It was the root cause of a calamity of territorial bisection and national division which the Korean people had never experienced during their long history of 21950,21948 years.
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If the lines — which increase incrementally in width as they advance up or down, right or left — are one color on one side of the bisection, they are a different color on the other side.
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Samurai Shodown is about the parts of fighting games I like (tense exchanges of blows interrupted by immediate bisection) without the parts that I love watching but haven't had the focus to do, like 4th-dimensional chess setplay, labyrinthine pressure strings, and impossible aerial movement.
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Urschel, a 6-foot, 3-inch (1.9 m), 300-pound (136 kg) player who joined the Ravens from Penn State University, is studying applied mathematics at MIT and was the co-author of a research paper titled "Spectral Bisection of Graphs and Connectedness," that was published in 2014, the same year he began his pro career.
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For multiple roots, no method was much faster than bisection. In fact, the only methods that were as fast as bisection were three new methods introduced by Galdino. But even they were only a little faster than bisection.
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In computer networking, if the network is bisected into two partitions, the bisection bandwidth of a network topology is the bandwidth available between the two partitions. Bisection should be done in such a way that the bandwidth between two partitions is minimum. Bisection bandwidth gives the true bandwidth available in the entire system. Bisection bandwidth accounts for the bottleneck bandwidth of the entire network.
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For a linear array with n nodes bisection bandwidth is one link bandwidth. For linear array only one link needs to be broken to bisect the network into two partitions. Bisection of linear array network For ring topology with n nodes two links should be broken to bisect the network, so bisection bandwidth becomes bandwidth of two links. Bisection of a ring network For tree topology with n nodes can be bisected at the root by breaking one link, so bisection bandwidth is one link bandwidth.
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When solving one equation, or just a few, using a computer, the bisection method is an adequate choice. Although bisection isn't as fast as the other methods—when they're at their best and don't have a problem—bisection nevertheless is guaranteed to converge at a useful rate, roughly halving the error with each iteration - gaining roughly a decimal place of accuracy with every 3 iterations. For manual calculation, by calculator, one tends to want to use faster methods, and they usually, but not always, converge faster than bisection. But a computer, even using bisection, will solve an equation, to the desired accuracy, so rapidly that there's no need to try to save time by using a less reliable method—and every method is less reliable than bisection.
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Uvula piercings may migrate leading to bisection of the uvula, which is harmless.
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Therefore bisection bandwidth represents bandwidth characteristics of the network better than any other metric.
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The user can start a bisection session with a specified range of revisions from which the revision control system proposes a revision to test, the user tells the system whether the revision tested as "good" or "bad", and the process repeats until the specific "bad" revision has been identified. Other revision control systems, such as Bazaar or Subversion, support bisection through plugins or external scripts. Phoronix Test Suite can do bisection automatically to find performance regressions.
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Although the bisection method can be completed manually, one of its main advantages is that it can be easily automated. It can thus fit into existing test automation processes: failures in exhaustive automated regression tests can trigger automated bisection to localize faults. Ness and Ngo focused on its potential in Cray's continuous delivery-style environment in which the automatically isolated bad changeset could be automatically excluded from builds. The revision control systems Fossil, Git and Mercurial have built-in functionality for code bisection.
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To help deal with this problem, automated tools allow specific changesets to be ignored during a bisection search.
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For code bisection it is desirable that each revision in the search space can be built and tested independently.
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In numerical analysis, Brent's method is a root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less-reliable methods. The algorithm tries to use the potentially fast- converging secant method or inverse quadratic interpolation if possible, but it falls back to the more robust bisection method if necessary. Brent's method is due to Richard Brent and builds on an earlier algorithm by Theodorus Dekker.
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They allow extending bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation.
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Although the bisection method is robust, it gains one and only one bit of accuracy with each iteration. Other methods, under appropriate conditions, can gain accuracy faster.
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Warneckea cordiformis is a species of plant in the family Melastomataceae. The species is found in Mozambique, and is currently Critically endangered due to the bisection of Namacubi Forest.
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Bisection is in LSPACE having an algorithmic complexity of O(\log N) with N denoting the number of revisions in the search space, and is similar to a binary search.
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Since 48 = 24 × 3, a regular tetracontaoctagon is constructible using a compass and straightedge.Constructible Polygon As a truncated icositetragon, it can be constructed by an edge-bisection of a regular icositetragon.
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Since 96 = 25 × 3, a regular enneacontahexagon is constructible using a compass and straightedge.Constructible Polygon As a truncated tetracontaoctagon, it can be constructed by an edge-bisection of a regular tetracontaoctagon.
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As 24 = 23 × 3, a regular icositetragon is constructible using a compass and straightedge.Constructible Polygon As a truncated dodecagon, it can be constructed by an edge-bisection of a regular dodecagon.
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A few steps of the bisection method applied over the starting range [a1;b1]. The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous functions for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root.
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Zero-order methods consist of methods which make use of zero-order interval arithmetic.Hansen, E.R. Global optimization using interval analysis, Marcel Dekker Inc, New York 1992 A representative example is interval bisection.
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Since 60 = 22 × 3 × 5, a regular hexacontagon is constructible using a compass and straightedge.Constructible Polygon As a truncated triacontagon, it can be constructed by an edge-bisection of a regular triacontagon.
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Since 120 = 23 × 3 × 5, a regular 120-gon is constructible using a compass and straightedge.Constructible Polygon As a truncated hexacontagon, it can be constructed by an edge-bisection of a regular hexacontagon.
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Since 64 = 26 (a power of two), a regular hexacontatetragon is constructible using a compass and straightedge.Constructible Polygon As a truncated triacontadigon, it can be constructed by an edge-bisection of a regular triacontadigon.
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Since the bracketing interval's length is halved at each step, the bisection method's error is, on average, halved with each iteration. The method gains roughly a decimal place of accuracy, for each 3 iterations.
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An exception would be if the computer program had to solve equations very many times during its run. Then the time saved by the faster methods could be significant. Then, a program could start with Newton's method, and, if Newton's isn't converging, switch to regula falsi, maybe in one of its improved versions, such as the Illinois or Anderson–Björck versions. Or, if even that isn't converging as well as bisection would, switch to bisection, which always converges at a useful, if not spectacular, rate.
