206 Sentences With "unordered" | Random Sentence Generator

She sees it as her duty, an ordering of things in an unordered stream.

Do you have a computer file that is a long, unordered list that must be sorted?

AARON DAVID MILLER, FORMER MIDDLE EAST NEGOTIATOR This decision was unordered and untethered to any foreign policy consideration.

Now I get a jug of unordered detergent every day and my phone seems to know I'm watching reruns of 'Downton Abbey.

After some hemming and hawing with both uniformed and plainclothes police officers, as well as building security, five protesters were allowed a few feet inside the vestibule of 212 5th Ave to leave Bezos his unordered shipment.

There are a number of other companies out there looking to put their own spin on how to "wrangle" or read unstructured or otherwise unordered data, to tap into what IDC estimates as $210 billion opportunity by 2020.

These processes have gotten me two things: a ZIP archive containing HTML records of all my data, and a folder containing around a thousand unordered and unlabeled photos that's less of a streamlined memory lane and more of a disorientating nostalgia junction.

Nomagic, which has developed way for a robotic arm to identify an item from an unordered selection, pick it up and then pack it into a box, is today announcing that it has raised $8.6 million in funding, one of the largest-ever seed rounds for a Polish startup.

Players can also choose to be unordered. Your Order is determined by your first chosen ability. Some orders include the Noble, Rogue, Elementalist, and of course, Unordered. Unordered characters still advance, but do so without the benefit of a guild.

Unordered activities are used when sub-activities of an activity do not have a pre-defined sequence in which they need to be carried out. Only sub-activities can be unordered. Unordered activities are represented as sub-activities without transitions within an activity, as is represented in Figure 3. Sometimes an activity consists of both sequential and unordered sub-activities.

In an undirected graph, an unordered pair of vertices is called connected if a path leads from x to y. Otherwise, the unordered pair is called disconnected. A connected graph is an undirected graph in which every unordered pair of vertices in the graph is connected. Otherwise, it is called a disconnected graph.

The associative containers are similar to the unordered associative containers in C++ standard library, the only difference is that the unordered associative containers, as their name implies, do not order their elements.

In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a1, a2,... an}. .

Each of the 45 circles is denoted by an unordered pair of duads.

The Latin name "factorisatio numerorum" had been used previously. MathWorld uses the term unordered factorization.

One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory. The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered pitch-class intervals, see interval class.

Built-in functions and libraries allow lists to also be used as associative arrays and ordered and unordered sets.

HyperCast provides a best-eﬀort communication service (unreliable, unordered, possible duplication) for application messages, which are referred to as overlay messages.

The unordered associative containers are similar to the associative containers in the C++ Standard Library but have different constraints. As their name implies, the elements in the unordered associative containers are not ordered. This is due to the use of hashing to store objects. The containers can still be iterated through like a regular associative container.

This is a list of tone rows and series. For a list of unordered collections, see set (music), Forte number, list of pitch-class sets, and trope (music).

In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records.

In mathematics, an unordered pair or pair set is a set of the form {a, b}, i.e. a set having two elements a and b with no particular relation between them. In contrast, an ordered pair (a, b) has a as its first element and b as its second element. While the two elements of an ordered pair (a, b) need not be distinct, modern authors only call {a, b} an unordered pair if a ≠ b.

Interval class . In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (; ), is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 ≡ 7 (mod 12). See modular arithmetic for more on modulo 12.

The standard provides comparison predicates to compare one floating-point datum to another in the supported arithmetic format. Any comparison with a NaN is treated as unordered. −0 and +0 compare as equal.

The programming languages Clojure, Scala, and Frege use a persistent variant of hash array mapped tries for their native hash map type. The Haskell library "unordered- containers" uses the same to implement persistent map and set data structures.Johan Tibell, A. Announcing unordered-containers 0.2 Another Haskell library "stm-containers" adapts the algorithm for use in the context of software transactional memory.Nikita Volkov, Announcing the "stm- containers" library, 2014 A Javascript HAMT library based on the Clojure implementation is also available.

In mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.) Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors.

In algebraic topology, the symmetric product of a topological space consists of unordered -tuples of distinct points in . The infinite symmetric product is the colimit of this process, and appears in the Dold–Thom theorem.

PelC contains a parallel beta-helix folding motif. The majority of the regular secondary structure is composed of parallel beta-sheets (about 30%). The individual strands of the sheets are connected by unordered loops of varying length.

Record Collector included the album in their unordered 2000 list of "10 Classic Albums from 21 Genres for the 21st Century", whilst Robert Dimery included the album in the book 1001 Albums You Must Hear Before You Die.

Collection types model groups of values. Sets are finite unordered collections in which duplication between values is suppressed. Sequences are finite ordered collections (lists) in which duplication may occur and mappings represent finite correspondences between two sets of values.

Three-taxon analysis (3ia). Modified from Figure 1 from this paper:Grand A, Corvez A, Duque Velez LM, Laurin M. 2013. Phylogenetic inference using discrete characters: performance of ordered and unordered parsimony and of three-item statements. Biol J Linn Soc.

For unordered access as defined in the java.util.Map interface, the java.util.concurrent.ConcurrentHashMap implements java.util.concurrent.ConcurrentMap. The mechanism is a hash access to a hash table with lists of entries, each entry holding a key, a value, the hash, and a next reference.

In coding theory, a balanced code is a binary forward error correction code for which each codeword contains an equal number of zero and one bits. Balanced codes have been introduced by Donald Knuth; they are a subset of so-called unordered codes, which are codes having the property that the positions of ones in a codeword are never a subset of the positions of the ones in another codeword. Like all unordered codes, balanced codes are suitable for the detection of all unidirectional errors in an encoded message. Balanced codes allow for particularly efficient decoding, which can be carried out in parallel.

Also, two negative bands were present on the CD spectrum. In an aqueous environment, mastoparan took on a nonhelical, unordered form. In this case, only one negative band was observed on the CD spectrum. Adding phosphate buffer to mastoparan resulted in no effect.

Unrooted binary trees have also been called free binary trees,. cubic trees,. ternary trees and unrooted ternary trees,.. However, the "free binary tree" name has also been applied to unrooted trees that may have degree-two nodes. and to rooted binary trees with unordered children,.

This is applied in all filesystem based synchronizations (where the data is ordered). Many practical applications of this are discussed or referenced above. It is sometimes possible to transform the problem to one of unordered data through a process known as shingling (splitting the strings into shingles).

A priority queue is a concept like "a list" or "a map"; just as a list can be implemented with a linked list or an array, a priority queue can be implemented with a heap or a variety of other methods such as an unordered array.

In music theory, equivalence class is an equality (=) or equivalence between properties of sets (unordered) or twelve-tone rows (ordered sets). A relation rather than an operation, it may be contrasted with derivation.Schuijer (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.85. .

Along with the Büyük Zafer crew, Arka Sıradakiler includes a large array of characters: students, teachers, families, friends, and fictional characters. The main characters, teacher Kemal and the crew, are listed first; all other characters are listed unordered. Only main, supporting, and recurring characters are listed.

The domains on the left, complex and chaotic, are "unordered": cause and effect can be deduced only with hindsight or not at all.Koskela, Lauri; Kagioglou, Mike (2006). "On the Metaphysics of Production" . Proceedings of the 13th Annual Conference on Lean Construction, Sydney, Australia, July 2005 (37–45), 42–43.

There are model formulations for linear and nonlinear regression, robust estimation, discrete choice (including binary choice, ordered choice and unordered multinomial choice), censoring and truncation, sample selection, loglinear models, survival analysis, quantile regression (linear and count), panel data, stochastic frontier and data envelopment analysis, count data, and time series.

Dictionaries/Maps store references to objects with a lookup key to access the object's values. One example of a key is an identification card. The base interface for dictionaries/maps is called Map. Sets are unordered collections that can be iterated and contain each element at most once.

Whittall 2008, 139. as for example in his Requiem Canticles: Basic row forms from Stravinsky's Requiem Canticles: P R I IR Klavierstücke I–IV which, "retained only the rudiments of the 12-note series."Leeuw 2005, 176–77. Unordered sets from the third of Stockhausen's Klavierstücke I–IV .

Conversely, given a selection algorithm, one can easily get an unordered partial sort (k smallest elements, not in order) in O(n) time by iterating through the list and recording all elements less than the kth element. If this results in fewer than k − 1 elements, any remaining elements equal the kth element. Care must be taken, due to the possibility of equality of elements: one must not include all elements less than or equal to the kth element, as elements greater than the kth element may also be equal to it. Thus unordered partial sorting (lowest k elements, but not ordered) and selection of the kth element are very similar problems.

If the original space X is a manifold, its ordered configuration spaces are open subspaces of the powers of X and are thus themselves manifolds. The configuration space of distinct unordered points is also a manifold, while the configuration space of not necessarily distinct unordered points is instead an orbifold. A configuration space is a type of classifying space or (fine) moduli space. In particular, there is a universal bundle \pi\colon E_n\to C_n which is a sub-bundle of the trivial bundle C_n\times X\to C_n, and which has the property that the fiber over each point p\in C_n is the n element subset of X classified by p.

In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two- graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs.

C++'s Standard Template Library provides the `multimap` container for the sorted multimap using a self-balancing binary search tree, and SGI's STL extension provides the `hash_multimap` container, which implements a multimap using a hash table. As of C++11, the Standard Template Library provides the `unordered_multimap` for the unordered multimap.

An indexed view has the same storage structure as an indexed table. A table without a clustered index is stored in an unordered heap structure. However, the table may have non-clustered indices to allow fast retrieval of rows. In some situations the heap structure has performance advantages over the clustered structure.

