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653 Sentences With "edges in"

How to use edges in in a sentence? Find typical usage patterns (collocations)/phrases/context for "edges in" and check conjugation/comparative form for "edges in". Mastering all the usages of "edges in" from sentence examples published by news publications.

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There are a few rough edges in the Podcasts app.
You can sense the frayed edges in the sound of it.
The alcoholic blur pushes away the sharp edges in his mind.
A light musical beat edges in—slow at first, with a steady uptick.
The cameras detect edges in your environment and use them as anchor points.
The Dawson City movies have degraded around their edges in a characteristic way.
We like to think of our hair and edges in the same vein.
The company promised to do away with all of the "unnecessary edges" in the process.
And it has frayed around the edges in the absence of such a primary focus.
Uruguay had 4 shots, to Russia's 1 and slight edges in possession and pass accuracy.
But deforestation isn't an organized shrinking of the rainforest, paring it down from the edges in.
At the next layer, the network might have neurons that simply detect edges in the image.
To show up in places on the edges, in the cracks, to create new, novel systems?
For example, there's a selection tool, but it doesn't follow the defined edges in the image.
Bauer may have softened some of his edges in recent years, but not in this instance.
Clinton had been presumed to have the advantage based on her edges in national and state polls.
Critic's Notebook Yes, it's better to see this great flutter of planes, volumes and edges in person.
Many people have a taste for thoroughly browned foods, crusty corners and inky, bittersweet edges — in moderation.
Laying edges in this style is unique to black hairstyles so I don't wanna hear about nordic hairstyles.
This may be accomplished by a number of means, and one is to intelligently identify edges in the image.
Women only exist on the edges in "Uncut Gems," which stars Adam Sandler as an adrenaline-fueled diamond dealer.
Rather than muting their personalities, these songwriters-slash-performers lend cred and rougher edges in addition to catchy choruses.
His edges in heavily white Iowa and New Hampshire are only in the high single digits and low double digits.
She penned many poetry collections, including nappy edges in 1978, as well as a plethora of novels and children's books.
Probably its best comparison point was Wired, but it felt a bit rougher around the edges, in a good way.
Also, if using store-bought tortillas, dip the edges in some water [combined with] a couple of tablespoons of oil.
The candidates seized Sunday's debate as an opportunity to show off their hard edges in front of a national audience.
And what that does is it preserves every single gradient — all the gradients and edges in the picture are perfectly preserved.
Softening The Edges In polite conversation with friends and relatives, we are all taught to soften the edges of our conflict.
While it's somewhat rough around the edges in spots, Hound has the makings of a serious competitor in the voice recognition space.
Yes, there are rough edges in the software, and the folding screen doesn't feel as premium as other screens in this price category.
The manuscript's pages have been remounted onto new ones, because the book was singed around the edges in a library fire in 1731.
After a tragedy dramatically changes the network, they sand down its rough edges in their memories, recalling the parts that made them happiest.
Christiansen makes note that figures crowded at the canvas edges in Valentin's work suggest a dynamic entering and exiting of the cinematic frame.
She's still rough around the edges in the ring, and her meteoric rise to prominence over the Four Horsewomen seems to rankle some.
It detects the edges in your drawing and then uses that as a structured starting point for the randomized duals of adversarial image generation.
And I think a lot of where you see his influence is on the edges — in the rhetoric and the approach in the primary.
It has a screen that's about 6.5 inches diagonally (depending on how you count the curved edges) in a fairly tall 19.5:9 aspect ratio.
She also has the clearest path to be the nominee, with a polling and organizational edges in Iowa and a geographic connection in New Hampshire.
Whenever you need to pack it back up, you simply turn it inside out, fold the edges in, and stuff it into the interior pocket.
Their hardline views on immigration often left them on the edges in the Senate, fighting broader bipartisan immigration reform efforts every step of the way.
Throughout Mark Leibovich's new book Big Game, the ghoulish results of an NFL career — memory loss, physical degeneration, grief — materialize on the edges, in discordant places.
You had people testing the edges in serious ways too, from Andy Carvin's real-time curation of the Arab Spring to Teju Cole's experiments in storytelling.
Dallas concentrated on keeping the ball and waiting for its chances and earned big edges in total passes (643-341) and possession percentage (64.1 to 35.9).
Edges in the graph indicate when an entity was recognized for a photo, when a specific response was given for a photo, and visual similarities between photos.
Peppy, silly hits like "Rio" and "Hungry Like the Wolf" had the Brooklyn audience dancing and singing along, ignoring some scratchy edges in Mr. Le Bon's voice.
The other phones that Nathaniel mentioned, the G6 and the Xioami Mi Mix, both have screens that are pushed to the edges in a very similar manner.
It turned out, she'd used the eyeshadow in a way I never had — just on the outer edges, in a really flattering shape — and it looked great!
Add the potatoes and use a spatula to tuck the edges in, creating sides all around in a hockey puck shape about 1¼ inches (3 cm) tall.
HoloLens, at least as I understand it from Lauren Goode and Tom Warren, is impressive but still a little rough around the edges in its current beta form.
Right now, the Galaxy Fold is for people who can handle some rough edges in exchange for trying out a gadget that's unlike anything else on the market.
All the money is going to the outside edges, in New York and San Francisco, and all the local stores, local advertising is being hurt in the middle.
But this is so reductive, sanding off all of Outer Wilds most unique edges in order to sell something frighteningly fresh in the comfortable uniform of the familiar.
A social network is, after all, itself a graph—a mathematical structure consisting of various objects (or nodes) connected by links (or edges) in various configurations with varying complexities.
Mightn't they sand down their edges in an effort to repair the party's image, improve its fortunes and make certain that it didn't lose yet more seats in 2018?
Like the Roomba s9+, the Braava Jet m6 has also been designed with edges in mind, and it's also equipped with the same smart mapping functionality as its vacuuming sibling.
Imagine quickly navigating though an ebook by grabbing and bending the edge of the case, not unlike how you'd grab the page edges in a real book to flip through it.
But the 2016 Democratic primary was far from a level playing field, with Clinton holding clear edges in everything from money to organization to, yes, the tacit support of the Democratic National Committee.
The S7 appears to have a much friendlier look, doing away with the S6's harsh edges in favor of something, well, a little more like the iPhone 6 and 6S's round edges.
If we connect the edges in our mind's eye, as we might instinctively do, we will recognize that the three forms add up to a rectangle made of three distinct but related shapes.
When I was a graduate student in computer science in the early 2000s, computers were barely able to detect sharp edges in photographs, let alone recognize something as loosely defined as a human face.
Those who prefer lateral living should head to 50 St. Edmunds Terrace, which, technically edges in with a Primrose Hill address, as it is adjacent to the park, though closer to neighboring St. John's Wood.
Its first step might have been to include one of Ms. Mohamedi's drawings from the show downstairs; their idiosyncratic grids often imply infinite expansion beyond their edges in a way that local Minimalism rarely does.
Their music is jubilant and rough around the edges in a way that's best experienced live; for those looking to start their New Year's revels a few nights early, the band offers an optimal soundtrack.nublu.
Hunt grew up in DIY contexts, playing in electronic and noise acts with names like Mom's Spaghetti, and her work is still wonderfully rough around the edges in a way that such a lineage would suggest.
They nest on cliff edges in the remote northern reaches of Canada and Alaska and are fierce predators, primarily of ptarmigan (a bird in the grouse family with feathered feet to help them walk in the snow).
It edges in that direction in the final episode, which focuses on Korey Wise, who (unlike the other four) was 16 at the time of his arrest and thus committed to the adult rather than the juvenile system.
Every six to ten years, during the hot season, mosquitoes would pick it up from infected monkeys and spread it to a few loggers, hunters, and farmers at the forests' edges in the northwestern part of the country.
As the sky sharpened at its edges in pink, slashing tongues, I could see, finally, through a gap in the cliffs, a long curve of juniper-covered hills rolling and tumbling southward before breaking up into open country.
Douthat: Honestly, I think the age of #MeToo should cast some serious doubt on the theory — I won't call it "cant," but I do think it edges in that direction — that celibacy simply and straightforwardly causes priestly misbehavior.
It relies primarily on front-facing cameras to detect edges in the environment and use them as reference points, so the headset can tell how far you've walked in real space and translate that into virtual motion as well.
Which means that in only a few months, the Trump administration will have ended a decades-long pact that softened the rough edges in the US-Russia struggle for military superiority — and could reignite Cold War tensions once more.
Also on The Jay & Farhad Show, Gurman discussed hearing that there would be a number of small design tweaks across the operating system, making it a bit more colorful, adding rounded edges in some places, and updating a few icons.
This says that if you have a planar graph (a network of vertices and edges in the plane) that stays connected if you remove one or two vertices, then there is a convex polyhedron that has exactly the same connectivity pattern.
Young, Shapley, and Chariker demonstrated that their feedback-rich model was able to reproduce the orientation of edges in objects—from vertical to horizontal and everything in between—based on only slight changes in the weak LGN input coming into the model.
Some of her renderings of water even take on the appearance of flowing hair, like the rippling waves in "Something Vanished Over Paradise" (2009), or the jagged edges in "Cut my ropes, let me fall" (2008), suggesting perhaps drowned bodies within the ocean.
But the intense moralism in those controversies, and their reverent invocations of "diversity" and "identity," suggest a desperation to excuse or cover the soulless Mammonism that grips students seeking to carve out competitive edges in the world that Stephen Schwarzman has made.
Ingredients that have been left to sit alongside one another for a long while simply lose some of their sharp edges in the process for the sake of a greater good, in much the same way as individuals morph into a family.
"As they ended the ceremony, exchanging 'Hell Yeahs' instead of 'I Dos,' 10 BASE jumper 'flower girls' lined along the cliff edges in tutus and jumped off one-by-one, releasing 5,000 flower petals that had been packed in their parachutes," the site states.
That matters because the way to create a partisan gerrymander is to group together a whole bunch of heavily Democratic precincts in order to create a single district that serves as a vote sink while giving the GOP smaller, but still nearly insurmountable, edges in the others.
It's nearly impossible for critical feedback to make it in, especially from the outer edges where the farmers are working, to the central planning committee in time to affect decisions, and then for those decisions to make it back to the edges in time to be useful.
But it's also a testament to the engineers and designers at Apple who have worked to minimize "edges" in the OS. You are never "scolded" by hitting a dead end—you reach a soft bounce at worst, and so, for me at least, exploration is encouraged.
In another interview, he told the Associated Press his finale isn&apost an apology for the previous film, but specific scenes in "TROS" appear to say the opposite, smoothing over and explaining away some rough edges in the eighth film involving Snoke, Luke Skywalker, and Rey.
The presidency is the least gerrymandered branch of the federal government (the Electoral College gives the GOP about a 2-point edge, enough to make Trump president but smaller than their edges in the House or Senate) and therefore the prize Democrats have the best odds of capturing.
The new Echo kind of, sort of, edges in that direction with improved audio, but the Google Home Max and Apple HomePod offer up similar visions for a future in which smart assistants are a nice bonus on a device focused on delivering high-quality, floor-rumbling, room-filling audio.
Related: Iraqis Are Bombarding Fallujah With 50,000 Civilians Trapped Inside The Norwegian Refugee Council said it had lost contact with people in the city center, while more than 1200 people had escaped from the city's outer edges in the past 24 hours, more than doubling the number of civilains already staying in NRC supported-camps.
And given that this fall is going to be enacted by Ms. Houdyshell, a performer with a gift for finding original edges in familiar shapes, you can assume that you're going to be emotionally shaken, if not stirred, by the end of this MCC Theater production, directed at a faltering pace by Liesl Tommy.
For example, whereas the Fold's screens are compromised — the exterior features a skinny and small 4.6-inch screen with huge bezels all around it and the unfolded larger interior screen has a cutout for the selfie cameras in the upper right — the Mate X's screens are larger and stretch closer towards the edges in all modes.
They contend that his new immigration message is designed merely to soften his sharp edges in the eyes of moderate white Republicans and independents, who are turned off by Trump's more controversial statements but also don't want to support Hillary ClintonHillary Diane Rodham ClintonLewandowski on potential NH Senate run: If I run, 'I'm going to win' Fighter pilot vs.
The story began like a fairy tale offered up to the rest of the planet: the giddy opening of infinite spaces and labyrinths of intelligence; the vertiginous feeling of having all the known world within one's grasp; the joy, for those living at the edges in remote villages or peripheral nations, of gaining access to globalized methods of socialization and personal growth.
Full leather, blind stamped and tooled, goffered edges in gold.
Brandy Mary's leek orchid grows on stream edges in a small area near Cabramurra and Talbingo.
The residual capacity for some path is the minimum residual capacity of all edges in that path.
The number of operations in each of these procedures is equivalent to the number of edges in T_1 that are not in T_2 plus the number of edges in T_2 that are not in T_1. The sum of the operations is equivalent to a transformation from T_1 to T_2, or vice versa.
The path between the valence-5 vertices is two edges in a row, and then a turn and one more edge.
An interesting generalization of the network- motifs, activity motifs are over occurring patterns that can be found when nodes and edges in the network are annotated with quantitative features. For instance, when edges in a metabolic pathways are annotated with the magnitude or timing of the corresponding gene expression, some patterns are over occurring given the underlying network structure.
Black-tailed prairie dogs were rarely seen feeding more than 16 ft (5 m) from colony edges in Wind Cave National Park.
In all of the algorithms below, m is the number of edges in the graph and n is the number of vertices.
Atractaspis branchi lives in primary rainforest and rainforest edges in the western part of the Upper Guinea forests in Guinea and Liberia.
BBC Introducing included Jaded Edges in their best of 2013 hour on BBC London The band are planning upcoming shows and future releases for early 2014.
Open deciduous forest, clearings and edges in evergreen forest, abandoned hill cultivation with some trees; often near water. Mostly 200–800 m, fairly regularly to 1,700 m.
Marshall, Joe. "Turnover in Tampa Bay". Sports Illustrated. 7 January 1980 Going into the matchup, the Eagles were expected to have edges in playoff and quarterback experience.
The Norseman gimlet is found on valley edges in a small area in the Goldfields-Esperance region of Western Australia near Norseman where it grows in loamy soils.
These leaf beetles are heat-loving. They can be found predominantly in thickets and forest edges, in the plane or on dry warm slopes, from about April to July.
Springer, New Delhi each will extract the edges in respect to its direction. A combined use of compass masks of different directions could detect the edges from different angles.
In the mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph G = (V, E) is the minimum number of bicliques (that is complete bipartite subgraphs), needed to cover all edges in E. A collection of bicliques covering all edges in G is called a biclique edge cover, or sometimes biclique cover. The bipartite dimension of G is often denoted by the symbol d(G).
These plants grow in sunny areas and calcareous soils, on semiarid grasslands, slopes and forest edges. In the Alps they can be found at an altitude of above sea level.
This species is found in cool mountain forest, especially at the edges, in clearings, along roadsides and near streams, and in second growth and bushy pastures. It breeds from to nearly altitude.
An MBST in this case is called a Minimum Bottleneck Spanning Arborescence (MBSA). The graph on the right is an example of MBSA, the red edges in the graph form a MBSA of .
The species name refers to the dark edges in the forewing., 2010: Review of East African Cochylini (Lepidoptera, Tortricidae) with description of new species. Norwegian Journal of Entomology 57 (2): 81-108. Abstract: .
Intuitively, an agreement forest of size for two phylogenetic trees is a forest which can be obtained from both trees by removing edges in each tree and subsequently suppressing internal nodes of degree .
Camerini proposed an algorithm used to obtain a minimum bottleneck spanning tree (MBST) in a given undirected, connected, edge-weighted graph in 1978. It half divides edges into two sets. The weights of edges in one set are no more than that in the other. If a spanning tree exists in subgraph composed solely with edges in smaller edges set, it then computes a MBST in the subgraph, a MBST of the subgraph is exactly a MBST of the original graph.
Culture and Organization, 13, 223–237.Herrmann, A. F., Barnhill, J. J., & Poole, M. C. (2013). Ragged edges in the fractured future: A co-authored organizational autoethnography. Journal of Organizational Ethnography, 2, 57-75.
Mounting sharp flint edges in a wood or bone handle is the key innovation in microliths, essentially because the handle gives the user protection against the flint and also improves leverage of the device.
Net of a dodecahedron. All edges in this net have true length. In geometry, true length is any distance between points that is not foreshortened by the view type.Manual of Engineering Drawing 2009, , pp.
Obsidian is hard, brittle, and amorphous; it therefore fractures with sharp edges. In the past, it was used to manufacture cutting and piercing tools, and it has been used experimentally as surgical scalpel blades.
Like many WPA murals, these contained images of Springfield and Massachusetts history in a bold, proletarian style, full of expressive movement and hard edges. In six panels, these murals now decorate Springfield's federal building.
Let be a (finite and simple) graph with vertices. We denote by the degree of a vertex in , i.e. the number of incident edges in to . Then, Ore's theorem states that if then is Hamiltonian.
Lochhead began playing professional baseball in 1896 as a pitcher and shortstop for the Stockton team in the California League. He also played for Sacramento Gilt Edges in the Pacific Coast League from 1898 to 1900.
In a mesh structure, nodes are either corner (only two neighbours), border (only three neighbours) or interior (with four neighbours). The number of edges in a mesh of size a x b is m=2ab-a-b.
The small-lipped white spider orchid is common in the area between Eneabba and Gingin, where it grows in seasonal swamps, near creeks and on lake edges in the Geraldton Sandplains and Swan Coastal Plain biogeographic regions.
This method is sensitive to noise and can easily detect false edges and lose real edges. # In the traditional Canny edge detection algorithm, there will be two fixed global threshold values to filter out the false edges. However, as the image gets complex, different local areas will need very different threshold values to accurately find the real edges. In addition, the global threshold values are determined manually through experiments in the traditional method, which leads to complexity of calculation when a large number of different images need to be dealt with.
In K.J. Schneider, J.F.T. Bugental & J.F. Pierson (Eds.) The handbook of humanistic psychology: Leading edges in theory, research and practice (pp. 5-20). Thousand Oaks, CA: Sage Publications Carl Rogers was trained in psychoanalysis before developing humanistic psychology.
Its natural habitat is in is in forest edges in hilly areas. Scutellaria brachyspica is a perennial, growing to 50 cm tall. Its blue-white flowers are clustered in a short terminal spikes. It blooms from May to June.
Each leaf can contain up to 17 primary leaflets that are lanceolate in shape with toothed edges. In between the primary leaflets, secondary leaflets can be found which are much smaller than the primary leaflets and are also toothed.
A board roof of the board-on-board type with grooved edges in Sweden A board roof or boarded roof"Boarded roof" def. 1.Davies, Nikolas, and Erkki Jokiniemi. Dictionary of Architecture and Building Construction. Amsterdam: Elsevier/Architectural, 2008. 43. Print.
This number is called the circuit rank of the graph, and it equals m-n+c where m is the number of edges in the graph, n is the number of vertices, and c is the number of connected components..
The second issue is that phase equalization is essential for an analog television signal. Without it dispersion causes the loss of integrity of the original wave-shape and is seen as smearing of what were originally sharp edges in the picture.
Their breeding habitats are brushy areas and forest edges in eastern North America. The prairie warbler's nests are open cups, which are usually placed in a low area of a tree or shrub. Incubation period is 12 to 13 days.
The degree sum formula implies that every r-regular graph with n vertices has nr/2 edges. In particular, if r is odd then the number of edges must be divisible by r, and the number of vertices must be even.
The cross for next of kin is bronze and similar to the cross without swords, but smaller in size. Unlike the others, it is attached to a ribbon in black with edges in red, yellow, and red (the colours of the Spanish flag).
At the rising edges of the square wave, each sinusoidal component has a rising phase; the phases have maximal congruency at the edges. This corresponds to the human-perceived edges in an image where there are sharp changes between light and dark.
In the mathematical field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle. The triangle graph is also known as the cycle graph C_3 and the complete graph K_3.
The uppersides of the hindwings have a smaller golden-yellow area at the base and several yellow spots at the edges. In both sexes the undersides are similar to the uppersides. The abdomen is yellow, while the head and thorax are black.
In 1973, she began to soften some of the edges in her works, a trend that would continue the next few years; this resulted in a myriad of horizontal landscape compositions often containing a few or even only one thin hard edge line.
The leaves are lightly sericeous (hairy) and have wavy edges. In cultivation the tree ideally reaches up to 6 metres (20 feet) in diameter, although can be maintained to a smaller size. The tree is fast-growing and has some frost-tolerance.
In this special case, the maximum number of events processed by a kinetic heap can be shown to be exactly the number of edges in the transitive closure of the tree structure of the heap, which is for a tree of height .
Path contraction occurs upon the set of edges in a path that contract to form a single edge between the endpoints of the path. Edges incident to vertices along the path are either eliminated, or arbitrarily (or systematically) connected to one of the endpoints.
The expected performance is a result of the random sampling step. The effectiveness of the random sampling step is described by the following lemma which places a bound on the number of F-light edges in G thereby restricting the size of the second subproblem.
In addition, the outer automorphisms of the group of permutations swap one side of the bipartition for the other. As Coxeter showed, any path of up to five edges in the Tutte–Coxeter graph is equivalent to any other such path by one such automorphism.
Fast algorithms include the WSPD spanner and the Theta graph which both construct spanners with a linear number of edges in O(n \log n) time. If better weight and vertex degree is required the Greedy spanner can be computed in near quadratic time.
Fountainea nobilis is a quite rare "leaf butterfly". The dorsal sides of the upperwings are reddish with dark brown edges. In the females the dorsal sides are usually brown, with clearer edges. On the hindwings there are a few small white and black eyespots.
Berkhoudt, who studied the bill of the mallard, had findings consistent with those of Krogis for the dorsal surface of the upper bill, noting also that the density of Grandry corpuscles increased greatly near the nostrils. In the ventral skin of the lower bill of the mallard, the density of Grandry corpuscles increased toward the tip of the bill and toward the bill edges. In the bill mucosa which lines the inside of the lower and upper bill, Berkhoudt noted that the concentration of Grandry corpuscles was highest at the outer edges. In the tongue, Grandry corpuscles were dispersed very sparsely on the dorsal surface only.
Thus, if the original graph has n vertices and m edges then at depth d of the tree each subproblem is on a graph of at most n/4d vertices. Also the tree has at most log4n levels. Left paths of a binary tree are circled in blue To reason about the recursion tree let the left child problem be the subproblem in the recursive call in step 3 and the right child problem be the subproblem in the recursive call in step 5. Count the total number of edges in the original problem and all subproblems by counting the number of edges in each left path of the tree.
As a special case of Turán's theorem, for r = 2, one obtains: :Mantel's Theorem. The maximum number of edges in an -vertex triangle-free graph is \lfloor n^2/4 \rfloor. In other words, one must delete nearly half of the edges in to obtain a triangle-free graph. A strengthened form of Mantel's theorem states that any hamiltonian graph with at least n2/4 edges must either be the complete bipartite graph Kn/2,n/2 or it must be pancyclic: not only does it contain a triangle, it must also contain cycles of all other possible lengths up to the number of vertices in the graph .
P. × eminens takes after P. fruticosa in preferring open, steppe-like habitat, although it also grows in forest edges. In the wild it is chiefly found in central Europe, in the western part of the range of P. fruticosa and largely over-lapping and supplanting it there.
This melaleuca occurs in the south-west of Western Australia and on the south coast as far east as Esperance in the Jarrah Forest, Swan Coastal Plain and Warren biogeographic regions. It grows on swamp edges, in low woodland and heath in peaty soil and sand.
The Canny edge detector is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. It was developed by John F. Canny in 1986. Canny also produced a computational theory of edge detection explaining why the technique works.
The cubic (n=3) Bézier triangle is defined by 10 control points and is the lowest order Bézier triangle that has an internal control point, not located on the edges. In all cases, the edges of the triangle will be Bézier curves of the same degree.
The rear of the frill consisted of the rounded parietal bones. They too had osteoderms attached to their edges, in this case called epiparietals. Each parietal had five of them, conventionally numbered "p1" to "p5". The fifth and fourth epiparietals, the ones in front, resembled the episquamosals.
A queue layout of a given graph is defined by a total ordering of the vertices of the graph together with a partition of the edges into a number of "queues". The set of edges in each queue is required to avoid edges that are properly nested: if ab and cd are two edges in the same queue, then it should not be possible to have in the vertex ordering. The queue number qn(G) of a graph G is the minimum number of queues in a queue layout.. Equivalently, from a queue layout, one could process the edges in a single queue using a queue data structure, by considering the vertices in their given ordering, and when reaching a vertex, dequeueing all edges for which it is the second endpoint followed by enqueueing all edges for which it is the first endpoint. The nesting condition ensures that, when a vertex is reached, all of the edges for which it is the second endpoint are ready to be dequeued.
At that time Fliegerstaffel 3 changed to the AMIR badge. The original badge was a red equilateral triangle with white outer edges. In this badge was the head of a white Bulldog with black spot over the right eye and black collar. Underneath “3ème ESCADRILLE” was written in black.
Picotee edges in flower Picotee describes flowers whose edge is a different colour than the flower's base colour.Daily Dictionary entry for picotee (URL accessed June 16, 2006) The word originates from the French picoté, meaning 'marked with points'.The Oxford Dictionary of English, page 1331. Oxford University Press, 2005.
Salvia tolimensis is a perennial shrub endemic to a very small region in Colombia (Tolima) growing on streamsides, scrublands, and forest edges in wet conditions at elevation. The plant is a vigorous undershrub, about high, with narrow ovate leaves that are long and wide. The purple flowers are long.
More generally, a matroid is called graphic whenever it is isomorphic to the graphic matroid of a graph, regardless of whether its elements are themselves edges in a graph. The bases of a graphic matroid M(G) are the spanning forests of G, and the circuits of M(G) are the simple cycles of G. The rank in M(G) of a set X of edges of a graph G is r(X)=n-c where n is the number of vertices in the subgraph formed by the edges in X and c is the number of connected components of the same subgraph. The corank of the graphic matroid is known as the circuit rank or cyclomatic number.
C-vine on 4 variables D-vine on 4 variables R-vine on 5 variables A vine on n variables is a nested set of connected trees where the edges in the first tree are the nodes of the second tree, the edges of the second tree are the nodes of the third tree, etc. A regular vine or R-vine on n variables is a vine in which two edges in tree are joined by an edge in tree j + 1 only if these edges share a common node, j = 1, …, n − 2\. The nodes in the first tree are univariate random variables. The edges are constraints or conditional constraints explained as follows.
Sambucus sieboldiana, commonly called the Japanese red elder, is a deciduous shrub in the moschatel family (Adoxaceae). It is native to East Asia, where it is found in Japan and Korea.Sambucus racemosa ssp. sieboldiana (in Japanese), Flora of Mikawa Its natural habitat is in thickets and forest edges, in low elevations.
Most competitors quickly adopted the raised label and edges. In 1955, RCA Victor purchased the recording contract of Elvis Presley from Sun Records for the then-astronomical sum of $35,000. Presley would become RCA Victor's biggest-selling recording artist. His first gold record was "Heartbreak Hotel", recorded in January 1956.
The most likely evolutionary rationale for this effect is that it enhances edges in the visual field, thus facilitating the recognition of shapes and objects. 192x192pxThis is a different concept from contrast, which by itself refers to one object's difference in color and luminance compared to its surroundings or background.
Their black-capped lory inhabits the primary forest and forest edges in most lowland areas up to 1000m (sporadically to 1750m), but not monsoon forest or coconut plantations. It is usually found in pairs and occasionally in groups of 10 or more. Their diet includes pollen, nectar, flowers, fruit and insects.
The Erdős–Stone theorem extends Turán's theorem by bounding the number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar bounds in extremal graph theory can be proven for any excluded subgraph, depending on the chromatic number of the subgraph.
The ruin passed from the counts of Hanau-Lichtenberg to the landgraves of Hesse, then to the Bishopric of Speyer and finally to the state of Rhineland-Palatinate. The State Office of Castles, Palaces and Antiquities installed safety measures (such as railings along stairways and around the cliff edges) in the 1970s.
If the tank is too small, the sharks have to spend more time actively swimming than they would in the wild, where they have space to glide. Also, sharks in small, circular tanks often spend most of their time circling along the edges in only one direction, causing asymmetrical stress on their bodies.
It is unclear whether this decoration was unique to dancers or if women commonly had it applied. Male dancers had short hairLexová 2000, p. 62. and typically wore the standard men's dress viz. skirt; in the Old and Middle Kingdoms, they would also wear an apron with round edges in the front.
The golden trout has golden flanks with red, horizontal bands along the lateral lines on each side and about 10 dark, vertical, oval marks (called "parr marks") on each side. Dorsal, lateral and anal fins have white leading edges. In their native habitat, adults range from long. Fish over are considered large.
Thus the inside of the island is lower than its edges. In time the inner lagoon lost its saltiness and all that remains today are two small lakes, wetlands and marshy taro fields. Therefore, Fuvahmulah is a small Atoll that closed and filled in with silt, like Nukutavake in the Central Pacific.
The Sacrament of the Last Supper (1955): The canvas of this surrealist masterpiece by Salvador Dalí is a golden rectangle. A huge dodecahedron, with edges in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.Hunt, Carla Herndon and Gilkey, Susan Nicodemus. Teaching Mathematics in the Block pp.
In 1936, Bremer fitted the sails with Dekkerised leading edges. In that year the mill was sold to De Goede Verwachting Coöperatie. The stage was renewed in 1961 and in 1967 the mill was sold to the Gemeente Peize. The mill was restored in 1971-72 by millwright Alserda of Doezum, Groningen.
Edges (sometimes produced as Edges: A Song Cycle) is a work of musical theatre by Pasek & Paul. It is a song cycle about coming of age, growth and self- discoveryKeyes, Bob. "Coming-of-age musical 'Edges' in Maine debut", Portland Press Herald, 2006-06-29, p. D9. of people mostly in their 20s.
Once a receptor is active, it inhibits adjacent receptors. This inhibition creates contrast, highlighting edges. In the Hermann grid illusion, the gray spots that appear at the intersections at peripheral locations are often explained to occur because of lateral inhibition by the surround in larger receptive fields.Pinel, J. (2005) Biopsychology (6th ed.).