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Unlike other genital modifications, the glans tissue does not have a tendency to re-adhere to itself or heal closed. A meatotomy may be extended to subincision or genital bisection, which are both much more complex and serious modifications.
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Bisection is a method used in software development to identify change sets that result in a specific behavior change. It is mostly employed for finding the patch that introduced a bug. Another application area is finding the patch that indirectly fixed a bug.
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It was mined in March 1978. The diamond was purchased by Mouw Diamond Cutting in Johannesburg in partnership with William Goldberg of New York City. The diamond was marked for bisection by Rose Mouw, the spouse of Jacob Mouw, the founder of Mouw Diamond Cutting.
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Each of the patients of VR went through 3 weeks of 5-day-a-week 30-minute intervals emerged in these programs. The controls went through the equivalent time in traditional rehabilitation therapies. Each patient took the star cancellation test, line bisection test, and Catherine Bergego Scale (CBS) 24 hours before and after the three-week treatment to assess the severity of unilateral spatial neglect. The VR group showed a higher increase in the star cancellation test and CBS scores after treatment than the control group (p<0.05), but both groups did not show any difference in the line bisection test and K-MBI before and after treatment.
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In 1940 he published a new method for excavating root systems called the bisect-wash method. That is described as follows: “A smooth face of soil is cut through the plant axis vertically to sufficient breadth and depth to insure inclusion of the farthest ramifications of the root system in the plane of the bisection. Horizontal and perpendicular lines are marked off on this face with cord, the interval suited to the size of the root system. Then by means of a fine jet of water the soil is removed from the whole of the face of the bisection to a depth of one or two inches.
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NUMAlink 8 is the eighth generation of the interconnect, introduced in 2017 and used in the HPE Superdome Flex. NUMAlink 8 is capable of 853.33 GB/s of bisection peak bandwidth(64 links are cut) for up to 32 socket system and 48TB of coherent shared memory.
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The first post office opened in Stanley in 1887. On 1 January 1891 a need for 1/2d stamps resulted in the authorization of bisection and surcharge of existing 1d stamps. 1/2d stamps arrived in September, but the bisects were allowed until 11 January 1892.
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Bartlett's bisection theorem is an electrical theorem in network analysis attributed to Albert Charles Bartlett. The theorem shows that any symmetrical two-port network can be transformed into a lattice network.Bartlett, AC, "An extension of a property of artificial lines", Phil. Mag., vol 4, p902, November 1927.
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There are 5 receptive subtests (3 auditory comprehension, 2 visual comprehension) and 16 expressive subtest (5 repetition, 3 naming, 4 reading, 4 writing) Neuropsychological deficits that could be associated with aphasia are tested in 6 subtests (line bisection, semantic memory, word fluency, recognition memory, gesture object use, arithmetic).
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Line DE bisects line AB at D, line EF is a perpendicular bisector of segment AD at C, and line EF is the interior bisector of right angle AED In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the segment bisector (a line that passes through the midpoint of a given segment) and the angle bisector (a line that passes through the apex of an angle, that divides it into two equal angles). In three-dimensional space, bisection is usually done by a plane, also called the bisector or bisecting plane.
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A visualization of the 1-factor algorithm. Again, we consider a single-ported machine. A trivial algorithm, is to send (p-1) asynchronous messages into the network for each processor. The performance of this algorithm is poor, which is due to congestion arising because of the bisection width of the network.
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Parabola and tangent The above proofs of the reflective and tangent bisection properties use a line of calculus. Here a geometric proof is presented. In this diagram, F is the focus of the parabola, and T and U lie on its directrix. P is an arbitrary point on the parabola.
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The network consists of a total of 3n^3/2 processors are built around n^2 factor networks called TSE networks. Each factor network consists of n leaf nodes. The diameter and bisection width of the OMTSE network is shown to be 6 log n − 1 and (n^3)/4.
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Simple and intermediate systems are characterized by lists or trees of dependencies among their components or subsystems. More complex systems contain cyclical dependencies or interactions (feedback loops). Such systems are less amenable to "bisection" troubleshooting techniques. It also helps to start from a known good state, the best example being a computer reboot.
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Newton's method assumes the function f to have a continuous derivative. Newton's method may not converge if started too far away from a root. However, when it does converge, it is faster than the bisection method, and is usually quadratic. Newton's method is also important because it readily generalizes to higher-dimensional problems.
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For the bisection algorithm to identify a single changeset which caused the behavior being tested to change, the behavior must change monotonically across the search space. For a Boolean function such as a pass/fail test, this means that it only changes once across all changesets between the start and end of the search space. If there are multiple changesets across the search space where the behavior being tested changes between false and true, then the bisection algorithm will find one of them, but it will not necessarily be the root cause of the change in behavior between the start and the end of the search space. The root cause could be a different changeset, or a combination of two or more changesets across the search space.
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Theoretical support for the importance of this measure of network performance was developed in the PhD research of Clark Thomborson (formerly Clark Thompson). Thomborson proved that important algorithms for sorting, Fast Fourier transformation, and matrix-matrix multiplication become communication-limited—as opposed to CPU-limited or memory-limited—on computers with insufficient bisection width. F. Thomson Leighton's PhD research tightened Thomborson's loose bound on the bisection width of a computationally-important variant of the De Bruijn graph known as the shuffle-exchange graph. Based on Bill Dally's analysis of latency, average case throughput, and hot-spot throughput of m-ary n-cube networks for various m, It can be observed that low-dimensional networks, in comparison to high- dimensional networks (e.g.
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Though regula falsi always converges, usually considerably faster than bisection, there are situations that can slow its convergence – sometimes to a prohibitive degree. That problem isn't unique to regula falsi: Other than bisection, all of the numerical equation-solving methods can have a slow-convergence or no-convergence problem under some conditions. Sometimes, Newton's method and the secant method diverge instead of converging – and often do so under the same conditions that slow regula falsi's convergence. But, though regula falsi is one of the best methods, and even in its original un-improved version would often be the best choice; for example, when Newton's isn't used because the derivative is prohibitively time-consuming to evaluate, or when Newton's and Successive-Substitutions have failed to converge.
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Brent's method is a combination of the bisection method, the secant method and inverse quadratic interpolation. At every iteration, Brent's method decides which method out of these three is likely to do best, and proceeds by doing a step according to that method. This gives a robust and fast method, which therefore enjoys considerable popularity.