In a passing reference to this piece, the Dutch composer Ton de Leeuw presents these same five notes in ascending scale order, which he describes as "rudiments of the 12-note series", but does not explain whether his diagram is to be understood as an ordered row or an unordered collection . This same set, treated as unordered, has been taken as a starting point for a lengthy analysis by David , while Christoph von Blumröder (1993, 109–54) has published one nearly as long favouring Maconie's view. One reviewer has judged Blumröder's analysis as a conclusive demonstration that the tetrachord is in fact the compositional basis, while conceding that Harvey and Lewin's view remains a valid construal of the piece viewed as a finished product .

The sort operation transforms an unordered set of elements into an ordered set of elements. The most common implementation on GPUs is using radix sort for integer and floating point data and coarse- grained merge sort and fine-grained sorting networks for general comparable data.Merrill, Duane. Allocation-oriented Algorithm Design with Application to GPU Computing.

The Great Piece of TurfThe work is sometimes referred to as the Large Piece of Turf, or The Large Turf. () is a watercolor painting by Albrecht Dürer. The painting was created at Dürer's workshop in Nuremberg in 1503. It is a study of a seemingly unordered group of wild plants, including dandelion and greater plantain.

In every unordered tree there is a distinguished partition of the set of nodes into sibling sets. Two non-root nodes , belong to the same sibling set if . The root node forms the singleton sibling set }. A tree is said to be locally finite or finitely branching if each of its sibling sets is finite.

In 2006 the premier US martial arts magazine "Black Belt" published an unordered list of the "deadliest fighters on the planet" – the criteria was no deceased fighters and no mixed-martial artists, and attempted to subjectively rate the men according to how skilled they were in their prime, with Terry O'Neill listed No.1 .

Schoenberg 1975, 218. It is commonly considered a form of serialism. Schoenberg's fellow countryman and contemporary Hauer also developed a similar system using unordered hexachords or tropes—but with no connection to Schoenberg's twelve-tone technique. Other composers have created systematic use of the chromatic scale, but Schoenberg's method is considered to be historically and aesthetically most significant.

When all the operands of an instruction in an issue queue are ready, that instruction is ready to issue. The issue queues pick ready instructions to send to the various functional units each cycle. Non-ready instructions stay in the issue queues. This unordered removal of instructions from the issue queues can make them large and power-consuming.

The deficiency and unordered developments led to establishments in laneways. However, the problems arise from the essences in dwelling. A laneway house's issues with privacy, noise and smells suggest many potential ruins to the quality of life. Shim and Howard initiated the project by buying a junker lot, near Queen and Leslie, shoved with abandoned cars.

The solution to this modeling issue is to divide the main activity in different parts. In Figure 4 an example is illustrated, which clarifies the necessity to be able to model unordered activities. The example is taken from the requirements analysis workflow of the Unified Process. The main activity, “describe candidate requirements”, is divided into two parts.

The fundamental concept of musical set theory is the (musical) set, which is an unordered collection of pitch classes . More exactly, a pitch-class set is a numerical representation consisting of distinct integers (i.e., without duplicates) . The elements of a set may be manifested in music as simultaneous chords, successive tones (as in a melody), or both.

An important aspect of these stemmas is that they are "unordered", i.e. they do not reflect actual word order. For Tesnière, structural order (hierarchical order) preceded linear order in the mind of a speaker. A speaker first conceives of what he/she wants to say, whereby this conception consists of words organized hierarchically in terms of connections (structural order).

The fundamental difference between context-free grammars and parsing expression grammars is that the PEG's choice operator is ordered. If the first alternative succeeds, the second alternative is ignored. Thus ordered choice is not commutative, unlike unordered choice as in context-free grammars. Ordered choice is analogous to soft cut operators available in some logic programming languages.

If six unordered points are given on a conic section, they can be connected into a hexagon in 60 different ways, resulting in 60 different instances of Pascal's theorem and 60 different Pascal lines. This configuration of 60 lines is called the Hexagrammum Mysticum. with a reference to Veblen and Young, Projective Geometry, vol. I, p.

Each pair of distinct siblings is incomparable in . This is why the word unordered is used in the definition. Such a terminology might become misleading when all sibling sets are singletons, i.e. when the set of all nodes is totally ordered (and thus well-ordered) by In such a case we might speak about a singly-branching tree instead.

The Kuboyama's definition of "rooted ordered trees" makes use of the horizontal order as a definitory relation. (See also Suppes. ) Using the notation and terminology introduced so far, the definition can be expressed as follows. An ordered tree is a structure such that conditions (1-5) are satisfied: # is a partial order that is an unordered tree.

In graph theory, a recursive tree (i.e., unordered tree) is a non-planar labeled rooted tree. A size-n recursive tree is labeled by distinct integers 1, 2, ..., n, where the labels are strictly increasing starting at the root labeled 1. Recursive trees are non-planar, which means that the children of a particular node are not ordered. E.g.

In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list. It is related to the quicksort sorting algorithm. Like quicksort, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. Like quicksort, it is efficient in practice and has good average-case performance, but has poor worst-case performance.

It is a trivial task when the convex polygon is specified in a traditional for polygons way, i.e., by the ordered sequence of its vertices v_1,\dots, v_m. When the input list of vertices (or edges) is unordered, the time complexity of the problems becomes O(m log m). A matching lower bound is known in the algebraic decision tree model of computation.

The XML elements in an XOXO document are: ; `

unordered

An unordered tree is well-founded if the strict partial order is a well-founded relation. In particular, every finite tree is well-founded. Assuming the axiom of dependent choice a tree is well-founded if and only if it has no infinite branch. Well-founded trees can be defined recursively - by forming trees from a disjoint union of smaller trees.

The allotropic forms of silicon range from a single crystalline structure to a completely unordered amorphous structure with several intermediate varieties. In addition, each of these different forms can possess several names and even more abbreviations, and often cause confusion to non-experts, especially as some materials and their application as a PV technology are of minor significance, while other materials are of outstanding importance.

A strong advantage of the ACE procedure is the ability to incorporate variables of quite different type in terms of the set of values they can assume. The transformation functions \theta(y), \varphi_i(x_i) assume values on the real line. Their arguments can, however, assume values on any set. For example, ordered real and unordered categorical variables can be incorporated in the same regression equation.

Revised version in Information and Control, 68 (1986), 86–104. and Vardi independently showed the descriptive complexity result that the polynomial-time computable properties of linearly ordered structures are definable in FO(LFP), i.e. in first-order logic with a least fixed point operator. However, FO(LFP) is too weak to express all polynomial-time properties of unordered structures (for instance that a structure has even size).

Q also included it in their unordered list of the 50 best albums of 1989. In 1989, German publication Tempo ranked the album at number 69 in their list of "The 100 Best Albums of the 80's." In 1995, Q included The Raw & the Cooked in its publication "In Our Lifetime: Q's 100 Best Albums 1986–94", a list compiled to celebrate its 100th issue.

The most common measures of evaluation are precision, recall, and f-score. They are computed using unordered sets of documents. These measures must be extended, or new measures must be defined, in order to evaluate the ranked retrieval results that are standard in modern search engines. In a ranked retrieval context, appropriate sets of retrieved documents are naturally given by the top k retrieved documents.

Whereas eventual consistency is only a liveness guarantee (updates will be observed eventually), strong eventual consistency (SEC) adds the safety guarantee that any two nodes that have received the same (unordered) set of updates will be in the same state. If, furthermore, the system is monotonic, the application will never suffer rollbacks. Conflict- free replicated data types are a common approach to ensuring SEC.

Early-build genomes are quite fragmented, with unordered and unoriented contigs. Using Strand-seq provides directionality information to accompany the sequence, which ultimately helps resolve the placement of contigs. Contigs present in the same chromosome will exhibit the same directionality, provided SCE events have not occurred. Conversely, contigs present in different chromosomes will only exhibit the same directionality in 50% of the Strand-seq libraries.

Allen Forte defines transposition so as to apply to unordered sets of other than twelve pitches: :the addition mod 12 of any integer k in S to every integer p of P. thus giving, "12 transposed forms of P".Forte (1964). "A Theory of Set-Complexes for Music", p. 149, Journal of Music Theory 8/2:136–83. cited in Schuijer (2008), p. 57.

BPS incorporates two basic operations: "merge" and "move". Although there is active debate on exactly how "move" should be formulated, the differences between the current proposals are relatively minute. The following description follows Chomsky's original proposal. Merge is a function that takes two objects (say α and β) and merges them into an unordered set with a label (either α or β, in this case α).

The opposite is partitioning, the use of methods to create segments from entire sets, most often through registral difference. In music using the twelve-tone technique a partition is, "a collection of disjunct, unordered pitch-class sets that comprise an aggregate."Alegant (2001), p.2. It is a method of creating segments from sets, most often through registral difference, the opposite of derivation used in derived rows.

Originally algorithmic induction methods extrapolated ordered sequences of strings. Methods were needed for dealing with other kinds of data. A 1999 report,"Two Kinds of Probabilistic Induction," The Computer Journal, Vol 42, No. 4, 1999. (pdf version) generalizes the Universal Distribution and associated convergence theorems to unordered sets of strings and a 2008 report,"Three Kinds of Probabilistic Induction, Universal Distributions and Convergence Theorems" 2008.

Besides, underpricing is also affected by the firm idiosyncratic factors such as its business model. Thus it is difficult to determine a clear price which is compounded by the different goals issuers and investors have. The problem with developing algorithms to determine underpricing is dealing with noisy, complex, and unordered data sets. Additionally, people, environment, and various environmental conditions introduce irregularities in the data.