Greya variata is a moth of the family Prodoxidae. It is found in herb-rich meadows and along forest edges in the central Rocky Mountains at the border between the United States and Canada. The wingspan is 11–13 mm. The forewings have a dark brown base and two pale tan-coloured patches.
Verandah beams have stop-chamfered edges in places. The slender, cylindrical timber verandah posts with square base and top are modern replicas of the original posts, which were more finely detailed. Paired columns are located at the main entrance. The timber verandah decking is supported on rendered brick piers with metal ant caps.
With mirroring, is the mirror image of (with the mirror axis between processors and ). Mirroring only works for even . It can be proven that a coloring with the desired properties exists for all . When mirroring is used to construct , each processor can independently compute the color of its incident edges in time.
If the minimum cost edge e of a graph is unique, then this edge is included in any MST. Proof: if e was not included in the MST, removing any of the (larger cost) edges in the cycle formed after adding e to the MST, would yield a spanning tree of smaller weight.
Carex rosea distribution is in essentially the eastern portion of North America. Its habitat is in dry-moist woodlands. It can adapt to various soil types and it can also live in rich ravines, and wood edges. In Canada, C. rosea is distributed from Nova Scotia and southern Quebec west to MN and eastern NE.
Along with crossings, circular versions of problems of optimizing the lengths of edges in a circular layout, the angular resolution of the crossings, or the cutwidth (the maximum number of edges that connects one arc of the circle to the opposite arc) have also been considered,; ; ; . but many of these problems are NP-complete..
The subgraphs formed by the edges in each equivalence class are the biconnected components of the given graph. Thus, the biconnected components partition the edges of the graph; however, they may share vertices with each other. credit the definition of this equivalence relation to ; however, Harary does not appear to describe it in explicit terms.
A new pair of sails were fitted in 1923 at a cost of ƒ565. The sails were fitted with Dekker streamlined leading edges in 1937 by millwright Westra of Franeker. A diesel engine was installed as auxiliary power in 1961 and the Archimedes' screw was renewed. The mill ceased working a few years later.
Overcast stitches may be reversible, as when they are used to join together crochet block pieces of afghan blankets. There are several different kinds of overcast stitches. A straight overcast stitch is used for finishing edges in eyelets and cutwork. A blanket stitch, used to finish edges of wool blankets, is another common overcast stitch.
In general, defocus reduces the sharpness and contrast of the image. What should be sharp, high-contrast edges in a scene become gradual transitions. Fine detail in the scene is blurred or even becomes invisible. Nearly all image-forming optical devices incorporate some form of focus adjustment to minimize defocus and maximize image quality.
In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph for a non-complete graph H. It is named after Paul Erdős and Arthur Stone, who proved it in 1946, and it has been described as the “fundamental theorem of extremal graph theory”.
T. nogelii H.-Schaff. (= nogellii Lang) (75 e). The smallest species, recognizable by the hindwing beneath bluish grey ornamented with red macular bands, which are dotted with black at their edges. In the typical form, from Asia Minor and Turkey, the forewing bears a red discal patch and the hind wing a red transverse spot before the anal area.
Originally given to Arikus (Eric according to the latest released novella "Perfect Shadow") Daadrul. Once bonded, the silver ka'kari makes the user impervious to blades and other metals. The Globe of Edges in Cenaria was thought to be the silver ka'kari, but was a forgery. This could be the item that Garoth Ursuul wanted but is never made specific.
Wheels used in speed skating are usually round or elliptical in profile, and do not literally have edges. The terminology is carried over from ice skate blades, which have edges. In inline skating, being "on an inside edge" refers to skating with the wheel of the skate leaning inwards (i.e. medially: right skate leaning left, and vice versa).
To replace that mill, the drainage mill Flikkezijlsterpoldermolen was moved from Farmsum, Groningen by millwright Van Ausselt of Coevorden. Repairs were made to the mill in 1938 and the following year the sails were fitted with streamlined leading edges. In 1945, the mill lost a pair of sails and ceased work. It was restored in 1988.
Instead this set of edges is the union of a dual spanning tree with a small set of extra edges whose number is determined by the genus of the surface on which the graph is embedded. The extra edges, in combination with paths in the spanning trees, can be used to generate the fundamental group of the surface..
Ranjit Barot (born 1959) is an Indian film score composer, music director, music arranger, drummer and singer based in Mumbai, India. He is a longtime associate of A. R. Rahman. He has been described by guitar legend John McLaughlin as "one of the leading edges in drumming", and is now part of John McLaughlin and the 4th Dimension.
Appending an edge and a vertex to P2 gives P3, the path with three vertices. Denote the vertices by v1, v2, and v3. Label the two edges in the following way: the edge (v1, v2) is labeled 1 and (v2, v3) labeled 2. The induced labelings on v1, v2, and v3 are then 1, 0, and 2 respectively.
While glass looks like an easy surface to keep clean, glass cutting boards can damage knives because of the high hardness of the material. Cutting on glass tends to dent, roll or even chip knife edges in a rapid manner. Additionally, if used for chopping instead of slicing, glass can shatter or chip itself, contaminating food.
C. m. madagarensis has a vivid pale or cold blue beak, with a dark tip and cutting edges in adult males, and a dark brown with similar pattern in adult female. Juveniles have a black bill with pale pink base. The iris is sky-blue or greenish blue in males, and brown in females and juveniles.
This also implies that, community search is more suitable for finding communities from big graphs. (3) Support for dynamically evolving graphs. Almost all the graphs in real life are often evolving over time. Since community detection often uses the same global criterion to find communities, they are not sensitive of the updates of nodes and edges in graphs.
Their primary breeding habitats are open areas, mountainsides and forest edges in western North America from southern Alaska through British Columbia and the Pacific Northwest to California, nesting further north (Alaska) than any other hummingbird. The female builds a nest in a protected location in a shrub or conifer. Males are promiscuous, mating with several females.
A graph and two of its cuts. The dotted line in red is a cut with three crossing edges. The dashed line in green is a min-cut of this graph, crossing only two edges. In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph.
Summit of Cerro Cabrillo and Morro Bay estuary Black Hill in the park. Morro Bay State Park is a state park on the Morro Bay lagoon, in western San Luis Obispo County, on the Central Coast of California. On the lagoon's northeastern and eastern edges in the park, there are saltwater and brackish marshes that support thriving bird populations.
Similarly, if you traverse all nine edges in the walk "blue- blue-red—blue-blue-red—blue-blue-red", you will always end up at the vertex marked in green, no matter where you started. The road coloring theorem states that for a certain category of directed graphs, it is always possible to create such a coloring.
Bilinear interpolation works by interpolating pixel color values, introducing a continuous transition into the output even where the original material has discrete transitions. Although this is desirable for continuous-tone images, this algorithm reduces contrast (sharp edges) in a way that may be undesirable for line art. Bicubic interpolation yields substantially better results, with an increase in computational cost.
Given an edge-colored graph G = (V,E), a rainbow matching M in G is a set of pairwise non-adjacent edges, that is, no two edges share a common vertex, such that all the edges in the set have distinct colors. A maximum rainbow matching is a rainbow matching that contains the largest possible number of edges.
Tozzia alpina is a herbaceous, perennial plant, reaching heights of . The quadrangular stem is hairless in the lower part, hairy on the edges in the middle and upper part. The simple, bright green leaves are broad, ovate, serrate, with a length of 1 to 3.5 centimeters, a rounded or slightly heart-shaped basis, and a sharp upper end.
Any toroidal graph has chromatic number at most 7. The complete graph K7 provides an example of toroidal graph with chromatic number 7. Any triangle-free toroidal graph has chromatic number at most 4. By a result analogous to Fáry's theorem, any toroidal graph may be drawn with straight edges in a rectangle with periodic boundary conditions.
In applied mathematical analysis, piecewise functions have been found to be consistent with many models of the human visual system, where images are perceived at a first stage as consisting of smooth regions separated by edges. In particular, shearlets have been used as a representation system to provide sparse approximations of this model class in 2D and 3D.
Since there are m clause components, and the selection of sets of internal edges, L, within each clause component is independent of the selection of sets of internal edges in other clause components, so one can multiply everything to get the weight of Z^M. So, the weight of each Z^M, where M induces a satisfying assignment, is 12^m. Further, where M does not induce a satisfying assignment, M is not proper with respect to some C_j, so the product of the weights of internal edges in Z^M will be 0. The clause component is a weighted, directed graph with 7 nodes with edges weighted and nodes arranged to yield the properties specified above, and is given in Appendix A of Ben-Dor and Halevi (1993).
The galena forms mats of octahedral crystals, the sphalerite is dense and anhedral and the marcasite powdery or displays its coxcomb habit. The lodes are mylonitized at the edges; the sulfide mineral aggregates within this zone are sheared. Secondary mineralisations cover the central fracture surfaces and the mylonitic edges. In the core region geodes of quartz and of chalcedony can occur.
Signal upsampling via the traditional interpolation followed by smoothing for denoising evidently distorts the edges in the original ideal or downsampled signal. The edge- preserving interpolation followed by the edge-preserving filters is proposed in e.g., to upsample a no-flash RGB photo guided using a high resolution flash RGB photo, and a depth image guided using a high resolution RGB photo.
In adult Endothiodons the lower jaw teeth are pear shaped in cross section, compressed distolaterally, and has posterior serrated edges while the upper jaw teeth have anterior serrated edges. In the juveniles, the lower jaw is a lot smaller and more slender. The lower jaw contains one functional tooth row with 5-6 teeth. The teeth are small, conical, and pointed.
Each half-edge has exactly one previous half-edge, next half-edge and twin. DCEL is more than just a doubly linked list of edges. In the general case, a DCEL contains a record for each edge, vertex and face of the subdivision. Each record may contain additional information, for example, a face may contain the name of the area.
Everything was set thick and very low to the ground, while the produce in Chinatown was oversized. No edges in the film are completely straight. She explained, "We wanted there to be this perfect imperfection in the world to feel more handmade and personal and warm." Shi explained how she worked with a good number of female supervisors on her team for Bao.
The user interface allows the customization of these parameters: the user can select the minimum frequency of the edges returned. There is an option for viewing and comparing the female or male reference connectomes. The connectomes of women contain significantly more edges than those of men, and a larger portion of the edges in the connectomes of women run between the two hemispheres.
The corresponding dessins take the form of path graphs, alternating between black and white vertices, with n edges in the path. Due to the connection between Shabat polynomials and Chebyshev polynomials, Shabat polynomials themselves are sometimes called generalized Chebyshev polynomials.Jones, G. and Streit, M. "Galois groups, monodromy groups and cartographic groups", p.43 in Schneps & Lochak (2007) pp.25-66.
SRM then sorts those edges in a priority queue and decides whether or not to merge the current regions belonging to the edge pixels using a statistical predicate. One region-growing method is the seeded region growing method. This method takes a set of seeds as input along with the image. The seeds mark each of the objects to be segmented.
Pseudophilautus tanu occurs in forest-edges in open shrub areas of the lowland wet zone of Sri Lanka, above sea level. Males have been found sitting on leaves of shrubs about above the ground. Pseudophilautus tanu is a common species within its habitat. In Kanneliya, it was the most common species in the fern-dominated habitat, along with Pseudophilautus hoipollo.
Directional Cubic Convolution Interpolation (DCCI) is an edge-directed image scaling algorithm created by Dengwen Zhou and Xiaoliu Shen. By taking into account the edges in an image, this scaling algorithm reduces artifacts common to other image scaling algorithms. For example, staircase artifacts on diagonal lines and curves are eliminated. The algorithm resizes an image to 2x its original dimensions, minus 1.
There are three thoracial segments, each bearing a leg, and five abdominal segments. The fourth abdominal segment bears an organ known as a "dens", and at the tip of this is a structure known as a "mucro". This species has mucros with smooth outer edges and saw-edged inner edges. In females, the appendage on the fifth abdominal segment is unforked.
The maroon-bellied parakeet is common in woodland, and forest edges. In the northern part of its range, it mainly lives in highlands up to 1,400 m (4,600 ft), but elsewhere it is primarily found in lowlands up to 1,000 m (3,300 ft). Tolerates disturbance well and even lives in urban parks (e.g., Rio de Janeiro and São Paulo) and feeds in gardens.
The IAR.22 was a wooden, low-wing monoplane with a fixed conventional undercarriage, seating two in tandem, open cockpits. The wings were built around two spruce box spars, with plywood webs; plywood covered the whole wing except for the fabric trailing edges. In plan, the wings were straight-tapered, with most of the taper on the trailing edge, but with rounded tips.
The matching problem can be generalized by assigning weights to edges in G and asking for a set M that produces a matching of maximum (minimum) total weight: this is the maximum weight matching problem. This problem can be solved by a combinatorial algorithm that uses the unweighted Edmonds's algorithm as a subroutine. Kolmogorov provides an efficient C++ implementation of this.
Each colony grows by asexual budding from a single zooid known as the ancestrula, which is round rather than shaped like a normal zooid. This occurs at the tips of "trunks" or "branches" in forms that have this structure. Encrusting colonies grow round their edges. In species with calcareous exoskeletons, these do not mineralize until the zooids are fully grown.
Stylidium weeliwolli is only known from a few locations in northwestern Western Australia, but it is locally abundant at these locations. Its habitat is recorded as being sandy soils on watercourse edges, in wet areas, and a variety of other conditions in the presence of many companion plants. S. aceratum is most closely related to S. calcaratum.Lowrie, A., and Kenneally, K.F. (1998).
The idea behind the algorithm is as follows: as long as there is a path from the source (start node) to the sink (end node), with available capacity on all edges in the path, we send flow along one of the paths. Then we find another path, and so on. A path with available capacity is called an augmenting path.
Ručnik pattern on the flag of Belarus A Rushnyk has many uses. The very basic rushnik is colloquially called the utyralnyk or wiper and serves as a towel. The utyralnyk either has no designs on it or it has very narrow strip on the edges. In contrast, a nabozhnyk is a highly decorated Rushnyk composing of embroidery and of lace.
Finally, disorder in shift successions, causes an intermediate between alpha and gamma structures, called the delta (δ) form. The TiCl6 share edges in each form, with 3.60 Å being the shortest distance between the titanium cations. This large distance between titanium cations precludes direct metal-metal bonding. In contrast, the trihalides of the heavier metals hafnium and zirconium engage in metal-metal bonding.
That is, G1 and G2 can be represented on the same set of n vertices with no edges in common. The Hajnal–Szemerédi theorem is the special case of this conjecture in which G2 is a disjoint union of cliques. provides a similar but stronger condition on Δ1 and Δ2 under which such a packing can be guaranteed to exist.
The Adamoli-Cattani was intended to be the smallest practical biplane around the most powerful engine available to them, a le Rhône M. The result was a reasonably conventional design, other than that the wings featured hinged leading edges in place of conventional ailerons. The Farina Coach Building factory in Turin began construction of the prototype; the Officine Moncenisio in Condove completed it.
In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance. Notice that there may be more than one shortest path between two vertices. If there is no path connecting the two vertices, i.e.
Icaricia acmon, the Acmon blue, is a North American butterfly. It ranges mainly in California but can be seen north to Oregon and south through Baja California. The tops of the wings are blue with dark edges in males and brown in females. Its underside is white with black spots for both sexes with a red- orange band on the hindwing.
Its habitat is recorded as being wet sands at swamp edges in association with grasslands and sedgelands. Due to its weak stem, this species often threads its way through supporting branches and leaves of the dense grass and sedge cover. S. fissilobum is most closely related to S. aquaticum and S. oviflorum. Its conservation status has been assessed as data deficient.
Once n-1 F-light edges have been added to H none of the subsequent edges considered are F-light by the cycle property. Thus, the number of F-light edges in G is bounded by the number of F-light edges considered for H before n-1 F-light edges are actually added to H. Since any F-light edge is added with probability p this is equivalent to flipping a coin with probability p of coming up heads until n-1 heads have appeared. The total number of coin flips is equal to the number of F-light edges in G. The distribution of the number of coin flips is given by the inverse binomial distribution with parameters n-1 and p. For these parameters the expected value of this distribution is (n-1)/p.
A graph is 1-planar if it has a drawing with at most one crossing per edge. Intuitively, this restriction makes it easier to cause this crossing to be at right angles, and the 4n − 10 bound on the number of edges of straight-line RAC drawings is close to the bounds of 4n − 8 on the number of edges in a 1-planar graph, and of 4n − 9 on the number of edges in a straight-line 1-planar graph. Every RAC drawing with 4n − 10 edges is 1-planar.. Additionally, every outer-1-planar graph (that is, a graph drawn with one crossing per edge with all vertices on the outer face of the drawing) has a RAC drawing.. However, there exist 1-planar graphs with 4n − 10 edges that do not have RAC drawings..
The ribbon for troops held in reserve (Band für Reservetruppen) was blue with thin white edges. In the center were wide stripes of white, black and white. The ribbon for Johanniter Orden recipients was suspended from the ribbon of the House Order of Hohenzollern (Bande des Hausordens von Hohenzollern). This ribbon is white, with a black central stripe and black stripes near the edge.
They won the regular season in 1995 and in 2012. BWC Schools' histories by annals would show competitive edges in B1G and PAC12 head-to-head duels. Cal Poly San Luis Obispo became a perennial Beach Top 10 performer, with HC Todd Rogers. As of 2018 the BWC is the only NCAA conference to sponsor an official pairs bracket following the awarding of a Team Championship.
It ranges from dense forest to riverine forest and forest edges. In the forest it typically lives in the subcanopy at between 8–30 m. The green malkoha feeds primarily on insects, particularly caterpillars, beetles, grasshoppers and crickets; it will also take frogs, slugs, fruit, seeds and leaves. It moves through the tangled vegetation with a series of small hops, snatching prey as it travels.
This species is most commonly visible at the end of the rainy season, but sparsely found in the post-monsoon months. It is common but not abundant in most habitats. The spotted small flat (Sarangesa purendra), though, is more common in the arid regions. It occurs in openings and edges in both the evergreen and semi-evergreen forests, deciduous forests, and scrub & short grassland savannahs.
The brimstone canary or bully canary, (Crithagra sulphuratus), is a small passerine bird in the finch family. It is a resident breeder in central and southern Africa. This species is found in open, lightly wooded habitats, such as hillsides with trees or scrub and forest edges. In South Africa it occurs mainly in coastal areas, inhabiting coastal bush, shrubs along streams, gardens, and areas with rank vegetation.
The building was constructed of Yorkshire stone from the local quarries at Dacre Bank, Harehills, Meanwood and Weetwood. Corson was a perfectionist and instructed the contractors in how to dress and lay the stones to minimise weathering. The roof is made of Westmoreland slate. The entrance steps are made of Shap granite; a tough, slip proof material commonly used for kerb edges in Leeds.
The Paraguayan punaré, Thrichomys pachyurus, is a caviomorph rodent of South America from the spiny rat family. With its skull averaging 55 mm long, it is the largest species in the genus Thrichomys. It is found in savannas and forest edges in southwestern Brazil and northern Paraguay within the cerrado ecoregion. The species tolerates a degree of habitat disturbance, and is considered abundant throughout its range.
Oxford English Dictionary, 2nd ed.: Codex: "a manuscript volume" A codex much like the modern book is bound by stacking the pages and securing one set of edges in a form analogous to modern bookbinding by a variety of methods over the centuries. Modern books are divided into paperback or softback and those bound with stiff boards, called hardbacks. Elaborate historical bindings are called treasure bindings.
The nebula surrounds the variable star RU Coronae Australis, which has an average apparent magnitude of 12.9 and is a WC class Wolf–Rayet star. IC 1297 is small, at only 7 arcseconds in diameter; it has been described as "a square with rounded edges" in the eyepiece, elongated in the north-south direction. Descriptions of its color encompass blue, blue-tinged green, and green-tinged blue.
By showing how to derive a sequence of this type by choosing a tree, a root for the tree, and an ordering for the edges in the tree, he shows that there are Tnn! possible sequences of this type. And by counting the number of ways in which a partial sequence can be extended by a single edge, he shows that there are nn − 2n! possible sequences.
A drawing of the Petersen graph with slope number 3 In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the graph in which vertices are represented as points in the Euclidean plane and edges are represented as line segments that do not pass through any non-incident vertex.
According to Heins, the Perepiteia produces magnetic friction which somehow gets turned into a magnetic boost. Using an electric motor, the drive shaft is attached to a steel rotor with small round magnets lining its outer edges. In this set-up of a simple generator, the rotor spins so that the magnets pass by a wire coil just in front of them, generating electrical energy.
Phytolacca japonica is a species of flowering plant in the pokeweed family (Phytolaccaceae). It native to eastern Asia, where it is found in China and Japan (from the Kantō region westward).Phytolacca japonica (in Japanese), Flora of Mikawa Its natural habitat is in forests edges, in ravines and along riversides.Phytolacca japonica Flora of China Phytolacca japonica is an herbaceous perennial, growing to 1.5 meters tall.
A line perfect graph. The edges in each biconnected component are colored black if the component is bipartite, blue if the component is a tetrahedron, and red if the component is a book of triangles. In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle.
In central Europe this beetle lives in the grass layer and detritus, feeding on scale insects, aphids, and especially Psocoptera. It occurs in marshes, including peatbogs, on marshy shores, in meadows, at wet forest edges, in flood-plain forests, and in dry habitats such as karst, sandy, and stone quarries, wastelands, and in fields. This is a rather rare species.Koch, K., Die Käfer Mitteleuropas, Ökologie. Vol.
Curvelets have been used in place of the Gaussian filter and gradient estimation to compute a vector field whose directions and magnitudes approximate the direction and strength of edges in the image, to which steps 3 - 5 of the Canny algorithm are then applied. Curvelets decompose signals into separate components of different scales, and dropping the components of finer scales can reduce noise[12].
The eye socket is almost completely surrounded by a ring of bone. Incisors are distinctly narrow. Overall, the animal displays a mix of New World porcupine cranial characters, spiny rat cranial characters, and characters that set it apart from all other rodents. The bristle-spined rat is restricted to remnant forests and forest edges in the Atlantic coastal forests on the east coast of Brazil.
Tellurium has properties similar to sulfur and selenium. In the anhydrous form Na2TeO3 the tellurium atoms are 6 coordinate, three Te-O at 1.87 Å and three at 2.9 Å, with distorted octahedra sharing edges. In the pentahydrate, Na2TeO3.5H2O there are discrete tellurite anions, TeO32− which are pyramidal. The Te-O distance is 1.85 - 1.86 Å and the O-Te-O angle is close to 99.5°.
Graphium eurypylus has a wingspan reaching about . The basic colour of the uppersides of the wings is black, with a chain of yellowish or greenish spots at the edges. In the middle of the forewings there is a large yellowish or greenish area. The undersides of the wings are similar to the uppersides, but the basic colour is brownish and the spots are paler or whitish.
Steady and separated incompressible potential flow around a plate in two dimensions,Batchelor (2000), p. 499, eq. (6.13.12). with a constant pressure along the two free streamlines separating from the plate edges. In the second half of the 19th century, focus shifted again towards using inviscid flow theory for the description of fluid drag—assuming that viscosity becomes less important at high Reynolds numbers.
A biclique cover of the ten-vertex crown graph The number of edges in a crown graph is the pronic number n(n − 1). Its achromatic number is n: one can find a complete coloring by choosing each pair {ui, vi} as one of the color classes. Crown graphs are symmetric and distance-transitive. describe partitions of the edges of a crown graph into equal-length cycles.
The species has a shrill, staccato, chattering call and a sharp, screaming call but is usually silent outside the breeding season. It is fairly common in the southern and western parts of Madagascar but more local in the north and east and absent from the central plateau. It occurs from sea level up to 2000 metres. It inhabits clearings and edges in forest and woodland.
The five edges in each matching quintet are distinguishable, since corresponding non- central edges are mirror images of each other. There are 12!/2 ways to arrange the central edges, since an odd permutation of the corners implies an odd permutation of these pieces as well. There are 211 ways that they can be flipped, since the orientation of the twelfth edge depends on the preceding eleven.
The ' r(H) of a hypergraph H is the maximum cardinality of any of the edges in the hypergraph. If all edges have the same cardinality k, the hypergraph is said to be uniform or k-uniform, or is called a k-hypergraph. A graph is just a 2-uniform hypergraph. The degree d(v) of a vertex v is the number of edges that contain it.
The original ribbon was plain purple, with the addition of a thin vertical red stripe for military awards. A silver laurel branch was added diagonally to the ribbon for both types of award in 1933. The ribbon changed to rose pink with pearl grey edges in July 1937, with an addition pearl grey vertical stripe for military awards, and stayed in this version until its revocation.
Lilium kesselringianum is a large herbaceous member of the lily family. It is native to North and South Caucasus as well as northern Turkey.Kew World Checklist of Selected Plant Families It grows from sea level along the Black Sea up into the mountains to subalpine level on forest edges, in brushlands, and in grassy meadows.Misczenko, Pavel Ivanovich 1914. Trudy Byuro po Prikladnoi Botanike 7:251.
New anamorphic optics were built by Panavision which were very different from CinemaScope lenses which used optical ground glass elements set in a frame to create the anamorphic image. The problem with these lenses, however, was that whatever was in the center of the image tended to be stretched wider than whatever was at the edges. In close-up shots, this distortion was particularly noticeable.
The dimension of a graph is written: \dim G. For example, the Petersen graph can be drawn with unit edges in E^2, but not in E^1: its dimension is therefore 2 (see the figure to the right). This concept was introduced in 1965 by Paul Erdős, Frank Harary and William Tutte. It generalises the concept of unit distance graph to more than 2 dimensions.
All PAR lamps except those with narrow or very narrow lenses produce an intense oval pool of light, some with fixed focus and soft edges. In order to adjust the orientation of the oval, the lamp must be rotated. The number associated with a PAR light (e.g.: Par 64, Par 36, Par 16) indicates the diameter of the lamp in eighths of an inch.
The network probability matrix describes the probability structure of a network based on the historical presence or absence of edges in a network. For example, individuals in a social network are not connected to other individuals with uniform random probability. The probability structure is much more complex. Intuitively, there are some people whom a person will communicate with or be connected more closely than others.
In the undirected edge- disjoint paths problem, we are given an undirected graph and two vertices and , and we have to find the maximum number of edge-disjoint s-t paths in . The Menger's theorem states that the maximum number of edge-disjoint s-t paths in an undirected graph is equal to the minimum number of edges in an s-t cut-set.
Electrostrymon joya, the muted hairstreak, is a butterfly of the family Lycaenidae. It was described by Paul Dognin in 1895. It is found from southern Texas and Mexico to Ecuador, Peru and Tobago,"Electrostrymon Clench, 1961" at Markku Savela's Lepidoptera and Some Other Life Forms as well as on the Netherlands Antilles. The habitat consists of openings and edges in tropical semideciduous river forests and second growth.
Every transitively reduced st-planar graph, a directed acyclic planar graph with a single source and a single sink, both on the outer face of some embedding of the graph, has a dominance drawing. The left-right algorithm for finding these drawings sets the x coordinate of every vertex to be its position in a depth-first search ordering of the graph, starting with s and prioritizing edges in right-to-left order, and by setting the y coordinate to be obtained in the same way but prioritizing edges in left-to-right order. Typical dominance drawing algorithms include another phase of compaction after this coordinate assignment, shifting vertices down and to the left as much as possible while preserving the properties of a dominance drawing. The resulting drawing lies within an n × n integer grid, and displays many of the symmetries of the underlying topological embedding.
The problem may be generalized for a set of forbidden subgraphs S: find the maximal number of edges in an n-vertex graph which does not have a subgraph isomorphic to any graph from S.Handbook of Discrete and Combinatorial Mathematics By Kenneth H. Rosen, John G. Michaels p. 590 There are also hypergraph versions of forbidden subgraph problems that are much more difficult. For instance, Turán's problem may be generalized to asking for the largest number of edges in an n-vertex 3-uniform hypergraph that contains no tetrahedra. The analog of the Turán construction would be to partition the vertices into almost equal subsets V_1, V_2, V_3, and connect vertices x,y,z by a 3-edge if they are all in different V_is, or if two of them are in V_i and the third is in V_{i+1} (where V_4=V_1).
Note that this case is analogous to the balls into bins model. It proves that, if d bins are picked randomly for each ball, then it is possible to select one bin for each ball such that the bins are all distinct (the maximum load is 1). In the general cake model, where the value functions are different, the probabilities of the edges in the implication graph are dependent.
In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising Tatar, Nurollah, et al. "High-Resolution Satellite Stereo Matching by Object-Based Semiglobal Matching and Iterative Guided Edge- Preserving Filter." IEEE Geoscience and Remote Sensing Letters (2020): 1-5.. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g.
A graph and two of its cuts. The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some sense.
3D computer animation combines 3D models of objects and programmed or hand "keyframed" movement. These models are constructed out of geometrical vertices, faces, and edges in a 3D coordinate system. Objects are sculpted much like real clay or plaster, working from general forms to specific details with various sculpting tools. Unless a 3D model is intended to be a solid color, it must be painted with "textures" for realism.
There is another great circle path of interest that alternately passes through opposing cell vertices, then along an edge. This path consists of 6 cells and 6 edges. Both the above great circle paths have dual great circle paths in the 600-cell. The 10 cell face to face path above maps to a 10 vertices path solely traversing along edges in the 600-cell, forming a decagon.
Some of the Melbourne bands he played in from 1976 to 1978 included Thunder and Edges. In 1979 he co-founded a Melbourne-based band called Cheks (renamed Deckchairs Overboard when they moved to Sydney in 1982). He lived with Deborah Conway of Do-Ré-Mi during the early 1980s, while playing regularly in Love Party. Hester later worked with Conway in Rose Amongst Thorns (1990–1991) and Ultrasound (1995).
In Costa Rica it is a common bird from altitude in the lower and middle levels of wet mountain forests and adjacent semi-open areas like clearings with shade trees, second growth and woodland edges. In the heavy rains of the wet season, it will descend to sea level. In the South American part of its range it mainly occurs between , but can be found at altitudes of .