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Many annelids (segmented worms) are capable of regeneration. For example, Chaetopterus variopedatus and Branchiomma nigromaculata can regenerate both anterior and posterior body parts after latitudinal bisection. The relationship between somatic and germline stem cell regeneration has been studied at the molecular level in the annelid Capitella teleta. Leeches, however, appear incapable of segmental regeneration.
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Ness and Ngo outlined linear search and binary search methods of performing this isolation. Code bisection has the goal of minimizing the effort to find a specific change set. It employs a divide and conquer algorithm that depends on having access to the code history which is usually preserved by revision control in a code repository.
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With the escaping air and pressure, it included bisection of his thoracoabdominal cavity, which resulted in expulsion of all of the internal organs of his chest and abdomen, except the trachea and a section of small intestine, and of the thoracic spine. These were projected some distance, one section being found vertically above the exterior pressure door.
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In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm for complex polynomials, extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane. It uses the Schur-Cohn test to test increasingly smaller disks for the presence or absence of roots.
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The result is a bisection of the root system which may be drawn in detail. A second face perpendicular to the first gives a half bisection which may be used as a check against the first to insure a representative sample of the entire root system.” In 1939 he published a paper showing that warts or tumors on the bark of Celtis are probably initiated by mechanical injury. He wrote letters published in the American association for the advancement of science on common uses of plants for Christmas decoration, commenting on them as a fire hazard and the potential to have chemicals such as ammonium sulfate or calcium chloride absorbed through the cut and of the tree which can make the tree less flammable along with the method to do so.
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Another objective function used for graph partitioning is Conductance which is the ratio between the number of cut edges and the volume of the smallest part. Conductance is related to electrical flows and random walks. The Cheeger bound guarantees that spectral bisection provides partitions with nearly optimal conductance. The quality of this approximation depends on the second smallest eigenvalue of the Laplacian λ2.
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Golden triangles inscribed in a logarithmic spiral The golden triangle is used to form some points of a logarithmic spiral. By bisecting one of the base angles, a new point is created that in turn, makes another golden triangle. The bisection process can be continued infinitely, creating an infinite number of golden triangles. A logarithmic spiral can be drawn through the vertices.
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One side portal and the Brautportal, the main entrance to the Marienkirche. Buttresses (along with flying buttresses) and balustrades characterise the image of the chancel. The exterior of the chancel underlies a bisection emerging from the ambulatory and the clerestory. The buttress of the Marienkirche in Osnabrück is given a very vivid design by the pinnacles as well as the neo-Gothic balustrades.
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Punchbowl has a relatively small shopping centre, although the selection is diverse. It thrived until the advent of Roselands and Bankstown Square in the late 1960s and its bisection by the upgrading of Punchbowl Road in the 1970s. It is centred on Punchbowl railway station, along The Boulevarde and Punchbowl Road. Local businesses and clubs reflect the diversity of the population.
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Bananal Island (, ) is a large river island formed from the bisection of the Araguaia River, in southwestern Tocantins, Brazil. The island is formed by a fork in a very flat section of the Araguaia River. Bananal Island is the second largest fluvial island in the world and the largest without an ocean coastline, at long and wide.Island Superlatives Its total area is .
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The oldest complete algorithm for real-root isolation results from Sturm's theorem. However, it appears to be much less efficient than the methods based on Descartes' rule of signs and Vincent's theorem. These methods divide into two main classes, one using continued fractions and the other using bisection. Both method have been dramatically improved since the beginning of 21st century.
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With these improvements they reach a computational complexity that is similar to that of the best algorithms for computing all the roots (even when all roots are real). These algorithms have been implemented and are available in Mathematica (continued fraction method) and Maple (bisection method). Both implementations can routinely find the real roots of polynomials of degree higher than 1,000.
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The simplest root-finding algorithm is the bisection method. Let be a continuous function, for which one knows an interval such that and have opposite signs (a bracket). Let be the middle of the interval (the midpoint or the point that bisects the interval). Then either and , or and have opposite signs, and one has divided by two the size of the interval.
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Virtual reality therapy has two promising potential benefits for treatment of hemispatial neglect patients. These include improvement of diagnostic techniques and as a supplement to rehabilitation techniques. Current diagnostic techniques usually involve pen and paper tests like the line bisection test. Though these tests have provided relatively accurate diagnostic results, advances in virtual reality therapy (VRT) have proven these tests to not be completely thorough.
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This conversion procedure starts by using the property of a lattice where a common series element in all arms can be taken outside the lattice as two series elements (as shown above). By repeatedly applying this property, components can be extracted from within the lattice structure. Finally, by means of Bartlett's bisection theorem,Bartlett A.C., "An Extension of a Property of Artificial Lines", Phil. Mag.
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Ascot has a station on a bisection of the railway line from London Waterloo to Reading, Bagshot, Aldershot and Guildford, originally built by the London & South Western Railway and now operated by South Western Railway. As a consequence of the frequent service on this line, Ascot is now a commuter centre with its residents in both directions (westwards to Reading and eastwards to London).
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This was an early and convenient method to use if you had access to an astrolabe as many astrologers and mathematicians of the time would have had. The method involved copying the projections of the celestial sphere onto a plane surface. A vertical line was drawn with a line at the angle of the latitude drawn on the bisection of the vertical with the celestial sphere.
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For real roots, see next sections. The Lehmer–Schur algorithm uses the Schur–Cohn test for circles; a variant, Wilf's global bisection algorithm uses a winding number computation for rectangular regions in the complex plane. The splitting circle method uses FFT-based polynomial transformations to find large-degree factors corresponding to clusters of roots. The precision of the factorization is maximized using a Newton-type iteration.
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The first two iterations of the false position method. The red curve shows the function and the blue lines are the secants. The convergence rate of the bisection method could possibly be improved by using a different solution estimate. The regula falsi method calculates the new solution estimate as the -intercept of the line segment joining the endpoints of the function on the current bracketing interval.
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The temporal lobe controls auditory and visual memories, language, and some hearing and speech. Cortical folds and white matter in horizontal bisection of head The cerebrum contains the ventricles where the cerebrospinal fluid is produced and circulated. Below the corpus callosum is the septum pellucidum, a membrane that separates the lateral ventricles. Beneath the lateral ventricles is the thalamus and to the front and below this is the hypothalamus.