J. Chem. Phys., 43:1806-1818, 1965 to unordered solids,Rist, G. H., and Hyde, J. S.: Ligand ENDOR of Metal Complexes in Powders. J. Chem. Phys. 52:4633-4643m 1970 to flavoproteinsEhrenberg, A., Eriksson, L. E. G., Hyde, J. S., Electron-nuclear double resonance from Flavin free radicals in NADPH dehydrogenase (“old yellow enzyme”). Biochim. Biophys. Acta., 167:482-484, 1968. and to copper proteins.

Statistical frameworks and mapping models are used to identify imprinting effects on genes and complex traits. Allelic parent-of -origin influences the vary in phenotype that derive from the imprinting of genotype classes. These models of mapping and identifying imprinting effects include using unordered genotypes to build mapping models. These models will show classic quantitative genetics and the effects of dominance of the imprinted genes.

A partial premiere of book2 was performed by the composer and Yvonne Loriod at the Wigmore Hall, London, in March 1957. This was Boulez's first appearance in the UK as a performer . The same performers gave the premiere of the complete second book, with two different versions of chapter2, in a chamber-music concert of the Donaueschinger Musiktage on Saturday, 21 October 1961 . Olivier Messiaen's Mode de valeurs et d'intensités highest of three unordered divisions of the mode (; ) or, less precisely, "three series forms [caption: "for pitch, duration, dynamics, and articulation"]...treated as unordered collections," ()—which Boulez, "the pupil intending to teach the master a lesson," adapted as an ordered series for his Structures Ia Structures I was the last and most successful of Boulez's works to use the technique of integral serialism , wherein many parameters of a piece's construction are governed by serial principles, rather than only pitch.

The importance of blending order. The top produces an incorrect result with unordered alpha blending, while the bottom correctly sorts the geometry. Note lower visibility of the skeletal structure without correct depth ordering. Image from ATI Mecha Demo Order-independent transparency (OIT) is a class of techniques in rasterisational computer graphics for rendering transparency in a 3D scene, which do not require rendering geometry in sorted order for alpha compositing.

Released in March 1998, Crazy on the Weekend had some critical success including a five star review in Uncut. It featured in the year end best of lists for Uncut, Les Inrockuptibles (both unordered) and Mojo (#15). Despite the critical success, the album sold poorly and the band never recorded again. Singer-songwriter Gavin Clark went on to form the band Clayhill and made several guest appearances on recordings by Unkle.

In the programming language C++, unordered associative containers are a group of class templates in the C++ Standard Library that implement hash table variants. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard: `unordered_set`, `unordered_map`, `unordered_multiset`, `unordered_multimap`. Each of these containers differ only on constraints placed on their elements.

A still further class of controlled grammars is the class of grammars with parallelism in the application of a rewrite operation, in which each rewrite step can (or must) rewrite more than one non-terminal simultaneously. These, too, come in several flavors: Indian parallel grammars, k-grammars, scattered context grammars, unordered scattered context grammars, and k-simple matrix grammars. Again, the variants differ in how the parallelism is defined.

On December 15, 1966, Wilson attempted to ease Capitol's concerns over the album's delay by delivering a handwritten note that contained an unordered, preliminary track listing, which later provoked much speculation about the album. Capitol prepared record sleeves that listed these songs on the reverse side with the disclaimer "see label for correct playing order". Preliminary mixes (and in some cases many) were created for several of these tracks.

Azemiopsin is a polypeptide molecule consisting of 21 residues, which does not contain cysteine residues or disulfide bridges. Its amino acid sequence is DNWWPKPPHQGPRPPRPRPKP and its molecular weight 2540 Da. Azemiopsin predominantly contains beta-structures: 62% consists of beta-structure (beta sheet + beta-turn), 34% consists of unordered structure, and the remaining 4% consist of alpha helix. This suggests that the polypeptide may likely adopt a hairpin-like structure.

Some run an unordered analysis, and order characters that show a clear order of transition in the resulting tree (which practice might be accused of circular reasoning). Some authorities refuse to order characters at all, suggesting that it biases an analysis to require evolutionary transitions to follow a particular path. It is also possible to apply differential weighting to individual characters. This is usually done relative to a "cost" of 1.

The Manhattan bottle service club Arena was sued in 2007 for their version of the clip joint scam. In December 2007, a patron knowingly purchased a $350 bottle of vodka, but was not told of a three bottle minimum. At the end of the night, he was presented with a $1050 tab that included two unordered bottles. When he refused to pay, the Arena bouncers beat him up.

Cataloging of segmental duplications was originally difficult due to its inconspicuousness, large size, and high degree of sequence similarity. This led to issues of interpreting separate loci as one sequence as these duplications are over-represented in unordered and unassigned contigs. Furthermore, these duplications are more prevalent within the pericentromeric and subtelomeric regions. BACs containing intrachromosomal duplications can be made and their duplication pattern can be characterized using FISH.

On the other hand, rotation can be used "to select the place in the redo list where the next undo operation will put the command". The list of redo is therefore unordered. "To undo an isolated command, the user has to undo a number of steps, rotate the redo list, and then redo a number of steps". For redo the list has to be rotated until the wanted command is above.

Schreier completed his master's degree On tournament elimination systems in 1932 under the direction of Hugo Steinhaus. Schreier correctly conjectured that to determine the second largest number in an unordered list requires at least n + \lceil \log_2 n \rceil -2 comparisons.On tournament elimination systems, J. Schreier - Mathesis Polska, 1932 In 1934, he completed his doctorate, On finite base in topological groups under Banach.O skończonej bazie w grupach topologicznych In 1932 he married Zofia Rosenblatt.

SAIL, the Stanford Artificial Intelligence Language, was developed by Dan Swinehart and Bob Sproull of the Stanford AI Lab in 1970. It was originally a large ALGOL 60-like language for the PDP-10 and DECSYSTEM-20. SAIL's main feature is a symbolic data system based upon an associative store (based on the LEAP system of Jerry Feldman and Paul Rovner). Items may be stored as unordered sets or as associations (triples).

In combinatorics, an unordered subset of objects, such as pitch classes, is called a combination, and an ordered subset a permutation. Musical set theory is best regarded as a field that is not so much related to mathematical set theory, as an application of combinatorics to music theory with its own vocabulary. The main connection to mathematical set theory is the use of the vocabulary of set theory to talk about finite sets.

Notational conventions vary from author to author, but sets are typically enclosed in curly braces: {} , or square brackets: [] . Some theorists use angle brackets to denote ordered sequences , while others distinguish ordered sets by separating the numbers with spaces . Thus one might notate the unordered set of pitch classes 0, 1, and 2 (corresponding in this case to C, C, and D) as {0,1,2}. The ordered sequence C-C-D would be notated or (0,1,2).

Stata is a commercial package. Stata's implementation of IRT includes 1, 2 and 3 parameter logistic models, graded response models, partial credit and generalized partial credit models, rating scale models, and a nominal response model for unordered categorical responses. It is driven by a control panel that allows the user to specify the model, examine fit numerically and graphically and investigate differential item functioning from a single interface Stata's IRT manual online.

Similarly, the album's producer Mark Tucker said the album had been "repeatedly hailed" as "their best yet". The Daily Telegraph included the album in its unordered list of the "Best Folk Music Albums of 2012". In January 2013, the duo were nominated in the Songlines Music Awards. The album charted at number 73 in the UK Album Chart, becoming their second album to chart after Arrogance Ignorance and Greed, which reached number 170.

On August 1, 2016, Washington State Attorney General Bob Ferguson filed a lawsuit against Comcast Corporation in King County Superior Court, alleging the company's own documents reveal a pattern of illegally deceiving their customers to pad their bottom line by tens of millions of dollars.Office of the Attorney General. . Retrieved August 1, 2016 The FCC issued a $2.3 million fine to Comcast after finding that the company was charging customers for unordered services and equipment.

Let f : Γ → Γ be a combinatorial map. A turn is an unordered pair e, h of oriented edges of Γ (not necessarily distinct) having a common initial vertex. A turn e, h is degenerate if e = h and nondegenerate otherwise. A turn e, h is illegal if for some n ≥ 1 the paths fn(e) and fn(h) have a nontrivial common initial segment (that is, they start with the same edge).

Olmstead 2008, 218, 291. Sessions's usual method was to use a row to control the full chromaticism and motivic-intervallic cohesion that already marks his music from before 1953. He treats his rows with great freedom, however, typically using pairs of unordered complementary hexachords to provide “harmonic” aspects without determining note-by-note melodic succession, or conversely using the row to supply melodic thematic material while freely composing the subsidiary parts.Morgan 1991, 294–95.

The configuration space of all unordered pairs of points on the circle is the Möbius strip. In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single point in a high- dimensional space. In mathematics, they are used to describe assignments of a collection of points to positions in a topological space.

Box Frenzy is the debut studio album by English rock band Pop Will Eat Itself. It was released on 26 October 1987 in the United Kingdom by Chapter 22 Records and in the United States by Rough Trade Records. At the end of 1987, the NME ranked the album at number 49 in their list of the top 50 "Albums of the Year". Q also included it in their unordered list of the year's 50 best albums.rocklistmusic.co.uk/qlists.

A k-tuple point (double, triple, etc.) of an immersion is an unordered set } of distinct points with the same image . If M is an m-dimensional manifold and N is an n-dimensional manifold then for an immersion in general position the set of k-tuple points is an -dimensional manifold. Every embedding is an immersion without multiple points (where ). Note, however, that the converse is false: there are injective immersions that are not embeddings.