Salvia maximowicziana is a perennial plant that is found growing on grasslands, forests, and forest edges in China, at elevation. It grows tall, with circular-cordate to ovate-cordate leaves that are typically long and wide. The upper leaf surface is nearly smooth, or lightly covered with hairs, while the underside has glandular hairs on the veins. The inflorescence is of loose racemes or panicles, with a corolla.
These low-growing and rather handsome little plants have clumps of downy, light green, heart-shaped leaves with serrated edges. In late spring, small loose umbel of delicate bell-shaped to lily-liked flowers born terminally on drooping spikes arise from the base, some 6-8in high. Flowers are magenta, pink, white and yellow. They are dormant in some months, and as spring begins, stems and leaves quickly start to reproduce.
The embalmers likely used a sharp instrument on the skull. The left side of the lower face includes a large defect involving her left cheek, left maxillary sinus, alveolar process, and part of her left mandible. There are sharp edges in this bony defect, with no evidence of attempted healing or sclerosis. Fragments of the broken lateral wall of the left maxillary sinus were located within the antral cavity.
Relationships between regions can then be included in models of how a disease spreads from place to place. To accomplish this, STEM represents the world as a "graph". The nodes in the graph correspond to places or regions, and the edges in the graph describe relationships or connections between regions. Both the nodes and the edges can be labeled or "decorated" with a variety of denominator data and models.
No better worst-case time bound is possible because, for any fixed value of β smaller than one, there exist point sets in general position (small perturbations of a regular polygon) for which the β-skeleton is a dense graph with a quadratic number of edges. In the same quadratic time bound, the entire β-spectrum (the sequence of circle-based β-skeletons formed by varying β) may also be calculated.
The Petersen family. The generalized Petersen graph G(n,k) is formed by connecting the vertices of a regular n-gon to the corresponding vertices of a star polygon with Schläfli symbol {n/k}.; . For instance, in this notation, the Petersen graph is G(5,2): it can be formed by connecting corresponding vertices of a pentagon and five-point star, and the edges in the star connect every second vertex.
The marvellous spatuletail (Loddigesia mirabilis) is a medium-sized (up to 15 cm long) white, green and bronze hummingbird adorned with blue crest feathers, a brilliant turquoise gorget, and a black line on its white underparts. It is the only member of the monotypic genus Loddigesia. It is sexually dimorphic. Distribution of Loddigesia mirabilis in Peru A Peruvian endemic, this species is found on forest edges in the Río Utcubamba region.
Buddleja candida is a small deciduous shrub widely distributed from north-east India through south east Xizang (Tibet) to the provinces of Sichuan and Yunnan in western China, growing on forest edges, in mountain thickets, and along riverbanks, at altitudes of 1000 - 2500 m. Named and described by Dunn in 1920, the shrub was introduced to cultivation in the west in 1928.Stuart, D. (2006). Buddlejas. RHS Plant Collector Guide.
Nesting sites are often near a stream, or otherwise perhaps near a ravine with wide view but sometimes varies from deep forest to isolated trees on village edges. In the peri-urban green spaces of Singapore, changeable hawk-eagles nested mostly on Albizia trees, which are among the fastest-growing and tallest trees in these secondary forests.Tan, K.H. (2005). The status and distribution of Changeable Hawk-eagle (Nisaetus cirrhatus) in Singapore.
Less preferred habitat are shrubland, farmlands and forest edges. In particular American yellow warblers will come to suburban or less densely settled areas, orchards and parks, and may well breed there. Outside the breeding season, these warblers are usually encountered in small groups, but while breeding they are fiercely territorial and will try to chase away any conspecific intruder that comes along. These birds feed mainly on arthropods, in particular insects.
Flames had engulfed the entire amidships section of the stricken landing ship, and explosions tore holes in the stricken ship's side. The jagged edges in turn ripped gashes in Willmarth's hull at the waterline. One hole, unfortunately, opened up one of the destroyer escort's fuel tanks, and the oil leaking out made further close operations hazardous. Willmarth stood clear while dense smoke from the burning LST further complicated firefighting.
The real-time image processing involves reducing the resolution, enhancing contrast, detecting the edges in the image and converting it into a spatio- temporal pattern of stimulation delivered to the electrode array on the retina. The majority of electronics can be incorporated into the associated external components, allowing for a smaller implant and simpler upgrades without additional surgery. The external electronics provides full control over the image processing for each patient.
A path of four upward-sloping edges in a set of 17 points. By the Erdős–Szekeres theorem, every set of 17 points has a path of this length that slopes either upward or downward. The 16-point subset with the central point removed has no such path. In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.
Edge-directed interpolation algorithms aim to preserve edges in the image after scaling, unlike other algorithms, which can introduce staircase artifacts. Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), Edge- Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional Cubic Convolution Interpolation (DCCI). A 2013 analysis found that DCCI had the best scores in PSNR and SSIM on a series of test images.
The distance is the length of a shortest path connecting the vertices. Unless lengths of edges are explicitly provided, the length of a path is the number of edges in it. The distance matrix resembles a high power of the adjacency matrix, but instead of telling only whether or not two vertices are connected (i.e., the connection matrix, which contains boolean values), it gives the exact distance between them.
The morphology of this species is variable, the fronds vary in shape and color. They can measure up to 10 cm long, they are flat, lobed at the edges and in some cases wavy. The color can vary from light brown, yellow and in some cases with light red to discolored edges. In the margins, the reproductive structures are presented, which when they are released, have a whitish coloration.
The primitive graph operations that the algorithm uses are to enumerate the vertices of the graph, to store data per vertex (if not in the graph data structure itself, then in some table that can use vertices as indices), to enumerate the out-neighbours of a vertex (traverse edges in the forward direction), and to enumerate the in-neighbours of a vertex (traverse edges in the backward direction); however the last can be done without, at the price of constructing a representation of the transpose graph during the forward traversal phase. The only additional data structure needed by the algorithm is an ordered list L of graph vertices, that will grow to contain each vertex once. If strong components are to be represented by appointing a separate root vertex for each component, and assigning to each vertex the root vertex of its component, then Kosaraju's algorithm can be stated as follows. # For each vertex u of the graph, mark u as unvisited.
Brian Alspach and Heather Gavlas established necessary and sufficient conditions for the existence of a decomposition of a complete graph of even order minus a 1-factor into even cycles and a complete graph of odd order into odd cycles. Their proof relies on Cayley graphs, in particular, circulant graphs, and many of their decompositions come from the action of a permutation on a fixed subgraph. They proved that for positive even integers m and n with 4\leq m\leq n , the graph K_n-I (where I is a 1-factor) can be decomposed into cycles of length m if and only if the number of edges in K_n-I is a multiple of m. Also, for positive odd integers m and n with 3≤m≤n, the graph K_n can be decomposed into cycles of length m if and only if the number of edges in K_n is a multiple of m.
The nine-vertex Paley graph, a balanced tripartite graph with 18 edges, each belonging to exactly one triangle Several views of the Brouwer–Haemers graph, a non-tripartite 20-regular graph with 81 vertices in which each edge belongs to exactly one triangle In combinatorial mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or (6,3)-problem asks for the maximum number of edges in a graph in which every edge belongs to a unique triangle. Equivalently it asks for the maximum number of edges in a balanced bipartite graph whose edges can be partitioned into a linear number of induced matchings, or the maximum number of triples one can choose from n points so that every six points contain at most two triples. The problem is named after Imre Z. Ruzsa and Endre Szemerédi, who first proved that its answer is smaller than n^2 by a slowly-growing (but still unknown) factor.
In a hypergraph H = (V, E), each edge of E may contain more than two vertices of V. The degree of a vertex v in V is, as before, the number of edges in E that contain v. But in a hypergraph we can also consider the degree of subsets of vertices: given a subset U of V, deg(U) is the number of edges in E that contain all vertices of U. Thus, the degree of a hypergraph can be defined in different ways depending on the size of subsets whose degree is considered. Formally, for every integer d ≥ 1, degd(H) is the minimum of deg(U) over all subsets U of V that contain exactly d vertices. Thus, deg1(H) corresponds to the definition of a degree of a simple graph, namely the smallest degree of a single vertex; deg2(H) is the smallest degree of a pair of vertices; etc.
A Shannon multigraph with degree six and edge multiplicity three, requiring nine colors in any edge coloring For multigraphs, in which multiple parallel edges may connect the same two vertices, results that are similar to but weaker than Vizing's theorem are known relating the edge chromatic number , the maximum degree , and the multiplicity , the maximum number of edges in any bundle of parallel edges. As a simple example showing that Vizing's theorem does not generalize to multigraphs, consider a Shannon multigraph, a multigraph with three vertices and three bundles of parallel edges connecting each of the three pairs of vertices. In this example, (each vertex is incident to only two out of the three bundles of parallel edges) but the edge chromatic number is (there are edges in total, and every two edges are adjacent, so all edges must be assigned different colors to each other). In a result that inspired Vizing,, p. 136.
A PageRank-based algorithm could identify important protein targets in the pathogen organism better than a method considering only the number of incoming edges (in-degree) of a node in the metabolic network. The reason for this is that some already known, important protein targets do not have a high degree (are not hubs) and also, perturbing some hubs could result in unwanted physiological effects.Russell RB, Aloy P (2008). "Targeting and tinkering with interaction networks".
The species has been found in heavy, barrier-beach forest, in pine-barrens undergrowth (both typical or heavy and grassy), on the borders of pine barrens, on swamp edges, in heavy deciduous forest, and in heavy oak woods. In Florida it has been found in mesic hammock, xeric hammock, scrub, and sand hill habitats. Individuals may be found under dead leaves, pine needles (particularly beneath shortleaf pine), logs, beneath loose bark, or wandering at night.
GQL is a query language specifically for property graphs. A property graph closely resembles a conceptual data model, as expressed in an entity–relationship model or in a UML class diagram (although it does not include n-ary relationships linking more than two entities). Entities or concepts are modelled as nodes, and relationships as edges, in a graph. Property graphs are multigraphs: there can be many edges between the same pair of nodes.
The medal is suspended by a ribbon wide and long of dark blue with the edges in the German national colors, black-red-gold. The service ribbon of the medal is in the same colors as the suspension ribbon. The service ribbon is wide and high, with the edge stripes of black-red-gold wide each. In the center of the ribbon is worn a wide representation of the obverse of the medal.
In Central Europe C. undecimpunctata feeds on aphids associated with grasses - in fields, in ruderal biotopes, on steppe (including Pannonian steppe), stone quarries, wastelands, dry forest edges in meadows and coastal meadow, in open habitats with grasses, near rivers. Frequently in biotopes with Ammophila arenaria it also occurs on alluvial soils, detritus, on dead grass and in biotopes with Salix purpurea.Koch, K., Die Käfer Mitteleuropas, Ökologie. Vol. 2 (Goecke und Evers Verlag, Krefeld, 1989).
Over the years Altadena has been subject to attempted annexation by Pasadena. Annexation was stopped in 1956 by community campaigns, though it has been resurrected several times since by Pasadena without success. Had the annexation succeeded, Pasadena would be the 108th largest city in the United States. While Altadena long refused wholesale annexation by neighboring Pasadena, the larger community nibbled at its edges in several small annexations of neighborhoods through the 1940s.
In this regard, some dependency grammars employ an arrow convention. Arguments receive a "normal" dependency edge, whereas adjuncts receive an arrow edge.See Eroms (2000) and Osborne and Groß (2012) in this regard. In the following tree, an arrow points away from an adjunct toward the governor of that adjunct: ::Argument picture 2 The arrow edges in the tree identify four constituents (= complete subtrees) as adjuncts: At one time, actually, in congress, and for fun.
In graph theory, Berge's lemma states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there is no augmenting path (a path that starts and ends on free (unmatched) vertices, and alternates between edges in and not in the matching) with M. It was proven by French mathematician Claude Berge in 1957 (though already observed by Petersen in 1891 and Kőnig in 1931).
Blakley et al. have described how the technique used by BioFabric, which they refer to as a cartographic representation, can be used to compare the networks A and B by juxtaposing the edges in (A ∖ B), (A ∩ B), and (B ∖ A), a technique that is evocative of a Venn Diagram. Rossi and Magnani. have developed ranked sociograms, which is a BioFabric-like presentation where the node ordering is based upon a ranking metric.
Multigraphs of both Königsberg Bridges and Five room puzzles have more than two odd vertices (in orange), thus are not Eulerian and hence the puzzles have no solutions. degree. Therefore, this is an Eulerian graph. Following the edges in alphabetical order gives an Eulerian circuit/cycle. In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices).
Minimal Bottleneck Spanning Tree In an undirected graph and a function , let be the set of all spanning trees Ti. Let B(Ti) be the maximum weight edge for any spanning tree Ti. We define subset of minimum bottleneck spanning trees S′ such that for every and we have for all i and k. The graph on the right is an example of MBST, the red edges in the graph form a MBST of .
Waves and wind then act to compress these ice particles into larger plates, of several meters in diameter, called pancake ice. These float on the ocean surface, and collide with one another, forming upturned edges. In time, the pancake ice plates may themselves be rafted over one another or frozen together into a more solid ice cover, known as consolidated pancake ice. Such ice has a very rough appearance on top and bottom.
This frog is endemic to Colombia and Ecuador, being found on the western slopes of the Western Cordilleras and the Central Cordilleras in Colombia, and in the Ecuadorean provinces of Carchi, Cotopaxi, Pichincha and Santo Domingo de los Tsáchilas. Its altitudinal range is between . It is to be found in foliage in swamps and near streams, in cloud forest, by forest edges, in pastures and by roadsides, but never far from forests.
Lieutenant Lenore "Lonnie" Ellen Henderson (Kathy Evison; seasons 2 & 3) signed aboard the seaQuest DSV-II as a helmsman in 2021. As a first generation naval officer, she was a bit rough around the edges in terms of proper protocol. She successfully was able to smuggle her stuffed bear Addison aboard seaQuest, much to the consternation of Commander Ford. Henderson initially showed an interest in Lieutenant O'Neill and the two spent some shore leave together.
Titus, K., & Mosher, J. A. (1981). Nest-site habitat selected by woodland hawks in the central Appalachians. The Auk, 98(2), 270-281. Forest edges, in particular, tend to be key as these are peak hunting grounds for these hawks.Millsap, B. A., Madden, K. Murphy, R. K. & Campbell, D. (2012). Demography and Population Dynamics of Cooper’s Hawks in Albuquerque, New Mexico, with an Emphasis on Non-breeding Adult Floaters: Annual Progress Report, Year Two.
In the ant colony optimization algorithms, an artificial ant is a simple computational agent that searches for good solutions to a given optimization problem. To apply an ant colony algorithm, the optimization problem needs to be converted into the problem of finding the shortest path on a weighted graph. In the first step of each iteration, each ant stochastically constructs a solution, i.e. the order in which the edges in the graph should be followed.
The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.
The male painted bunting was once a very popular caged bird, but its capture and holding is currently illegal. Trapping for overseas sale may still occur in Central America. Populations are primarily declining due to habitat being lost to development, especially in coastal swamp thickets and woodland edges in the east and riparian habitats in migration and winter in the Southeastern United States and Mexico. They are protected by the U.S. Migratory Bird Act.
In sewing and tailoring, facing is a small piece of fabric, separate or a part of the fabric itself, used to finish the fabric edges. Facing makes a garment look professionally finished with the seams well hidden inside the folds of the facing. Facing is mostly used to finish the edges in necklines, armholes, hems and openings. They are also used widely in all other sewing like quilts and home decor items like curtain hems.
Thus, it becomes easy to find edges in the picture and trace the image onto the tracing paper. Pure cellulose fiber is translucent, and it is the air trapped between fibers that makes paper opaque and look white. If the fibers are refined and beaten until all the air is taken out, then the resulting sheet will be translucent. Translucent papers are dense and contain up to 10% moisture at 50% humidity.
Euryops chrysanthemoides is indigenous to southern Africa, where it occurs in the Eastern Cape, along the coast and inland, to KwaZulu-Natal, Mpumalanga and Swaziland. It is usually found on forest edges, in riverine bush and in ravines, as well as in coastal scrub, grassland and disturbed areas. It is a ruderal weed in New South Wales, although it is not invasive in all places where it is cultivated or has naturalized.
Data-flow optimizations, based on data-flow analysis, primarily depend on how certain properties of data are propagated by control edges in the control flow graph. Some of these include: ;Common subexpression elimination: In the expression `(a + b) - (a + b)/4`, "common subexpression" refers to the duplicated `(a + b)`. Compilers implementing this technique realize that `(a + b)` will not change, and so only calculate its value once.Aho, Sethi, and Ullman, Compilers, pp. 592–594.
Here denotes the graph derived from G by contracting edges in F (by the Cut property, these edges belong to the MST). Each Boruvka step takes linear time. Since the number of vertices is reduced by at least half in each step, Boruvka's algorithm takes O(m log n) time. A second algorithm is Prim's algorithm, which was invented by Vojtěch Jarník in 1930 and rediscovered by Prim in 1957 and Dijkstra in 1959.
The language was designed with the power and capability of SQL (standard query language for the relational database model) in mind, but Cypher was based on the components and needs of a database built upon the concepts of graph theory. In a graph model, data is structured as nodes (vertices in math and network science) and relationships (edges in math and network science) to focus on how entities in the data are connected and related to one another.
In graph theory, the Y-Δ transform means replacing a Y subgraph of a graph with the equivalent Δ subgraph. The transform preserves the number of edges in a graph, but not the number of vertices or the number of cycles. Two graphs are said to be Y-Δ equivalent if one can be obtained from the other by a series of Y-Δ transforms in either direction. For example, the Petersen family is a Y-Δ equivalence class.
In the mathematical field of graph theory, the bull graph is a planar undirected graph with 5 vertices and 5 edges, in the form of a triangle with two disjoint pendant edges. It has chromatic number 3, chromatic index 3, radius 2, diameter 3 and girth 3. It is also a self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex- connected graph and a 1-edge-connected graph.
The 60 faces are deltoids or kites. The short and long edges of each kite are in the ratio 1: ≈ 1:1.539344663... The angle between two short edges in a single face is arccos()≈118.2686774705°. The opposite angle, between long edges, is arccos()≈67.783011547435° . The other two angles of each face, between a short and a long edge each, are both equal to arccos()≈86.97415549104°. The dihedral angle between any pair of adjacent faces is arccos()≈154.12136312578°.
Because of the span difference, these leaned outwards at 45°, allowing them to carry ailerons on their trailing edges. In addition, it was claimed, these provided the lateral stability more usually secured with dihedral as well as producing additional lift. The fuselage and empennage of the AS-27 were conventional, with its cockpit over the lower wing. Its fixed conventional undercarriage had arched leaf spring cantilever main legs with cable bracing, together with a steerable tailwheel.
Rhododendron laetum is a rhododendron species native to the Anggi Lakes area of the Arfak Mountains in Indonesia and western New Guinea, where it grows at forest edges, in open marsh, and in swamps at the edge of lakes. It is a shrub that grows to 3 m in height, with leaves that are broadly elliptic or sub- ovate-elliptic, 40–95 × 25–53 mm in size. Flowers are deep yellow, flushing with red or orange as they age.
This species is known as acebiño in Spanish and azevinho in Portuguese. It is a shrub or small tree up to 6.5 meters tall sometimes 10 m high, evergreen, with a gray trunk. It has glossy ovate leaves, 5–7 cm long by and 2.5–4 cm wide, usually whole rounded edges in the leaves and only a few small spines; iota obtuse or rounded. The leaves have ovate to ovate to lanceolate, bright and whole.
Most of the work on classification problems has focused on three dimensions, particularly on the classification of crystal nets, i.e., of periodic graphs that could serve as descriptions or designs for placement of atoms or molecular objects, with bonds indicated by edges, in a crystal. One of the more popular classification criteria is graph isomorphism, not to be confused with crystallographic isomorphism. Two periodic graphs are often called topologically equivalent if they are isomorphic, although not necessarily homotopic.
After a match is over, players earn experience to slowly level up and may randomly obtain new equipment. The equipment equipped may gives some edges in the battle as different items gives different effects to the players during the Combat stage. There are two currencies, earned in-game gold and gems. Gold is used to slightly enhance existing equipment and gems may be used to give more gameplay turns or play the slot machine which awards powerful equipment.
In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed by Joel Spencer. He used a branching process to formally prove the optimal achievable bound under some side conditions.
If only two of them are chosen, their end-vertices must be adjacent in the two 5-cycles, which is not possible. Hence 4 of them are chosen. Assume that the top edge of the cut is not chosen (all the other cases are the same by symmetry). Of the 5 edges in the outer cycle, the two top edges must be chosen, the two side edges must not be chosen, and hence the bottom edge must be chosen.
A plane graph (in blue) and its medial graph (in red). In the mathematical discipline of graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were introduced in 1922 by Ernst Steinitz to study combinatorial properties of convex polyhedra, although the inverse construction was already used by Peter Tait in 1877 in his foundational study of knots and links.
The Karger–Stein variant of Karger's algorithm provides a faster randomized algorithm for determining the connectivity, with expected runtime O(n^2\log^3 n). A related problem: finding the minimum k-edge-connected spanning subgraph of G (that is: select as few as possible edges in G that your selection is k-edge-connected) is NP-hard for k\geq 2.M.R. Garey and D.S. Johnson. Computers and Intractability: a Guide to the Theory of NP-Completeness.
This prevents the ejector blades from striking the back of a mold liner on narrow slugs. As the slug is pushed from the mold, the slug passes a set of knife edges in the knife block, which trims off any small irregularities in the casting and produces a slug of exactly the desired point thickness. From there, the slug drops into the galley tray which holds the lines in the order in which they were cast.
The wrought-iron gates in front came from the North Reformed Dutch Church, which closed in 1875. The chapel's Byzantine interior features Guastavino tile vaulting in intricate patterns on almost every curved surface. Three stained glass windows by John La Farge adorn the apse; other windows are by D. Maitland Armstrong, Henry Wynd Young, and J. Gordon Guthrie. The chapel contains an "Altar for Peace" by George Nakashima, a wooden table with natural edges in his signature style.
Ravi Kannan, Santosh Vempala and Adrian Vetta proposed a bicriteria measure to define the quality of a given clustering. They said that a clustering was an (α, ε)-clustering if the conductance of each cluster (in the clustering) was at least α and the weight of the inter-cluster edges was at most ε fraction of the total weight of all the edges in the graph. They also look at two approximation algorithms in the same paper.
Reviews for the series have been positive, with warm notices from USA Today and Entertainment Weekly. Darren Staley of America's Comedy writes "The show is at all times smart, unpredictable, thought-provoking, and funny as hell," arguing that "It's the best podcast out there right now." Writing for IFC, Ron Mwangaguhunga called Macdonald "a comedic force with which to be reckoned," noting that the show was "a bit rough around the edges," in its first episode.
The large, iron sword pommel survived along with the guard, four gold hoops from the hilt and six gold rivets. The pommel is broadly triangular and is inlaid with plaques of gold foil decorated with incised animal interlace with nicked edges in the late Anglo-Saxon Trewhiddle style, which can be dated to the late 9th century. The form of the pommel is typical of Petersen's late 9th-century type L.Petersen, J. 1919. De Norske Vikingesverd.
There is a spot on the southern end known as Kudhuheraival (forest of a small islet), which indicates there was a small separate islet over there in ancient times. The channel connecting the lagoon with the ocean was closed by massive coral boulders in the past. Thus the inside of the island is lower than its edges. In time the inner lagoon lost its saltiness and all that remains today are two small lakes, wetlands and marshy taro fields.
Formally, let be any graph, and let be any subset of vertices of . Then the induced subgraph is the graph whose vertex set is and whose edge set consists of all of the edges in that have both endpoints in .. The same definition works for undirected graphs, directed graphs, and even multigraphs. The induced subgraph may also be called the subgraph induced in by , or (if context makes the choice of unambiguous) the induced subgraph of .
The disjointness graph of G, denoted D(G), is constructed in the following way: for each edge in G, make a vertex in D(G); for every two edges in G that do not have a vertex in common, make an edge between their corresponding vertices in D(G). In other words, D(G) is the complement graph of L(G). A clique in D(G) corresponds to an independent set in L(G), and vice versa.
Taipei was not known to be prosperous until after World War II. Starting in the 1950s, Night markets formed in Taipei's old urban areas and later settlements were set up across the city's edges. In the 1970s, night markets spread into new suburbs and manufacturing areas. There were also traveling periodic night markets that could even be found in rural towns. By the 1980s, anyone could buy a full range of goods even in a remote area.
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q). Dihedra have also been called bihedra,. flat polyhedra, or doubly covered polygons.
6-connected pixels are neighbors to every pixel that touches one of their corners (which includes pixels that touch one of their edges) in a hexagonal grid or stretcher bond rectangular grid. There are several ways to map hexagonal tiles to integer pixel coordinates. With one method, in addition to the 4-connected pixels, the two pixels at coordinates \textstyle(x+1,y+1) and \textstyle(x-1,y-1) are connected to the pixel at \textstyle(x,y).
In the former, the objective function in the minimization is the Wiener index of the connector, whereas in the latter, the objective function is the sum of the weights of the edges in the connector. The optimum solutions to these problems may differ, given the same graph and set of query vertices. In fact, a solution for the Steiner tree problem may be arbitrarily bad for the minimum Wiener connector problem; the graph on the right provides an example.
Epichloë hybrida was one of the first Epichloë hybrids identified. Although the date of the hybridization event is not known with any certainty, an upper bound of ~300,000 years has been estimated. The colony morphology of E. hybrida Lp1 is a compact form with wavy edges, in contrast to the morphology of either parent. Conidia stained with DAPI, which binds to DNA, show only a single nucleus, confirming that E. hybrida is mononucleate and not simply an interspecies dikaryon.
In optimization, 3-opt is a simple local search algorithm for solving the travelling salesman problem and related network optimization problems. 3-opt analysis involves deleting 3 connections (or edges) in a network (or tour), to create 3 sub-tours. Then the 7 different ways of reconnecting the network are analysed to find the optimum one. This process is then repeated for a different set of 3 connections, until all possible combinations have been tried in a network.
Some complex systems, for example, are also complex networks, which have properties such as phase transitions and power- law degree distributions that readily lend themselves to emergent or chaotic behavior. The fact that the number of edges in a complete graph grows quadratically in the number of vertices sheds additional light on the source of complexity in large networks: as a network grows, the number of relationships between entities quickly dwarfs the number of entities in the network.
Lemma- Let H be a subgraph of G formed by including each edge of G independently with probability p and let F be the minimum spanning forest of H. The expected number of F-light edges in G is at most n/p where n is the number of vertices in G To prove the lemma examine the edges of G as they are being added to H. The number of F-light edges in G is independent of the order in which the edges of H are selected since the minimum spanning forest of H is the same for all selection orders. For the sake of the proof consider selecting edges for H by taking the edges of G one at a time in order of edge weight from lightest to heaviest. Let e be the current edge being considered. If the endpoints of e are in two disconnected components of H then e is the lightest edge connecting those components and if it is added to H it will be in F by the cut property.
A major use of partial transparency is to produce "soft edges" in graphics so that they blend into their background. See also monochrome or with shades of gray and anti-aliasing. Partial transparency can also be used to make an image less prominent, such as a watermark or other logo; or to render something see-through, such as a ghostly apparition in a video game. Animating the alpha channel in an image-editing program can allow smooth transitions between different images.
When comparing two strands of DNA, colored de Bruijn graphs are frequently used to identify errors. These errors, often polymorphisms, cause bubbles, similar to the ones mentioned above, to form. Currently there are four main algorithms used to generalize the data and locate bubbles. The four algorithms extend de Bruijn graphs by allowing the nodes and edges in the graph to be colored by the samples from which they were observedIqbal, Z., Caccamo, M., Turner, I., Flicek, P., & McVean, G. (2012).
In order to prove this generalized form of the theorem, Petersen first proved that a 4-regular graph can be factorized into two 2-factors by taking alternate edges in a Eulerian trail. He noted that the same technique used for the 4-regular graph yields a factorization of a 2k-regular graph into two k-factors.Mulder, H. "Julius Petersen’s theory of regular graphs". Discrete Mathematics, 100 (1992) 157-175 North-Holland To prove this theorem, it is sufficient to consider connected graphs.
When a new pulse of magma forced its way upward, the edges in contact with the older magma cooled rapidly forming a kind of "skin" of fine-grained granite. Since fine-grained granite is less porous, this "outer skin" sealed the magma body and helped to trap rare elements and water inside. Over time, the water and rare elements were concentrated along the edges of the magma. While the magma cooled and crystallized, the water content of the remaining liquid magma increased rapidly.
DCDi by Faroudja (directional correlational de-interlacing) technology DCDi by Faroudja is an advanced deinterlacing algorithm for upconverting and deinterlacing standard definition NTSC content for display on high-definition flat panel TVs. DCDi by Faroudja corrects several deinterlacing issues, including visible jagged edges in an image, cross-color artifacts and includes Film mode processing.Genesis Microchip technical overview Faroudja DCDi Cinema was developed around higher performance 10-bit processing with extended picture enhancement controls, an active color management system and 3D Noise Reduction.
The S8 Active features tougher materials designed for protection against shock, shatter, water and dust, with a metal frame and a tough texture for improved grip that makes the S8 Active have a rugged design. The Active's screen measures the same size as the standard S8 model but loses the curved edges in favor of a metal frame. The S8 and S8+ received positive reviews. Their design and form factor received praise, while critics also liked the updated software and camera optimizations.
The nodules coalesce early in the course of disease, such that the nodules may only be seen as soft fluffy edges in the periphery. When the nodules are centered on the hilar regions, the chest x-ray may develop what is called the "butterfly," or "batwing" appearance. The nodules may also have a segmental or lobar distribution. Air alveolograms and air bronchograms can also be seen which indicate fluid in the alveoli with air in the terminal bronchioles indicating disease is alveolar.
In 2010, Jonah contributed a cover of the New Order song "Dream Attack" to the tribute album Ceremony - A New Order Tribute, endorsed by Peter Hook of New Order, which benefited The Salford Foundation Trust. Cordy also produced a remix of "Ceremony" performed by sister act Yes But No which was included in the double album. In August 2011, his first full-length album, the eight song Cosmonauts was released worldwide, followed by On the Edges in 2014 and The Movies in 2018.