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Some special cases of Slerp admit more efficient calculation. When a circular arc is to be drawn into a raster image, the preferred method is some variation of Bresenham's circle algorithm. Evaluation at the special parameter values 0 and 1 trivially yields p0 and p1, respectively; and bisection, evaluation at ½, simplifies to , normalized. Another special case, common in animation, is evaluation with fixed ends and equal parametric steps.
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These methods employ hill-climbing algorithms to progressively approach the best tree. However, it has been shown that there can be "tree islands" of suboptimal solutions, and the analysis can become trapped in these local optima. Thus, complex, flexible heuristics are required to ensure that tree space has been adequately explored. Several heuristics are available, including nearest neighbor interchange (NNI), tree bisection reconnection (TBR), and the parsimony ratchet.
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Q is a computer software package for molecular dynamics (MD) simulation (current release: Q6). Unlike other MD codes, it has specialized since its conception (Marelius et al. 1998) on three specific types of free energy calculations. These calculations are based on the methods: empirical valence bond (EVB), free energy perturbation (FEP), and linear interaction energy (LIE), as well as, more recently, also path integral calculations using the bisection quantum classical path (BQCP) approach.
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Significant reductions in unilateral neglect symptoms were seen in 2002 by Frassinetti et al. Improvements in visual-motor, visual-verbal, behavioral, and spatial cognitive tasks were observed to last up to 5 weeks after a twice-daily, two-week prism adaptation program. The standard tests included visual motor tasks such as line cancellation, line bisection and drawing by copying or memory. The visual- verbal tasks included object description, object naming and word reading.
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The Churn and the Thames feed the waters of a western bisection of the Cotswold Water Park, converted since the 1970s from redundant gravel beds between Cirencester and Cricklade. In 2006, the national government was engaged in a planning study to analyse methods of mitigating future flooding associated with the Churn. However, the river is known to stop flowing completely at times; in September 2011 the river bed was completely dry at Latton.
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A single by-pass for switching was located between the two. The track and two cars completed basic testing in 1976, and were turned over for passenger use between the two buildings. Although the ACT system was later removed, the Fairlane mall's layout retains several vestigial signs of its former presence, notably the bisection of its central interior court.Milford During the project's lifetime there were numerous expressions of interest in the ACT system.
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The above formula is also used in the secant method, but the secant method always retains the last two computed points, and so, while it is slightly faster, it does not preserve bracketing and may not converge. The fact that regula falsi always converges, and has versions that do well at avoiding slowdowns, makes it a good choice when speed is needed. However, its rate of convergence can drop below that of the bisection method.
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While the above removes the unknown \lambda from the formula, it introduces an additional point of complexity: we can no longer compute the blocking probability directly, and must use an iterative method instead. While a fixed-point iteration is tempting, it has been shown that such an iteration is sometimes divergent when applied to f. Alternatively, it is possible to use one of bisection or Newton's method, for which an open source implementation is available.
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He published a treatment of geometrically symmetrical 2-port networks in 1927 and is responsible for Bartlett's bisection theorem which shows that any symmetrical network can be transformed into a symmetrical lattice network.Belevitch, V, "Summary of the History of Circuit Theory", Proceedings of the IRE, vol 50, p850, May, 1962. He also patented the idea of using the method of an active amplifier with "negative resistance" to cancel the inductance of a telephone line.
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Decades later, Giovanni Domenico Cassini, redid the meridian in the same basilica. His work resolved the apparent conflicts between Ptolemy’s solar theory and Kepler’s “bisection of eccentricity” using the diameter of the sun’s image as an inverse substitute for the sun’s distance from the earth. His precise work ended up proving the validity of Copernican theory condemned by the church. After Galileo, scientists consciously identified ways to stay in alignment with the church as much as possible.
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Many types of genital modification are performed at the behest of the individual, for personal, sexual, aesthetic or cultural reasons. Penile subincision, or splitting of the underside of the penis, is widespread in the traditional cultures of Indigenous Australians. This procedure has taken root in Western body modification culture, the modern primitives. Meatotomy is a form that involves splitting of the glans penis alone, while bisection is a more extreme form that splits the penis entirely in half.
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Typically, the method is used in combination with some other method which finds approximate eigenvalues: the standard example is the bisection eigenvalue algorithm, another example is the Rayleigh quotient iteration, which is actually the same inverse iteration with the choice of the approximate eigenvalue as the Rayleigh quotient corresponding to the vector obtained on the previous step of the iteration. There are some situations where the method can be used by itself, however they are quite marginal.
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The Black Hills of Yavapai County (in Yavapai: Waulkayauayau - "pine tableland") are a large mountain range of central Arizona in southeast Yavapai County. It is bordered by the Verde Valley to the east. The northwest section of the range is bisected from the southeast section by Interstate 17, which is the main route connecting Phoenix to Sedona, Oak Creek Canyon, and Flagstaff. This bisection point is the approximate center of the mostly northwest by southeast trending range.
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In some cases the conditions on the function that are necessary for convergence are satisfied, but the point chosen as the initial point is not in the interval where the method converges. This can happen, for example, if the function whose root is sought approaches zero asymptotically as goes to or . In such cases a different method, such as bisection, should be used to obtain a better estimate for the zero to use as an initial point.
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County residents failed to ratify the bill, and in 1853 the legislature instead bisected the county into eastern and western sections, creating Ozaukee County. Port Washington became the seat of the new county, and the Washington County seat moved to West Bend. The bisection was controversial. When Washington County officials from West Bend arrived in Port Washington to correct relevant county records, they were run out of town, and Ozaukee County officials refused to hand over the records for several months.
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The third model that describes bimodality in the occupancy frequency distribution is based on the scaling pattern of occupancy under a self-similar assumption of species distributions (called the occupancy probability transition [OPT] model). The OPT model is based on Harte et al.'s bisection scheme (although not on their probability rule) and the recursion probability of occupancy at different scales. The OPT model has been shown to support two empirical observations: #That bimodality is prevalent in interspecific occupancy frequency distributions.
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For example, the half of bdgh is acfg. One sees immediately that it is only feasible when the numeral to be halved does not contain an a (or, if the numeral is extended, an odd number of as). In other words, an abbreviated numeral is odd if it contains an a and even if it does not. With these basic operations (doubling and halving), we can adapt all the binary algorithms starting by, but not limited to, the Bisection method and Dichotomic search.