In 2004, Total Film named Brazil the 20th-greatest British movie of all time. In 2005, Time film reviewers Richard Corliss and Richard Schickel included Brazil in an unordered list of the 100 best films of all time. In 2006, Channel 4 voted Brazil one of the "50 Films to See Before You Die", shortly before its broadcast on FilmFour. The film also ranks at number 83 in Empire magazine's list of the 500 Greatest Films of All Time.

He would have unordered taxis turning up during the night, sometimes three or four times a night, to take him to the airport. He would receive calls from strangers enquiring about his health, although he had an unlisted number. A heart specialist came to his house at three o'clock in the morning because he had been told by police headquarters that Whitrod was having a heart attack. He had a large load of gravel he had not purchased dumped on his front garden.

The foundation of Shieber's Algorithm is based on the Earley Parser for CFG, however, it does not require the ID/LP Grammar to be converted into a different grammar in order to be parsed. ID rules can be parsed in a separate form, S ->ID {V, NP, S}, from the LP rules, V < S. Shieber compared parsing of a CFG to an ordered ID/LP Grammar string and Barton compared the parsing of a UCFG to an unordered ID/LP Grammar string.

The Wuhuan, on the other hand, were evidently unprepared for battle as they were not in proper formations, nor did they attempt to take the initiative by harassing Cao Cao's march. Undaunted, Cao Cao climbed a slope to observe the enemy's formations. He saw that the Wuhuan were unordered, and immediately unleashed his soldiers to exploit this weakness. With Cao Cao's general Zhang Liao leading the offensive, the light force swiftly defeated the Wuhuan cavalry, and Cao Chun's brigade captured Tadun.

Whenever index notation is used the indexed objects form a family. For example, consider the following sentence: Here (vi)i ∈ {1, ..., n} denotes a family of vectors. The i-th vector vi only makes sense with respect to this family, as sets are unordered and there is no i-th vector of a set. Furthermore, linear independence is only defined as the property of a collection; it therefore is important if those vectors are linearly independent as a set or as a family.

Their scheme allows these trees to be encoded in a number of bits that is close to the information-theoretic lower bound (the base-2 logarithm of the Wedderburn–Etherington number) while still allowing constant-time navigation operations within the tree.. use unordered binary trees, and the fact that the Wedderburn–Etherington numbers are significantly smaller than the numbers that count ordered binary trees, to significantly reduce the number of terms in a series representation of the solution to certain differential equations..

The names of enumerators need not be semantically complete or compatible in any sense. For example, an enumerated type called color may be defined to consist of the enumerators Red, Green, Zebra, Missing, and Bacon. In some languages, the declaration of an enumerated type also intentionally defines an ordering of its members; in others, the enumerators are unordered; in others still, an implicit ordering arises from the compiler concretely representing enumerators as integers. Some enumerator types may be built into the language.

Its unordered pitch-class content in normal form is 01348 (e.g., C–C–E–E–G), its Forte number is 5-z17,Michiel Schuijer, Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts (Eastman Studies in Music 60), Rochester: University of Rochester Press, 2008, p.109. .Allen Forte, "The Golden Thread: Octatonic Music in Webern's Early Songs, with Certain Historical Reflections", in Webern Studies, edited by Kathryn Bailey, pp.74–110. New York: Cambridge University Press, 1996, p.98n21. .

The traversal maps constitute a partial unary algebra that forms a basis for representing trees as linked data structures. At least conceptually,there are parent links, sibling adjacency links, and first / last child links. This also applies to unordered trees in general, which can be observed on the dentry data structure in the Linux VFS. Similarly to the "V-S-H-L±" system of partial orders, there are pairs of traversal maps that uniquely determine the whole ordered tree structure.

Sauti recites the slokas of the Mahabharata. The text was described by some early 20th-century Indologists as unstructured and chaotic. Hermann Oldenberg supposed that the original poem must once have carried an immense "tragic force" but dismissed the full text as a "horrible chaos."Hermann Oldenberg, Das Mahabharata: seine Entstehung, sein Inhalt, seine Form, Göttingen, 1922, Moritz Winternitz (Geschichte der indischen Literatur 1909) considered that "only unpoetical theologists and clumsy scribes" could have lumped the parts of disparate origin into an unordered whole.

Environmental scanning isn't always as effective or useful in an organizational setting for several reasons. The volume of the information received through the scanning process can be disadvantageous when attempting to translate and make sense of the information as some information may get overlooked or just missed entirely. Because of the volume of information its hard to decipher what is important or not so management and key information may be missed. Another way vital information can be missed is if the information is unordered and unorganized.

Genotypes measure the unordered combination of alleles at each site, whereas haplotypes are the two sequences of alleles that have been inherited together from the individual's parents. When there are N heterozygous genotypes present in an individual's set of genotypes, there will be 2^{N} possible pairs of haplotypes that could underlie the genotypes. For example, when N=2, we have the following haplotypes: AA/TT, AT/TA, TA/AT, and TT/AA. If there are missing genotypes then the number of possible haplotype pairs increases.

Its square is widely called the discriminant, though some sources call the Vandermonde polynomial itself the discriminant. The discriminant (the square of the Vandermonde polynomial: \Delta=V_n^2) does not depend on the order of terms, as (-1)^2=1, and is thus an invariant of the unordered set of points. If one adjoins the Vandermonde polynomial to the ring of symmetric polynomials in n variables \Lambda_n, one obtains the quadratic extension \Lambda_n[V_n]/\langle V_n^2-\Delta\rangle, which is the ring of alternating polynomials.

Scherzo (Allegro moderato in Newbould's edition) in D major, Last 4 measures of the third movement, featuring the motif that opened it (notice the end barline). While being made up of several unordered sections, in Newbould's opinion, the movement is complete. The third movement was at first labelled "scherzo", despite being in . After a writing a few measures, Schubert left it aside, instead filling the page with counterpoint exercises testing the compatibility of the elements, in order to give the original opening a logical continuation.

Rather than acting on segments, phonological processes act on distinctive features within prosodic groups. Prosodic groups can be as small as a part of a syllable or as large as an entire utterance. Phonological processes are unordered with respect to each other and apply simultaneously (though the output of one process may be the input to another). The second most prominent natural phonologist is Patricia Donegan (Stampe's wife); there are many natural phonologists in Europe, and a few in the U.S., such as Geoffrey Nathan.

RELAX NG provides very strong support for unordered content. That is, it allows the schema to state that a sequence of patterns may appear in any order. RELAX NG also allows for non-deterministic content models. What this means is that RELAX NG allows the specification of a sequence like the following: When the validator encounters something that matches the "odd" pattern, it is unknown whether this is the optional last "odd" reference or simply one in the zeroOrMore sequence without looking ahead at the data.

However, AMD has not announced whether ASF will be used in products, and if so, in what timeframe. More recently, IBM announced in 2011 that Blue Gene/Q had hardware support for both transactional memory and speculative multithreading. The transactional memory could be configured in two modes; the first is an unordered and single- version mode, where a write from one transaction causes a conflict with any transactions reading the same memory address. The second mode is for speculative multithreading, providing an ordered, multi-versioned transactional memory.

It is often desirable to know the unordered amino acid composition of a protein prior to attempting to find the ordered sequence, as this knowledge can be used to facilitate the discovery of errors in the sequencing process or to distinguish between ambiguous results. Knowledge of the frequency of certain amino acids may also be used to choose which protease to use for digestion of the protein. The misincorporation of low levels of non-standard amino acids (e.g. norleucine) into proteins may also be determined.

Hall of Fame museum curator James Henke, along with "the museum's curatorial staff and numerous rock critics and music experts", created an unordered list of "500 Songs That Shaped Rock and Roll". The list is part of a permanent exhibit at the museum, and was envisioned as part of the museum from its opening in 1995. It contains songs recorded from the 1920s through the 1990s. The oldest song on the list is "Wabash Cannonball", written circa 1882 and credited to J. A. Roff.

Immunogens can be targeted to various cellular compartments to improve antibody or cytotoxic T-cell responses. Secreted or plasma membrane-bound antigens are more effective at inducing antibody responses than cytosolic antigens, while cytotoxic T-cell responses can be improved by targeting antigens for cytoplasmic degradation and subsequent entry into the major histocompatibility complex (MHC) class I pathway. This is usually accomplished by the addition of N-terminal ubiquitin signals. The conformation of the protein can also affect antibody responses. “Ordered” structures (such as viral particles) are more effective than unordered structures.

A typical example of a monotone function is the following function on the cycle with 6 elements: : : : A function is called an embedding if it is both monotone and injective. Equivalently, an embedding is a function that pushes forward the ordering on : whenever , one has . As an important example, if is a subset of a cyclically ordered set , and is given its natural ordering, then the inclusion map is an embedding. Generally, an injective function from an unordered set to a cycle induces a unique cyclic order on that makes an embedding.

We take a tree where each node has an arbitrary degree of unordered nodes and split it into paths. We call this the represented tree. These paths are represented internally by auxiliary trees (here we will use splay trees), where the nodes from left to right represent the path from root to the last node on the path. Nodes that are connected in the represented tree that are not on the same preferred path (and therefore not in the same auxiliary tree) are connected via a path-parent pointer.

Consider the general case when the input to the algorithm is a finite unordered set of points on a Cartesian plane. An important special case, in which the points are given in the order of traversal of a simple polygon's boundary, is described later in a separate subsection. If not all points are on the same line, then their convex hull is a convex polygon whose vertices are some of the points in the input set. Its most common representation is the list of its vertices ordered along its boundary clockwise or counterclockwise.