The games run well in DOSBox on modern operating systems. Also the Gold Box Companion has been developed to smooth out some of the rough edges in the programming of some of the games. Some of the early games, for instance, do not allow turning off Quick Fight, which sets characters to automatic in combat. GOG.com released the Pool of Radiance and Savage Frontier Gold Box series digitally on August 20, 2015, as a part of "Forgotten Realms: The Archives - Collection Two".
Convolve the image with a Sobel filter to extract edges. Using this filtered image create a graph using pixels as nodes with edges in four directions (up, down, left right). Edges are weighted with features gathered from the Sobel filter making it less costly to stay on an edge. Several different cost methods are possible but the most important is the gradient magnitude Live-Wire 2-D DP graph search algorithm in pseudocode algorithm Livewire is input: s {Start (or seed) pixel.
With the recent explosion of publicly available high throughput biological data, the analysis of molecular networks has gained significant interest. The type of analysis in this content are closely related to social network analysis, but often focusing on local patterns in the network. For example, network motifs are small subgraphs that are over-represented in the network. Activity motifs are similar over-represented patterns in the attributes of nodes and edges in the network that are over represented given the network structure.
Sujinho is a latin jazz collaboration album between Otis Jackson Jr., an American hip hop producer and MC known as Madlib, and Ivan Conti, drummer for the Brazilian funk band Azymuth. This album features Brazilian samba music and Latin Jazz, one of Madlib's interests (he had covered Azymuth's "Papa" on Yesterdays New Quintet's Angles Without Edges in 2001.) Sujinho has been released twice, once in the Netherlands on Kindred Spirits in 2x vinyl and in the US on Mochilla Records in CD format.
For each vertex we store the list of adjacencies (out-edges) in order of the planarity of the graph (for example, clockwise with respect to the graph's embedding). We then initialize a counter i = n + 1 and begin a Depth-First Traversal from s. During this traversal, the adjacency list of each vertex is visited from left-to-right as needed. As vertices are popped from the traversal's stack, they are labelled with the value i, and i is then decremented.
Graphs and networks have two phases: disconnected (fragmented) and connected. In the connected phase every node is connected by an edge to at least one other node and for any pair of nodes, there is at least one path (sequence of edges) joining them. The Erdős–Rényi model shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases. This avalanche amounts to a sudden phase change in the size of the largest connected subgraph.
The fractal properties of the network can be seen in its underlying tree structure. In this view, the network consists of the skeleton and the shortcuts. The skeleton is a special type of spanning tree, formed by the edges having the highest betweenness centralities, and the remaining edges in the network are shortcuts. If the original network is scale-free, then its skeleton also follows a power-law degree distribution, where the degree can be different from the degree of the original network.
Whether features in a digital image are sharp enough to achieve sub-pixel resolution can be quantified by measuring the point spread function (PSF) of an isolated point in the image. If the image does not contain isolated points, similar methods can be applied to edges in the image. It is also important when attempting sub-pixel resolution to keep image noise to a minimum. This, in the case of a stationary scene, can be measured from a time series of images.
Finally, Alon applies an observation of , that selecting alternating subsets of edges in an Euler tour of the graph partitions it into two regular subgraphs, to split the edge coloring problem into two smaller subproblems, and his algorithm solves the two subproblems recursively. The total time for his algorithm is . For planar graphs with maximum degree , the optimal number of colors is again exactly . With the stronger assumption that , it is possible to find an optimal edge coloring in linear time .
Since the total number of neighbors of all vertices is just the number of edges in the graph, the algorithm takes time linear in the number of edges, its input size.. Partition refinement also forms a key step in lexicographic breadth-first search, a graph search algorithm with applications in the recognition of chordal graphs and several other important classes of graphs. Again, the disjoint set elements are vertices and the set represent sets of neighbors, so the algorithm takes linear time...
With the recent explosion of publicly available high throughput biological data, the analysis of molecular networks has gained significant interest. The type of analysis in this context is closely related to social network analysis, but often focusing on local patterns in the network. For example, network motifs are small subgraphs that are over-represented in the network. Similarly, activity motifs are patterns in the attributes of nodes and edges in the network that are over-represented given the network structure.
Information about the relative importance of nodes and edges in a graph can be obtained through centrality measures, widely used in disciplines like sociology. For example, eigenvector centrality uses the eigenvectors of the adjacency matrix corresponding to a network, to determine nodes that tend to be frequently visited. Formally established measures of centrality are degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, subgraph centrality and Katz centrality. The purpose or objective of analysis generally determines the type of centrality measure to be used.
A partition of the complete bipartite graph K4,4 into three forests, showing that it has arboricity three. The figure shows the complete bipartite graph K4,4, with the colors indicating a partition of its edges into three forests. K4,4 cannot be partitioned into fewer forests, because any forest on its eight vertices has at most seven edges, while the overall graph has sixteen edges, more than double the number of edges in a single forest. Therefore, the arboricity of K4,4 is three.
Unlike most other types of drill bits, they are not practical to use as hand tools. The bit includes a center point which guides it throughout the cut (and incidentally spoils the otherwise flat bottom of the hole). The cylindrical cutter around the perimeter shears the wood fibers at the edge of the bore, and also helps guide the bit into the material more precisely. The tool in the image has a total of two cutting edges in this cylinder.
All of these phases exhibit the ferroelectric effect apart from the cubic phase. The high temperature cubic phase is easiest to describe, as it consists of regular corner-sharing octahedral TiO6 units that define a cube with O vertices and Ti-O-Ti edges. In the cubic phase, Ba2+ is located at the center of the cube, with a nominal coordination number of 12. Lower symmetry phases are stabilized at lower temperatures and involve movement of the Ti4+ to off-center positions.
The pygmy eagle primarily resides in lowland forests and forest edges in New Guinea. They enjoy nesting in closed forestry but have also been seen in open habitat and forest edges. The bird seems to be sparsely distributed throughout the hilly forests of New Guinea; however much of the forests of New Guinea are inaccessible so the eagle may be more abundant than it seems. One of the densely forested parts of New Guinea is Vogelkop or Bird's Head Peninsula.
Additional forms of mechanical stresses include ice and sand scour, as well as dislodgment by water-borne rocks, logs, etc. For each of these climate stresses, species exist that are adapted to and thrive in the most stressful of locations. For example, the tiny crustacean copepod Tigriopus thrives in very salty, high intertidal tidepools, and many filter feeders find more to eat in wavier and higher flow locations. Adapting to such challenging environments gives these species competitive edges in such locations.
This makes studies of many substances, such as numerous liquids impossible using soft x-ray absorption. One of the most notable applications in which x-ray Raman scattering is superior to soft x-ray absorption is the study of soft x-ray absorption edges in high pressure. Whereas high-energy x-rays may pass through a high-pressure apparatus like a diamond anvil cell and reach the sample inside the cell, soft x-rays would be absorbed by the cell itself.
Devon County Council introduced triangular-ended fingerposts with edges in four different colours to illustrate the suitability of the route for various types of vehicles, from black (for most vehicles, on A- and B-roads), through blue and brown to fully white fingers, indicating local access only. This system was entitled the Functional Road Network. Suffolk County Council, too, adopted the use of Transport Heavy typefaces on square-ended fingers, and here distances over three miles are still given to the nearest quarter.
The engines were mounted ahead of the leading edges in long fairings that also housed the main landing gear. The oil radiators were nearby in the leading edges of the outer wing panels which tapered strongly to semi-elliptical tips and had about 5° dihedral. Their fuselages were oval in cross-section and tapered rearwards to pointed extremities. Each had a glazed or semi-glazed nose and a cockpit, under raised, multi-part glazing, placed ahead of the leading edge.
Joinery throughout is of red cedar, as are the interior floorboards, with japanned edges in the main rooms. There is a cedar mantelpiece in the dining room and a grey marble mantelpiece with gilt mirror in the parlour, surrounding back-to-back fireplaces. The internal walls bear early paintwork, including a plain dado strip along the hallway. A servant's entrance leads from the dining room to a gable-roofed timber kitchen house, with servant's room, attached to the rear verandah.
Sometimes, the edges in a graph have personalities: each edge has its own selfish interest. An example is a communication network, in which each edge is a computer that possibly belongs to a different person. Different computers have different transmission speeds, so every edge in the network has a numeric weight equal to the number of milliseconds it takes to transmit a message. Our goal is to send a message between two points in the network in the shortest time possible.
Kakutani's theorem for n-simplices can be used to prove the theorem for an arbitrary compact, convex S. Once again we employ the same technique of creating increasingly finer subdivisions. But instead of triangles with straight edges as in the case of n-simplices, we now use triangles with curved edges. In formal terms, we find a simplex which covers S and then move the problem from S to the simplex by using a deformation retract. Then we can apply the already established result for n-simplices.
Taxidermied bird at the Natural History Museum of Geneva The red-bellied grackle is endemic to Colombia where it is found in all three Andean ranges at altitudes of above sea level. Its natural habitat is tropical forest, but the trees are increasingly being felled for timber and to make way for agriculture, and little virgin forest remains within its range. However, it can tolerate some disturbance and can be seen at forest edges, in plantations, on cleared land, in scrub, over pasture and beside roads.
Liatris cymosa, also known as Aggie-land gayfeather or branched blazing star, is a plant species in the aster family Asteraceae and genus Liatris. It is native to east central Texas in North America, where it is found in habitats such as post oak woodlands, fields, fence rows, woodland openings and edges, in clay soils. It blooms in mid to late summer with purple flower heads. It is of conservation concern. It grows from rounded or sometimes elongated corms, that produce stems 20 to 75 centimeters tall.
Opti-Scan 3D can offer you single click inspection, mobile large volume scanning and is also the world's only system that can measure edges in 3D. The Opti-Probe is an Optical CMM system that allows the user to inspect larger objects. The Opti-Probe can be used on the factory floor and is compatible with other InspecVision systems. In 2017 InspecVision launched the Accuity system which is an automated, large field of view, telecentric gauging system that can scan in both 2D and 3D.
It is native to Europe, growing further north than most other species in the genus Ophrys, in Scandinavia, Finland and the Baltic states, and as far south as Greece and Spain. – interpretation of codes In the UK it is a rare species, with a southern distribution. The plant favours sites with damp, alkaline, unimproved soil. It can be found growing in beech woodlands, on forest edges, in scrub, on limestone pavement, limestone grassland, in chalk pits and wet meadows, on cliffs as well as on disused railways.
MAFFS-equipped Air National Guard C-130 Hercules drops fire retardant on wildfires in Southern California Red-dyed line of fire retardant stands out clearly on this Arizona hill, to control the Alambre Fire Early fire retardants were mixtures of water and thickening agents, and later included borates . and ammonium phosphates. Generally, fire retardants are dropped from aircraft or applied by ground crews around a wildfire's edges in an effort to contain its spread. This allows ground crews time to work to extinguish the fire.
Just like in marching cubes, the intersections of these edges with the isosurface are approximated by linearly interpolating the values at the grid points. Adjacent cubes share all edges in the connecting face, including the same diagonal. This is an important property to prevent cracks in the rendered surface, because interpolation of the two distinct diagonals of a face usually gives slightly different intersection points. An added benefit is that up to five computed intersection points can be reused when handling the neighbor cube.
The key insight to the algorithm is a random sampling step which partitions a graph into two subgraphs by randomly selecting edges to include in each subgraph. The algorithm recursively finds the minimum spanning forest of the first subproblem and uses the solution in conjunction with a linear time verification algorithm to discard edges in the graph that cannot be in the minimum spanning tree. A procedure taken from Borůvka's algorithm is also used to reduce the size of the graph at each recursion.
The steps themselves are solid, one piece, die-cast aluminium or steel. Yellow demarcation lines are sometimes added to indicate their edges. In most escalator models manufactured after 1950, both the riser and the tread of each step is cleated (given a ribbed appearance) with comb-like protrusions that mesh with the comb plates on the top and bottom platforms and the succeeding steps in the chain. Seeberger escalators featured flat treads and smooth risers; other escalator models have cleated treads and smooth risers.
The linear attenuation coefficients can hence be expanded as In contrast-enhanced imaging, high-atomic-number contrast agents with K absorption edges in the diagnostic energy range may be present in the body. K-edge energies are material specific, which means that the energy dependence of the photo-electric effect is no longer separable from the material properties, and an additional term can be added to Eq. () according to where a_K and f_K are the material coefficient and energy dependency of contrast- agent material K.
The colour of foliage may be green, red or brown, and "ranges from fine and hair-like, sometimes with curled tips, to quite broad with a noticeable midrib and sometimes razor sharp edges". In this Carex panicea, the upper spike contains male flowers, and the lower spike contains female flowers. The flowers of Carex are small and are combined into spikes, which are themselves combined into a larger inflorescence. The spike typically contains many flowers, but can hold as few as one in some species.
The optic flow experienced by a rotating observer (in this case a fly). The direction and magnitude of optic flow at each location is represented by the direction and length of each arrow. Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene. Optical flow can also be defined as the distribution of apparent velocities of movement of brightness pattern in an image.
In the following definitions, the hypergraph is denoted by H=(V,E). H is called a k-uniform hypergraph if every edge in E consists of exactly k vertices. P is a hypergraph packing if it is a subset of edges in H such that there is no pair of distinct edges with a common vertex. H is a (D_0,\epsilon)-good hypergraph if there exists a D_0 such that for all x,y \in V and D\geq D_0 and both of the following conditions hold.
The seminal vesicles form in the 13th instar, when also the penis reaches is final adult form by the ventral fusing of its rolled edges. In comparison to males, the female’s genitalia lobes elongate in succeeding moultings. In the 10th nymphal instar, a second, anterior pair of lobes develops from the intersegmental membrane between abdominal segments 8 and 9 and extends to the ninth sternum’s cleft in the 11th instar. In the following 12th instar, both pairs of genitalia lobes are almost of equal length.
In graph theory, Turán's theorem is a result on the number of edges in a Kr+1-free graph. An -vertex graph that does not contain any -vertex clique may be formed by partitioning the set of vertices into parts of equal or nearly equal size, and connecting two vertices by an edge whenever they belong to two different parts. The resulting graph is the Turán graph . Turán's theorem states that the Turán graph has the largest number of edges among all -free -vertex graphs.
There is a spot in the southern end known as a Kudhuheraivali (the forest of the small islet), which indicates that there was a separate little island in that area in ancient times. But long ago the channel connecting the lagoon with the ocean was closed by massive coral boulders. Thus the inside of the island is lower than its edges. In time the inner lagoon lost its saltiness and all that remains today are two small lakes(Kulhi), wetlands and marshy taro fields.
Animation on The Jungle Book commenced on May 2, 1966. While many of the later Disney feature films had animators being responsible for single characters, in The Jungle Book the animators were in charge of whole sequences, since many have characters interacting with one another. The animation was done by xerography, with character design, led by Ken Anderson, employing rough, artistic edges in contrast to the round animals seen in productions such as Dumbo. Anderson also decided to make Shere Khan resemble his voice actor, George Sanders.
Sumner's proof that claw-free connected graphs of even order have perfect matchings: removing the two adjacent vertices v and w that are farthest from u leaves a connected subgraph, within which the same removal process may be repeated. and, independently, proved that every claw-free connected graph with an even number of vertices has a perfect matching., pp. 120–124. That is, there exists a set of edges in the graph such that each vertex is an endpoint of exactly one of the matched edges.
The point on the leading edge used to define the chord may be either the surface point of minimum radius p.18 or the surface point that maximizes chord length. The wing, horizontal stabilizer, vertical stabilizer and propeller of an aircraft are all based on aerofoil sections, and the term chord or chord length is also used to describe their width. The chord of a wing, stabilizer and propeller is determined by measuring the distance between leading and trailing edges in the direction of the airflow.
In Late Triassic and Early Jurassic there were two stages of rifting involving extension and subsistence on the western margin of Iberia. It also extended the western margin. The Iberian Abyssal Plain, off the west coast of Portugal and Spain, formed 126 Ma. This separated Newfoundland's Grand Banks, with Galica Bank and Flemish Cap being split at 118 Ma. By Early Cretaceous, 110 Ma rifting occurs on west and north west edges. In the Mesozoic, Late Jurassic Africa started moving east, and the Alpine Tethys opened.
Aichmophobia () is a kind of specific phobia, the morbid fear of sharp things, such as pencils, needles, knives, a pointing finger, or even the sharp end of an umbrella and different sorts of protruding corners or sharp edges in furnitures and building constructions/materials. It is derived from the Greek aichmē (point) and phobos (fear). This fear may also be referred to as belonephobia or enetophobia. Sometimes this general term is used to refer to what is more specifically called fear of needles, or needle phobia.
Caloscypha is a fungal genus in the family Caloscyphaceae (order Pezizales). A monotypic genus, it contains the single species Caloscypha fulgens, commonly known as the spring orange peel fungus, the golden cup, or the dazzling cup. It is a cup fungus, typically up to in diameter, with a bright to pale orange interior and orange; specimens that are old or bruised often have an olive- green discoloration, especially around the edges. In North America, it is usually found on the ground in forest litter near conifers.
When surgeons have problems with an endoscopic forehead lift, -- in about one percent of cases -- they finish the procedure by switching to the open forehead lift method. Complications are said to be rare and minor when a forehead lift is performed by a surgeon trained in the technique. However, it is possible for the surgical process to damage the nerves that control eyebrow and forehead movements. Hair loss can also occur along the scar edges in the scalp when an incision is made through the hairline.
A useful property of G_\phi is that its cycle covers correspond to variable assignments for \phi. For a cycle cover Z of G_\phi, one can say that Z induces an assignment of values for the variables in \phi just in case Z contains all of the external edges in x_i's T-cycle and none of the external edges in x_i's F-cycle for all variables x_i that the assignment makes true, and vice versa for all variables x_i that the assignment makes false. Although any given cycle cover Z need not induce an assignment for \phi, any one that does induces exactly one assignment, and the same assignment induced depends only on the external edges of Z. The term Z is considered an incomplete cycle cover at this stage, because one talks only about its external edges, M. In the section below, one considers M-completions to show that one has a set of cycle covers corresponding to each M that have the necessary properties. The sort of Z's that don't induce assignments are the ones with cycles that "jump" inside the clause components.
If a network contains communities or groups that are only loosely connected by a few inter- group edges, then all shortest paths between different communities must go along one of these few edges. Thus, the edges connecting communities will have high edge betweenness (at least one of them). By removing these edges, the groups are separated from one another and so the underlying community structure of the network is revealed. The algorithm's steps for community detection are summarized below # The betweenness of all existing edges in the network is calculated first.
In 2009, Mashable reported that Viralheat has more features than free services, with a lower price than most paid options. A contributor review in PRWeek in 2012 said Viralheat's strengths were its sentiment analysis, simplicity, price and customer service, but that its filtering tools were "a little rough around the edges." In March 2013, Network World tested eight social media management tools. The reviewer found that Viralheat was the lowest cost, and supported more social media sites than competitors, but lacked the features to support multi-user accounts needed for large (enterprise) customers.
As a simple example, say we wish to find the maximum spanning forest of a graph. That is, given a graph and a weight for each edge, find a forest containing every vertex and maximizing the total weight of the edges in the tree. This problem arises in some clustering applications. If we look at the definition of the forest matroid above, we see that the maximum spanning forest is simply the independent set with largest total weight -- such a set must span the graph, for otherwise we can add edges without creating cycles.
The power graph greedy algorithm relies on two simple steps to perform the decomposition: The first step identifies candidate power nodes through a hierarchical clustering of the nodes in the network based on the similarity of their neighboring nodes. The similarity of two sets of neighbors is taken as the Jaccard index of the two sets. The second step performs a greedy search for possible power edges between candidate power nodes. Power edges abstracting the most edges in the original network are added first to the power graph.
The happens-before order subsumes the program order; if one action occurs before another in the program order, it will occur before the other in the happens-before order. In addition, releases and subsequent acquisitions of locks form edges in the happens-before graph. A read is allowed to return the value of a write if that write is the last write to that variable before the read along some path in the happens-before order, or if the write is not ordered with respect to that read in the happens-before order.
The property graph data model therefore deliberately prevents nesting of graphs, or treating nodes in one graph as edges in another. Each property graph may have a set of labels and a set of properties that are associated with the graph as a whole. Current graph database products and projects often support a limited version of the model described here. For example, Apache Tinkerpop forces each node and each edge to have a single label; Cypher allows nodes to have zero to many labels, but relationships only have a single label (called a reltype).
A simple technical way to solve this problem is to extend the input graph to a complete bipartite graph, by adding artificial edges with very large weights. These weights should exceed the weights of all existing matchings, to prevent appearance of artificial edges in the possible solution. As shown by Mulmuley, Vazirani and Vazirani, the problem of minimum weight perfect matching is converted to finding minors in the adjacency matrix of a graph. Using the isolation lemma, a minimum weight perfect matching in a graph can be found with probability at least ½.
To do this it finds all k-cliques in a network, that is all the complete sub-graphs of k-nodes. It then defines two k-cliques to be adjacent if they share k-1 nodes, that is this is used to define edges in a clique graph. A community is then defined to be the maximal union of k-cliques in which we can reach any k-clique from any other k-clique through series of k-clique adjacencies. That is communities are just the connected components in the clique graph.
Another commonly used algorithm for finding communities is the Girvan–Newman algorithm. This algorithm identifies edges in a network that lie between communities and then removes them, leaving behind just the communities themselves. The identification is performed by employing the graph-theoretic measure betweenness centrality, which assigns a number to each edge which is large if the edge lies "between" many pairs of nodes. The Girvan–Newman algorithm returns results of reasonable quality and is popular because it has been implemented in a number of standard software packages.
Other landscape-scale studies maintain that human impact is likely the main determinant of landscape pattern over much of the globe. Landscapes may become substitutes for biodiversity measures because plant and animal composition differs between samples taken from sites within different landscape categories. Taxa, or different species, can “leak” from one habitat into another, which has implications for landscape ecology. As human land use practices expand and continue to increase the proportion of edges in landscapes, the effects of this leakage across edges on assemblage integrity may become more significant in conservation.
The upperside of the abdomen has a broad, grey dorsal stripe and the lateral stripe is vivid yellow. The forewing upperside is similar to Xylophanes rhodochlora, but the ground colour is bronzy green with pearly reflections, the discal spot is smaller and the first and fourth postmedian lines are darker green, highlighted along their inner edges in pearly grey. The fringe is orange. The marginal area of the forewing underside is of the same general brick-red colour as the rest of the wing, barely delineated by a grey line.
Mantel's Theorem (1907) and Turán's Theorem (1941) were some of the first milestones in the study of Extremal graph theory. In particular, Turán's theorem would later on become a motivation for the finding of results such as the Erdős-Stone-Simonovits Theorem (1946). This result is surprising because it connects the chromatic number with the maximal number of edges in an H-free graph. An alternative proof of Erdős-Stone-Simonovits was given in 1975, and utilised the Szemerédi regularity lemma, an essential technique in the resolution of extremal graph theory problems.
The corresponding Belyi pair forms a transformation of the Riemann sphere that, if one places the pole at ∞, can be represented as a polynomial. Conversely, any polynomial with 0 and 1 as its finite critical values forms a Belyi function from the Riemann sphere to itself, having a single infinite- valued critical point, and corresponding to a dessin d'enfant that is a tree. The degree of the polynomial equals the number of edges in the corresponding tree. Such a polynomial Belyi function is known as a Shabat polynomial,Girondo & González-Diez (2012) p.
A left path begins at either a right child or the root and includes all nodes reachable through a path of left children. The left paths of a binary tree are shown circled in blue in the diagram on the right. Each edge in a left child problem is selected from the edges of its parent problem (less the edges contracted in the Borůvka steps) with probability 1/2. If a parent problem has x edges then the expected number of edges in the left child problem is at most x/2.
Clique percolation methods may be generalized by recording different amounts of overlap between the various k-cliques. This then defines a new type of graph, a clique graph, where each k-clique in the original graph is represented by a vertex in the new clique graph. The edges in the clique graph are used to record the strength of the overlap of cliques in the original graph. One may then apply any community detection method to this clique graph to identify the clusters in the original graph through the k-clique structure.
This sign at the entrance of the forest advises visitors to "please be careful". Belanglo State Forest is a planted forest, of mainly pine but some native forestry around the edges, in the Australian state of New South Wales; its total area is about 3,800 hectares. The Belanglo State Forest is located south of Berrima in the Southern Highlands, three kilometres west of the Hume Highway between Sydney and Canberra. The forest is owned by the New South Wales Government and contains some of the earliest pine plantings in the state.
The land around the barrow is cultivated up to its edges; in 1992, it was planted with barley crops. Originally the barrow probably stood larger; in 1923 an elliptical section surrounding the southwest circumference was recorded as approximately higher than the field, suggesting that it was once a part of the barrow. That the barrow's finds were not in the centre of its present dimensions also suggests that its original dimensions were somewhat different. Slippage of the barrow's soil may also help explain the changed dimensions, and the recorded reduction in height over time.
Traditionally, this is done by hanging the cheese in a muslin bag or a loosely woven cotton gauze called cheesecloth and letting the whey drip off, which gives quark its distinctive shape of a wedge with rounded edges. In industrial production, however, cheese is separated from whey in a centrifuge and later formed into blocks. Variations in quark preparation occur across different regions of Germany and Austria. Most of the Austrian and other Central and Eastern European varieties contain less whey and are therefore drier and more solid than the German and Scandinavian ones.
Adaptive histogram equalization (AHE) is a computer image processing technique used to improve contrast in images. It differs from ordinary histogram equalization in the respect that the adaptive method computes several histograms, each corresponding to a distinct section of the image, and uses them to redistribute the lightness values of the image. It is therefore suitable for improving the local contrast and enhancing the definitions of edges in each region of an image. However, AHE has a tendency to overamplify noise in relatively homogeneous regions of an image.
This combination of equipment was far from optimal for downhill skiing. During the downhill portions the skis are turned by rotating them onto their edges; in traditional cable bindings, the heel is free to lift from the ski to allow a striding motion, and the system offers little support for edging. The introduction of ski lifts, especially after World War II, led to the specialization of downhill as a separate sport, and new equipment evolved to meet this market. One example was the "Kandahar" style cable bindings, which added small metal hooks near the heel.
If a spanning tree does not exist, it combines each disconnected component into a new super vertex, then computes a MBST in the graph formed by these super vertices and edges in the larger edges set. A forest in each disconnected component is part of a MBST in original graph. Repeat this process until two (super) vertices are left in the graph and a single edge with smallest weight between them is to be added. A MBST is found consisting of all the edges found in previous steps.
The Petersen graph is nonplanar. Any nonplanar graph has as minors either the complete graph K_5, or the complete bipartite graph K_{3,3}, but the Petersen graph has both as minors. The K_5 minor can be formed by contracting the edges of a perfect matching, for instance the five short edges in the first picture. The K_{3,3} minor can be formed by deleting one vertex (for instance the central vertex of the 3-symmetric drawing) and contracting an edge incident to each neighbor of the deleted vertex.
That is, a proper edge coloring is the same thing as a partition of the graph into disjoint matchings. If the size of a maximum matching in a given graph is small, then many matchings will be needed in order to cover all of the edges of the graph. Expressed more formally, this reasoning implies that if a graph has edges in total, and if at most edges may belong to a maximum matching, then every edge coloring of the graph must use at least different colors., p. 134.
Map matching example with GraphHopperMap matching is the problem of how to match recorded geographic coordinates to a logical model of the real world, typically using some form of Geographic Information System. The most common approach is to take recorded, serial location points (e.g. from GPS) and relate them to edges in an existing street graph (network), usually in a sorted list representing the travel of a user or vehicle. Matching observations to a logical model in this way has applications in satellites navigation, GPS tracking of freight, and transportation engineering.
Zarankiewicz wrote works on cut-points in connected spaces, on conformal mappings, on complex functions and number theory, and triangular numbers. The Zarankiewicz problem is named after Zarankiewicz. This problem asks, for a given size of (0,1)-matrix, how many matrix entries must be set equal to 1 in order to guarantee that the matrix contains at least one a × b submatrix is made up only of 1's. An equivalent formulation in extremal graph theory asks for the maximum number of edges in a bipartite graph with no complete bipartite subgraph Ka,b.
Accordingly, let be a graph on vertices that is not Hamiltonian, and let be formed from by adding edges one at a time that do not create a Hamiltonian cycle, until no more edges can be added. Let and be any two non-adjacent vertices in . Then adding edge to would create at least one new Hamiltonian cycle, and the edges other than in such a cycle must form a Hamiltonian path in with and . For each index in the range , consider the two possible edges in from to and from to .
81–85 In a three- dimensional Euclidean space, lines with true length are parallel to the projection plane. For example, in a top view of a pyramid, which is an orthographic projection, the base edges (which are parallel to the projection plane) have true length, whereas the remaining edges in this view are not true lengths. The same is true with an orthographic side view of a pyramid. If any face of a pyramid was parallel to the projection plane (for a particular view), all edges would demonstrate true length.
The lower jaw was down-turned at the front and the teeth were distinct in having additional as well as third cutting edges in some of the hindmost teeth. The forelimbs were robust and had three fingers which bore large claws, and the feet had four toes supporting the foot—apart from therizinosaurs, all theropods had three-toed feet. The front of the pelvis was adapted to support the enlarged belly. The pubic bone was turned backwards, a feature that is only seen in birds and the dinosaurs most closely related to them.
A demo for Prim's algorithm based on Euclidean distance. In computer science, Prim's (also known as Jarník's) algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. The algorithm operates by building this tree one vertex at a time, from an arbitrary starting vertex, at each step adding the cheapest possible connection from the tree to another vertex.
This injury should be differentiated from the developmental "apophysis" which is the secondary ossification center of the metatarsal bone. It is normally occurring at this site in adolescents. Differentiation is possible by characteristics such as absence of sclerosis of the fractured edges (in acute cases) and orientation of the lucent line: transverse (at 90 degrees) to the metatarsal axis for the fracture (due to avulsion pull by the peroneus brevis muscle inserting at the proximal tip) – and parallel to the metatarsal axis in the case of the apophysis.