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The physical arrangement of their components and values are symmetric or antimetric as in the ladder example above. However, it is not a necessary condition for electrical antimetry. For example, if the example networks of figure 1 have an additional identical T-section added to the left-hand side as shown in figure 2, then the networks remain topologically symmetric and antimetric. However, the network resulting from the application of Bartlett's bisection theoremBartlett, AC, "An extension of a property of artificial lines", Phil. Mag.
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The results thus demonstrate that the use of the bisection method in combination with a power- scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales. This model further provokes the Harte-Maddux debate: Harte et al. demonstrated that the power law form of the species–area relationship may be derived from a bisected, self-similar landscape and a community-level probability rule. However, Maddux showed that this self-similarity model generates biologically unrealistic predictions.
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A common error is the failure to include numbers on the left side of a picture when drawing an analogue clock from memory, for example, all of the numbers may be positioned on the right side of the clock face. Another paper-and- pencil task is the line bisection task. In this exercise, patients are required to divide a horizontal line halfway along. Patients with neglect will often bisect the line to the right of the true centre, leaving the left portion of the line unattended to.
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Various ways for improving Akritas–Collins bisection algorithm have been proposed. They include a method for avoiding storing a long list of polynomials without losing the simplicity of the changes of variables, the use of approximate arithmetic (floating point and interval arithmetic) when it allows getting the right value for the number of sign variations, the use of Newton's method when possible, the use of fast polynomial arithmetic, shortcuts for long chains of bisections in case of clusters of close roots, bisections in unequal parts for limiting instability problems in polynomial evaluation. All these improvement lead to an algorithm for isolating all real roots of a polynomial with integer coefficients, which has the complexity (using soft O notation, , for omitting logarithmic factors) :\tilde O (n^2(k+t)), where is the degree of the polynomial, is the number of nonzero terms, is the maximum of digits of the coefficients. The implementation of this algorithm appears to be more efficient than any other implemented method for computing the real roots of a polynomial, even in the case of polynomials having very close roots (the case which was previously the most difficult for the bisection method).
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For orbits with e > 0.8, an initial value of E0 = π should be used. If e is identically 1, then the derivative of f, which is in the denominator of Newton's method, can get close to zero, making derivative-based methods such as Newton-Raphson, secant, or regula falsi numerically unstable. In that case, the bisection method will provide guaranteed convergence, particularly since the solution can be bounded in a small initial interval. On modern computers, it is possible to achieve 4 or 5 digits of accuracy in 17 to 18 iterations.
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The golden triangle can be characterized as an isosceles triangle ABC with the property that bisecting the angle C produces a new triangle CXB which is a similar triangle to the original. If angle BCX = α, then XCA = α because of the bisection, and CAB = α because of the similar triangles; ABC = 2α from the original isosceles symmetry, and BXC = 2α by similarity. The angles in a triangle add up to 180°, so 5α = 180, giving α = 36°. So the angles of the golden triangle are thus 36°-72°-72°.
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The bisection was controversial. When Washington County officials from West Bend arrived in Port Washington to correct relevant county records, they were run out of town, and Ozaukee County officials refused to hand over the records for several months. The town population reached 2,500 in 1853 and continued to increase, with an influx of immigrants from Germany and Luxembourg between 1853 and 1865. In the 1860s, William Knell developed the Knellsville community in the northern part of the town as a stagecoach stop on the Green Bay Road.
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Reputedly, four locals even tricked the international commission sent to mark the border by moving the temporary border stones overnight in order to include more of the village in Bulgaria. As a consequence of this bisection, the village's population has declined significantly on either side of the border. For example, the Serbian part had a population of 485 in 1948; by 2002, it had decreased to 53, of whom 47 Serbs (88.67%), 4 Yugoslavs (7.54%) and 2 Bulgarians (3.77%). The Bulgarian part of Strezimirovci is only inhabited by 25 people as of June 2008.
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In order to assess not only the type but also the severity of neglect, doctors employ a variety of tests, most of which are carried out at the patient's bedside. Perhaps one of the most-used and quickest is the line bisection. In this test, a line a few inches long is drawn on a piece of paper and the patient is then asked to dissect the line at the midpoint. Patients exhibiting, for example, left-sided neglect will exhibit a rightward deviation of the line's true midpoint.
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The aforementioned bisection renders "05" and "00" on the left and right side of the score, respectively. Amarin's version were also pentagonal shaped, but impressed with an "A" on one side with "74" on the opposing. Motofen is higher priced than both Imodium and Lomotil, does not have a generic equivalent, and is only available by prescription in the United States. Many United States insurance companies do not include Motofen as one of their formulary drugs, causing consumers to pay the highest copay, if it is covered by their health insurance at all.
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The British decimal fifty pence (50p) coin – often informally pronounced fifty pee – is a unit of currency equalling one half of a pound sterling. It is a seven-sided coin formed as an equilateral-curve heptagon, or Reuleaux polygon, a curve of constant width, meaning that the diameter is constant across any bisection. Its obverse has featured the profile of Queen Elizabeth II since the coin's introduction in 1969. Four different portraits of the Queen have been used, with the latest design by Jody Clark being introduced in 2015.
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The secant method does not require that the root remain bracketed, like the bisection method does, and hence it does not always converge. The false position method (or ) uses the same formula as the secant method. However, it does not apply the formula on x_{n-1} and x_{n-2}, like the secant method, but on x_{n-1} and on the last iterate x_k such that f(x_k) and f(x_{n-1}) have a different sign. This means that the false position method always converges.
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Also bisection by a Western Power line across the hill, which corresponds with the old border of the Greenmount National Park, has created an eyesore, as well as a serious point of erosion. It has also been the site of aircraft warning lights, since removed, and currently has a police communication tower on the western edge. It also has a mobile telephone tower with Optus and Telstra equipment near Padbury Road. Road access through the Greenmount National Park has been closed due to vandalism, except where permission and keys have been obtained from the Department of Environment and Conservation regional office in Mundaring.