The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that. One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well.

The number of distinct operations in a system that map a set into itself is the set's degree of symmetry . The degree of symmetry, "specifies the number of operations that preserve the unordered pcsets of a partition; it tells the extent to which that partition's pitch- class sets map into (or onto) each other under transposition or inversion". Every set has at least one symmetry, as it maps onto itself under the identity operation T . Transpositionally symmetric sets map onto themselves for T where does not equal 0 (mod 12).

The problem of synchronizing unordered data (also known as the set reconciliation problem) is modeled as an attempt to compute the symmetric difference S_A \oplus S_B = (S_A - S_B) \cup (S_B - S_A) between two remote sets S_A and S_B of b-bit numbers. Some solutions to this problem are typified by: ;Wholesale transfer: In this case all data is transferred to one host for a local comparison. ;Timestamp synchronization: In this case all changes to the data are marked with timestamps. Synchronization proceeds by transferring all data with a timestamp later than the previous synchronization.

From the fragments of unordered scenes left by Büchner, Berg selected 15 to form a compact structure of three acts with five scenes each. He adapted the libretto himself, retaining "the essential character of the play, with its many short scenes, its abrupt and sometimes brutal language, and its stark, if haunted, realism..."Walsh, pp. 61–63 The plot depicts the everyday lives of soldiers and the townspeople of a rural German-speaking town. Prominent themes of militarism, callousness, social exploitation, and casual sadism are brutally and uncompromisingly presented.

The long stem of a verb is the one that is formed by attaching - -eo/-a after a consonant. Both sometimes called gerunds, the verb form that ends in se and the one that ends in -ko juxtapose two actions, the action in the subclause and the action in the main clause. The difference between them is that with se the action in the subclause necessarily came first, while -ko conveys more of an unordered juxtaposition. se is frequently used to imply causation, and is used in many common expressions like manna se pan.

I was surprised." Paul Cooper of Pitchfork felt the album was "ambitious and innovative." In 1999, French magazine Trax included the album in their unordered list of "The 50 Best Techno Albums 1989-1989," while in 2017, Mixmag ranked the album at number 5 in their list of "The 10 best 90s techno albums". They said Slater delivered an "epic" album where "every track is potent to keep listeners locked in," and felt that the record "sounds like an invasion from an off-world colony of dance freaks.

For a binary (two-state) character, this makes little difference. For a multi-state character, unordered characters can be thought of as having an equal "cost" (in terms of number of "evolutionary events") to change from any one state to any other; complementarily, they do not require passing through intermediate states. Ordered characters have a particular sequence in which the states must occur through evolution, such that going between some states requires passing through an intermediate. This can be thought of complementarily as having different costs to pass between different pairs of states.

If the notes are ordered, a decatonic set has 3,628,800 permutations,Wyble, Jimmy (2011). Concepts for the Classical and Jazz Guitar, p.2. Mel Bay. . however, in twelve tone equal temperament only six unordered ten note sets exist, 10-1—10-6: # (all pitch classes but t & e) # (all but 9 & e) # (all but 8 & e) # (all but 7 & e) # (all but 6 & e) # (all but 5 & e) Given that two of the notes from the chromatic scale are missing and only two whole tones are possible, all 10-note scales are cohemitonic scales.

Acknowledged as one of the best aerobatic pilots in the UK, S/L Janusz Żurakowski from the A&AEE; at RAF Boscombe Down gave a spectacular display at the Farnborough Air Show in June 1946, with the Martin-Baker MB 5, an aircraft he considered superlative and better in many ways than the Spitfire. An MB 5 replica, nearing completion . If serial production had been authorised, the aircraft would have served over Germany during WW2. Instead, the RAF directed its attention towards jet-powered fighters with the MB 5 remaining unordered.

Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation (also called rotation), or multiplicative operations (such as the cycle of fourths and cycle of fifths transforms). These may produce reorderings of the members of the set, or may simply map the set onto itself. Order is particularly important in the theories of composition techniques originating in the 20th century such as the twelve-tone technique and serialism. Analytical techniques such as set theory take care to distinguish between ordered and unordered collections.

OPUS is an efficient algorithm for rule discovery that, in contrast to most alternatives, does not require either monotone or anti-monotone constraints such as minimum support.Webb, Geoffrey I. (1995); OPUS: An Efficient Admissible Algorithm for Unordered Search, Journal of Artificial Intelligence Research 3, Menlo Park, CA: AAAI Press, pp. 431-465 online access Initially used to find rules for a fixed consequent it has subsequently been extended to find rules with any item as a consequent. OPUS search is the core technology in the popular Magnum Opus association discovery system.

Englewood Cliffs, New Jersey: Prentice-Hall. . Prime form of five pitch class set from Igor Stravinsky's In memoriam Dylan ThomasWhittall (2008), p.127. Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form A set by itself does not necessarily possess any additional structure, such as an ordering or permutation. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.

The predecessor to BLAST, FASTA, can also be used for protein and DNA similarity searching. FASTA provides a similar set of programs for comparing proteins to protein and DNA databases, DNA to DNA and protein databases, and includes additional programs for working with unordered short peptides and DNA sequences. In addition, the FASTA package provides SSEARCH, a vectorized implementation of the rigorous Smith- Waterman algorithm. FASTA is slower than BLAST, but provides a much wider range of scoring matrices, making it easier to tailor a search to a specific evolutionary distance.

Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, for locating a given value in an unordered table. When it is applicable, however, backtracking is often much faster than brute force enumeration of all complete candidates, since it can eliminate many candidates with a single test. Backtracking is an important tool for solving constraint satisfaction problems, such as crosswords, verbal arithmetic, Sudoku, and many other puzzles.

Problems which are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit probably can't be efficiently simulated on classical computers (see Quantum supremacy). The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or an unordered list. Shor's algorithms runs much (almost exponentially) faster than the best-known classical algorithm for factoring, the general number field sieve.

Some strikers attempted to wrest the rifles from the soldiers, and one was injured in the advance of bayonets. A cry arose of "Stick to it; give it to them; don't fall back!" and some protesters began to throw rocks and fire pistols at the troops; several men were injured, at least one seriously. The troops returned fire and used their bayonets, beginning with a single unordered shot, and continuing in a volley for nearly ten minutes. When the firing ceased, an estimated 20 men, women and children had been killed, with another 29 wounded.

VPEC-T ("vee-pec-tee") is used where interaction between agents and communication between parties can easily result in ambiguity. This form of analysis is particularly applicable where it is likely that the interaction and communication context is unordered, complex or chaotic, and liable to result in misunderstanding. It is identified as a new way of carrying out enterprise architecture, and also identified as a way to design services. VPEC-T was first conceived as a framework to aid those studying information systems, where the conflicting viewpoints of the parties involved could be a barrier to proper understanding.

"Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the ostinato". Additionally, John Covach argues that the strict distinction between the two, emphasized by authors including Perle, is overemphasized: > The distinction often made between Hauer and the Schoenberg school—that the > former's music is based on unordered hexachords while the latter's is based > on an ordered series—is false: while he did write pieces that could be > thought of as "trope pieces", much of Hauer's twelve-tone music employs an > ordered series.John Covach quoted in Whittall 2008, 24.

A GraphML file consists of an XML file containing a `graph` element, within which is an unordered sequence of `node` and `edge` elements. Each `node` element should have a distinct `id` attribute, and each `edge` element has `source` and `target` attributes that identify the endpoints of an edge by having the same value as the `id` attributes of those endpoints. Here is what a simple undirected graph with two nodes and one edge between them looks like: Additional features of the GraphML language allow its users to specify whether edges are directed or undirected, and to associate additional data with vertices or edges.

When he finds out that she cannot be admitted against her will, he is determined to help her "hit rock bottom", as he somewhat proudly mentions he was able to do with Jan.The Office - Season 5 In the episode "The Promotion" it's revealed that Creed and Meredith have had sex. Creed didn't remember this until he makes another pass at her.The Office - Season 6 In the season seven episode "PDA" Dwight reads an unordered list of people who have had sex in the office which includes Meredith and Creed, meaning that they possibly had sex together in the office.

It is relatively easy to generate three-taxon statements (3is); that is, statements of the form "A and B are more closely related to one another than to C". Once each group of three taxa has been considered, the method constructs a tree that is consistent with as many three-item statements as possible. Computer program that implement three-taxon analysis is LisBeth (for systematic and biogeographic studies). LisBeth have been freely released. A recent simulation-based study found that Three-taxon analysis yields good power and an error rate intermediate between parsimony with ordered states and parsimony with unordered states.

As grāmya is constantly threatened by encroachment, disease, hunger and death form jāṅgala and āraṇya, so is the tangible world under constant threat from the intangible world of the spirits. The world of the forest is the "world of the wild, unordered, uncontrolled, hungry beings of destruction". The world of the forest and the world of the spirits are therefore seen as mirror images of each other. The wild animals threatening the human cultivator and his fields such as the tiger, the snake, the wild- boar, and the bison, find their mirror images in their corresponding būtas Pilli, Naga, Paňjurli and Maisandaya.

M23 is the point stabilizer of the action of the Mathieu group M24 on 24 points, giving it a 4-transitive permutation representation on 23 points with point stabilizer the Mathieu group M22. M23 has 2 different rank 3 actions on 253 points. One is the action on unordered pairs with orbit sizes 1+42+210 and point stabilizer M21.2, and the other is the action on heptads with orbit sizes 1+112+140 and point stabilizer 24.A7. The integral representation corresponding to the permutation action on 23 points decomposes into the trivial representation and a 22-dimensional representation.