Edge thinning is a technique used to remove the unwanted spurious points on the edges in an image. This technique is employed after the image has been filtered for noise (using median, Gaussian filter etc.), the edge operator has been applied (like the ones described above , canny or sobel ) to detect the edges and after the edges have been smoothed using an appropriate threshold value. This removes all the unwanted points and if applied carefully, results in one pixel thick edge elements. Advantages: # Sharp and thin edges lead to greater efficiency in object recognition.
Shortly after, Luby and Alon et al. independently improved on this result, bringing the maximal independent set problem into the realm of NC_2 with an O(\log^2n) runtime using O(mn^2) processors, where m is the number of edges in the graph. In order to show that their algorithm is in NC_2, they initially presented a randomized algorithm that uses O(m) processors but could be derandomized with an additional O(n^2) processors. Today, it remains an open question as to if the maximal independent set problem is in NC_1.
The main fuel tank was behind the cabin and between the wing spars, with a smaller fuel tank in the engine nacelle that was fed by a fuel pump. The Wasp Jr. radial engine was mounted as a pusher, which made passenger egress safer, and reduced cabin noise. Starting was accomplished with an inertial hand starter. The wings were built around two spruce spars, with ribs and leading and trailing edges in spot welded chromium-molybdenum alloy (chrome- moly) steel, all covered in fabric sealed and tightened with aircraft dope.
In this graph, removing one vertex in the center produces three odd components, the three five-vertex lobes of the graph. Therefore, by the Tutte–Berge formula, it has at most (1−3+16)/2 7 edges in any matching. In the mathematical discipline of graph theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte's theorem on perfect matchings, and is named after W. T. Tutte (who proved Tutte's theorem) and Claude Berge (who proved its generalization).
In a line graph L(G), each vertex of degree k in the original graph G creates k(k − 1)/2 edges in the line graph. For many types of analysis this means high-degree nodes in G are over-represented in the line graph L(G). For instance, consider a random walk on the vertices of the original graph G. This will pass along some edge e with some frequency f. On the other hand, this edge e is mapped to a unique vertex, say v, in the line graph L(G).
In graph theory, a maximally-matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching in the graph. An alternative term is allowed edge. A fundamental problem in matching theory is: given a graph G, find the set of all maximally-matchable edges in G. This is equivalent to finding the union of all maximum matchings in G (this is different than the simpler problem of finding a single maximum matching in G). Several algorithms for this problem are known.
Waverley has had several colour schemes in her life. At launch her paddle boxes were painted black, in 1959 they were painted white, then back to black but with white edges in 1972, then finally back to all black in 1977. The two gold stripes along the hull were removed in 1954 but restored during the 2000 rebuild. Today, Waverley has the LNER 1947 livery of red, white and black funnels, traditional brown-grained (or "scumbled") superstructure and black paddle-wheel boxes, decorated with gold lettering on each side.
However, in testing against more modern engines, the Tesla Turbine had expansion efficiencies far below contemporary steam turbines and far below contemporary reciprocating steam engines. It does suffer from other problems such as shear losses and flow restrictions, but this is partially offset by the relatively massive reduction in weight and volume. Some of Tesla turbine's advantages lie in relatively low flow rate applications or when small applications are called for. The disks need to be as thin as possible at the edges in order not to introduce turbulence as the fluid leaves the disks.
H.aurescens is typically found in the understorey of lowland humid tropical forests, particularly near streams, and only rarely at forest edges. In Brazil it has been observed in tall forest impacted by logging, seen feeding at flowers in the canopy of “a small patch of semi-deciduous forest surrounded by terra firme”. Cotton observed it in both varzea forest and terra firme but not in riverine vegetation. Another Brazilian study found them in terra firme in both the wet and dry seasons but in várzea only during the dry season.
In 1997, Sós was awarded the Széchenyi Prize. One of her results is the Kővári–Sós–Turán theorem concerning the maximum possible number of edges in a bipartite graph that does not contain certain complete subgraphs. Another is the following so- called friendship theorem proved with Paul Erdős and Alfréd Rényi: if, in a finite graph, any two vertices have exactly one common neighbor, then some vertex is joined to all others. In number theory, Sós proved the three-gap theorem, conjectured by Hugo Steinhaus and proved independently by Stanisław Świerczkowski.
Colias chippewa may be a subspecies of Colias palaeno see Grieshuber & Lamas, 2007; however, C. chippewa is considered a separate species from C. palaeno by Guppy and Shepard (2001)John Shepard, Crispin Guppy, 2001 Butterflies of British Columbia University of British Columbia Press. . on the basis of work by V. K. Tuzov (which they quote). He found that, in the Magadan region of Siberia, the two forms were sympatric but locally separated C. chippewa was restricted to stream-edges in dry tundra and C.palaeno was found only in low-elevation forested swamps.
The deckle edge could be trimmed off, but this extra step would add to the cost of the book. Beginning in the early 1800s with the invention of the Fourdrinier machine, paper was produced in long rolls and the deckle edge became mostly obsolete. Although there was some deckle on the ends of the rolls, it was cut off, and the individual sheets cut out from the roll would have no deckle in any case. With the appearance of smooth edges in the 19th century, the deckle edge slowly emerged as a status symbol.
Fairy orchid grows in forest and woodland in moist places, often in steep, rocky places but also in swamps and at lake edges. In New Zealand it sometimes occurs around hot springs. The distribution is not well understood because the flowers are small and ephemeral but it has been recorded in south-east Queensland, the coast and tablelands of New South Wales, near-coastal areas of Victoria east of Wilsons Promontory and in Tasmania. In New Zealand it is confined to the North Island, mainly between Te Paki and Rotorua.
Commodore Stockton, the senior military officer in California, appointed Larkin as Naval agent, and Larkin returned to Monterey. The apparently peaceful conquest of California soon began to fray at the edges in southern California. Revolts broke out in Los Angeles, and the occupation forces under Archibald Gillespie and his 30-40 men were driven out. José Castro returned, and Larkin moved his family to Yerba Buena (San Francisco) as the Californios throughout the province were attempting to repel the thinly spread out California Battalion garrison troops and Navy forces.
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e. the smallest total weight of the edges which if removed would disconnect the source from the sink. The max-flow min-cut theorem is a special case of the duality theorem for linear programs and can be used to derive Menger's theorem and the Kőnig–Egerváry theorem.
Similarly the subsonic leading and trailing are those portions of the wing edge where the components of the free stream velocity normal to the edge are subsonic. Delta wings have supersonic leading and trailing edges; in contrast arrow wings have a subsonic leading edge and a supersonic trailing edge. When designing a supersonic airfoil two factors that must be considered are shock and expansion waves. Whether a shock or expansion wave is generated at different locations along an airfoil depends on the local flow speed and direction along with the geometry of the airfoil.
The leaves are 4–12 cm long and 2.5–5 cm broad, arranged alternately on the stems with an elliptical shape and finely serrated edges. In the fall the foliage turns yellow, red or purple. The flowers are up to 8 cm wide, with five white petals with orange anthers; they are shaped like those of the related Camellia, round and flat to somewhat cupped. They are produced in summer, generally in June until the end of August; each flower is short-lived, but many are produced that open over many weeks.
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others.
The overhaul replaced the original wall tiles, old signs, and incandescent lighting to the 1970s modern look wall tile band and tablet mosaics, signs and fluorescent lights. It also fixed staircases and platform edges. In the early 1990s, the station received another major repair, which included an upgrade for ADA-accessibility and modernized wall tiling. The MTA repaired the staircases, re-tiling for the walls, installed new tiling on the floors, upgraded the station's lights and the public address system, installing ADA safety threads along the platform edge, new signs, and new track-beds in both directions.
First, if planar regions separated by the graph are not triangulated, i.e. do not have exactly three edges in their boundaries, we can add edges without introducing new vertices in order to make every region triangular, including the unbounded outer region. If this triangulated graph is colorable using four colors or fewer, so is the original graph since the same coloring is valid if edges are removed. So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.
S. occidentalis grows on sticks and twigs. Depending on their age, the fruit bodies of S. occidentalis may range in shape from deep cups to saucers to discs in maturity, and they can reach diameters up to . In young specimens, the edges of the cup are curled inwards, and crenulate (with small rounded scallops); the cup edges in older specimens become laciniate (with jagged edges cut into irregular segments). The cups rest atop a stem that is small to medium-sized, up to long and 1.5–2 mm thick, and attached centrally or to the side to the underside of the cup.
The median graph representing all solutions to the example 2-satisfiability instance whose implication graph is shown above. The set of all solutions to a 2-satisfiability instance has the structure of a median graph, in which an edge corresponds to the operation of flipping the values of a set of variables that are all constrained to be equal or unequal to each other. In particular, by following edges in this way one can get from any solution to any other solution. Conversely, any median graph can be represented as the set of solutions to a 2-satisfiability instance in this way.
The gills are squarely attached to the stem, and flushed with pink in maturity. The cap of the M. polygramma fruit body is in diameter, and initially egg- to cone-shaped, but expands to become conic to bell-shaped or nearly convex with an abrupt small umbo, or at times plane with a conic umbo. On young fruit bodies, the cap margin is slightly curved inward, and frequently has scalloped edges; in maturity the margin flares out, or is recurved and wavy. The surface of the cap is initially covered with short, fine whitish or grayish hairs that often persist until near maturity.
It was reported in 1775 by Sir Percival Pott in climbing boys or chimney sweepers. It is the first industrially related cancer to be found. Potts described it: > It is a disease which always makes it first attack on the inferior part of > the scrotum where it produces a superficial, painful ragged ill-looking sore > with hard rising edges…in no great length of time it pervades the skin, > dartos and the membranes of the scrotum, and seizes the testicle, which it > inlarges [sic], hardens and renders truly and thoroughly distempered. Whence > it makes its way up the spermatic process into the abdomen.
Most investigations of Rossby waves have been done on those in Earth's atmosphere. Rossby waves in the Earth's atmosphere are easy to observe as (usually 4-6) large-scale meanders of the jet stream. When these deviations become very pronounced, masses of cold or warm air detach, and become low- strength cyclones and anticyclones, respectively, and are responsible for day- to-day weather patterns at mid-latitudes. The action of Rossby waves partially explains why eastern continental edges in the Northern Hemisphere, such as the Northeast United States and Eastern Canada, are colder than Western Europe at the same latitudes.
The army of Charles Robert Anjou ambushed by Basarab's army at Posada from Vienna Illuminated Chronicle manuscript (1330) The Vlach (Romanian) warriors rolled down rocks over the cliff edges in a place where the Hungarian mounted knights could neither escape from them nor climb the heights to dislodge the Vlach warriors. Some historians claim that the Cumans aided the Wallachians in the battle. Still in the Hungarian army there was a substantial Cuman-Hungarian contingent so this variant is very improbable. In 1324, Wallachia was a vassal of Hungary, and Robert referred to Basarab as "our Transalpine Voivode".
The optimal path around the track for the lowest lap time. In drag racing it is about the center portion of the lane, where the cars can gain traction quicker. ;Groove a tire: see Sipe ;Ground effect: A method of creating downforce by the shape of the car's body, notably by shaping the underside of the car in combination with the car's lateral edges in order to trap and dramatically slow the airflow running underneath the car, effectively turning the entire car into a wing. ;Gurney, Gurney flap: A small lip placed at the trailing edge of a race car's aerodynamic wing.
A graph with 16 vertices and 6 bridges (highlighted in red) An undirected connected graph with no bridge edges In graph theory, a bridge, isthmus, cut- edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components.. Equivalently, an edge is a bridge if and only if it is not contained in any cycle. For a connected graph, a bridge can uniquely determine a cut. A graph is said to be bridgeless or isthmus-free if it contains no bridges. Another meaning of "bridge" appears in the term bridge of a subgraph.
Reducing Minimum weight bipartite matching to minimum cost max flow problem Given a bipartite graph G = (A ∪ B, E), the goal is to find the maximum cardinality matching in G that has minimum cost. Let w: E → R be a weight function on the edges of E. The minimum weight bipartite matching problem or assignment problem is to find a perfect matching M ⊆ E whose total weight is minimized. The idea is to reduce this problem to a network flow problem. Let G′ = (V′ = A ∪ B, E′ = E). Assign the capacity of all the edges in E′ to 1.
A unique advantage of MRI is that it provides not only the phase image but also the magnitude image. In principle, the contrast change, or equivalently the edge, on a magnitude image arises from the underlying change of tissue type, which is the same cause for the change of susceptibility. This observation is translated into mathematics in MEDI, where edges in a QSM which do not exist in the corresponding magnitude image are sparsified by solving a weighted l_1 norm minimization problem. MEDI has also been validated extensively in phantom, in vitro and ex vivo experiments.
This leads to establishing rasterization rules to guarantee the above conditions. One set of such rules is called a top-left rule, which states that a pixel is rasterized if and only if # its center lies completely inside the triangle. Or # its center lies exactly on the triangle edge (or multiple edges in case of corners) that is (or, in case of corners, all are) either top or left edge. A top edge is an edge that is exactly horizontal and lies above other edges, and a left edge is a non-horizontal edge that is on the left side of the triangle.
The dual graph of this embedding has four vertices forming a complete graph with doubled edges. In the torus embedding of this dual graph, the six edges incident to each vertex, in cyclic order around that vertex, cycle twice through the three other vertices. In contrast to the situation in the plane, this embedding of the cube and its dual is not unique; the cube graph has several other torus embeddings, with different duals. Many of the equivalences between primal and dual graph properties of planar graphs fail to generalize to nonplanar duals, or require additional care in their generalization.
In computer vision, the Marr–Hildreth algorithm is a method of detecting edges in digital images, that is, continuous curves where there are strong and rapid variations in image brightness. The Marr–Hildreth edge detection method is simple and operates by convolving the image with the Laplacian of the Gaussian function, or, as a fast approximation by difference of Gaussians. Then, zero crossings are detected in the filtered result to obtain the edges. The Laplacian-of-Gaussian image operator is sometimes also referred to as the Mexican hat wavelet due to its visual shape when turned upside-down.
The intersection of the unit cube with the cutting plane x_1 + x_2 + x_3 \geq 2. In the context of the Traveling salesman problem on three nodes, this (rather weak) inequality states that every tour must have at least two edges. In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems.
Ignoring work done in recursive subproblems the total amount of work done in a single invocation of the algorithm is linear in the number of edges in the input graph. Step 1 takes constant time. Borůvka steps can be executed in time linear in the number of edges as mentioned in the Borůvka step section. Step 3 iterates through the edges and flips a single coin for each one so it is linear in the number of edges. Step 4 can be executed in linear time using a modified linear time minimum spanning tree verification algorithm.
Since the work done in one iteration of the algorithm is linear in the number of edges the work done in one complete run of the algorithm (including all recursive calls) is bounded by a constant factor times the total number of edges in the original problem and all recursive subproblems. Each invocation of the algorithm produces at most two subproblems so the set of subproblems forms a binary tree. Each Borůvka step reduces the number of vertices by at least a factor of two so after two Borůvka steps the number of vertices has been reduced by a factor of four.
The problem arises because if a vertex is in n different k-cliques it will contribute to n(n-1)/2 edges in such a clique graph. A simple solution is to let each vertex common to two overlapping kcliques to contribute a weight equal to 1/n when measuring the overlap strength of the two k-cliques. In general the clique graph viewpoint is a useful way of finding generalizations of standard clique-percolation methods to get any round problems encountered. It even shows how to describe extensions of these methods based on other motifs, subgraphs other than kcliques.
Let M be a maximum matching and consider an alternating chain such that the edges in the path alternates between being and not being in M. If the alternating chain is a cycle or a path of even length, then a new maximum matching M′ can be found by interchanging the edges found in M and not in M. For example, if the alternating chain is (m1, n1, m2, n2, ...), where mi ∈ M and ni ∉ M, interchanging them would make all ni part of the new matching and make all mi not part of the matching.
In graph theory, a moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief propagation on graphical models. The moralized counterpart of a directed acyclic graph is formed by adding edges between all pairs of non- adjacent nodes that have a common child, and then making all edges in the graph undirected. Equivalently, a moral graph of a directed acyclic graph is an undirected graph in which each node of the original is now connected to its Markov blanket.
Canny edge detection applied to a photograph So far, the strong edge pixels should certainly be involved in the final edge image, as they are extracted from the true edges in the image. However, there will be some debate on the weak edge pixels, as these pixels can either be extracted from the true edge, or the noise/color variations. To achieve an accurate result, the weak edges caused by the latter reasons should be removed. Usually a weak edge pixel caused from true edges will be connected to a strong edge pixel while noise responses are unconnected.
Quazatron was a Spectrum version of Paradroid, which was written by Graftgold partner Andrew Braybrook in 1985. Although a direct conversion was considered, it was felt that the Spectrum couldn't handle screen-scrolling as smoothly as the Commodore 64. However, Steve Turner had been working on an isometric landscape engine for the Spectrum called Ziggurat and decided to use this with the Paradroid game mechanics, control system and patrol paths. This new isometric perspective (drawing visual comparisons with Marble Madness) also provided an additional gameplay aspect – opposing droids could be pushed off edges in order to damage them.
The red and blue components for this pixel are obtained from the neighbors. For a green pixel, two red neighbors can be interpolated to yield the red value, also two blue pixels can be interpolated to yield the blue value. This simple approach works well in areas with constant color or smooth gradients, but it can cause artifacts such as color bleeding in areas where there are abrupt changes in color or brightness especially noticeable along sharp edges in the image. Because of this, other demosaicing methods attempt to identify high- contrast edges and only interpolate along these edges, but not across them.
Similar to the 92 series, the frame is constructed of a light alloy, and the slide and barrel are constructed of steel. The slide is also in itself a whole new design. The rough edges in the previous 92 models were smoothed out, for a more "snag-free" design. Included with the pistol is an accessory rail cover, which protects the rail when an accessory is not attached. Magazine capacities available for the 90-Two 9×19mm are: 10-round single-stack, 15 or 17-round double-stack; the 90-Two 9×21mm IMI: 15 round double-stack, the 90-Two .
This 3-regular planar graph has 16 vertices and 24 edges, but only 7 edges in any maximum matching. Therefore, it requires four colors in any edge coloring. A matching in a graph is a set of edges, no two of which are adjacent; a perfect matching is a matching that includes edges touching all of the vertices of the graph, and a maximum matching is a matching that includes as many edges as possible. In an edge coloring, the set of edges with any one color must all be non-adjacent to each other, so they form a matching.
For instance, the 16-vertex planar graph shown in the illustration has edges. In this graph, there can be no perfect matching; for, if the center vertex is matched, the remaining unmatched vertices may be grouped into three different connected components with four, five, and five vertices, and the components with an odd number of vertices cannot be perfectly matched. However, the graph has maximum matchings with seven edges, so . Therefore, the number of colors needed to edge-color the graph is at least 24/7, and since the number of colors must be an integer it is at least four.
However, unlike the bipod on the Type 64, the version on the Type 89 is easily removable as it is clamped onto the barrel behind the bayonet lug with a clothes-pin style spring mechanism and retained with a lever-like lock. Also, the Type 89's handguard is molded with inlets along its lower edges in order to accommodate the legs of the bipod if they are folded inwards for storage. The Type 06 rifle grenade is designed for the Type 89. The attachment of the M203 grenade launcher is possible with the proper adapter.
The sign of a path is the product of the signs of its edges. Thus a path is positive only if there are an even number of negative edges in it (where zero is even). In the mathematical balance theory of Frank Harary, a signed graph is balanced when every cycle is positive. He proves that a signed graph is balanced when (1) for every pair of nodes, all paths between them have the same sign, or (2) the graph partitions into a pair of subgraphs, each consisting of positive edges, but connected by negative edges.
There were three premaxillary teeth. In the Early Jurassic Abrictosaurus, Heterodontosaurus, and Lycorhinus, the first two premaxillary teeth were small and conical, while the much larger third tooth resembled the canines of carnivoran mammals and is often called the caniniform or 'tusk'. A lower caniniform, larger than the upper, took the first position in the dentary and was accommodated by the arched diastema of the upper jaw when the mouth was closed. These caniniforms were serrated on both the anterior and posterior edges in Heterodontosaurus and Lycorhinus, while those of Abrictosaurus bore serrations only on the anterior edge.
This constraint is known as sunflower intersection. Simultaneous embedding is closely related to thickness, the minimum number of planar subgraphs that can cover all of the edges of a given graph, and geometric thickness, the minimum number of edge colors needed in a straight-line drawing of a given graph with no crossing between same-colored edges. In particular, the thickness of a given graph is two, if the graph's edges can be partitioned into two subgraphs that have a simultaneous embedding, and the geometric thickness is two, if the edges can be partitioned into two subgraphs with simultaneous geometric embedding.
The possible causes of the difference between individual connectomes were also investigated. It has been found that the macro-scale connectomes of women contain significantly more edges than those of men, and a larger portion of the edges in the connectomes of women run between the two hemispheres. In addition, connectomes generally exhibit a small-world character, with overall cortical connectivity decreasing with age. The aim of the as of 2015 ongoing HCP Lifespan Pilot Project is to identify connectome differences between 6 age groups (4–6, 8–9, 14–15, 25–35, 45–55, 65–75).
In a given region it is sometimes arranged that all television transmitters are located in roughly the same direction and use frequencies spaced closely enough that a single antenna suffices for all. A single transmitter location may transmit signals for several channels. CABD (communal antenna broadcast distribution) is a system installed inside a building to receive free-to-air TV/FM signals transmitted via radio frequencies and distribute them to the audience. Analog television signals are susceptible to ghosting in the image, multiple closely spaced images giving the impression of blurred and repeated images of edges in the picture.
PhoneArena argued that the S7 Edge was not a phablet, as it has a narrow and compact build with a physical footprint more in line with the smaller-screened Nexus 5X, due primarily to its use of a display with curved edges. In 2017, several manufacturers began to release smartphones with displays taller than the conventional 16:9 aspect ratio used by the majority of devices, and diagonal screen sizes often around 6 inches. However, in these cases, the sizes of the devices are more compact than 16:9 aspect ratio devices with equivalent diagonal screen sizes.
See the figure below for an example, where E11 is the East edge of the yellow tile, E21 is the West edge of the red tile, and both E21 and E22 are the North edges. A basic move, transferring a hinge between two tiles to another pair of edges In order to carry out such a move, the hinge being moved cannot cross another hinge. Thus, the two hinges on a tile can take up one of five relative positions (see figure below). The positions are encoded as a number in the range from -2 to +2, called the wrap.
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges. In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark (BDS stands for Blanuša Descartes Szekeres). Isaacs also discovered one 30-vertex snark that does not belongs to the BDS family and that is not a flower snark — the double-star snark. As a snark, the double-star graph is a connected, bridgeless cubic graph with chromatic index equal to 4.
Within each lens there is a basal convex upward layer from which the landscape rises. The 'hedge' layer is about 5 mm thick, marked at the top by many small bumps. The 'trees', arborescent structures, extend upwards from the hedge and are relatively constant in height at about 4-5 cm, although somewhat shorter near the lens edges. In most cases the lenses contain only a single layer of the landscape, but two, or exceptionally three layers may be developed, known as double and triple landscape marble respectively, each growing up from the crest of the underlying layer.
For example, a 2003 study in North Carolina found the tree of heaven was present on 1.7% of all highway and railroad edges in the state and had been expanding its range at the rate of 4.76% counties per year. Similarly, another study conducted in southwestern Virginia determined that the tree of heaven is thriving along approximately 30% of the state's interstate highway system length or mileage. It sometimes enters undisturbed areas as well and competes with native plants. In western North America it is most common in mountainous areas around old dwellings and abandoned mining operations.
Several authors have proven results relating the minimum weight triangulation to other triangulations in terms of the approximation ratio, the worst-case ratio of the total edge length of the alternative triangulation to the total length of the minimum weight triangulation. In this vein, it is known that the Delaunay triangulation has an approximation ratio of \Theta(n),. A weaker bound was given by . and that the greedy triangulation (the triangulation formed by adding edges in order from shortest to longest, at each step including an edge whenever it does not cross an earlier edge) has an approximation ratio of \Theta(\sqrt n).
In graph theory, a Pfaffian orientation of an undirected graph G is an orientation (an assignment of a direction to each edge of the graph) in which every even central cycle is oddly oriented. In this definition, a cycle C is even if it contains an even number of edges. C is central if the subgraph of G formed by removing all the vertices of C has a perfect matching; central cycles are also sometimes called alternating circuits. And C is oddly oriented if each of the two orientations of C is consistent with an odd number of edges in the orientation.
The pyrrhuloxia is a year-round resident of desert scrub and mesquite thickets, in the U.S. states of Arizona, New Mexico, and Texas and woodland edges in Mexico. It occupies the southwestern half of Texas, roughly the southern third of New Mexico, and southeastern region of Arizona. Its range includes areas from the west to east coast of Mexico north of the Sierra Madre del Sur, Trans-Mexican Volcanic Belt, and Isthmus of Tehuantepec, while excluding the Sierra Madre Occidental. An individual of the species has reportedly been seen as far away from its dominant range as Costa Mesa, California, in Orange County.
When the capacities are integers, the runtime of Ford–Fulkerson is bounded by O(E f) (see big O notation), where E is the number of edges in the graph and f is the maximum flow in the graph. This is because each augmenting path can be found in O(E) time and increases the flow by an integer amount of at least 1, with the upper bound f. A variation of the Ford- Fulkerson algorithm with guaranteed termination and a runtime independent of the maximum flow value is the Edmonds–Karp algorithm, which runs in O(VE^2) time.
Under Soviet rule, the Union Republic – situated in what is now modern-day Uzbekistan – utilized a flag derived from the flag of the Soviet Union and representing Communism, that was approved in 1952. ' The flag is similar to the Soviet design but with the blue stripe in 1/5 width and the two 1/100 white edges in between. Uzbekistan declared itself independent on September 1, 1991, approximately three months before the dissolution of the Soviet Union. A search for a national flag began soon after, with a contest being held to determine the new design.
M2, M3 and M4 Mycielski graphs Applying the Mycielskian repeatedly, starting with the one-edge graph, produces a sequence of graphs Mi = μ(Mi−1), sometimes called the Mycielski graphs. The first few graphs in this sequence are the graph M2 = K2 with two vertices connected by an edge, the cycle graph M3 = C5, and the Grötzsch graph M4 with 11 vertices and 20 edges. In general, the graph Mi is triangle-free, (i−1)-vertex-connected, and i-chromatic. The number of vertices in Mi for i ≥ 2 is 3 × 2i−2 − 1 , while the number of edges for i = 2, 3, . . .
A progressive mesh is a data structure which is created as the original model of the best quality simplifies a suitable decimation algorithm, which removes step by step some of the edges in the model (edge-collapse operation). It is necessary to undertake as many simplifications as needed to achieve the minimal model. The resultant model, in a full quality, is then represented by the minimal model and by the sequence of inverse operations to simplistic (vertex split operation). This forms a hierarchical structure which helps to create a model in the chosen level of detail.
Atomic cycles are a generalization of chordless cycles, that contain no n-chords. Given some cycle, an n-chord is defined as a path of length n connecting two points on the cycle, where n is less than the length of the shortest path on the cycle connecting those points. If a cycle has no n-chords, it is called an atomic cycle, because it cannot be decomposed into smaller cycles.. In the worst case, the atomic cycles in a graph can be enumerated in O(m2) time, where m is the number of edges in the graph.
The cill, also spelled sill, is a narrow horizontal ledge protruding a short way into the chamber from below the upper gates. Allowing the rear of the boat to "hang" on the cill is the main danger when descending a lock, and the position of the forward edge of the cill is usually marked on the lock side by a white line. The edge of the cill is usually curved, protruding less in the center than at the edges. In some locks, there is a piece of oak about thick which protects the solid part of the lock cill.
" She also complimented Adam Holender's cinematography and commented that he makes the film "extraordinarily handsome, with a sharply sunlit look that brings out the hard edges in its urban landscapes. The subject and visual style could not be more forcefully matched." Although he did not find its second half believable, Owen Gleiberman of Entertainment Weekly gave the film a B rating and called Nelson a "wondrous young actor". James Berardinelli called Jackson's supporting role "an example of an actor at his most focused" and called Fresh "an atypical thriller -- a film that succeeds because it defies many conventions of its genre.
A graph operation called lifting is central in a concept called immersions. The lifting is an operation on adjacent edges. Given three vertices v, u, and w, where (v,u) and (u,w) are edges in the graph, the lifting of vuw, or equivalent of (v,u), (u,w) is the operation that deletes the two edges (v,u) and (u,w) and adds the edge (v,w). In the case where (v,w) already was present, v and w will now be connected by more than one edge, and hence this operation is intrinsically a multi-graph operation.
Dracaena mannii Baker or small-leaved dragon tree, is a small to medium-sized tree, though recorded up to 30 m tall with stem to 2 m in diameter in Cameroon and Gabon. It occurs from Senegal to Angola along the African west coast, is widespread in tropical Africa and is found along the African east coast from Kenya to Kosi Bay in northern KwaZulu-Natal. It prefers lowland, submontane and montane forests which are either moist and evergreen, swampy or on coastal dunes. It is also found along forest edges, in clearings and on river banks from sea level to 1,800 metres.
In the illustration, every odd cycle in the graph contains the blue (the bottommost) vertices, so removing those vertices kills all odd cycles and leaves a bipartite graph. The edge bipartization problem is the algorithmic problem of deleting as few edges as possible to make a graph bipartite and is also an important problem in graph modification algorithmics. This problem is also fixed-parameter tractable, and can be solved in time O\left(2^k m^2\right), where k is the number of edges to delete and m is the number of edges in the input graph.
89 They were expected to cover the entire surface of the ice rink, without "an apparent struggle for speed", because it required the use of good flow and deep edges in skating. Dancers were not allowed to cross the center link of rinks in a regulation-sized arena (100 x 200 feet). Competitors were "judged for their mastery of fundamental elements" and CDs "provided an essential comparison of the dancers' technical skills". There was some latitude given to competitors that allowed them to "demonstrate their own personal style", usually done with using a variety of leg and/or arm movements.