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The school of the parish of St Mary Magdalen, Holmwood, was built in 1844 and enlarged in 1870 and 1884. The village prospered from the increased traffic and from the presence of large country houses such as Anstie Grange and Holmwood Park. The former led to the founding of such places as the cottages and travellers' inn in Mid Holmwood, and relatively well-to-do villas such as The Dutch House in South Holmwood.The Dutch House The village saw a bisection from its cricket ground on Holmwood Common, with the extension of the turnpike road, now the A24, in 1971.
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The evaluation of quantile functions often involves numerical methods, as the example of the exponential distribution above is one of the few distributions where a closed-form expression can be found (others include the uniform, the Weibull, the Tukey lambda (which includes the logistic) and the log-logistic). When the cdf itself has a closed-form expression, one can always use a numerical root-finding algorithm such as the bisection method to invert the cdf. Other algorithms to evaluate quantile functions are given in the Numerical Recipes series of books. Algorithms for common distributions are built into many statistical software packages.
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In principle, exact recovery can be solved in its feasible range using maximum likelihood, but this amounts to solving a constrained or regularized cut problem such as minimum bisection that is typically NP-complete. Hence, no known efficient algorithms will correctly compute the maximum-likelihood estimate in the worst case. However, a wide variety of algorithms perform well in the average case, and many high- probability performance guarantees have been proven for algorithms in both the partial and exact recovery settings. Successful algorithms include spectral clustering of the vertices, semidefinite programming,, forms of belief propagation,, and community detection among others.
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The core layers contain (k/2)2 core switches where each of the core switches is connected to one aggregate layer switch in each of the pods. The fat tree topology can offer up to 1:1 oversubscription ratio and full bisection bandwidth , depending on the each rack's total bandwidth versus the bandwidth available at the tree's highest levels. Higher tree branches are typically oversubscribed to their lower branches by a ratio of 1:5, with the problem compounding at the highest tree levels, including up to 1:80 or 1:240, at the highest levels Greenberg, Albert, et al.
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Then compute the series yi and xi as above. If yi > f(0) for any i < n, then the initial estimate x1 was too low, leading to too large an area A. If yn < f(0), then the initial estimate x1 was too high. Given this, use a root-finding algorithm (such as the bisection method) to find the value x1 which produces yn−1 as close to f(0) as possible. Alternatively, look for the value which makes the area of the topmost layer, xn−1(f(0) − yn−1), as close to the desired value A as possible.
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As at February 2016 several citywide cycle routes pass through the suburb. This includes Wynnum Road, which has a shared pedestrian/bicycle path due to narrow traffic lanes, Canara Street-Crown Street-Macrossan Avenue, which is line-marked as a Bicycle Awareness Zone (yellow stencil stylized bicycle marked on edge of vehicle travel lane), and Bennetts Road, which has formal bicycle lanes south of Agnew Street. Packs of cyclists are commonplace along these routes early on weekend mornings. The hilly terrain in the suburb's north and east sides, busy traffic conditions and bisection by the Cleveland railway line also impose some impediment to local walking opportunities.
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Bisection of arbitrary angles has long been solved. Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice the area of a given polygon. Three problems proved elusive, specifically, trisecting the angle, doubling the cube, and squaring the circle. The problem of angle trisection reads: Construct an angle equal to one-third of a given arbitrary angle (or divide it into three equal angles), using only two tools: # an unmarked straightedge, and # a compass.
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Bottenhorn Plateaux in the Gladenbach Uplands, i.M. 480 m to 500 m above NN Geological map of Middle Hesse The western Middle Hesse belongs to the Rhenish Massif and is therefore its oldest part (formed during the Palaeozoic around 300 to 500 million years ago). This, initially single, mountain chain was uplifted again during the Alpine folding and finally took on the morphology visible today: the vulcanites of the Westerwald and its bisection by the rivers Lahn and Dill with raised fault blocks (Dill Basin) like the Limburg Basin that were broken again during the Tertiary. Depositions of loess and the availability of water resulted in its early settlement.
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This system gradually dies out and leaves the surface smooth, only the row of infrasutural tubercles survives in an enlarged but depressed form. And springing from these some sinuous oblique and slightly irregular longitudinal puckerings appear on the body whorl, which is nearly bisected by the sharpish, slightly expressed, finely tubercled carina. This bisection of the body whorl arises from the great prolongation and tumidity of the base On this base, below the carina, are five narrow, equally parted, spiral threads, and two intra-umbilical ones, which are more contiguous. Besides this larger system of sculpture, the whole surface is covered with minute, oblique, irregular, and interrupted puckerings of the epidermis.
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As 10 = 2 × 5, a power of two times a Fermat prime, it follows that a regular decagon is constructible using compass and straightedge, or by an edge- bisection of a regular pentagon.. An alternative (but similar) method is as follows: #Construct a pentagon in a circle by one of the methods shown in constructing a pentagon. #Extend a line from each vertex of the pentagon through the center of the circle to the opposite side of that same circle. Where each line cuts the circle is a vertex of the decagon. #The five corners of the pentagon constitute alternate corners of the decagon.
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Problems of sufficient simplicity are solved directly. For example, to sort a given list of n natural numbers, split it into two lists of about n/2 numbers each, sort each of them in turn, and interleave both results appropriately to obtain the sorted version of the given list (see the picture). This approach is known as the merge sort algorithm. The name "divide and conquer" is sometimes applied to algorithms that reduce each problem to only one sub-problem, such as the binary search algorithm for finding a record in a sorted list (or its analog in numerical computing, the bisection algorithm for root finding).
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Bisection of an angle using a compass and straightedge An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The exterior or external bisector is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles.
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It then replaces by the subset that it has determined to contain the bottleneck weight, and starts the next iteration with this new set . The number of subsets into which can be split increases exponentially with each step, so the number of iterations is proportional to the iterated logarithm function, , and the total time is . In a model of computation where each edge weight is a machine integer, the use of repeated bisection in this algorithm can be replaced by a list-splitting technique of , allowing to be split into smaller sets in a single step and leading to a linear overall time bound..
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Dvorkin et al. used a camera system that immersed the patient into a virtual reality world and required the patient to grasp or move object in the world, through tracking of arm and hand movements. These techniques revealed that pen and paper tests provide relatively accurate qualitative diagnoses of hemispatial neglect patients, but VRT provided accurate mapping into a 3-dimensional space, revealing areas of space that were thought to be neglected but which patients had at least some awareness. Patients were also retested 10 months from initial measurements, during which each went through regular rehabilitation therapy, and most showed measurably less neglect on virtual reality testing whereas no measurable improvements were shown in the line bisection test.