When viewing ƒ as a labelling of the elements of N, the latter may be thought of as arranged in a sequence, and the labels as being successively assigned to them. A requirement that ƒ be injective means that no label can be used a second time; the result is a sequence of labels without repetition. In the absence of such a requirement, the terminology "sequences with repetition" is used, meaning that labels may be used more than once (although sequences that happen to be without repetition are also allowed). For an unordered selection the same kind of distinction applies.

While the link between signified and signifier (as per Saussure) may be separately represented in a junction grammar, the interfacing between J-rule structuring and the coding extant in other components of the model is provided by context-sensitive coding grammars formulated as algorithms in an appropriate pattern matching language. For example, JG incorporates a lexical coding grammar consisting of lexical rules (L-rules) which encodes unordered sememic structuring as ordered lexical strings in a separate coding space.See, for example, Billings, Floyd and Thompson, Tracy (1972). “Proposals for Ordering Well-formed Syntactic Statements.” LINGUISTICS SYMPOSIUM: AUTOMATIC LANGUAGE PROCESSING, 30–31 March 1972.

Scheduling parent-teacher conferences involves finding a time that suits both parents and teachers with their existing time constraints and finding locations for the meetings. If all meetings would be independent without any dependencies, the planning of the meetings simplifies to unordered timetabling rather than full-scale scheduling where events need to be scheduled in a certain order, often because the output of one event forms an input for another. In most cases, certain dependencies exist: parents prefer not to wait too long between different interviews but need long enough breaks to move from one location to another or locations in close proximity.

In terms of the relational model of databases, a table can be considered a convenient representation of a relation, but the two are not strictly equivalent. For instance, a SQL table can potentially contain duplicate rows, whereas a true relation cannot contain duplicate rows that we call as tuples. Similarly, representation as a table implies a particular ordering to the rows and columns, whereas a relation is explicitly unordered. However, the database system does not guarantee any ordering of the rows unless an `ORDER BY` clause is specified in the `SELECT` statement that queries the table.

They can also be finite, countably infinite, or uncountably infinite. For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}, commonly written {H, T}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}. If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}. For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).

Serialism is one of the most important post-war movements among the high modernist schools. Serialism, more specifically named "integral" or "compound" serialism, was led by composers such as Pierre Boulez, Bruno Maderna, Luigi Nono, and Karlheinz Stockhausen in Europe, and by Milton Babbitt, Donald Martino, Mario Davidovsky, and Charles Wuorinen in the United States. Some of their compositions use an ordered set or several such sets, which may be the basis for the whole composition, while others use "unordered" sets. The term is also often used for dodecaphony, or twelve-tone technique, which is alternatively regarded as the model for integral serialism.

In number theory, a multiplicative partition or unordered factorization of an integer n is a way of writing n as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number n is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions, discussed in , which are additive partitions of finite sequences of positive integers, with the addition made pointwise. Although the study of multiplicative partitions has been ongoing since at least 1923, the name "multiplicative partition" appears to have been introduced by .

Recall that an edge in a tree is an unordered set of two nodes. Each edge in a vine is associated with a constraint set, being the set of variables (nodes in first tree) reachable by the set membership relation. For each edge, the constraint set is the union of the constraint sets of the edge's two members called its component constraint sets (for an edge in the first tree, the component constraint sets are empty). The constraint associated with each edge is now the symmetric difference of its component constraint sets conditional on the intersection of its constraint sets.

Narrative is an elementary need of people, according to the "homo narrans" theory, and personal narrative is the "paradigm of human communication," one of the main activities performed on a daily basis. Narratives have the power to lend orderliness to unordered experiences, personal narratives reflect social organization and cultural values, and are intertwined with social evaluation of people and their actions. At the core of personal narrative is a moral evaluation of self. The moral proposition present in all first-person narratives is, "I am a good person," or that the speaker acted wrong, and learned what was right.

Pitchfork Media named the song the sixth best song of 2010, with the staff writing "it's all of My Beautiful Dark Twisted Fantasy's pathology and genius in digest form, the vicarious, timeless thrill of hearing a crazy talented person act crazy and talented." Rolling Stone placed the song at position 40 amongst their 50 best tracks of the year. The song was on an unordered list of the 20 best songs of the year by Spin, with critic Charles Aaron musing that "as if he's inciting an Afro-futurist convocation, Kanye creates the theme music for his spectacularly ambivalent "superhero" alter ego."Aaron, Charles (2010-12-08).

In computer science, a search data structure is any data structure that allows the efficient retrieval of specific items from a set of items, such as a specific record from a database. The simplest, most general, and least efficient search structure is merely an unordered sequential list of all the items. Locating the desired item in such a list, by the linear search method, inevitably requires a number of operations proportional to the number n of items, in the worst case as well as in the average case. Useful search data structures allow faster retrieval; however, they are limited to queries of some specific kind.

That is, an ordered n-tuple is in the same orbit as any other that is a re-ordered version of it. A path in the n-fold symmetric product is the abstract way of discussing n points of X, considered as an unordered n-tuple, independently tracing out n strings. Since we must require that the strings never pass through each other, it is necessary that we pass to the subspace Y of the symmetric product, of orbits of n-tuples of distinct points. That is, we remove all the subspaces of X^n defined by conditions x_i = x_j for all 1\le i.

Genetic data are particularly amenable to character-based phylogenetic methods such as maximum parsimony because protein and nucleotide sequences are naturally discrete: A particular position in a nucleotide sequence can be either adenine, cytosine, guanine, or thymine / uracil, or a sequence gap; a position (residue) in a protein sequence will be one of the basic amino acids or a sequence gap. Thus, character scoring is rarely ambiguous, except in cases where sequencing methods fail to produce a definitive assignment for a particular sequence position. Sequence gaps are sometimes treated as characters, although there is no consensus on how they should be coded. Characters can be treated as unordered or ordered.

In the eye-color example above, it is possible to leave it unordered, which imposes the same evolutionary "cost" to go from brown-blue, green-blue, green-hazel, etc. Alternatively, it could be ordered brown-hazel-green-blue; this would normally imply that it would cost two evolutionary events to go from brown-green, three from brown-blue, but only one from brown-hazel. This can also be thought of as requiring eyes to evolve through a "hazel stage" to get from brown to green, and a "green stage" to get from hazel to blue, etc. For many characters, it is not obvious if and how they should be ordered.

In a recursive tree with n vertices, the vertices are labeled by the numbers from 1 to n, and the labels must decrease along any path to the root of the tree. These trees are unordered, in the sense that there is no distinguished ordering of the children of each vertex. In a random recursive tree, all such trees are equally likely. Alternatively, a random recursive tree can be generated by starting from a single vertex, the root of the tree, labeled 1, and then for each successive label from 2 to n choosing a random vertex with a smaller label to be its parent.

A directed graph with three vertices (blue circles) and three edges (black arrows). In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points), together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as edges (also called links or lines), and for a directed graph are also known as arrows.

The problem of computing the kth smallest (or largest) element of a list is called the selection problem and is solved by a selection algorithm. Although this problem is difficult for very large lists, sophisticated selection algorithms have been created that can solve this problem in time proportional to the number of elements in the list, even if the list is totally unordered. If the data is stored in certain specialized data structures, this time can be brought down to O(log n). In many applications all order statistics are required, in which case a sorting algorithm can be used and the time taken is O(n log n).

In Bayesian spam filtering, an e-mail message is modeled as an unordered collection of words selected from one of two probability distributions: one representing spam and one representing legitimate e-mail ("ham"). Imagine there are two literal bags full of words. One bag is filled with words found in spam messages, and the other with words found in legitimate e-mail. While any given word is likely to be somewhere in both bags, the "spam" bag will contain spam-related words such as "stock", "Viagra", and "buy" significantly more frequently, while the "ham" bag will contain more words related to the user's friends or workplace.

ATS at Work, (1943) After the war, he was professor of painting at the Royal College of Art 1948–1957, and was elected a full member of the Royal Academy in 1954. At this period, he was in demand for official portraits, and executed commissions of amongst others Princess Elizabeth (1946) and Prime Minister Clement Attlee (1947). He changed direction from 1957, resigning from the Royal College of Art and the Royal Academy and returning to abstraction, working outside England in Europe and North America. From 1971 onwards he was inspired to return to figurative painting in the form of large-scale studio still-lives, unordered, unarranged and apparently random.

This corps was created on October 10, 1863, from the remnants of XX and XXI Corps, both of which had suffered heavy casualties at Chickamauga. It was initially commanded by Gordon Granger and its division commanders were Philip Sheridan, Charles Cruft, and Thomas J. Wood. It served with distinction in the famous unordered attack on Missionary Ridge at Chattanooga, and served in the Knoxville and Atlanta Campaigns. During John B. Hood's Franklin-Nashville Campaign, General William T. Sherman left the IV (and XXIII Corps), under the overall command of General George H. Thomas, to defend Tennessee, and the corps was heavily engaged in the battles at Spring Hill, Franklin, and Nashville.

Satyricon is a chamber opera by Bruno Maderna with a libretto adapted by Ian Strasfogel and the composer from Petronius. It was written during Maderna's last illness in 1973 and premièred as part of the Holland Festival on 16 March 1973, in Scheveningen, Netherlands. The work consists of 16 unordered numbers (with the option of placing taped numbers between them) and the collage effect extends to the music, which relies heavily on pastiche. It is uncertain to what extent this "open" form was a product of the composer’s inclination to semi-improvisational music theatre, or to the urgency of composition at a time when Maderna’s terminal illness was increasingly becoming evident .