Some minor sections in the central area were abandoned, and there were some extensions to the system at the outer edges. In order to operate the services, which ran on standard gauge track, the Corporation ordered ten bogie double deck cars with open tops from the Electric Railway and Tramway Carriage Works of Preston. The trams were stabled in the Lochee Depot, and were subsequently fitted with top covers. These were followed by eight trams purchased from G.F. Milnes & Co. of Birkenhead in 1902, which were also open topped double deck vehicles, and were later fitted with tiop covers.
In mathematics, an edge cycle cover (sometimes called simply cycle coverCun- Quan Zhang, Integer flows and cycle covers of graphs, Marcel Dekker,1997.) of a graph is a family of cycles which are subgraphs of G and contain all edges of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case the set of the cycles constitutes a spanning subgraph of G. If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.
Due to its geometric realization having some double edges where 4 faces meet, it's considered a degenerate uniform polyhedron but not strictly a uniform polyhedron. The number of edges is ambiguous, because the underlying abstract polyhedron has 360 edges, but 120 pairs of these have the same image in the geometric realization, so that the geometric realization has 120 single edges and 120 double edges where 4 faces meet, for a total of 240 edges. The Euler characteristic of the abstract polyhedron is −96. If the pairs of coinciding edges in the geometric realization are considered to be single edges, then it has only 240 edges and Euler characteristic 24.
It also included fixing staircases and platform edges. In 2001, the station received a major refurbishment, including upgrading the station for ADA compliance, restoring the original late 1910s tiling, repairing the staircases, re-tiling the walls, new tiling on the floors, upgrading the station's lights and the public address system, installing ADA yellow safety threads along the platform edge, new signs, and new trackbeds in both directions. The 2002 artwork here is called Memories of Twenty-Third Street by Keith Godard. The platform walls feature mosaics depicting hats that famous people of the Flatiron District wore, including Oscar Wilde, Sarah Bernhardt, and W. E. B. Du Bois.
The model is based on the idea of fitness, an inherent competitive factor that nodes may have, capable of affecting the network's evolution. According to this idea, the nodes' intrinsic ability to attract links in the network varies from node to node, the most efficient (or "fit") being able to gather more edges in the expense of others. In that sense, not all nodes are identical to each other, and they claim their degree increase according to the fitness they possess every time. The fitness factors of all the nodes composing the network may form a distribution ρ(η) characteristic of the system been studied.
In the entablature above it is a wooden "IHS" Christogram from the middle of which rises the vertical line of a wooden cross at the gable apex. On either side of the entrance section are recessed narrow Gothic arched windows in molded surrounds set with tinted glass, one horizontal mullion at centre and two curved ones curving inward from the edges, in contrast to those on the entrance transom. On each side of the pavilion is a similarly treated, narrower window. At the roofline of the entrance pavilion is a plain frieze; above it on either side of the entrance projection are louvered vents.
One of the outer edges in 1991 The city also underwent massive construction during the 1960s, with developers building new modular structures above older ones. The city became extremely densely populated and "a world unto its own," an enclave, with over 33,000 people in 300 buildings occupying little more than . As a result, the city reached its maximum size by the late 1970s and early 1980s; a height restriction of 13 to 14 storeys had been imposed on the city due to the flight path of planes heading toward Kai Tak Airport. As well as limiting building height, the proximity of the airport subjected residents to serious noise pollution.
More generally, every planar graph of minimum degree at least three either has an edge of total degree at most 12, or at least 60 edges that (like the edges in the triakis icosahedron) connect vertices of degrees 3 and 10. If all triangular faces of a polyhedron are vertex-disjoint, there exists an edge with smaller total degree, at most eight. Generalizations of the theorem are also known for graph embeddings onto surfaces with higher genus. The theorem cannot be generalized to all planar graphs, as the complete bipartite graphs K_{1,n-1} and K_{2,n-2} have edges with unbounded total degree.
In a complete undirected graph G = (V, E), if we sort the edges in nondecreasing order of the distances: d(e1) ≤ d(e2) ≤ … ≤ d(em) and let Gi = (V, Ei), where Ei = {e1, e2, …, ei}. The k-center problem is equivalent to finding the smallest index i such that Gi has a dominating set of size at most k. Although Dominating Set is NP-complete, the k-center problem remains NP- hard. This is clear, since the optimality of a given feasible solution for the k-center problem can be determined through the Dominating Set reduction only if we know in first place the size of the optimal solution (i.e.
Whereas intaglio methods worked by creating furrows into which the acid was poured to create 'holes' in the plate and the ink then poured over the entire surface, Blake wrote and drew directly onto the plate with an acid-resistant material known as a stop-out. He would then embed the plate’s edges in strips of wax to create a self-contained tray and pour the acid about a quarter of an inch deep, thus causing the exposed parts of the plate to melt away, and the design and/or text to remain slightly above the rest of the plate, i.e. in relief, like a modern rubber stamp.
Intuitively, adding an edge of fixed length to a graph reduces its number of degrees of freedom by one, so the 2n − 3 edges in a Laman graph reduce the 2n degrees of freedom of the initial point placement to the three degrees of freedom of a rigid graph. However, not every graph with 2n − 3 edges is rigid; the condition in the definition of a Laman graph that no subgraph can have too many edges ensures that each edge contributes to reducing the overall number of degrees of freedom, and is not wasted within a subgraph that is already itself rigid due to its other edges.
Haddow 1967, p. 9. The early aircraft had structural deficiencies and their machine guns were installed beyond the reach of the pilot so that when they jammed, there was nothing the pilot could do about it. These problems were later rectified with the strengthening of the airframe and the repositioning of the guns. While the original Aviatik D-I design by Julius von Berg was sound, the Series 115 aircraft license-produced by the Lohner firm at Wien-Floridsdorf were notorious for failures along the wing trailing edges in high speed maneuvers, as Lohner had deviated from Aviatik specifications by employing thinner, lighter wing ribs.
This process does not add any vertices to the subdivision (therefore, the size remains O(n)), and can be performed in O(n log n) time by plane sweep (it can also be performed in linear time, using polygon triangulation). Therefore, there is no loss of generality, if we restrict our data structure to the case of monotone subdivisions, as we do in this section. The weakness of the slab decomposition is that the vertical lines create additional segments in the decomposition, making it difficult to achieve O(n) storage space. Edelsbrunner, Guibas, and Stolfi discovered an optimal data structure that only uses the edges in a monotone subdivision.
Block 1 includes elliptical leading edges in the compressor, smaller low-pressure turbine tip clearances, and new coating for the high- pressure compressor drum, as well as an upgrade to the engine control (FADEC) software. The EP2 package entered testing in May 2013 and was scheduled to be available for delivery in mid 2014. This package aims to provide a further 0.8% reduction in fuel burn on top of the improvements offered by the EP package. Changes include better sealing of the low-pressure turbine, improvements to fan blade tip clearances, and other changes derived from the engines developed for the Boeing 787 and Airbus A350.
This is because the corresponding problem that defines PPAD, known as END OF THE LINE, can be reduced (in a straightforward way) to the above search for an additional odd-degree vertex (essentially, just by ignoring the directions of the edges in END OF THE LINE). There is an un- oriented version of the Sperner lemma known to be complete for PPA. The consensus-halving problem, which is a computational version of the Hobby-Rice theorem, is known to be complete for PPA. The problem of searching for a second Hamiltonian cycle on a 3-regular graph is a member of PPA, but is not known to be complete for PPA.
RIXS is element and orbital specific: chemical sensitivity arises by tuning to the absorption edges of the different types of atoms in a material. RIXS can even differentiate between the same chemical element at sites with inequivalent chemical bondings, with different valencies or at inequivalent crystallographic positions as long as the X-ray absorption edges in these cases are distinguishable. In addition, the type of information on the electronic excitations of a system being probed can be varied by tuning to different X-ray edges (e.g., K, L or M) of the same chemical element, where the photon excites core-electrons into different valence orbitals.
For instance, the figure shows the vertices of the graph placed on a cycle, with the internal diagonals of the cycle forming a matching. By subdividing the cycle edges into two matchings, we can partition the Heawood graph into three perfect matchings (that is, 3-color its edges) in eight different ways. Every two perfect matchings, and every two Hamiltonian cycles, can be transformed into each other by a symmetry of the graph.. There are 28 six-vertex cycles in the Heawood graph. Each 6-cycle is disjoint from exactly three other 6-cycles; among these three 6-cycles, each one is the symmetric difference of the other two.
The distance between two people/nodes in a collaboration graph is called the collaboration distance.. Thus the collaboration distance between two distinct nodes is equal to the smallest number of edges in an edge-path connecting them. If no path connecting two nodes in a collaboration graph exists, the collaboration distance between them is said to be infinite. The collaboration distance may be used, for instance, for evaluating the citations of an author, a group of authors or a journal. In the collaboration graph of mathematicians, the collaboration distance from a particular person to Paul Erdős is called the Erdős number of that person.
It was observed that in fact several edges may be drawn in the same "page"; the book thickness of the graph is the minimum number of halfplanes needed for such a drawing. Alternatively, any finite graph can be drawn with straight-line edges in three dimensions without crossings by placing its vertices in general position so that no four are coplanar. For instance, this may be achieved by placing the ith vertex at the point (i,i2,i3) of the moment curve. An embedding of a graph into three- dimensional space in which no two of the cycles are topologically linked is called a linkless embedding.
Tessa Virtue and Scott Moir (2009) demonstrating an ice dance hold The ISU defines a step sequence in ice dance as "a series of prescribed or un-prescribed steps, turns and movements in a Rhythm Dance or a Free Dance". Step sequences have three divisions: types, groups, and styles. There are two types of step sequences: not-touching or in hold. Not-touching step sequences must include matching and/or mirror footwork; both ice dancers must skate as close to each other as possible, not more than two arm lengths apart, without touching, except when they are skating turns and edges in opposite directions for short distances.
A graph with attributes Various attributes can be applied to graphs, nodes and edges in DOT files. These attributes can control aspects such as color, shape, and line styles. For nodes and edges, one or more attribute–value pairs are placed in square brackets ([]) after a statement and before the semicolon (which is optional). Graph attributes are specified as direct attribute–value pairs under the graph element, where multiple attributes are separated by a comma or using multiple sets of square brackets, while node attributes are placed after a statement containing only the name of the node, but not the relations between the dots.
The pectoral fins are hyaline whilst the pelvic fins are translucent yellow, becoming more solidly and opaquely yellow with black posterior edges in fine specimens (again, alpha males are particularly notable in this regard). The eye is a notable feature of this fish, the upper half of the iris being an intense red, in some specimens almost gemstone-ruby in appearance. The colour of this part of the iris is an indicator of the health of the fish: if this red colouration fades, or worse still turns grey, then this is an indicator of serious disease in the fish. In common with many characins, the lemon tetra possesses an adipose fin.
The skull of Colobomycter is considered one of the most enigmatic found in any of the parareptiles primarily due to the presence of greatly enlarged caniniform teeth possessing serrated edges in the premaxilla and, to a lesser extent, the maxilla. The length of the premaxillary fang is greater than half the height of the skull. Modesto & Reisz (2008) note that "The large size of the first premaxillary tooth is [otherwise] unheard of among early reptiles." The taxon also possesses unusual "folding" of the dentine at the bases of its larger marginal teeth, a state known as polyplycodont (a condition also seen to have evolved independently in diadectomorphs, ichthyosaurs, and mosasaurs).
Padbury station was demolished in 1968 and houses were built on the site in 1975. The line through Verney Junction was mothballed in 1993, leaving the stationmaster's house as a private residence and the platform edges in an overgrown state. , the Government has funded works to reopen the main line between Oxford and Cambridge through Verney Junction (by 2025),Autumn statement: Chancellor invests in new transport links for the regionITV Anglia, 23 November 2016 but there are no known plans to reopen this branch. In January 2019, advocacy group the Campaign for Better Transport released a report in which they listed the line as Priority 2 for reopening.
As with its vertex counterpart, an edge coloring of a graph, when mentioned without any qualification, is always assumed to be a proper coloring of the edges, meaning no two adjacent edges are assigned the same color. Here, two distinct edges are considered to be adjacent when they share a common vertex. An edge coloring of a graph may also be thought of as equivalent to a vertex coloring of the line graph , the graph that has a vertex for every edge of and an edge for every pair of adjacent edges in . A proper edge coloring with different colors is called a (proper) -edge-coloring.
The female zebra mbuna is polymorphic, that is to say it occurs in two different colour forms. In one morph the head and body colour is pale brownish-grey, with similar coloured dorsal, anal and caudal fins, the pectoral fins have grey rays and clear membranes, and the black pelvic fins have white leading edges. In the other colour morph the throat is brown and the head and body are dark brown to black, the body having blue highlights. The dorsal and caudal fins are a similar brown/black colour and so are the anal fins, but on them, the trailing edges have a number of yellow spots.
It can contain regular digon lunes as {2}θ,φ, where θ and φ are two dihedral angles. For example, a regular hosotope {2,p,q} has digon faces, {2}2π/p,2π/q, where its vertex figure is a spherical platonic solid, {p,q}. Each vertex of {p,q} defines an edge in the hosotope and adjacent pairs of those edges define lune faces. Or more specifically, the regular hosotope {2,4,3}, has 2 vertices, 8 180° arc edges in a cube, {4,3}, vertex figure between the two vertices, 12 lune faces, {2}π/4,π/3, between pairs of adjacent edges, and 6 hosohedral cells, {2,p}π/3.
When r is a divisor of n, the Turán graph is symmetric and strongly regular, although some authors consider Turán graphs to be a trivial case of strong regularity and therefore exclude them from the definition of a strongly regular graph. The Turán graph T(n,\lceil n/3\rceil) has 3a2b maximal cliques, where 3a + 2b = n and b ≤ 2; each maximal clique is formed by choosing one vertex from each partition subset. This is the largest number of maximal cliques possible among all n-vertex graphs regardless of the number of edges in the graph (Moon and Moser 1965); these graphs are sometimes called Moon–Moser graphs.
If an n-vertex graph has a RAC drawing with straight edges, it can have at most 4n − 10 edges. This is tight: there exist RAC-drawable graphs with exactly 4n − 10 edges. For drawings with polyline edges, the bound on the number of edges in the graph depends on the number of bends that are allowed per edge. The graphs that have RAC drawings with one or two bends per edge have O(n) edges; more specifically, with one bend there are at most 5.5n edges and with two bends there are at most 74.2n edges.. Every graph has a RAC drawing with three bends per edge.
A directed graph with a synchronizing coloring The image to the right shows a directed graph on eight vertices in which each vertex has out-degree 2\. (Each vertex in this case also has in-degree 2, but that is not necessary for a synchronizing coloring to exist.) The edges of this graph have been colored red and blue to create a synchronizing coloring. For example, consider the vertex marked in yellow. No matter where in the graph you start, if you traverse all nine edges in the walk "blue-red-red—blue-red-red—blue-red-red", you will end up at the yellow vertex.
Kruskal's algorithm finds a minimum spanning forest of an undirected edge- weighted graph. If the graph is connected, it finds a minimum spanning tree. (A minimum spanning tree of a connected graph is a subset of the edges that forms a tree that includes every vertex, where the sum of the weights of all the edges in the tree is minimized. For a disconnected graph, a minimum spanning forest is composed of a minimum spanning tree for each connected component.) It is a greedy algorithm in graph theory as in each step it adds the next lowest-weight edge that will not form a cycle to the minimum spanning forest.
Whilst it is possible to define so-called gap-n morasses for n > 1, they are so complex that focus is usually restricted to the gap-1 case, except for specific applications. The "gap" is essentially the cardinal difference between the size of the "small approximations" used and the size of the ultimate structure. A (gap-1) morass on an uncountable regular cardinal κ (also called a (κ,1)-morass) consists of a tree of height κ + 1, with the top level having κ+-many nodes. The nodes are taken to be ordinals, and functions between these ordinals are associated to the edges in the tree order.
Suurballe's algorithm performs the following steps: # Find the shortest path tree rooted at node by running Dijkstra's algorithm (figure C). This tree contains for every vertex , a shortest path from to . Let be the shortest cost path from to (figure B). The edges in are called tree edges and the remaining edges (the edges missing from figure C) are called non-tree edges. # Modify the cost of each edge in the graph by replacing the cost of every edge by . According to the resulting modified cost function, all tree edges have a cost of 0, and non-tree edges have a non-negative cost.
As Vienna was expanding rapidly around its edges, in 1893 Wagner proposed a project creating a new channel for the Wien river, a tributary of the Danube, and a grand boulevard with new buildings to line it. His project was accepted by the city government in 1894.Metzger, Rainer, Vienne des Anées 1900 (2018) Wagner was very critical of the historicism of the buildings which lined the Ringstrasse, the famous circular main boulevard of Vienna, which he termed a "stylistic masked ball". He presented his new ideas in an essay entitled Modern Architecture, published in 1896, calling for a new architecture whose forms expressed their functions.
It is a mainstay of Islamic architecture, especially Persian and Mughal architecture; in the latter the lowest arches often have scalloped edges. In Asia it typically has a less depressed form than in "Tudor"-style examples. In English architecture, it is often known as a Tudor arch, as it was a common architectural element during the reigns of the Tudor dynasty (1485–1603), though its use predates 1485 by several decades, and from about 1550 it was out of fashion for grand buildings. It is a blunted version of the pointed arch of Gothic architecture, of which Tudor architecture is the last phase in England.
It is NP-complete to determine the queue number of a given graph, or even to test whether this number is one., Corollary 3.9. However, if the vertex ordering of a queue layout is given as part of the input, then the optimal number of queues for the layout equals the maximum number of edges in a k-rainbow, a set of k edges each two of which form a nested pair. A partition of edges into queues can be performed by assigning an edge e that is the outer edge of an i-rainbow (and of no larger rainbow) to the ith queue.
Given a DSP program in Data flow graph(DFG) format and a unfolding factor J, unfolding process transforms the DSP program into a new one by duplicating the functional blocks and reconnecting the functional blocks while maintaining its DSP functionality. We call the program performed with factor J as J-unfolded DFG. In the J-unfolded DFG, for each node U in original DFG, there are J nodes in the transformed DFG with the same function as U. For each edge in the original DFG, there are J edges in the transformed DFG but its delay is only 1/J times to the original one.
Alternatively, each point of the diamond cubic structure may be given by four-dimensional integer coordinates whose sum is either zero or one. Two points are adjacent in the diamond structure if and only if their four-dimensional coordinates differ by one in a single coordinate. The total difference in coordinate values between any two points (their four-dimensional Manhattan distance) gives the number of edges in the shortest path between them in the diamond structure. The four nearest neighbors of each point may be obtained, in this coordinate system, by adding one to each of the four coordinates, or by subtracting one from each of the four coordinates, accordingly as the coordinate sum is zero or one.
Therefore, we have constructed an antichain and a partition into chains with the same cardinality. To prove Kőnig's theorem from Dilworth's theorem, for a bipartite graph G = (U,V,E), form a partial order on the vertices of G in which u < v exactly when u is in U, v is in V, and there exists an edge in E from u to v. By Dilworth's theorem, there exists an antichain A and a partition into chains P both of which have the same size. But the only nontrivial chains in the partial order are pairs of elements corresponding to the edges in the graph, so the nontrivial chains in P form a matching in the graph.
Unsharp masking has been applied to lower part of image, creating overshoot and undershoot and increasing acutance. Edge enhancement is an image processing filter that enhances the edge contrast of an image or video in an attempt to improve its acutance (apparent sharpness). The filter works by identifying sharp edge boundaries in the image, such as the edge between a subject and a background of a contrasting color, and increasing the image contrast in the area immediately around the edge. This has the effect of creating subtle bright and dark highlights on either side of any edges in the image, called overshoot and undershoot, leading the edge to look more defined when viewed from a typical viewing distance.
Traditional Ukrainian , before cooking and with crimped edges In other regions of Ukraine, the names pyrohy and pyrizhky refer to baked pies and buns as opposed to the boiled dumplings. The name of a popular type of Polish pierogi, pierogi ruskie ("Ruthenian pierogi"), is related to Rus', the historical region and naming of Eastern Slavs and the ancient kingdom from which Ukrainians descend. Varenyky are considered by Ukrainians as one of their national dishes and plays a fundamental role in Ukrainian culture. Contrary to many other countries that share these dumplings, Ukrainians tended to use fermented milk products (Ukrainian: kysle moloko or Ryazhenka) to bind the dough together; however, today eggs tend to be used instead.
Therefore, the sum of the size of the largest independent set \alpha(G) and the size of a minimum vertex cover \beta(G) is equal to the number of vertices in the graph. A vertex coloring of a graph G corresponds to a partition of its vertex set into independent subsets. Hence the minimal number of colors needed in a vertex coloring, the chromatic number \chi(G), is at least the quotient of the number of vertices in G and the independent number \alpha(G). In a bipartite graph with no isolated vertices, the number of vertices in a maximum independent set equals the number of edges in a minimum edge covering; this is Kőnig's theorem.
Another algorithm with the same approximation factor takes advantage of the fact that the k-center problem is equivalent to finding the smallest index i such that Gi has a dominating set of size at most k and computes a maximal independent set of Gi, looking for the smallest index i that has a maximal independent set with a size of at least k. It is not possible to find an approximation algorithm with an approximation factor of 2 − ε for any ε > 0, unless P = NP. Furthermore, the distances of all edges in G must satisfy the triangle inequality if the k-center problem is to be approximated within any constant factor, unless P = NP.
Earley parsers in particular have been used in compiler compilers where their ability to parse using arbitrary Context-free grammars eases the task of writing the grammar for a particular language. However their lower efficiency has led to people avoiding them for most compiler work. In bidirectional chart parsing, edges of the chart are marked with a direction, either forwards or backwards, and rules are enforced on the direction in which edges must point in order to be combined into further edges. In incremental chart parsing, the chart is constructed incrementally as the text is edited by the user, with each change to the text resulting in the minimal possible corresponding change to the chart.
Saint-Exupéry: A Biography, Pimlico 1994. of Saint-Exupéry, author Stacy Schiff described the campus as a "tidy red-roofed village unto itself" overlooking "sleepy" Fribourg. Ms Schiff's evocation of the self-contained, red-roofed village is quite accurate, but the campus did not overlook the city so much as it was perched on a flat, wooded plateau, nestled in an elbow high above the Sarine River, which over the eons had carved the bluff's curling cliffs. At its edges, in the woods beyond the unmarked perimeter of the campus, the plateau, now the site of the Swiss lycée Collège St Croix, gives way to those cliffs which fall 200 feet to the winding Saane/Sarine River below.
Therefore, the best known time bound for testing whether a graph is triangle- free, O(m1.41),, based on fast matrix multiplication. Here m is the number of edges in the graph, and the big O notation hides a large constant factor; the best practical algorithms for triangle detection take time O(m3/2). For median graph recognition, the time bound can be expressed either in terms of m or n (the number of vertices), as m = O(n log n). applies as well to testing whether a graph is a median graph, and any improvement in median graph testing algorithms would also lead to an improvement in algorithms for detecting triangles in graphs.
In static timing analysis, the word static alludes to the fact that this timing analysis is carried out in an input-independent manner, and purports to find the worst-case delay of the circuit over all possible input combinations. The computational efficiency (linear in the number of edges in the graph) of such an approach has resulted in its widespread use, even though it has some limitations. A method that is commonly referred to as PERT is popularly used in STA. However, PERT is a misnomer, and the so-called PERT method discussed in most of the literature on timing analysis refers to the critical path method (CPM) that is widely used in project management.
A perfect matching (red edges), in the Petersen graph. Since the Petersen graph is cubic and bridgeless, it meets the conditions of Petersen's theorem. A cubic (but not bridgeless) graph with no perfect matching, showing that the bridgeless condition in Petersen's theorem cannot be omitted In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: > Petersen's Theorem. Every cubic, bridgeless graph contains a perfect > matching.. In other words, if a graph has exactly three edges at each vertex, and every edge belongs to a cycle, then it has a set of edges that touches every vertex exactly once.
The emboss filter, also called a directional difference filter,"Computer imaging: Digital image analysis and processing (Second ed.)" by Scott E Umbaugh, (2010) will enhance edges in the direction of the selected convolution mask(s). When the emboss filter is applied, the filter matrix is in convolution calculation with the same square area on the original image. So it involves a large amount of calculation when either the image size or the emboss filter mask dimension is large. The emboss filter repeats the calculation as encoded in the filter matrix for every pixel in the image; the procedure itself compares the neighboring pixels on the image, leaving a mark where a sharp change in pixel value is detected.
For a regular graph of degree that does not have a perfect matching, this lower bound can be used to show that at least colors are needed. In particular, this is true for a regular graph with an odd number of vertices (such as the odd complete graphs); for such graphs, by the handshaking lemma, must itself be even. However, the inequality does not fully explain the chromatic index of every regular graph, because there are regular graphs that do have perfect matchings but that are not k-edge-colorable. For instance, the Petersen graph is regular, with and with edges in its perfect matchings, but it does not have a 3-edge-coloring.
A strong orientation of a given bridgeless undirected graph may be found in linear time by performing a depth first search of the graph, orienting all edges in the depth first search tree away from the tree root, and orienting all the remaining edges (which must necessarily connect an ancestor and a descendant in the depth first search tree) from the descendant to the ancestor.See e.g. and . If an undirected graph with bridges is given, together with a list of ordered pairs of vertices that must be connected by directed paths, it is possible in polynomial time to find an orientation of that connects all the given pairs, if such an orientation exists.
A spanning tree (blue heavy edges) of a grid graph In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with a minimum possible number of edges. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (but see spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself).
The Schönhardt polyhedron is combinatorially equivalent to the regular octahedron: its vertices, edges, and faces can be placed in one-to-one correspondence with the features of a regular octahedron. However, unlike the regular octahedron, three of its edges have concave dihedral angles, and these three edges form a perfect matching of the graph of the octahedron; this fact is sufficient to show that it cannot be triangulated. The six vertices of the Schönhardt polyhedron can be used to form fifteen unordered pairs of vertices. Twelve of these fifteen pairs form edges of the polyhedron: there are six edges in the two equilateral triangle faces, and six edges connecting the two triangles.
In it, the vertices can be connected by a path, such that every two edges in the path are at right angles to each other. A two-dimensional orthoscheme is a right triangle. A three-dimensional orthoscheme can be constructed from a cube by finding a path of three edges of the cube that do not all lie on the same square face, and forming the convex hull of the four points on this path. Dissection of a cube into six orthoschemes A dissection of a shape S (which may be any closed set in Euclidean space) is a representation of S as a union of other shapes whose interiors are disjoint from each other.
On the August 18, 2014 episode of Raw, reigning champion Brock Lesnar, who had won the title the night before at SummerSlam, was presented with a single championship belt, retiring the Big Gold Belt in the process. The current belt has a slightly updated design from the belt introduced by The Rock in 2013 as a result of WWE changing their corporate logo which was originally used for the WWE Network. It includes a large center plate dominated by a cut out of the current WWE logo inside an irregular heptagon with the capital words "World Heavyweight Champion" along the bottom edges, in very small print. The belt retains the gold divider bars introduced in the previous design.
Let G be a finite, strongly connected, directed graph where all the vertices have the same out- degree k. Let A be the alphabet containing the letters 1, ..., k. A synchronizing coloring (also known as a collapsible coloring) in G is a labeling of the edges in G with letters from A such that (1) each vertex has exactly one outgoing edge with a given label and (2) for every vertex v in the graph, there exists a word w over A such that all paths in G corresponding to w terminate at v. The terminology synchronizing coloring is due to the relation between this notion and that of a synchronizing word in finite automata theory.
A single fore-edge painting includes a painting on only one side of the book page edges. Generally, gilt or marbling is applied by the bookbinder after the painting has dried, so as to make the painting completely invisible when the book is closed and the pages are not fanned. A double fore- edge painting has paintings on both sides of the page margin so that one painting is visible when the leaves are fanned one way, and the other is visible when the leaves are fanned the other way. A triple fore-edge painting has, in addition to paintings on the edges, a third painting applied directly to the edges (in lieu of gilt or marbling).
For any cycle in a graph , one can form an -dimensional 0-1 vector that has a 1 in the coordinate positions corresponding to edges in and a 0 in the remaining coordinate positions. The cycle space of the graph is the vector space formed by all possible linear combinations of vectors formed in this way. In Mac Lane's characterization, is a vector space over the finite field with two elements; that is, in this vector space, vectors are added coordinatewise modulo two. A 2-basis of is a basis of with the property that, for each edge in , at most two basis vectors have nonzero coordinates in the position corresponding to .
A factor-critical graph, together with perfect matchings of the subgraphs formed by removing one of its vertices. In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph.) is a graph with vertices in which every subgraph of vertices has a perfect matching. (A perfect matching in a graph is a subset of its edges with the property that each of its vertices is the endpoint of exactly one of the edges in the subset.) A matching that covers all but one vertex of a graph is called a near-perfect matching. So equivalently, a factor-critical graph is a graph in which there are near-perfect matchings that avoid every possible vertex.
A planar embedding of a given graph is a drawing of the graph in the Euclidean plane, with points for its vertices and curves for its edges, in such a way that the only intersections between pairs of edges are at a common endpoint of the two edges. A minor of a given graph is another graph formed by deleting vertices, deleting edges, and contracting edges. When an edge is contracted, its two endpoints are merged to form a single vertex. In some versions of graph minor theory the graph resulting from a contraction is simplified by removing self-loops and multiple adjacencies, while in other version multigraphs are allowed, but this variation makes no difference to Wagner's theorem.
A line perfect graph. The edges in each biconnected component are colored black if the component is bipartite, blue if the component is a tetrahedron, and red if the component is a book of triangles. The line graph of the complete graph Kn is also known as the triangular graph, the Johnson graph J(n, 2), or the complement of the Kneser graph KGn,2. Triangular graphs are characterized by their spectra, except for n = 8.. See in particular Proposition 8, p. 262. They may also be characterized (again with the exception of K8) as the strongly regular graphs with parameters srg(n(n − 1)/2, 2(n − 2), n − 2, 4).
Each 4-connected (in the above sense) simple cubic graph on vertices defines a class of quantum mechanical j symbols. Roughly speaking, each vertex represents a 3-jm symbol, the graph is converted to a digraph by assigning signs to the angular momentum quantum numbers , the vertices are labelled with a handedness representing the order of the three (of the three edges) in the 3jm symbol, and the graph represents a sum over the product of all these numbers assigned to the vertices. There are 1 (6j), 1 (9j), 2 (12j), 5 (15j), 18 (18j), 84 (21j), 607 (24j), 6100 (27j), 78824 (30j), 1195280 (33j), 20297600 (36j), 376940415 (39j) etc. of these .
In some applications, such cycles are undesirable, and we wish to eliminate them and obtain a directed acyclic graph (DAG). One way to do this is simply to drop edges from the graph to break the cycles. Closely related are the feedback vertex set, which is a set of vertices containing at least one vertex from every cycle in the directed graph, and the minimum spanning tree, which is the undirected variant of the feedback arc set problem. A minimal feedback arc set (one that can not be reduced in size by removing any edges) has the additional property that, if the edges in it are reversed rather than removed, then the graph remains acyclic.
By the turn of the third millennium, the term bogan came to be employed more favourably to indicate a pride in being rough around the edges. In 2002, Michelle Griffin discussed the fact that "bogan" is no longer just being used as an insult, but is in fact a way to identify with the "Aussie" culture that many Anglo‐Saxon Australian citizens are proud of. In the past, bogan was a term of disdain, but nowadays it has become "cool" to be a bogan. Radio station Triple J held a "National Bogan Day" on 28 June 2002, which they commemorated by playing music by rock bands such as Cold Chisel, Midnight Oil, Rose Tattoo and AC/DC.
In this case each matrix can be encoded as a directed edge of a graph with n vertices. So all matrices together give a graph on n vertices with 2n directed edges. The identity holds provided that for any two vertices A and B of the graph, the number of odd Eulerian paths from A to B is the same as the number of even ones. (Here a path is called odd or even depending on whether its edges taken in order give an odd or even permutation of the 2n edges.) Swan showed that this was the case provided the number of edges in the graph is at least 2n, thus proving the Amitsur–Levitzki theorem.
Further, denote the set of all M-completions by L^M and the set of all resulting cycle covers of G_\phi by Z^M. Recall that construction of G_\phi was such that each external edge had weight 1, so the weight of Z^M, the cycle covers resulting from any M, depends only on the internal edges involved. We add here the premise that the construction of the clause components is such that the sum over possible M-completions of the weight of the internal edges in each clause component, where M is proper relative to the clause component, is 12. Otherwise the weight of the internal edges is 0.
Not-touching step sequences must include matching and/or mirror footwork; both ice dancers must skate as close to each other as possible, not more than two arm lengths apart, without touching, except when they are skating turns and edges in opposite directions for short distances. The dancers can switch from mirror to matching footwork, and vice versa, and they can cross each other's tracings (marks made in the ice by the skates). Step sequences in hold must be performed in any dance holds or any variation of dance holds, and must not last over one measure of music. Types of step sequences are separated into four Groups, based upon their difficulty.
Each middle caudal vertebra has two roughened structures that extend from the top of the back face onto the top surface of the vertebra. Finally, the bottom portion of each half of the haemal arches in the posterior caudal vertebrae is split fully into two articular facets. These traits form a unique combination not seen in other titanosaurs, along with the centrodiapophyseal laminae being widened on the top and bottom edges in the front and middle dorsal vertebrae (as also seen in Saltasaurus), and a rounded protrusion being present between the front and side trochanters of the fibula (also seen in Jainosaurus). A number of the bones of Lohuecotitan were internally pneumatized, including the cervical vertebrae, sacral vertebrae, and ilium.
Avions Fairey, the Fairey Aviation Company's Belgian subsidiary, was set up in 1930-1 to produce Fairey Fox and Firefly aircraft for the Belgian Air Force. Once production of the military aircraft was under way, its manager Ernest Oscar Tips found the time to design and build light aircraft of his own, first the single-seat Tipsy S and S.2 in 1935, then the two-seat Tipsy B. Although the latter was larger, the two aircraft types had much in common; both were single-engined low wing cantilever monoplanes, with wings tapered on the trailing edges. In detail, though, the planforms of the two aircraft were different. Both were built in Belgium by Avions Fairey and in the UK under licence.
250px Given three points x, y, z in the metric space X, by the triangle inequality there exist non-negative numbers a, b, c such that d(x,y) = a + b, \ d(x,z) = a + c, \ d(y,z) = b + c. Then the Gromov products are (y,z)_x = a, \ (x,z)_y = b, \ (x,y)_z = c. In the case that the points x, y, z are the outer nodes of a tripod then these Gromov products are the lengths of the edges. In the hyperbolic, spherical or euclidean plane, the Gromov product (A, B)C equals the distance p between C and the point where the incircle of the geodesic triangle ABC touches the edge CB or CA. Indeed from the diagram , so that .
Any counting formula involving vertices and faces that is valid for all planar graphs may be transformed by planar duality into an equivalent formula in which the roles of the vertices and faces have been swapped. Euler's formula, which is self-dual, is one example. Another given by Harary involves the handshaking lemma, according to which the sum of the degrees of the vertices of any graph equals twice the number of edges. In its dual form, this lemma states that in a plane graph, the sum of the numbers of sides of the faces of the graph equals twice the number of edges.. The medial graph of a plane graph is isomorphic to the medial graph of its dual.
The light that passes through the emulsion is absorbed by the anti-halation layer. This prevents any light from being reflected back through the emulsion from the rear surface of the base, or from anything behind the film, such as the pressure plate of the camera, and causing a halo-like effect around bright points or edges in the image. Still cameras, which handle less film and thus contend with less wear, typically hold their film in the gate with components painted or treated to be black, so reflections are less of an issue and few still films made use of anti-halation backings. The notable exception was Kodak's Kodachrome, which incorporated such a backing to aid with a very sensitive innermost layer.
Up to constant factors, z(n; t) also bounds the number of edges in an n-vertex graph (not required to be bipartite) that has no Kt,t subgraph. For, in one direction, a bipartite graph with z(n; t) edges and with n vertices on each side of its bipartition can be reduced to a graph with n vertices and (in expectation) z(n; t)/4 edges, by choosing n/2 vertices uniformly at random from each side. In the other direction, a graph with n vertices and no Kt,t can be transformed into a bipartite graph with n vertices on each side of its bipartition, twice as many edges, and still no Kt,t by taking its bipartite double cover., Theorem 2.3, p. 310.
Forsskaolea tenacissima is a member of the non-stinging nettles genus Forsskaolea and is in the same family as the stinging kind, Urticaceae. Described as "looking like a tough character that does not want or need a caress", F. tenacissima makes its home where not many plant species survive, in stony soils, road edges, in the gravel wadi and "in the rock crevices and water-receiving depressions" above the stone pavements of the Hamadas. Forsskaolea tenacissima was named in mourning of a student of Carl Linnaeus, a Swede named Peter Forsskål, who died while gathering botanical and zoological specimens from the Arabia Felix. Linnaeus named this plant Forsskaolea tenacissima because the plant was as stubborn and persistent as the student had been.
With a comeback show at The Hoxton Bar & Kitchen in June as part of The Artrocker New Blood Festival, the band released their come back single Jaded Edges in September 2013, announced as the first of a new series of singles to be released over the next year. Following a series of further London shows, the band released the single along with a video on YouTube, again directed by Templeton. The single received critical acclaim with Tom Robinson playlisting the track on his Fresh On The Net blog, Gary Crowley announcing it his 'Crowley Cracker' on his Amazing Radio show and Artrocker magazine calling it "possibly the strongest indie pop of the year". Radio One have also played the single with Jen Long calling it 'Big Indie'.
The Westerwald's permanent settlement and thereby its territorial history began with the Chatti (Hessians) pushing their way into the area after the Romans were driven out in the 3rd century. Placename endings such as –ar, –mar and –aha ("Haigraha" = Haiger) stemming from the Migration Period ("Völkerwanderung") can still be found now. These lie around the forest's outer edges in basins and dales whose soils and climate were favourable to early settlers, and include, for instance, Hadamar, Lahr and Wetzlar. From the 4th to the 6th century, the settlements from the time of the taking of the land arose in formerly pathless areas, taking endings such as –ingen and –heim, like Bellingen and Bladernheim; these lie on the broad, raised plains in the Upper Westerwald.
Traditional node-link methods for visualizing networks deteriorate in terms of legibility when dealing with large networks, due to the proliferation of edge crossings amassing as what are disparagingly termed 'hairballs'. BioFabric is one of a number of alternative approaches designed explicitly to tackle this scalability issue, choosing to do so by depicting nodes as lines on the horizontal axis, one per row; edges as lines on the vertical axis, one per column, terminating at the two rows associated with the endpoint nodes. As such, nodes and edges are each provided their own dimension (as opposed to solely the edges with nodes being non-dimensional points). BioFabric exploits the additional degree of freedom thus produced to place ends of incident edges in groups.
After application of non-maximum suppression, remaining edge pixels provide a more accurate representation of real edges in an image. However, some edge pixels remain that are caused by noise and color variation. In order to account for these spurious responses, it is essential to filter out edge pixels with a weak gradient value and preserve edge pixels with a high gradient value. This is accomplished by selecting high and low threshold values. If an edge pixel’s gradient value is higher than the high threshold value, it is marked as a strong edge pixel. If an edge pixel’s gradient value is smaller than the high threshold value and larger than the low threshold value, it is marked as a weak edge pixel.
If one aims at drawing a distinction between corner detectors and blob detectors, this can often be done in terms of their localization properties at corner structures. For a junction structure in the image domain that corresponds to an intersection of physical edges in the three-dimensional world, the localization properties of a corner detector will in most cases be much better than the localization properties that would be obtained from a blob detector. Hence, for the purpose of computing structure and motion from multiple views, corner detectors will in many cases have advantages compared to blob detectors in terms of smaller localization error. Notwithstanding this, blob descriptors have also been demonstrated to be useful when relating object models to temporal imagery.
In a simple graph G = (V, E), the degree of a vertex v, often denoted by deg(v) or δ(v), is the number of edges in E adjacent to v. The minimum degree of a graph, often denoted by deg(G) or δ(v), is the minimum of deg(v) over all vertices v in V. A matching in a graph is a set of edges such that each vertex is adjacent to at most one edge; a perfect matching is a matching in which each vertex is adjacent to exactly one edge. A perfect matching does not always exist, and thus it is interesting to find sufficient conditions that guarantee its existence. One such condition follows from Dirac's theorem on Hamiltonian cycles.
This tiling is uniform but not regular (it is by scalene triangles), and often regular tilings are used instead. A quotient of any tiling in the (2,3,7) family can be used (and will have the same automorphism group); of these, the two regular tilings are the tiling by 24 regular hyperbolic heptagons, each of degree 3 (meeting at 56 vertices), and the dual tiling by 56 equilateral triangles, each of degree 7 (meeting at 24 vertices). The order of the automorphism group is related, being the number of polygons times the number of edges in the polygon in both cases. :24 × 7 = 168 :56 × 3 = 168 The covering tilings on the hyperbolic plane are the order-3 heptagonal tiling and the order-7 triangular tiling.
The top two edges in the inner cycle must be chosen, but this completes a non-spanning cycle, which cannot be part of a Hamiltonian cycle. Alternatively, we can also describe the ten-vertex 3-regular graphs that do have a Hamiltonian cycle and show that none of them is the Petersen graph, by finding a cycle in each of them that is shorter than any cycle in the Petersen graph. Any ten-vertex Hamiltonian 3-regular graph consists of a ten-vertex cycle C plus five chords. If any chord connects two vertices at distance two or three along C from each other, the graph has a 3-cycle or 4-cycle, and therefore cannot be the Petersen graph.
This cancer was a manifestation of scrotal squamous cell carcinoma which had first been noted in 1775 by Sir Percival Pott in climbing boys or chimney sweepers. It was the first industrially related cancer to be identified and was originally called soot wart, then chimney sweeps cancer. He describes it: > It is a disease which always makes it first attack on the inferior part of > the scrotum where it produces a superficial, painful ragged ill-looking sore > with hard rising edges ... in no great length of time it pervades the skin, > dartos and the membranes of the scrotum, and seizes the testicle, which it > inlarges, hardens and renders truly and thoroughly distempered. Whence it > makes its way up the spermatic process into the abdomen.
There is a polynomial-time algorithm to determine the largest k for which a graph G is k-edge-connected. A simple algorithm would, for every pair (u,v), determine the maximum flow from u to v with the capacity of all edges in G set to 1 for both directions. A graph is k-edge-connected if and only if the maximum flow from u to v is at least k for any pair (u,v), so k is the least u-v-flow among all (u,v). If n is the number of vertices in the graph, this simple algorithm would perform O(n^2) iterations of the Maximum flow problem, which can be solved in O(n^3) time.
Let G = ((VG, EG), c) be an undirected graph with c(u,v) being the capacity of the edge (u,v) respectively. : Denote the minimum capacity of an s-t cut by λst for each s, t ∈ VG. : Let T = (VT,ET) be a tree with VT = VG, denote the set of edges in an s-t path by Pst for each s,t ∈ VT. Then T is said to be a Gomory–Hu tree of G if : λst = mine∈Pst c(Se, Te) for all s, t ∈ VG, where # Se and Te are the two connected components of T∖{e} in the sense that (Se, Te) form a s-t cut in G, and # c(Se, Te) is the capacity of the cut in G.
Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph G, and the goal is to find a matching containing as many edges as possible, that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this problem is equivalent to the task of finding a matching that covers as many vertices as possible. An important special case of the maximum cardinality matching problem is when G is a bipartite graph, whose vertices V are partitioned between left vertices in X and right vertices in Y, and edges in E always connect a left vertex to a right vertex.
Maitland, vol. 2, p. 811 Among his other works was The Baron, an extensive treatment of the history of English titles and offices, which is not extant, although some of the material he collected for it survives. His only surviving genealogical work, A Commentary Vpon ... Liber Domus DEI, a finished manuscript, describes the history of the families who came to England with William the Conqueror. Title page to corrupted version of Buck's History, misappropriated and published 1647 (2nd issue) by Buck's great-nephew His major prose work was The History of King Richard the Third, which he completed in 1619 and left in rough draft at his death, and which, in 1731, was burnt around the edges in the Cotton library fire.
The zone of a line l in a line arrangement is the collection of cells having edges belonging to l. The zone theorem states that the total number of edges in the cells of a single zone is linear. More precisely, the total number of edges of the cells belonging to a single side of line l is at most 5n − 1,, , . and the total number of edges of the cells belonging to both sides of l is at most \lfloor 9.5n\rfloor-1.. More generally, the total complexity of the cells of a line arrangement that are intersected by any convex curve is O(n α(n)), where α denotes the inverse Ackermann function, as may be shown using Davenport–Schinzel sequences.
Bedford and Cooke show that any assignment of values in the open interval (−1, 1) to the edges in any partial correlation vine is consistent, the assignments are algebraically independent, and there is a one- to-one relation between all such assignments and the set of correlation matrices. In other words, partial correlation vines provide an algebraically independent parametrization of the set of correlation matrices, whose terms have an intuitive interpretation. Moreover, the determinant of the correlation matrix is the product over the edges of (1 − ρ2ik;D(ik)) where ρik;D(ik) is the partial correlation assigned to the edge with conditioned variables i,k and conditioning variables D(ik). A similar decomposition characterizes the mutual information, which generalizes the determinant of the correlation matrix.
Numerous inexpensive imitations are now widely sold as puka shell necklaces. The majority of contemporary "puka shell necklaces" are not made from cone shells, but from other shells, or even from plastic. In addition, some strings of beads are currently sold that are made from cone shells, but the beads in these necklaces were not formed by natural processes. They were instead worked by hand from whole shells using pliers to break the shell down to the needed part, and then subjecting the rough results to tumble finishing, in order to give each bead more or less smooth edges in imitation of the natural wear-and- tear a shell receives when tumbled in the surf over long periods of time.
To a graph G there corresponds a signed complete graph Σ on the same vertex set, whose edges are signed negative if in G and positive if not in G. Conversely, G is the subgraph of Σ that consists of all vertices and all negative edges. The two-graph of G can also be defined as the set of triples of vertices that support a negative triangle (a triangle with an odd number of negative edges) in Σ. Two signed complete graphs yield the same two-graph if and only if they are equivalent under switching. Switching of G and of Σ are related: switching the same vertices in both yields a graph H and its corresponding signed complete graph.
A pusher mounted on a loader Steel trip edge snow pushers have a spring-loaded steel cutting edge mounted to the bottom of the moldboard that allow them to scrape the pavement. They employ a tripping system to allow them to pass over obstructions such as uneven pavement or raised manhole covers. There are three types of trip edges in use today: compression spring, torsion spring, and composite material springs. Both compression and torsion spring systems work similarly; the steel edge is mounted on a hinge and is held in place by the pressure of the springs; when the edge meets an obstruction the springs compress and allow the edge to flip back and under the pusher and to pass over the obstruction.
Both edge and vertex contraction techniques are valuable in proof by induction on the number of vertices or edges in a graph, where it can be assumed that a property holds for all smaller graphs and this can be used to prove the property for the larger graph. Edge contraction is used in the recursive formula for the number of spanning trees of an arbitrary connected graph, and in the recurrence formula for the chromatic polynomial of a simple graph. Contractions are also useful in structures where we wish to simplify a graph by identifying vertices that represent essentially equivalent entities. One of the most common examples is the reduction of a general directed graph to an acyclic directed graph by contracting all of the vertices in each strongly connected component.
Every pseudoforest on a set of n vertices has at most n edges, and every maximal pseudoforest on a set of n vertices has exactly n edges. Conversely, if a graph G has the property that, for every subset S of its vertices, the number of edges in the induced subgraph of S is at most the number of vertices in S, then G is a pseudoforest. 1-trees can be defined as connected graphs with equally many vertices and edges. Moving from individual graphs to graph families, if a family of graphs has the property that every subgraph of a graph in the family is also in the family, and every graph in the family has at most as many edges as vertices, then the family contains only pseudoforests.
The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices but has no complete bipartite subgraphs of a given size.. Reprint of 1978 Academic Press edition, . It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.. As cited by . The Kővári–Sós–Turán theorem, named after Tamás Kővári, Vera T. Sós, and Pál Turán, provides an upper bound on the solution to the Zarankiewicz problem. When the forbidden complete bipartite subgraph has one side with at most three vertices, this bound has been proven to be within a constant factor of the correct answer.
Black walnut is primarily a pioneer species similar to red and silver maple and black cherry. Because of this, black walnut is a common weed tree found along roadsides, fields, and forest edges in the eastern US. It will grow in closed forests, but is classified as shade intolerant; this means it requires full sun for optimal growth and nut production. Black walnut's native range extends across much of the eastern US. It is absent from the coastal plain south of North Carolina as well as the Mississippi Valley, and does not occur in the northern tier of the eastern US, where the frost-free season is too short for the nuts to develop. Its western range extends all the way to the eastern Great Plains, after which climate conditions become too dry for it.
An unrooted binary tree T may be transformed into a full rooted binary tree (that is, a rooted tree in which each non-leaf node has exactly two children) by choosing a root edge e of T, placing a new root node in the middle of e, and directing every edge of the resulting subdivided tree away from the root node. Conversely, any full rooted binary tree may be transformed into an unrooted binary tree by removing the root node, replacing the path between its two children by a single undirected edge, and suppressing the orientation of the remaining edges in the graph. For this reason, there are exactly 2n −3 times as many full rooted binary trees with n leaves as there are unrooted binary trees with n leaves.
Delighted with the novel style and form, he built some columns after that pattern for the Corinthians, determined their symmetrical proportions, and established from that time forth the rules to be followed in finished works of the Corinthian order. There is no way to corroborate Vitruvius's account, but since the elaborate design of the Corinthian column resembles other works attributed to Callimachus, the attribution seems reasonable to modern architectural historians. The complex and difficult design of the column's capital often required drilling to undercut the leaf edges. In the cella of the Erechtheion hung an ingenious golden lamp called asbestos lychnis invented by Callimachus, according to Pausanias' Description of Greece: it needed to be refilled with oil only once a year as the asbestos wick did not burn.
While traditional Canny edge detection provides relatively simple but precise methodology for edge detection problem, with more demanding requirements on the accuracy and robustness on the detection, the traditional algorithm can no longer handle the challenging edge detection task. The main defects of the traditional algorithm can be summarized as follows:[8] # A Gaussian filter is applied to smooth out the noise, but it will also smooth the edge, which is considered as the high frequency feature. This will increase the possibility of missing weak edges, and the appearance of isolated edges in the result. # For the gradient amplitude calculation, the old Canny edge detection algorithm uses the center in a small 2×2 neighborhood window to calculate the finite difference mean value to represent the gradient amplitude.
The input to the algorithm is an undirected graph with vertex set , edge set , and (optionally) numerical weights on the edges in . The goal of the algorithm is to partition into two disjoint subsets and of equal (or nearly equal) size, in a way that minimizes the sum of the weights of the subset of edges that cross from to . If the graph is unweighted, then instead the goal is to minimize the number of crossing edges; this is equivalent to assigning weight one to each edge. The algorithm maintains and improves a partition, in each pass using a greedy algorithm to pair up vertices of with vertices of , so that moving the paired vertices from one side of the partition to the other will improve the partition.
In the case of bipartite graphs or multigraphs with maximum degree , the optimal number of colors is exactly . showed that an optimal edge coloring of these graphs can be found in the near-linear time bound , where is the number of edges in the graph; simpler, but somewhat slower, algorithms are described by and . The algorithm of begins by making the input graph regular, without increasing its degree or significantly increasing its size, by merging pairs of vertices that belong to the same side of the bipartition and then adding a small number of additional vertices and edges. Then, if the degree is odd, Alon finds a single perfect matching in near-linear time, assigns it a color, and removes it from the graph, causing the degree to become even.
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this. Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the ϑ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph., p. 71.
If the front of the shadow volume is capped, the entire shadow volume may be offset slightly away from the light to remove any shadow self-intersections within the offset distance of the silhouette edge (this solution is more commonly used in shadow mapping). The basic steps for forming a shadow volume are: # Find all silhouette edges (edges which separate front-facing faces from back-facing faces) # Extend all silhouette edges in the direction away from the light- source # Add a front-cap and/or back-cap to each surface to form a closed volume (may not be necessary, depending on the implementation used) Illustration of shadow volumes. The image above at left shows a scene shadowed using shadow volumes. At right, the shadow volumes are shown in wireframe.
The vertex cover problem involves finding a set of vertices that touches every edge of the graph. It is NP-hard but can be approximated to within an approximation ratio of two, for instance by taking the endpoints of the matched edges in any maximal matching. Evidence that this is the best possible approximation ratio of a polynomial- time approximation algorithm is provided by the fact that, when represented as a semidefinite program, the problem has an integrality gap of two; this gap is the ratio between the solution value of the integer solution (a valid vertex cover) and of its semidefinite relaxation. According to the unique games conjecture, for many problems such as this the optimal approximation ratio is provided by the integrality gap of their semidefinite relaxation.
All tetrahedra can be inscribed in a parallelepiped. A tetrahedron is orthocentric if and only if its circumscribed parallelepiped is a rhombohedron. Indeed, in any tetrahedron, a pair of opposite edges is perpendicular if and only if the corresponding faces of the circumscribed parallelepiped are rhombi. If four faces of a parallelepiped are rhombi, then all edges have equal lengths and all six faces are rhombi; it follows that if two pairs of opposite edges in a tetrahedron are perpendicular, then so is the third pair, and the tetrahedron is orthocentric. A tetrahedron ABCD is orthocentric if and only if the sum of the squares of opposite edges is the same for the three pairs of opposite edges:Reiman, István, "International Mathematical Olympiad: 1976-1990", Anthem Press, 2005, pp. 175-176.
Brexia is a shrub or small tree, usually 3–7, but occasionally up to 10 m high with many branches, that are smooth with ridges early on but later becoming cylindrical. The leaves are evergreen, with a leaf stem mostly 1–2 cm long, but sometimes very short. The leathery leaf blades are between 3½ and 50 cm long and 2 and 11 cm wide, with large differences in shape, narrowly inverted egg-shaped to linear with teeth or even spines along the edges in young growth, while on mature shoots they may be narrowly to broadly inverted egg-shaped and the edge toothy to entire, with a rounded to indented tip, and wedged along the leaf stem or rounded at the base. The stipules are very narrow.
Equivalently, in this graph, edges exist between all real numbers and all real numbers of the form , where is any rational number. Each path in this graph, starting from any real number , alternates between numbers that differ from by a rational number plus an even multiple of and numbers that differ from by a rational number plus an odd multiple of . This alternation prevents from containing any cycles of odd length, so each of its finite subgraphs requires only two colors. However, in the Solovay model in which every set of real numbers is Lebesgue measurable, requires infinitely many colors, since in this case each color class must be a measurable set and it can be shown that every measurable set of real numbers with no edges in must have measure zero.
Their names given here were given by John Conway, extending Cayley's names for the Kepler-Poinsot polyhedra: along with stellated and great, he adds a grand modifier. Conway offered these operational definitions: #stellation – replaces edges by longer edges in same lines. (Example: a pentagon stellates into a pentagram) #greatening – replaces the faces by large ones in same planes. (Example: an icosahedron greatens into a great icosahedron) #aggrandizement – replaces the cells by large ones in same 3-spaces. (Example: a 600-cell aggrandizes into a grand 600-cell) John Conway names the 10 forms from 3 regular celled 4-polytopes: pT=polytetrahedron {3,3,5} (a tetrahedral 600-cell), pI=polyicoshedron {3,5,} (an icosahedral 120-cell), and pD=polydodecahedron {5,3,3} (a dodecahedral 120-cell), with prefix modifiers: g, a, and s for great, (ag)grand, and stellated.
A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, each edge has an orientation, from one vertex to another vertex. A path in a directed graph is a sequence of edges having the property that the ending vertex of each edge in the sequence is the same as the starting vertex of the next edge in the sequence; a path forms a cycle if the starting vertex of its first edge equals the ending vertex of its last edge. A directed acyclic graph is a directed graph that has no cycles.... Adding the red edges to the blue directed acyclic graph produces another DAG, the transitive closure of the blue graph.
Bindman (1978: 13) Blake's great innovation in relief etching was to print from the relief, or raised, parts of the plate rather than the intaglio, or incised, parts. Whereas intaglio methods worked by creating furrows into which the acid was poured to create 'holes' in the plate and the ink then poured over the entire surface, Blake wrote and drew directly onto the plate with an acid- resistant material known as a stop-out. He would then embed the plate's edges in strips of wax to create a self-contained tray and pour the acid about a quarter of an inch deep, thus causing the exposed parts of the plate to melt away, and the design and/or text to remain slightly above the rest of the plate, i.e. in relief, like a modern rubber stamp.
A simple maze in which the maze walls and the free space between the walls form two interdigitating trees A spanning tree may be defined as a set of edges that, together with all of the vertices of the graph, forms a connected and acyclic subgraph. But, by cut-cycle duality, if a set of edges in a planar graph is acyclic (has no cycles), then the set of edges dual to has no cuts, from which it follows that the complementary set of dual edges (the duals of the edges that are not in ) forms a connected subgraph. Symmetrically, if is connected, then the edges dual to the complement of form an acyclic subgraph. Therefore, when has both properties – it is connected and acyclic – the same is true for the complementary set in the dual graph.
Screen doors are in use at all three LINK Train stations and the Union and Pearson stations along the Union Pearson Express route to Toronto Pearson International Airport in Mississauga, Ontario. Greater Montreal's forthcoming Réseau express métropolitain (REM), the 67-kilometre-long driverless complementary suburban rapid transit network opening in three phases between 2021 and 2023 will feature screen doors at each of its 26 stations. With the advent of the REM on the horizon, advocating retrofits of platform edges in the Montreal Metro with doors to combat delays attributed to overcrowding is becoming increasingly customary. Were its type of door to be screen (full- height), then such installations might quash the fully underground system's notoriety whereby opening or passing through station entrance doors proves mightily troublesome due to the excessive windiness brought about by arriving or departing trains.
In the same way, one may consider an arbitrary sequence of enqueue and dequeue operations of a queue data structure, and form a graph that has these operations as its vertices, placed in order on the spine of a single page, with an edge between each enqueue operation and the corresponding dequeue. Then, in this graph, each two edges will either cross or cover disjoint intervals on the spine. By analogy, researchers have defined a queue embedding of a graph to be an embedding in a topological book such that each vertex lies on the spine, each edge lies in a single page, and each two edges in the same page either cross or cover disjoint intervals on the spine. The minimum number of pages needed for a queue embedding of a graph is called its queue number...
There are also four two-player courses (again with eight holes). The final hole is listed as "Dedede" and features King Dedede in a large machine that continually moves toward Kirby while deploying smaller versions of himself as the final boss. Kirby loses one of his health points (represented as a tomato icon in single-player, and a square with rounded edges in two-player mode) every time he makes a shot or gets hit by an enemy or an obstacle, and gains one every time he hits an enemy or lands in a hole. In the two-player mode, two health points are awarded for landing in the hole first, and two health points can also be lost if one player's Kirby is "attacked" by the other player's by using an ability (such as the tornado or the stone).
However, if a graph can be made Hamiltonian by the addition of vertices and edges it can also be made Hamiltonian by the addition of edges alone, so this extra freedom does not change the definition.For instance in a 2003 technical report "Book embeddings of graphs and a theorem of Whitney", Paul Kainen defines subhamiltonian graphs to be subgraphs of planar Hamiltonian graphs, without restriction on the vertex set of the augmentation, but writes that "in the definition of subhamiltonian graph, one can require that the extension only involve the inclusion of new edges." In a subhamiltonian graph, a subhamiltonian cycle is a cyclic sequence of vertices such that adding an edge between each consecutive pair of vertices in the sequence preserves the planarity of the graph. A graph is subhamiltonian if and only if it has a subhamiltonian cycle.