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Luke recognizes the disruption that Maul's existence is causing in the Force, and shuts down the life-support systems keeping the brain alive. In 2005, Dark Horse Comics published Star Wars: Visionaries, a compilation of non-canonical short comics made by the creators of Revenge of the Sith. One story, "Old Wounds", depicts Maul with longer horns on his head, having survived his bisection at Obi-Wan's hands, with his missing bottom half replaced with cybernetic legs, similar to those of General Grievous (and his eventual revival in The Clone Wars). He follows Obi-Wan throughout the galaxy, finally tracking him down on Tatooine a few years after the events of Revenge of the Sith.
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All points on the bisector are equidistant from F and T, but Q is closer to F than to T. This means that Q is to the left of , that is, on the same side of it as the focus. The same would be true if Q were located anywhere else on the parabola (except at the point P), so the entire parabola, except the point P, is on the focus side of . Therefore, is the tangent to the parabola at P. Since it bisects the angle ∠FPT, this proves the tangent bisection property. The logic of the last paragraph can be applied to modify the above proof of the reflective property.
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Individuals sustaining a severe bisection injury that is essentially a de facto hemicorporectomy would rarely reach a hospital before succumbing. A study that reviewed 267 cases of patients who sustained severe blunt and penetrating trauma, and who were in cardiopulmonary arrest, found that only 7 survived long-term, only four of whom returned to their previous neurologic level. Apart from the very low likelihood of surviving such an injury, even an operative hemicorporectomy is unlikely to be successful unless the patient has "sufficient emotional and psychological maturity to cope" and "sufficient determination and physical strength to undergo the intensive rehabilitation". Emergency rooms and ambulance service policies advise against the resuscitation of such patients.
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The bisection method consists roughly of starting from an interval containing all real roots of a polynomial, and divides it recursively into two parts until getting eventually intervals that contain either zero or one root. The starting interval may be of the form , where is an upper bound on the absolute values of the roots, such as those that are given in . For technical reasons (simpler changes of variable, simpler complexity analysis, possibility of taking advantage of the binary analysis of computers), the algorithms are generally presented as starting with the interval . There is no loss of generality, as the changes of variables and move respectively the positive and the negative roots in the interval .
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In the 19th century, several disparate mathematical properties were understood that would later be seen as consequences of compactness. On the one hand, Bernard Bolzano (1817) had been aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point, called a limit point. Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into two equal parts, and a part containing infinitely many terms of the sequence was selected. The process could then be repeated by dividing the resulting smaller interval into smaller and smaller parts—until it closes down on the desired limit point.
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At the time of its publication, Modern Primitives was the first text to attempt to comprehensively address the issues, aesthetics and meaning involved in the subject of body modification. The public knowledge of the term Modern Primitive is primarily due to the widespread popularity of this book. Many of the images in the book would have been familiar to persons involved in the movement, but the book exposed several "underground" practices to a vastly greater public, including graphic images of genital piercing and genital bisection and scarification. The book also advanced numerous urban legends regarding the history and origin of body piercing, which remain widespread to this day, most notably Doug Malloy (Richard Simonton)'s invented origins of various piercings.
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In one of Short's last letters home, her older sister Virginia claimed she had written that a movie director was going to give her a screen test. Pacios also cites Welles' familiarity with the site where the body was found and the magic act he performed to entertain soldiers during World War II. She believes that the bisection of the body was part of the killer's signature and an acting out of the perpetrator's obsession. Welles applied for his passport on January 24, 1947, the same day the killer mailed a packet to Los Angeles newspapers. Welles left the country for an extended stay in Europe 10 months after the murder without completing the editing of Macbeth, the film he was both directing and starring in.
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In 2008-09, concerned about the rapidly growing demand for cloud computing, the IT industry was contemplating converting the prevalent multi-rooted tree based network topology, of oversubscribed data center networks, to a fat tree topology or to a non-blocking full bisection bandwidth clos topology. The difficulty was that re-hauling these networks with complex aggregate layer network switches, as required in a fat tree network topology, or with thousands of simpler commodity network switches inter-connected with miles of wires as required in a clos network topology, was very expensive. In a study of a production mega data center, published in Oct. 2009, Bahl, Kandula, and Padhye showed that barring a few outliers, traffic demands could be met in existing, slightly-oversubscribed data center networks.
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Bokhari's research with Marsha Berger (Berger and Bokhari 1987) concerns versions of the partitioning problem in which different tasks may have greatly differing workloads; he gives as an application the distributed solution of nonlinear partial differential equations. The technique introduced in this paper, recursive co-ordinate bisection, repeatedly divides the geometric problem domain along co-ordinate axes into two subdomains of equal workload until the number of subdomains formed equals the number of processors. However, as Simon writes, although this method is conceptually very simple it tends to produce long and thin or even disconnected subdomains. A later refinement of this technique, parametric binary dissection (Bokhari, Crockett, and Nicol 1993) combines shape information with load balancing in its partitioning decisions in an attempt to mitigate this problem.
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Isabel Espinosa-Medina, working in the lab of French researcher Jean-François Brunet at IBENS, identified several transcription factors within pre-ganglionic neurons of the lower lumbar and sacral regions that are essential to neurogenesis. These transcription factors were only identified within other portions of the spinal cord, but they were not co-expressed in the developing cranium. This genomic similarity of the lumbrasacral region to the rest of the spinal cord lead to the conclusion that the sacral region of the spinal cord may actually be part of the sympathetic nervous system. The effect of this revision produces a simple bisection of the autonomic nervous system wherein the cranium is solely parasympathetic, and the spinal cord is solely sympathetic.
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To determine the zenith point of the circle, the telescope was directed vertically downwards at a basin of mercury, the surface of which formed an absolutely horizontal mirror. The observer saw the horizontal wire and its reflected image, and moving the telescope to make these coincide, its optical axis was made perpendicular to the plane of the horizon, and the circle reading was 180° \+ zenith point. In observations of stars refraction was taken into account as well as the errors of graduation and flexure. If the bisection of the star on the horizontal wire was not made in the centre of the field, allowance was made for curvature, or the deviation of the star's path from a great circle, and for the inclination of the horizontal wire to the horizon.