An algorithm is said to be constant time (also written as O(1) time) if the value of T(n) is bounded by a value that does not depend on the size of the input. For example, accessing any single element in an array takes constant time as only one operation has to be performed to locate it. In a similar manner, finding the minimal value in an array sorted in ascending order; it is the first element. However, finding the minimal value in an unordered array is not a constant time operation as scanning over each element in the array is needed in order to determine the minimal value.

Both of these individual histories are represented by the global history bcbdddcced, since the projection of this string onto the individual alphabets yields the individual histories. In the global history, the letters b and c can be considered to commute with the letters d and e, in that these can be rearranged without changing the individual histories. Such commutation is simply a statement that the first and second processes are running concurrently, and are unordered with respect to each other; they have not (yet) exchanged any messages or performed any synchronization. The letter a serves as a synchronization primitive, as its occurrence marks a spot in both the global and individual histories, that cannot be commuted across.

A new genus for non-spiniferous species could be phylogenetically supported, but transferring the new genus to the Slimonidae based on the loss of a feature which seems to have been lost independently in the two groups is not in line with common practice. The cladogram below displays the results of a phylogenetic analysis conducted by O. Erik Tetlie and Markus Poschmann in 2008, featuring seven species of Adelophthalmus and excluding other species on the grounds that they were too incompletely known. All characters were treated as unordered and given equal weight. Orcanopterus, part of a clade that also contains Grossopterus and Waeringopterus, was included in the analysis as an outgroup to polarise the characters.

M11 has a sharply 4-transitive permutation representation on 11 points, whose point stabilizer is sometimes denoted by M10, and is a non-split extension of the form A6.2 (an extension of the group of order 2 by the alternating group A6). This action is the automorphism group of a Steiner system S(4,5,11). The induced action on unordered pairs of points gives a rank 3 action on 55 points. M11 has a 3-transitive permutation representation on 12 points with point stabilizer PSL2(11). The permutation representations on 11 and 12 points can both be seen inside the Mathieu group M12 as two different embeddings of M11 in M12, exchanged by an outer automorphism.

In that case the computed integral can be assigned into its position in the array of two electron integrals by computing the required index from the p,q,r and s indices. In the 1960s it was essentially impossible to hold all of the two electron integrals in memory simultaneously. Therefore, M Yoshimine developed a sorting algorithm for two- electron integrals which reads the unordered list of integrals from a files and transforms it into an ordered list which is then written to another file. A by-product of this is that the file storing the ordered integrals does not need to contain the p,q,r,s indices for each integral.

A special case of racemic compounds are kryptoracemic compounds (or kryptoracemates), in which the crystal itself has handedness (is enantiomorphic), despite containing both enantiomorphs in a 1:1 ratio. ;Pseudoracemate (sometimes racemic solid solution): When there is no big difference in affinity between the same and opposite enantiomers, then in contrast to the racemic compound and the conglomerate, the two enantiomers will coexist in an unordered manner in the crystal lattice. Addition of a small amount of one enantiomer changes the melting point slightly or not at all. ;Quasiracemate: A quasiracemate is a co-crystal of two similar but distinct compounds, one of which is left-handed and the other right-handed.

The EcmaScript 6 standard has `for..of` for index-less iteration over generators, arrays and more: for (var item of array){ // Do stuff } Alternatively, function-based style: array.forEach(item => { // Do stuff }) For unordered iteration over the keys in an Object, JavaScript features the `for...in` loop: for (var key in object) { // Do stuff with object[key] } To limit the iteration to the object's own properties, excluding those inherited through the prototype chain, it is sometimes useful to add a hasOwnProperty() test, if supported by the JavaScript engine (for WebKit/Safari, this means "in version 3 or later"). for (var key in object) { if (object.hasOwnProperty(key)) { // Do stuff with object[key] } } ECMAScript 5 provided Object.

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.

The VOTable Working Group is in charge of the VOTable format, which is an XML standard for the interchange of data represented as a set of tables.Francois Ochsenbein & Roy Williams, IVOA VOTable Format Definition, "IVOA", 30/11/2009 In this context, a table is an unordered set of rows, each of a uniform format, as specified in the table metadata. Each row in a table is a sequence of table cells, and each of these contains either a primitive data type, or an array of such primitives. VOTable is derived from the Astrores format, itself modelled on the FITS Table format; VOTable was designed to be closer to the FITS Binary Table format.

Writing for Melody Maker in October 1997, Robin Bresnark gave Life thru a Lens a negative review; "There's nothing here... sure, Robbie Williams is as fascinating a hapless goon as we're ever likely to come across. But this album feels more like a press release than an album – and that's not what I call music." However, John Bush of AllMusic was very positive in his four and a half stars out of five review, calling the album "excellent" and "one of the best U.K. debuts of the '90s". Q ranked the album at number 43 in their 2004 list of "The 50 (+50) Best British Albums Ever" and in their unordered 2005 list of the "Ultimate Music Collection".

The term is derived by analogy from the 20th-century use of the word "tetrachord". Unlike the tetrachord and hexachord, there is no traditional standard scale arrangement of three notes, nor is the trichord necessarily thought of as a harmonic entity . Milton Babbitt's serial theory of combinatoriality makes much of the properties of three-note, four-note, and six-note segments of a twelve-tone row, which he calls, respectively, trichords, tetrachords, and hexachords, extending the traditional sense of the terms and retaining their implication of contiguity. He usually reserves the term "source set" for their unordered counterparts (especially hexachords), but does occasionally employ terms such as "source tetrachords" and "combinatorial trichords, tetrachords, and hexachords" instead (; ; ).

All known ribotoxins are proteins of between 130 and 150 amino acids that share at least two different elements of ordered secondary structure: a β-sheet, where the active center is located, and a short α-helix. The structural arrangement is very similar to that of other extracellular fungal RNases, which are not toxic, and constitute a family whose best known representative is the RNase T1 of Aspergillus oryzae. This explains why ribotoxins are considered the toxic representatives of the group. The observation of their three-dimensional structures reveals their functional differences in terms of toxicity, since ribotoxins present unordered, positively charged long loops, which are much shorter, and negatively charged, in their non-toxic "relatives".

The pyknon was an important criterion in the classification of melodic genera (). The Greek word πυκνόν is an adjective meaning "close", "compact", "close-packed", or "crowded" . In Ancient Greek music theory, this term is used to describe a pair of intervals within a tetrachord, the sum of which is less than the remainder of the tetrachord . Although in modern usage, a tetrachord may be any four-note segment of a scale, or indeed any (unordered) collection of four pitch classes, in ancient Greek music theory a tetrachord consists of a four- note segment of the Greater and Lesser Perfect Systems bounded by the interval of a perfect fourth, the outer notes of which remain fixed in all genera and therefore are called "standing notes" ().

The "strict ordering" of the Second Viennese school, on the other hand, "was inevitably tempered by practical considerations: they worked on the basis of an interaction between ordered and unordered pitch collections."Whittall 2008, 24. Rudolph Reti, an early proponent, says: "To replace one structural force (tonality) by another (increased thematic oneness) is indeed the fundamental idea behind the twelve-tone technique", arguing it arose out of Schoenberg's frustrations with free atonality,Reti 1958 providing a "positive premise" for atonality. In Hauer's breakthrough piece Nomos, Op. 19 (1919) he used twelve- tone sections to mark out large formal divisions, such as with the opening five statements of the same twelve-tone series, stated in groups of five notes making twelve five-note phrases.

ID and LP rules impose constraints on sentence strings; when dealing with large strings, the constraints of these rules can cause the parsed string to become infinite, thus making parsing difficult. The Earley Parser solves this by altering the format of an ID/LP Grammar into a Context Free Grammar (CFG), dividing the ID/LP Grammar into an Ordered Context Free Grammar (CFG) and Unordered Context Free Grammar (UCFG). This allows the two algorithms to parse strings more efficiently; in particular, the Earley Parser uses a point tracking method that follows a linear path established by the LP rules. In a CFG, LP rules do not allow repeated constituents in the parsed string, but an UCFG allows repeated constituents within the parsed strings.

Brahms wrote the waltzes rather quickly in the summer of 1869 as an unordered set of dances, with little regard for their ultimate arrangement. Likely he thought a home performer would simply pick and choose their favorites to be performed. The uncertainty of the ordering, grouping, and number of volumes lead to lengthy correspondence with his publisher, Simrock, with changes made up until the first performance, and within his own copy of the published first edition. The waltzes exist today in a single set of 18, but it is evident that Brahms made accommodations for the possibility of two books of nine waltzes, or even three books of six waltzes, giving numbers 6, 9, and 18 a particular sense of closure in their phrasing, gestures, and structure.

Entertainment Weekly included the album in its 2013 list of the 100 Greatest Albums Ever at number 78. In an unordered list of 500 essential albums compiled for Vanity Fair in 2013, English musician Elvis Costello included Post and mentioned "Hyperballad" as a highlight of the record. In the album's entry of the "Women Who Rock: The 50 Greatest Albums of All Time" list of 2012, Rolling Stone felt, "Björk's artistic stature grew by yards in the course of this strange, affecting work, by turns harshly industrial, meditative and neon jubilant." The album's influence has been identified as being increasingly palpable on the contemporary music landscape, and later reviews of the album also make note of the timeless aspect of the music.