Army Air Force analysts would later estimate 140 to , based on analysis of human visual acuity and other sighting details (such as estimated distance). Arnold said the objects were grouped together, as Ted BloecherThe UFO Wave of 1947 by Ted Bloecher, 1967; URL accessed March 7, 2007 writes, "in a diagonally stepped- down, echelon formation, stretched out over a distance that he later calculated to be five miles". Though they were moving on a more or less level horizontal plane, Arnold said the objects weaved from side to side ("like the tail of a Chinese kite" as he later stated), darting through the valleys and around the smaller mountain peaks. They would occasionally flip or bank on their edges in unison as they turned or maneuvered causing almost blindingly bright or mirror-like flashes of light.
The BSC was formed in 2000 by Bhob Rainey as a way to explore the dynamics of large group improvisation. The group also includes his nmperign partner Greg Kelley on trumpet, Mike Bullock on double bass, James Coleman on theremin, Chris Cooper on prepared guitar, Vic Rawlings on cello & electronics, Howard Stelzer on tapes, and Liz Tonne on voice. The group has released one CD on Grob entitled Good (2003) and has collaborated a number of times with pianist Steve Drury and his Callithumpian Consort (performing graphic scores by Stockhausen, Cardew and Christian Wolff), as well as with composer Christian Wolff in a realization of his graphic score, Edges. In 2010, the group released 23% Bicycle and/or Ribbons of the Natural Order, a download-only release which was made available by posting a tweet or "liking" it on Facebook.
As the thinness of the bread is a point of pride in the kitchen, a dense-textured white Pullman loaf is cut with a wide-bladed knife, which guides the cut; daylight should pass through the resulting fine pores. The peel of the cucumber is either removed or scored lengthwise with a fork before the cucumber is sliced. The slices of bread are carefully buttered all the way to the edges in the thinnest coating, which is only to prevent the bread from becoming damp with cucumber juice, and the slices of cucumber, which have been dashed with salt and lemon juice, are placed in the sandwich just before serving in order to prevent the sandwich from becoming damp enough to moisten the eater's fingers. The crusts of the bread are cut away cleanly, creating tea sandwiches.
Anterior wings the same, but towards their extremities becoming darker; the tips are angulated, and the edges a little scolloped; a dark line rises near the tips, which running across the wings ends near the middle of the posterior edges, but is there much fainter than at the tips. A small triangular transparent spot is situate near the centre of these wings, about three- eighths of an inch from the anterior edges. Posterior wings a little scolloped, being the same colour with the anterior next the abdomen, but darker towards the external edges. In the middle of these wings is a large eye, the pupil being black like velvet, surrounded with a narrow circle of a dark orange, round which is another cream-coloured circle, and this likewise is surrounded by a large border of a fine red-brown.
Conversely, if we are given a minimum edge dominating set with k edges, we can construct a maximal matching with k edges in polynomial time. Therefore, the problem of finding a minimum maximal matching is essentially equal to the problem of finding a minimum edge dominating set.. Both of these two optimization problems are known to be NP-hard; the decision versions of these problems are classical examples of NP-complete problems.. Edge dominating set (decision version) is discussed under the dominating set problem, which is the problem GT2 in Appendix A1.1. Minimum maximal matching (decision version) is the problem GT10 in Appendix A1.1. Both problems can be approximated within factor 2 in polynomial time: simply find an arbitrary maximal matching M.. Minimum edge dominating set (optimisation version) is the problem GT3 in Appendix B (page 370).
A recessed plate filter press does not use frames and instead has a recess in each plate with sloping edges in which the filter cloths lie, the filter cake builds up in the recess directly between two plates and when the plates are separated the sloping edges allow the cake to fall out with minimal effort. To simplify construction and usage the plates typically have a hole through the centre, passing through the filter cloth and around which it is sealed so that the slurry flows through the centre of each plate down the stack rather than inward from the edge of each plate. Although easier to clean, there are disadvantages to this method, such as longer cloth changing time, inability to accommodate filter media that cannot conform to the curved recess such as paper, and the possibility of forming uneven cake.
Breakdown is a local process, and in an insulating medium subjected to a high voltage difference begins at whatever point in the insulator the electric field first exceeds the local dielectric strength of the material. Since the electric field at the surface of a conductor is highest at protruding parts, sharp points and edges, in a homogeneous insulator like air or oil adjacent to a conductor breakdown usually starts at these points. If the breakdown is caused by a local defect in a solid insulator, such as a bubble in a ceramic insulator, it may remain limited to a small region; this is called partial discharge. In a gas adjacent to a sharp pointed conductor, local breakdown processes, corona discharge or brush discharge, can allow current to leak off the conductor into the gas as ions.
The number of edges in an n-vertex linkless graph is at most 4n − 10: maximal apex graphs with n > 4 have exactly this many edges, and proved a matching upper bound on the more general class of K6-minor-free graphs. observed that Sachs' question about the chromatic number would be resolved by a proof of Hadwiger's conjecture that any k-chromatic graph has as a minor a k-vertex complete graph. The proof by of the case k = 6 of Hadwiger's conjecture is sufficient to settle Sachs' question: the linkless graphs can be colored with at most five colors, as any 6-chromatic graph contains a K6 minor and is not linkless, and there exist linkless graphs such as K5 that require five colors. The snark theorem implies that every cubic linklessly embeddable graph is 3-edge-colorable.
If one is given a collection of unit disks (or their centres) in a space of any fixed dimension, it is possible to construct the corresponding unit disk graph in linear time, by rounding the centres to nearby integer grid points, using a hash table to find all pairs of centres within constant distance of each other, and filtering the resulting list of pairs for the ones whose circles intersect. The ratio of the number of pairs considered by this algorithm to the number of edges in the eventual graph is a constant, giving the linear time bound. However, this constant grows exponentially as a function of the dimension . It is NP-hard (more specifically, complete for the existential theory of the reals) to determine whether a graph, given without geometry, can be represented as a unit disk graph.
According to the Kővári–Sós–Turán theorem, every -vertex -biclique-free graph has edges, significantly fewer than a dense graph would have.. This work concerns the number of edges in biclique-free bipartite graphs, but a standard application of the probabilistic method transfers the same bound to arbitrary graphs. Conversely, if a graph family is defined by forbidden subgraphs or closed under the operation of taking subgraphs, and does not include dense graphs of arbitrarily large size, it must be -biclique-free for some , for otherwise it would include large dense complete bipartite graphs. As a lower bound, conjectured that every maximal -biclique-free bipartite graph (one to which no more edges can be added without creating a -biclique) has at least edges, where and are the numbers of vertices on each side of its bipartition..
If e is in the first subset of edges at v, these two edges are from u0 into v0 and from v1 into u1, while if e is in the second subset, the edges are from u0 into v1 and from v0 into u1. In the other direction, given a skew- symmetric graph G, one may form a polar graph that has one vertex for every corresponding pair of vertices in G and one undirected edge for every corresponding pair of edges in G. The undirected edges at each vertex of the polar graph may be partitioned into two subsets according to which vertex of the polar graph they go out of and come into. A regular path or cycle of a skew-symmetric graph corresponds to a path or cycle in the polar graph that uses at most one edge from each subset of edges at each of its vertices.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges. In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative- weight cycles, the longest path problem is NP-hard and the decision version of the problem, which asks whether a path exists of at least some given length, is NP-complete. This means that the decision problem cannot be solved in polynomial time for arbitrary graphs unless P = NP. Stronger hardness results are also known showing that it is difficult to approximate.
The graph K is needed to attach the pattern being matched to its context: if it is empty, the match can only designate a whole connected component of the graph G. In contrast a graph rewriting rule of the SPO approach is a single morphism in the category of labeled multigraphs and partial mappings that preserve the multigraph structure: r\colon L\rightarrow R. Thus a rewriting step is defined by a single pushout diagram. Practical understanding of this is similar to the DPO approach. The difference is, that there is no interface between the host graph G and the graph G' being the result of the rewriting step. From the practical perspective, the key distinction between DPO and SPO is how they deal with the deletion of nodes with adjacent edges, in particular, how they avoid that such deletions may leave behind "dangling edges".
Pott's early investigations contributed to the science of epidemiology and the Chimney Sweepers Act 1788. Pott describes chimney sweeps' carcinoma thus: > It is a disease which always makes it first attack on the inferior part of > the scrotum where it produces a superficial, painful ragged ill-looking sore > with hard rising edges.....in no great length of time it pervades the skin, > dartos and the membranes of the scrotum, and seizes the testicle, which it > inlarges, hardens and renders truly and thoroughly distempered. Whence it > makes its way up the spermatic process into the abdomen. He comments on the life of the boys: > The fate of these people seems peculiarly hard ... they are treated with > great brutality ... they are thrust up narrow and sometimes hot chimnies, > where they are bruised burned and almost suffocated; and when they get to > puberty they become ... liable to a most noisome, painful and fatal disease.
This graph has circuit rank because it can be made into a tree by removing two edges, for instance the edges 1–2 and 2–3, but removing any one edge leaves a cycle in the graph. In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making it into a tree or forest. It is equal to the number of independent cycles in the graph (the size of a cycle basis). Unlike the corresponding feedback arc set problem for directed graphs, the circuit rank is easily computed using the formula :r = m - n + c, where is the number of edges in the given graph, is the number of vertices, and is the number of connected components. .
It is possible to test whether a graph is bipartite, and to return either a two-coloring (if it is bipartite) or an odd cycle (if it is not) in linear time, using depth-first search. The main idea is to assign to each vertex the color that differs from the color of its parent in the depth-first search forest, assigning colors in a preorder traversal of the depth-first-search forest. This will necessarily provide a two-coloring of the spanning forest consisting of the edges connecting vertices to their parents, but it may not properly color some of the non- forest edges. In a depth-first search forest, one of the two endpoints of every non-forest edge is an ancestor of the other endpoint, and when the depth first search discovers an edge of this type it should check that these two vertices have different colors.
Reduction from closure to maximum flow As showed,. a maximum-weight closure may be obtained from G by solving a maximum flow problem on a graph H constructed from G by adding to it two additional vertices s and t. For each vertex v with positive weight in G, the augmented graph H contains an edge from s to v with capacity equal to the weight of v, and for each vertex v with negative weight in G, the augmented graph H contains an edge from v to t whose capacity is the negation of the weight of v. All of the edges in G are given infinite capacity in H. A minimum cut separating s from t in this graph cannot have any edges of G passing in the forward direction across the cut: a cut with such an edge would have infinite capacity and would not be minimum.
A plurality of college football analysts predicted that Mississippi State (MSU) would emerge victorious, including Pat Forde of Yahoo Sports, all six panelists from CBS Sports (although four of the six predicted that Rice would cover the 7-point spread), and Randy Chambers, a featured columnist for Bleacher Report. Chambers commented, CBS's Tony Moss concurred, noting, "Rice was a consistent winner this year and Mississippi State became bowl-eligible by the skin of its teeth. Still, it's hard to imagine a team that snuck by the likes of UAB and FAU beating someone from the SEC." Statistically, MSU held a slight edge in total offense and rushing yards allowed per game, and a significant edge in passing yards per game, whereas Rice held edges in points scored and points allowed per game, rushing yards per game, total yards allowed per game, and passing yards allowed per game.
G 63 AMG at Legendary 2014 The supercharged 5.4-litre V8 was replaced by the new 5.5-litre biturbo V8 for 2012 for better fuel consumption and lower emission. AMG made some more changes to the exterior as to give G 63 AMG more "brawl" appearance: single horizontal fin with twin chrome edges in the middle of radiator grille with more prominent three-point star ornament in the middle; new light-alloy wheel design; three enlarged airflow inlets on both sides and in middle of front bumper; vertical chrome stripes cover the small bumper guards; exterior rear- view mirrors are same as in GL-Class and ML-Class. The mechanical upgrade was AMG sports exhaust system with high-gloss chrome inserts, larger AMG high performance brakes with six-piston fixed calipers for front brakes from ML 63 AMG, and revised suspension and damper settings for more dynamic handling characteristics. The new E-SELECT gear selector from Mercedes-Benz SLS replaced the standard gear selector.
When measured both in terms of the number n of vertices and the number m of edges in a directed acyclic graph, transitive reductions can also be found in time O(nm), a bound that may be faster than the matrix multiplication methods for sparse graphs. To do so, apply a linear time longest path algorithm in the given directed acyclic graph, for each possible choice of starting vertex. From the computed longest paths, keep only those of length one (single edge); in other words, keep those edges (u,v) for which there exists no other path from u to v. This O(nm) time bound matches the complexity of constructing transitive closures by using depth first search or breadth first search to find the vertices reachable from every choice of starting vertex, so again with these assumptions transitive closures and transitive reductions can be found in the same amount of time.
The components that have no cycles are just trees, while the components that have a single cycle within them are called 1-trees or unicyclic graphs. That is, a 1-tree is a connected graph containing exactly one cycle. A pseudoforest with a single connected component (usually called a pseudotree, although some authors define a pseudotree to be a 1-tree) is either a tree or a 1-tree; in general a pseudoforest may have multiple connected components as long as all of them are trees or 1-trees. If one removes from a 1-tree one of the edges in its cycle, the result is a tree. Reversing this process, if one augments a tree by connecting any two of its vertices by a new edge, the result is a 1-tree; the path in the tree connecting the two endpoints of the added edge, together with the added edge itself, form the 1-tree's unique cycle.
A matroid is a mathematical structure in which certain sets of elements are defined to be independent, in such a way that the independent sets satisfy properties modeled after the properties of linear independence in a vector space. One of the standard examples of a matroid is the graphic matroid in which the independent sets are the sets of edges in forests of a graph; the matroid structure of forests is important in algorithms for computing the minimum spanning tree of the graph. Analogously, we may define matroids from pseudoforests. For any graph G = (V,E), we may define a matroid on the edges of G, in which a set of edges is independent if and only if it forms a pseudoforest; this matroid is known as the bicircular matroid (or bicycle matroid) of G... The smallest dependent sets for this matroid are the minimal connected subgraphs of G that have more than one cycle, and these subgraphs are sometimes called bicycles.
Conversely, every median graph G may be represented in this way as the solution set to a 2-satisfiability instance. To find such a representation, create a 2-satisfiability instance in which each variable describes the orientation of one of the edges in the graph (an assignment of a direction to the edge causing the graph to become directed rather than undirected) and each constraint allows two edges to share a pair of orientations only when there exists a vertex v such that both orientations lie along shortest paths from other vertices to v. Each vertex v of G corresponds to a solution to this 2-satisfiability instance in which all edges are directed towards v. Each solution to the instance must come from some vertex v in this way, where v is the common intersection of the sets Wuw for edges directed from w to u; this common intersection exists due to the Helly property of the sets Wuw.
The manual also includes techniques for fighting against a left-handed opponent. While many modern reference books state that rapiers were either blunt on their edges, or only had sharp edges in order to discourage blade grabs because they were not suitable for the cut, nearly 30% of the techniques included in Capoferro's treatise use the cut as a primary or secondary option. Capoferro's book was reprinted in Siena in 1629 by Ercole Gori, who had the plain backgrounds in twenty-seven of Schiamirossi's original illustrations replaced with intricate depictions of scenes from the Bible and Greek mythology; this version was reprinted in Bologna in 1652 by G. Longo. A third Siena printing was made in 1632 by Bernardino Capitelli, who omitted all of the introductory material and truncated the descriptions of the plays; he also commissioned new illustrations based on those of the first edition but scaled down to half size.
Animated example of a depth-first search For the following graph: alt=An undirected graph with edges AB, BD, BF, FE, AC, CG, AE a depth-first search starting at A, assuming that the left edges in the shown graph are chosen before right edges, and assuming the search remembers previously visited nodes and will not repeat them (since this is a small graph), will visit the nodes in the following order: A, B, D, F, E, C, G. The edges traversed in this search form a Trémaux tree, a structure with important applications in graph theory. Performing the same search without remembering previously visited nodes results in visiting nodes in the order A, B, D, F, E, A, B, D, F, E, etc. forever, caught in the A, B, D, F, E cycle and never reaching C or G. Iterative deepening is one technique to avoid this infinite loop and would reach all nodes.
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point set in the plane, the y-coordinates of the points, ordered by their x-coordinates, forms a sequence of numbers (unless two of the points have equal x-coordinates). With this translation between sequences and point sets, the Erdős–Szekeres theorem can be interpreted as stating that in any set of at least rs − r − s + 2 points we can find a polygonal path of either r − 1 positive-slope edges or s − 1 negative-slope edges. In particular (taking r = s), in any set of at least n points we can find a polygonal path of at least ⌊⌋ edges with same-sign slopes. For instance, taking r = s = 5, any set of at least 17 points has a four-edge path in which all slopes have the same sign.
In a 2002 interview in Blackjack Forum magazine, Blackjack Forum interview with Johnny Chang John Chang, an MIT undergrad who joined the team in late 1980 (and became MIT team co-manager in the mid-1980s and 1990s), reported that, in addition to classic card counting and blackjack team techniques, at various times the group used advanced shuffle and ace tracking techniques. While the MIT team's card counting techniques can give players an overall edge of about 2 percent, some of the MIT team's methods have been established as gaining players an overall edge of about 4 percent. In his interview, Chang reported that the MIT team had difficulty attaining such edges in actual play, and their overall results had been best with straight card counting. The MIT Team's approach was originally developed by Al Francesco, elected by professional gamblers as one of the original seven inductees into the Blackjack Hall of Fame.
In information visualization, Van Wijk is known for his research in texture synthesis, treemaps,.. and flow visualization... His work on map projection. won the 2009 Henry Johns Award of the British Cartographic Society for best cartographic journal article... He has twice been program co-chair for IEEE Visualization, and once for IEEE InfoVis. In 2007, he received an IEEE Technical Achievement Award for his visualization research.. In graph drawing, van Wijk has worked on the visualization of small-world networks. and on the depiction of abstract trees as biological trees.. He has also conducted user studies that showed that the standard depiction of directed edges in graph drawings using arrowheads is less effective at conveying the directionality of the edges to readers than other conventions such as tapering... He was one of two invited speakers at the 19th International Symposium on Graph Drawing in 2011,Graph Drawing 2011 program, retrieved 2011-11-10.
An isolated vertex cannot cover any edges, so in this case v cannot be part of any minimal cover. # If more than k^2 edges remain in the graph, and neither of the previous two rules can be applied, then the graph cannot contain a vertex cover of size k. For, after eliminating all vertices of degree greater than k, each remaining vertex can only cover at most k edges and a set of k vertices could only cover at most k^2 edges. In this case, the instance may be replaced by an instance with two vertices, one edge, and k=0 , which also has no solution. An algorithm that applies these rules repeatedly until no more reductions can be made necessarily terminates with a kernel that has at most k^2 edges and (because each edge has at most two endpoints and there are no isolated vertices) at most 2k^2 vertices.
The game is also considered to be rough around the edges in technical execution, with the lack of anti-aliasing and occasional "pop-in" rendering, as well as drops in frame rates when there was a significant amount of action on the screen. Infamous was released a few weeks before Radical Entertainment's Prototype, a game with many similar concepts including a character finding himself with super powers, a large open-world environment that can be traveled by climbing up buildings and gliding about the city, and several other comparisons. This led many game critics to compare and contrast the games. In his sarcastic Zero Punctuation review of Prototype, Ben "Yahtzee" Croshaw (who had initially praised Infamous as "huge, creative and fun,") compared the two games point for point, and determined that he could not tell which was the better game, and challenged the respective studios to "produce the best image of the rival game's main character wearing a women's bra" as a tiebreaker.
More than two months later, on October 17, the edition's segment anchor Lia Cruz and former Aksyon sa Tanghali segment anchor Marga Vargas are named as new rotating co-anchors to Lingao.Lia Cruz and Marga Vargas named new co-anchors of 'Aksyon Tonite' The primetime edition however, was spared from these changes and continued to be co-anchored by Valdez and Tulfo during the time.First on MNP: TV5 to switch to single-anchor format On December 1, 2016, Aksyon sa Umaga began its simulcast on Radyo5 until 6:00 AM. The move was made after News5 axed Balita Alas Singko on weekdays which ended on November 30. However, the Saturday and Sunday editions of Balita Alas Singko still continues to air because it occupies both on Radyo5 and AksyonTV and considering to be the only news content of News5 on weekends. However, it cannot be seen on TV5 because of its radio booth format with no field reporters and video reports. By December 19, 2016, the newscast's graphic package gained rounded edges (in exception in the flipper) with orange as the standard color.
Although listed as an open problem in the 1979 book Computers and Intractability,, [OPEN4], p. 286; update, p. 339. the computational complexity of the minimum chordal completion problem (also called the minimum fill-in problem) was quickly resolved: showed it to be NP-complete.. If the minimum chordal completion adds edges to a graph , then it is possible to find a chordal completion using at most added edges, in polynomial time.. The problem of finding the optimal set of edges to add can also be solved by a fixed-parameter tractable algorithm, in time polynomial in the graph size and subexponential in .. The treewidth (minimum clique size of a chordal completion) and related parameters including pathwidth and tree-depth are also NP-complete to compute, and (unless P=NP) cannot be approximated in polynomial time to within a constant factor of their optimum values; however, approximation algorithms with logarithmic approximation ratios are known for them.. Both the minimum fill-in and treewidth problems can be solved in exponential time. More precisely, for an -vertex graph, the time is ..
The dual of a simple graph need not be simple: it may have self-loops (an edge with both endpoints at the same vertex) or multiple edges connecting the same two vertices, as was already evident in the example of dipole multigraphs being dual to cycle graphs. As a special case of the cut-cycle duality discussed below, the bridges of a planar graph are in one-to-one correspondence with the self-loops of the dual graph.. For the same reason, a pair of parallel edges in a dual multigraph (that is, a length-2 cycle) corresponds to a 2-edge cutset in the primal graph (a pair of edges whose deletion disconnects the graph). Therefore, a planar graph is simple if and only if its dual has no 1- or 2-edge cutsets; that is, if it is 3-edge-connected. The simple planar graphs whose duals are simple are exactly the 3-edge-connected simple planar graphs.. This class of graphs includes, but is not the same as, the class of 3-vertex- connected simple planar graphs.
A bipartite graph with 4 vertices on each side, 13 edges, and no K3,3 subgraph, and an equivalent set of 13 points in a 4 × 4 grid, showing that z(4; 3) ≥ 13\. The number z(n, 2) asks for the maximum number of edges in a bipartite graph with n vertices on each side that has no 4-cycle (its girth is six or more). Thus, z(2, 2) = 3 (achieved by a three-edge path), and z(3, 2) = 6 (a hexagon). In his original formulation of the problem, Zarankiewicz asked for the values of z(n; 3) for n = 4, 5, and 6. The answers were supplied soon afterwards by Wacław Sierpiński: z(4; 3) = 13, z(5; 3) = 20, and z(6; 3) = 26.. The case of z(4; 3) is relatively simple: a 13-edge bipartite graph with four vertices on each side of the bipartition, and no K3,3 subgraph, may be obtained by adding one of the long diagonals to the graph of a cube.
Some designs were also subject to optical phenomena that could cause noticeably uneven color or other defects in the results. The other, more robust type was an essentially ordinary camera with a special sliding holder for the plates and filters that allowed each in turn to be efficiently shifted into position for exposure—an operation sometimes partly or even entirely automated with a pneumatic mechanism or spring-powered motor. When the three color-filtered photographs were not taken at the same time, anything in the scene that did not hold steady during the entire operation would exhibit colored "fringes" around its edges in the resulting color image. If it moved continuously across the scene, three separate strongly-colored "ghost" images could result. Such color artifacts are plainly visible in ordinary color composites of many of Prokudin-Gorsky's photographs, but special digital image processing software was used to artificially remove them, whenever possible, from the composites of all 1,902 of the images commissioned by the Library of Congress in 2004.
A 2-dimensional matching can be defined in a completely analogous manner. Let X and Y be finite, disjoint sets, and let T be a subset of X × Y. Now M ⊆ T is a 2-dimensional matching if the following holds: for any two distinct pairs (x1, y1) ∈ M and (x2, y2) ∈ M, we have x1 ≠ x2 and y1 ≠ y2. In the case of 2-dimensional matching, the set T can be interpreted as the set of edges in a bipartite graph G = (X, Y, T); each edge in T connects a vertex in X to a vertex in Y. A 2-dimensional matching is then a matching in the graph G, that is, a set of pairwise non-adjacent edges. Hence 3-dimensional matchings can be interpreted as a generalization of matchings to hypergraphs: the sets X, Y, and Z contain the vertices, each element of T is a hyperedge, and the set M consists of pairwise non-adjacent edges (edges that do not have a common vertex).
If the edges are sorted by their weights, then a modified version of Dijkstra's algorithm can compute the bottlenecks between a designated start vertex and every other vertex in the graph, in linear time. The key idea behind the speedup over a conventional version of Dijkstra's algorithm is that the sequence of bottleneck distances to each vertex, in the order that the vertices are considered by this algorithm, is a monotonic subsequence of the sorted sequence of edge weights; therefore, the priority queue of Dijkstra's algorithm can be implemented as a bucket queue: an array indexed by the numbers from 1 to (the number of edges in the graph), where array cell contains the vertices whose bottleneck distance is the weight of the edge with position in the sorted order. This method allows the widest path problem to be solved as quickly as sorting; for instance, if the edge weights are represented as integers, then the time bounds for integer sorting a list of integers would apply also to this problem.
However where high frequency information does occur (such as edges in the image) this is particularly important in terms of human perception of the image quality, and thus must be represented accurately in any high quality coding scheme. By considering the transformed coefficients as a tree (or trees) with the lowest frequency coefficients at the root node and with the children of each tree node being the spatially related coefficients in the next higher frequency subband, there is a high probability that one or more subtrees will consist entirely of coefficients which are zero or nearly zero, such subtrees are called zerotrees. Due to this, we use the terms node and coefficient interchangeably, and when we refer to the children of a coefficient, we mean the child coefficients of the node in the tree where that coefficient is located. We use children to refer to directly connected nodes lower in the tree and descendants to refer to all nodes which are below a particular node in the tree, even if not directly connected.
In contrast, in the model introduced by Erdős and Rényi, the graph is chosen uniformly at random among all -edge graphs; the number of edges is fixed, but the edges are not independent of each other, because the presence of an edge in one position is negatively correlated with the presence of an edge in a different position. Although these two models end up having similar properties, the model is often more convenient to work with due to the independence of its edges. In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model, developed in 1955 by Gilbert and Claude Shannon and independently in unpublished work in 1981 by Jim Reeds, is a probability distribution on permutations of a set of items that, according to experiments by Persi Diaconis, accurately models human-generated riffle shuffles. In this model, a deck of cards is split at a point chosen randomly according to a binomial distribution, and the two parts are merged together with the order of merging chosen uniformly at random among all possible mergers.
The dual polyhedron has a dual graph, a graph with one vertex for each face of the polyhedron and with one edge for every two adjacent faces. The same concept of planar graph duality may be generalized to graphs that are drawn in the plane but that do not come from a three-dimensional polyhedron, or more generally to graph embeddings on surfaces of higher genus: one may draw a dual graph by placing one vertex within each region bounded by a cycle of edges in the embedding, and drawing an edge connecting any two regions that share a boundary edge. An important example of this type comes from computational geometry: the duality for any finite set of points in the plane between the Delaunay triangulation of and the Voronoi diagram of . As with dual polyhedra and dual polytopes, the duality of graphs on surfaces is a dimension-reversing involution: each vertex in the primal embedded graph corresponds to a region of the dual embedding, each edge in the primal is crossed by an edge in the dual, and each region of the primal corresponds to a vertex of the dual.
Whether including K_0 as a valid graph is useful depends on context. On the positive side, K_0 follows naturally from the usual set-theoretic definitions of a graph (it is the ordered pair (V, E) for which the vertex and edge sets, V and E, are both empty), in proofs it serves as a natural base case for mathematical induction, and similarly, in recursively defined data structures K_0 is useful for defining the base case for recursion (by treating the null tree as the child of missing edges in any non-null binary tree, every non-null binary tree has exactly two children). On the negative side, including K_0 as a graph requires that many well-defined formulas for graph properties include exceptions for it (for example, either "counting all strongly connected components of a graph" becomes "counting all non-null strongly connected components of a graph", or the definition of connected graphs has to be modified not to include K0). To avoid the need for such exceptions, it is often assumed in literature that the term graph implies "graph with at least one vertex" unless context suggests otherwise.
The "girth" terminology generalizes the use of girth in graph theory, meaning the length of the shortest cycle in a graph: the girth of a graphic matroid is the same as the girth of its underlying graph.. The girth of other classes of matroids also corresponds to important combinatorial problems. For instance, the girth of a co-graphic matroid (or the cogirth of a graphic matroid) equals the edge connectivity of the underlying graph, the number of edges in a minimum cut of the graph. The girth of a transversal matroid gives the cardinality of a minimum Hall set in a bipartite graph: this is a set of vertices on one side of the bipartition that does not form the set of endpoints of a matching in the graph.. Any set of points in Euclidean space gives rise to a real linear matroid by interpreting the Cartesian coordinates of the points as the vectors of a matroid representation. The girth of the resulting matroid equals one plus the dimension of the space when the underlying set of point is in general position, and is smaller otherwise.
Since the clique problem is NP-complete, this polynomial-time many-one reduction shows that subgraph isomorphism is also NP- complete.. An alternative reduction from the Hamiltonian cycle problem translates a graph G which is to be tested for Hamiltonicity into the pair of graphs G and H, where H is a cycle having the same number of vertices as G. Because the Hamiltonian cycle problem is NP-complete even for planar graphs, this shows that subgraph isomorphism remains NP-complete even in the planar case. Subgraph isomorphism is a generalization of the graph isomorphism problem, which asks whether G is isomorphic to H: the answer to the graph isomorphism problem is true if and only if G and H both have the same numbers of vertices and edges and the subgraph isomorphism problem for G and H is true. However the complexity-theoretic status of graph isomorphism remains an open question. In the context of the Aanderaa–Karp–Rosenberg conjecture on the query complexity of monotone graph properties, showed that any subgraph isomorphism problem has query complexity Ω(n3/2); that is, solving the subgraph isomorphism requires an algorithm to check the presence or absence in the input of Ω(n3/2) different edges in the graph.

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