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In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw circles of equal radii and different centers. The segment is bisected by drawing intersecting circles of equal radius, whose centers are the endpoints of the segment and such that each circle goes through one endpoint. The line determined by the points of intersection of the two circles is the perpendicular bisector of the segment, since it crosses the segment at its center. This construction is in fact used when constructing a line perpendicular to a given line at a given point: drawing an arbitrary circle whose center is that point, it intersects the line in two more points, and the perpendicular to be constructed is the one bisecting the segment defined by these two points.
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In this single-stage procedure the urethra will be visualized (in the area of the defect), and the incision will be started at its mid-line (usually) using a bovie knife to dissect the dermal and sub-dermal layers until the associated musculature, corpus cavernosum, corpus spongiosum, and ventral urethral aspects are exposed. Particular care is used during the dissection to prevent damage to nerves and blood vessels (which could result in erectile dysfunction or loss of tactile sensation of the penis). The area of the defect is evaluated and marked both mid-line (laterally), and at the distal and proximal borders (transversely). Marked/labeled positioning sutures are secured (one, each) at the proximal and distal ends of the mid-line area of urethra closest to the bisection points.
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The bisection method (binary search) can also be used to transform decision into optimization. In this method, one maintains an interval of numbers, known to contain the optimal solution value, and repeatedly shrinks the interval by calling the decision algorithm on its median value and keeping only the half-interval above or below the median, depending on the outcome of the call. Although this method can only find a numerical approximation to the optimal solution value, it does so in a number of calls to the decision algorithm proportional to the number of bits of precision of accuracy for this approximation, resulting in weakly polynomial algorithms. Instead, when applicable, parametric search finds strongly polynomial algorithms, whose running time is a function only of the input size and is independent of numerical precision.
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Since the initial end-points and are chosen such that and are of opposite signs, at each step, one of the end-points will get closer to a root of . If the second derivative of is of constant sign (so there is no inflection point) in the interval, then one endpoint (the one where also has the same sign) will remain fixed for all subsequent iterations while the converging endpoint becomes updated. As a result, unlike the bisection method, the width of the bracket does not tend to zero (unless the zero is at an inflection point around which ). As a consequence, the linear approximation to , which is used to pick the false position, does not improve as rapidly as possible. One example of this phenomenon is the function : f(x) = 2x^3-4x^2+3x on the initial bracket [−1,1].
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After Darwin's writings, there was an effort to find evidence for the transmission of acquired characters; ultimately, the Lamarckian hypothesis of transmission of acquired characters was not supported by evidence, and was dismissed. August Weismann argued from the structure of the egg-cell and sperm-cell, and from how and when they are derived in the growth of the embryo from the egg, that it was impossible that a change in parental structure could produce a representative change in the germ or sperm-cells. The only evidence that seemed to support the Lamarckian hypothesis were the experiments of Charles Brown-Séquard, who produced epilepsy in guinea-pigs by bisection of the large nerves or spinal cord, which led him to believe that, in rare instances, the artificially-produced epilepsy and mutilation of the nerves was transmitted. The record of Brown-Séquard's original experiments was unsatisfactory, and attempts reproduce them were unsuccessful.
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Let : y(t) = f(t, y(t), y'(t)), \quad y(t_0) = y_0, \quad y(t_1) = y_1 be the boundary value problem. Let y(t; a) denote the solution of the initial value problem : y(t) = f(t, y(t), y'(t)), \quad y(t_0) = y_0, \quad y'(t_0) = a Define the function F(a) as the difference between y(t1; a) and the specified boundary value y1. : F(a) = y(t_1; a) - y_1 \, If F has a root a then the solution y(t; a) of the corresponding initial value problem is also a solution of the boundary value problem. Conversely, if the boundary value problem has a solution y(t), then y(t) is also the unique solution y(t; a) of the initial value problem where a = y'(t0), thus a is a root of F. The usual methods for finding roots may be employed here, such as the bisection method or Newton's method.
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The STM numerically solves equation 3 through an iterative process. This can be done using the bisection or Newton-Raphson Method, and is essentially solving for total head at a specified location using equations 4 and 5 by varying depth at the specified location. :H_2 = H_1 - h_f Equation 4 :H_2 = h_{vel} + h_{ele} Equation 5 In order to use this technique, it is important to note you must have some understanding of the system you are modeling. For each gradually varied flow transition, you must know both boundary conditions and you must also calculate length of that transition. (e.g. For an M1 Profile, you must find the rise at the downstream boundary condition, the normal depth at the upstream boundary condition, and also the length of the transition.) To find the length of the gradually varied flow transitions, iterate the “step length”, instead of height, at the boundary condition height until equations 4 and 5 agree. (e.g.
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After a third chapter relating the crossing number to graph parameters including skewness, bisection width, thickness, and (via the Albertson conjecture) the chromatic number, the final chapter of part I concerns the computational complexity of finding minimum-crossing graph drawings, including the results that the problem is both NP-complete and fixed-parameter tractable. In the second part of the book, two chapters concern the rectilinear crossing number, describing graph drawings in which the edges must be represented as straight line segments rather than arbitrary curves, and Fáry's theorem that every planar graph can be drawn without crossings in this way. Another chapter concerns 1-planar graphs and the associated local crossing number, the smallest number such that the graph can be drawn with at most crossings per edge. Two chapters concern book embeddings and string graphs, and two more chapters concern variations of the crossing number that count crossings in different ways, for instance by the number of pairs of edges that cross or that cross an odd number of times.
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However, in planar graphs, the Maximum-Cut Problem is dual to the route inspection problem (the problem of finding a shortest tour that visits each edge of a graph at least once), in the sense that the edges that do not belong to a maximum cut-set of a graph G are the duals of the edges that are doubled in an optimal inspection tour of the dual graph of G. The optimal inspection tour forms a self-intersecting curve that separates the plane into two subsets, the subset of points for which the winding number of the curve is even and the subset for which the winding number is odd; these two subsets form a cut that includes all of the edges whose duals appear an odd number of times in the tour. The route inspection problem may be solved in polynomial time, and this duality allows the maximum cut problem to also be solved in polynomial time for planar graphs.. The Maximum-Bisection problem is known however to be NP-hard..
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