With Theodore Slaman, Groszek showed that (if they exist at all) non-constructible real numbers must be widespread, in the sense that every perfect set contains one of them, and they asked analogous questions of the non-computable real numbers. With Slaman, she has also shown that the existence of a maximally independent set of Turing degrees, of cardinality less than the cardinality of the continuum, is independent of ZFC. In the theory of ordinal definable sets, an unordered pair of sets is said to be a Groszek–Laver pair if the pair is ordinal definable but neither of its two elements is; this concept is named for Groszek and Richard Laver, who observed the existence of such pairs in certain models of set theory.

The values are used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter storage addressing. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval, and storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space efficient form of data access which avoids the non-linear access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys.

In data storage and retrieval applications, use of a hash function is a trade off between search time and data storage space. If search time were unbounded, a very compact unordered linear list would be the best medium; if storage space were unbounded, a randomly accessible structure indexable by the key value would be very large, very sparse, but very fast. A hash function takes a finite amount of time to map a potentially large key space to a feasible amount of storage space searchable in a bounded amount of time regardless of the number of keys. In most applications, it is highly desirable that the hash function be computable with minimum latency and secondarily in a minimum number of instructions.

The significance of SMT is to significantly shift the previous emphasis on universal grammars to the concept which Chomsky and Berwick now call "merge". "Merge" is defined in their 2016 book when they state "Every computational system has embedded within it somewhere an operation that applies to two objects X and Y already formed, and constructs from them a new object Z. Call this operation Merge." SMT dictates that "Merge will be as simple as possible: it will not modify X or Y or impose any arrangement on them; in particular, it will leave them unordered, an important fact... Merge is therefore just set formation: Merge of X and Y yields the set {X, Y}."Chomsky and Berwick. Why Only Us?.

" In 2019, Pitchforks Mark Richardson wrote that the album was "weirdly beautiful and impossible... a place where the musical values of the past (instrumental proficiency, deliberate composition) met the digital future". In their lists of the best albums of 1998, TNT was ranked 12th by Magic, 32nd by Spex, 37th by Les Inrockuptibles and 58th by Muzik, and was also included in the unordered lists of 1998's best albums by Magnet and The Wire. The New York Times Neil Strauss ranked the album as the 5th best of 1998. In 2003, Pitchfork ranked the album at number 91 in its list of the "Top 100 Albums of the 1990s", with William Morris saying that "TNT was like a hypnotic snowglobe that refused to settle without ever having required shaking.

Many of the notions were first elaborated by Howard Hanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that. One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.

The model was proposed by Audrius Meškauskas and David Moore in 2004 and developed using the supercomputing facilities of the University of Manchester. The key idea of this model is that all parts of the fungal mycelium have identical field generation systems, field sensing mechanisms and growth direction altering algorithms. Under properly chosen model parameters it is possible to observe the transformation of the initial unordered mycelium structure into various forms, some of them being very like natural fungal fruit bodies and other complex structures. In one of the simplest examples, it is assumed that the hyphal tips try to keep a 45 degree orientation with relation to the Earth’s gravity vector field, and also generate some kind of scalar field that the growing tips try to avoid.

If one then also identified , then one obtains the Möbius strip. The diagonal of the square (the points where both coordinates agree) becomes the boundary of the Möbius strip, and carries an orbifold structure, which geometrically corresponds to "reflection" – geodesics (straight lines) in the Möbius strip reflect off the edge back into the strip. Notationally, this is written as T2/S2 – the 2-torus quotiented by the group action of the symmetric group on two letters (switching coordinates), and it can be thought of as the configuration space of two unordered points on the circle, possibly the same (the edge corresponds to the points being the same), with the torus corresponding to two ordered points on the circle. The Möbius strip is a two- dimensional compact manifold (i.e.

In music, unified field is the 'unity of musical space' created by the free use of melodic material as harmonic material and vice versa. The technique is most associated with the twelve-tone technique, created by its 'total thematicism' where a tone-row (melody) generates all (harmonic) material. It was also used by Alexander Scriabin, though from a diametrically opposed direction, created by his use of extremely slow harmonic rhythm which eventually led to his use of unordered pitch-class sets, usually hexachords (of six pitches) as harmony from which melody may also be created. (Samson 1977) It may also be observed in Igor Stravinsky's Russian period, such as in Les Noces, derived from his use of folk melodies as generating material and influenced by shorter pieces by Claude Debussy, such as Voiles, and Modest Mussorgsky.

Symbolically, Tn = (S1)n. The configuration space of unordered, not necessarily distinct points is accordingly the orbifold Tn/Sn, which is the quotient of the torus by the symmetric group on n letters (by permuting the coordinates). For n = 2, the quotient is the Möbius strip, the edge corresponding to the orbifold points where the two coordinates coincide. For n = 3 this quotient may be described as a solid torus with cross-section an equilateral triangle, with a twist; equivalently, as a triangular prism whose top and bottom faces are connected with a 1/3 twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical.

Olivier Messiaen's unordered series for pitch, duration, dynamics, and articulation from the pre-serial Mode de valeurs et d'intensités, upper division only—which Pierre Boulez adapted as an ordered row for his Structures I Punctualism (commonly also called "pointillism" or "point music") is a style of musical composition prevalent in Europe between 1949 and 1955 "whose structures are predominantly effected from tone to tone, without superordinate formal conceptions coming to bear" . In simpler terms: "music that consists of separately formed particles—however complexly these may be composed—[is called] punctual music, as opposed to linear, or group-formed, or mass-formed music" (, bolding in the source). This was accomplished by assigning to each note in a composition values drawn from scales of pitch, duration, dynamics, and attack characteristics, resulting in a "stronger individualizing of separate tones" . Another important factor was maintaining discrete values in all parameters of the music.

Linguistic models in MTT operate on the principle that language consists in a mapping from the content or meaning (semantics) of an utterance to its form or text (phonetics). Intermediate between these poles are additional levels of representation at the syntactic and morphological levels. Levels of representation in MTT Representations at the different levels are mapped, in sequence, from the unordered network of the semantic representation (SemR) through the dependency tree-structures of the syntactic representation (SyntR) to a linearized chain of morphemes of the morphological representation (MorphR) and, ultimately, the temporally-ordered string of phones of the phonetic representation (PhonR) (not generally addressed in work in this theory). The relationships between representations on the different levels are considered to be translations or mappings, rather than transformations, and are mediated by sets of rules, called "components", which ensure the appropriate, language-specific transitions between levels.

In some applications it may make sense to distinguish subtypes of unrooted binary trees: a planar embedding of the tree may be fixed by specifying a cyclic ordering for the edges at each vertex, making it into a plane tree. In computer science, binary trees are often rooted and ordered when they are used as data structures, but in the applications of unrooted binary trees in hierarchical clustering and evolutionary tree reconstruction, unordered trees are more common. Additionally, one may distinguish between trees in which all vertices have distinct labels, trees in which the leaves only are labeled, and trees in which the nodes are not labeled. In an unrooted binary tree with n leaves, there will be n − 2 internal nodes, so the labels may be taken from the set of integers from 1 to 2n − 1 when all nodes are to be labeled, or from the set of integers from 1 to n when only the leaves are to be labeled..

The Wire and AllMusic also included the album in their unordered lists of the best albums of the year. Numerous publications included Madvillainy in various lists of the best albums. Clash positioned it at number 47 in their list of top 100 albums of Clash lifetime, calling it "slapdash and dilapidated, wholly unconcerned with making sense", "defined by its flippancy and attitude to professionalism". The magazine also listed it on their list of ten best hip hop albums ever, calling it "one of this decade’s finest hip-hop albums" that "elevated the profile of both [artists] to whole new levels". Complex placed the album in their list of 100 best albums available on Spotify, calling it "dusty, weeded up, 22-song masterpiece that stood alone and brought us all into its own little world" and stating that "Madlib and MF Doom's classic wasn't meant for the radio, but it was too good to be kept to the underground".

Ancient writers refer to other works of Apollonius that are no longer extant: # Περὶ τοῦ πυρίου, On the Burning-Glass, a treatise probably exploring the focal properties of the parabola # Περὶ τοῦ κοχλίου, On the Cylindrical Helix (mentioned by Proclus) # A comparison of the dodecahedron and the icosahedron inscribed in the same sphere # Ἡ καθόλου πραγματεία, a work on the general principles of mathematics that perhaps included Apollonius's criticisms and suggestions for the improvement of Euclid's Elements # Ὠκυτόκιον ("Quick Bringing-to-birth"), in which, according to Eutocius, Apollonius demonstrated how to find closer limits for the value of than those of Archimedes, who calculated as the upper limit and as the lower limit # an arithmetical work (see Pappus) on a system both for expressing large numbers in language more everyday than that of Archimedes' The Sand Reckoner and for multiplying these large numbers # a great extension of the theory of irrationals expounded in Euclid, Book x., from binomial to multinomial and from ordered to unordered irrationals (see extracts from Pappus' comm. on Eucl. x., preserved in Arabic and published by Woepke, 1856).

Another measure in finance, one which views upside risk as unimportant compared to downside risk, is the downside beta. In the context of a binary variable, a simple statistical measure of risk is simply the probability that a variable will take on the lower of two values. There is a sense in which one risk A can be said to be unambiguously greater than another risk B (that is, greater for any reasonable risk function): namely, if A is a mean-preserving spread of B. This means that the probability density function of A can be formed, roughly speaking, by "spreading out" that of B. However, this is only a partial ordering: most pairs of risks cannot be unambiguously ranked in this way, and different risk functions applied to the estimated distributions of two such unordered risky variables will give different answers as to which is riskier. In the context of statistical estimation itself, the risk involved in estimating a particular parameter is a measure of the degree to which the estimate is likely to be inaccurate.

A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices.