Not only does Brown add the voice of a thoughtful struggler to his squealing weirdo and caustic thug, he sees to it that the tracks permute and evolve into something that feels thought through.
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"If I imagine randomly rearranging the atoms of the bacterium—so I just take them, I label them all, I permute them in space—I'm presumably going to get something that is garbage," he said earlier this month.
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This terminological ping-pong reaches its most excitable state in one of the collection's key longer poems, "light" (1984), in which the words "light" and "dark" — two of the most basic literary symbols — permute a series of verbs and prepositions that suffuse the movements with causality.
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This is illustrated below for the case n = 5. 1,2,3,4,5 ... Original Array 4,1,2,3,5 ... 1st iteration (Permute subset/Rotate subset) 5,1,2,3,4 ... 1st iteration (Swap) 3,5,1,2,4 ... 2nd iteration (Permute subset/Rotate subset) 4,5,1,2,3 ... 2nd iteration (Swap) 2,4,5,1,3 ... 3rd iteration (Permute subset/Rotate subset) 3,4,5,1,2 ... 3rd iteration (Swap) 1,3,4,5,2 ... 4th iteration (Permute subset/Rotate subset) 2,3,4,5,1 ... 4th iteration (Swap) 5,2,3,4,1 ... 5th iteration (Permute subset/Rotate subset) 1,2,3,4,5 ... 5th iteration (Swap) ... The final state of the array is in the same order as the original The induction proof for the claim is now complete, which will now lead to why Heap's Algorithm creates all permutations of array . Once again we will prove by induction the correctness of Heap's Algorithm. Basis: Heap's Algorithm trivially permutes an array of size as outputing is the one and only permutation of .
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Many operations on a Latin square produce another Latin square (for example, turning it upside down). If we permute the rows, permute the columns, and permute the names of the symbols of a Latin square, we obtain a new Latin square said to be isotopic to the first. Isotopism is an equivalence relation, so the set of all Latin squares is divided into subsets, called isotopy classes, such that two squares in the same class are isotopic and two squares in different classes are not isotopic. Another type of operation is easiest to explain using the orthogonal array representation of the Latin square.
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Microprocessor Report. One of the AltiVec units executes integer and floating-point instructions, and the other only permute instructions. The latter has three subunits for simple integer, complex integer and floating- point instructions. These units have pipelines of varying lengths: 10 stages for simple integer and permute instructions, 13 stages for complex integer instructions and 16 stage for floating-point instructions.
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However, jumbling moves are able to permute face center pieces between different orbits, thus leaving the puzzle in a state that cannot be solved by 180° twists alone.
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178 In this viewpoint, an affine transformation is a projective transformation that does not permute finite points with points at infinity, and affine transformation geometry is the study of geometrical properties through the action of the group of affine transformations.
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The shredding step can either permute all 8 bit-planes independently, or in groups of 4, depending on control bit 3. The permutation tables stay the same through all rounds of encryption on a given block, but if control bit 5 is set, then the tables are regenerated after each block.
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Equivalently, combine each input block with a key bit, and map the result through a 5→4 bit S-box. ## Mix adjacent 4-bit blocks using a maximum distance separable code over GF(24). ## Permute 4-bit blocks so that they will be adjacent to different blocks in following rounds.
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The system uses seven basic steps to solve a Rubik's Cube. # Build a 2x2x2 block # Expand to a 2x2x3 without destroying the 2x2x2 block # Correct edge orientation # Solve two complete layers # Permute the remaining corners # Orient the remaining corners # Permute the final edges Petrus invented three simple and flexible algorithms to complete the last three steps, which he named Niklas, Sune, and Allan. While the method stands alone as an efficient system for solving the Rubik's Cube, many modifications have been made over the years to stay on the cutting edge of competitive speedcubing. Many more algorithms have been added to shave seconds off the solution time, and steps 5+6 or 6+7 are often combined depending on the problems each case presents.
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A Fano subplane likewise satisfies suitable uniqueness conditions. To W21 append 3 new points and let the automorphisms in PΓL(3,4) but not in M21 permute these new points. An S(3,6,22) system W22 is formed by appending just one new point to each of the 21 lines and new blocks are 56 hyperovals conjugate under M21.
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Schönheit was commissioned by the music department of the Fundação Calouste Gulbenkian, Lisbon. Schönheit is the original trio of the subcycle comprising hours six to eleven, and as such is also the simplest. The other six trios permute its five main sections and add new material as insertions between them, creating introductions, codas, interludes, or cadenzas.
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The following modular law (for groups) holds for any Q a subgroup of S, where T is any other arbitrary subgroup (and both S and T are subgroups of some group G): :Q(S ∩ T) = S ∩ (QT). The two products that appear in this equality are not necessarily subgroups. If QT is a subgroup (equivalently, as noted above, if Q and T permute) then QT = ⟨Q ∪ T⟩ = Q ∨ T; i.e., QT is the join of Q and T in the lattice of subgroups of G, and the modular law for such a pair may also be written as Q ∨ (S ∩ T) = S ∩ (Q ∨ T), which is the equation that defines a modular lattice if it holds for any three elements of the lattice with Q ≤ S. In particular, since normal subgroups permute with each other, they form a modular sublattice.
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Recently many methods for transposon based random mutagenesis have been reported. This methods include, but are not limited to the following: PERMUTE-random circular permutation, random protein truncation, random nucleotide triplet substitution, random domain/tag/multiple amino acid insertion, codon scanning mutagenesis, and multicodon scanning mutagenesis. These aforementioned techniques all require the design of mini-Mu transposons. Thermo scientific manufactures kits for the design of these transposons.
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It can be twisted along its cuts to permute its pieces. The axial pieces are octahedral in shape, although this is not immediately obvious, and can only rotate around the axis they are attached to. The 6 edge pieces can be freely permuted. The trivial tips are so called because they can be twisted independently of all other pieces, making them trivial to place in solved position.
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A point of a parametric surface which is not regular is irregular. There are several kinds of irregular points. It may occur that an irregular point becomes regular, if one changes the parametrization. This is the case of the poles in the parametrization of the unit sphere by Euler angles: it suffices to permute the role of the different coordinate axes for changing the poles.
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Some methods permute the data and calculate a z-score using the distribution of correlations found between genes in permuted dataset. Some other approaches have also been used such as threshold selection based on clustering coefficient or random matrix theory. The problem with p-value based methods is that the final cutoff on the p-value is chosen based on statistical routines(e.g. a p-value of 0.01 or 0.05 is considered significant), not based on a biological insight.
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The CPU loads 4 numbers at once, multiplies them all in one SIMD- multiplication, and saves them all at once back to RAM. In theory, the speed can be multiplied by 4. SIMD instructions are widely used to process 3D graphics, although modern graphics cards with embedded SIMD have largely taken over this task from the CPU. Some systems also include permute functions that re-pack elements inside vectors, making them particularly useful for data processing and compression.
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An 800 MHz Motorola PowerPC 7450 on a Power Mac G4 CPU module PowerPC G4e design The PowerPC 7450 "Voyager"/"V'ger" was the only major redesign of the G4 processor. The 33-million transistor chip extended significantly the execution pipeline of 7400 (7 vs. 4 stages minimum) to reach higher clock speeds, improved instruction throughput (3 \+ branch vs. 2 \+ branch per cycle) to compensate for higher instruction latency, replaced an external L2 cache (up to 2 MB 2-way set associative, 64-bit data path) with an integrated one (256 KB 8-way set associative, 256-bit data path), supported an external L3 cache (up to 2 MB 8-way set associative, 64-bit data path), and featured many other architectural advancements. The AltiVec unit was improved with the 7450; instead of executing one vector permute instruction and one vector ALU (simple int, complex int, float) instruction per cycle like 7400/7410, the 7450 and its Motorola/Freescale-followers can execute two arbitrary vector instructions simultaneously (permute, simple int, complex int, float).
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In computational geometry, a standard technique to build a structure like a convex hull or Delaunay triangulation is to randomly permute the input points and then insert them one by one into the existing structure. The randomization ensures that the expected number of changes to the structure caused by an insertion is small, and so the expected running time of the algorithm can be bounded from above. This technique is known as randomized incremental construction.Seidel R. Backwards Analysis of Randomized Geometric Algorithms.
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The symmetries of the Dynkin diagram, , correspond to the outer automorphisms of in triality. Let now be a connected reductive group over an algebraically closed field. Then any two Borel subgroups are conjugate by an inner automorphism, so to study outer automorphisms it suffices to consider automorphisms that fix a given Borel subgroup. Associated to the Borel subgroup is a set of simple roots, and the outer automorphism may permute them, while preserving the structure of the associated Dynkin diagram.
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They can be solved by repeatedly applying two 4-twist sequences, which are mirror-image versions of each other. These sequences permute 3 edge pieces at a time and change their orientation differently, so that a combination of both sequences is sufficient to solve the puzzle. However, more efficient solutions (requiring a smaller total number of twists) are generally available (see below). The twist of any axial piece is independent of the other three, as is the case with the tips.
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RSD can also be defined for the more general setting in which the group has to select a single alternative from a set of alternatives. In this setting, RSD works as follows: First, randomly permute the agents. Starting with the set of all alternatives, ask each agent in the order of the permutation to choose his favorite alternative(s) among the remaining alternatives. If more than one alternative remains after taking the preferences of all agents into account, RSD uniformly randomizes over those alternatives.
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If then, Sym(M), the symmetric group on n letters is usually denoted by Sn. By Cayley's theorem, every group is isomorphic to some permutation group. The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry. The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation groups.
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In the complex plane a generalized circle is either a line or a circle. When completed with the point at infinity, the generalized circles in the plane correspond to circles on the surface of the Riemann sphere, an expression of the complex projective line. Linear fractional transformations permute these circles on the sphere, and the corresponding finite points of the generalized circles in the complex plane. To construct models of the hyperbolic plane the unit disk and the upper half-plane are used to represent the points.
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The layout of notes on the fretboard in standard tuning often forces guitarists to permute the tonal order of notes in a chord. The playing of conventional chords is simplified by open tunings, which are especially popular in folk, blues guitar and non-Spanish classical guitar (such as English and Russian guitar). For example, the typical twelve-bar blues uses only three chords, each of which can be played (in every open tuning) by fretting six strings with one finger. Open tunings are used especially for steel guitar and slide guitar.
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The real line in the complex plane gets permuted with circles and other real lines under Möbius transformations, which actually permute the canonical embedding of the real projective line in the complex projective line. Suppose A is an algebra over a field F, generalizing the case where F is the real number field and A is the field of complex numbers. The canonical embedding of P(F) into P(A) is :U_F[x, 1] \mapsto U_A[x, 1] , \quad U_F[1, 0] \mapsto U_A[1, 0]. A chain is the image of P(F) under a homography on P(A).
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In a general sequent of the form :\Gamma\vdash\Sigma both Γ and Σ are sequences of logical formulas, not sets. Therefore both the number and order of occurrences of formulas are significant. In particular, the same formula may appear twice in the same sequence. The full set of sequent calculus inference rules contains rules to swap adjacent formulas on the left and on the right of the assertion symbol (and thereby arbitrarily permute the left and right sequences), and also to insert arbitrary formulas and remove duplicate copies within the left and the right sequences.
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The permutation step swaps the positions of the words according to a constant pattern. Bit-level permutation is not achieved in this step, but this is not necessary since the MIX functions provides bit-level permutations in the form of bitwise rotations. The Permute step and rotation constants in the MIX functions are chosen in such a way that the overall effect is complete diffusion of all the bits in a data block. Because this permutation is fixed and independent of the key, the time needed to compute it does not provide information about the key or plaintext.
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Journal of Computer and System Sciences, 36: p.254–276. 1988. To demonstrate the power of these classes, consider the graph isomorphism problem, the problem of determining whether it is possible to permute the vertices of one graph so that it is identical to another graph. This problem is in NP, since the proof certificate is the permutation which makes the graphs equal. It turns out that the complement of the graph isomorphism problem, a co-NP problem not known to be in NP, has an AM algorithm and the best way to see it is via a private coins algorithm.
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There are two simple ways to obtain a new Markov triple from an old one (x, y, z). First, one may permute the 3 numbers x,y,z, so in particular one can normalize the triples so that x ≤ y ≤ z. Second, if (x, y, z) is a Markov triple then by Vieta jumping so is (x, y, 3xy − z). Applying this operation twice returns the same triple one started with. Joining each normalized Markov triple to the 1, 2, or 3 normalized triples one can obtain from this gives a graph starting from (1,1,1) as in the diagram.
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An input instance can be normalized by replacing, in each column, the character that occurs the most often with a, the character that occurs the second most often with b, and so forth. Given a solution to the normalized instance, the original instance can be found by remapping the characters of the solution to its original version in every column. The order of the columns does not contribute to the hardness of the problem. That means, if we permute all input strings according to a certain permutation π and obtain a solution string s to that modified instance, then π−1(s) will be a solution to the original instance.
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In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, retaining diffusion while transposing. An example of a 64-bit P-box which spreads the input S-boxes to as many output S-boxes as possible. In block ciphers, the S-boxes and P-boxes are used to make the relation between the plaintext and the ciphertext difficult to understand (see Shannon's property of confusion). P-boxes are typically classified as compression, expansion, and straight, depending on whether the number of output bits is less than, greater than, or equal to the number of input bits.
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Jessica Fridrich is a professor at Binghamton University, who specializes in data hiding applications in digital imagery. She is also known for documenting and popularizing the CFOP method (sometimes referred to as the "Fridrich method"), one of the most commonly used methods for speedsolving the Rubik's Cube, also known as speedcubing.Specializing in Problems That Only Seem Impossible to Solve, By Bina Venkataraman, Published: December 15, 2008, The New York Times She is considered as one of the pioneers of speedcubing, along with Lars Petrus. Nearly all of the fastest speedcubers have based their methods on Fridrich's, usually referred to as CFOP (Cross, First 2 Layers, Orient Last Layer, Permute Last Layer).
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The e5500 is based on the e500mc core and adds some new instructions introduced in the Power ISA 2.06 specification, namely some byte- and bit-level acceleration; Parity, Population count, Bit permute and Compare byte. The FPU is taken straight from the PowerPC e600 core, which is a classic fully pipelined dual precision IEEE 754 unit running at full core speed and supports conversion between 64-bit floats and integers, effectively twice as fast as the FPU in e500mc. The e5500 also introduces an enhanced branch prediction unit with an 8-entry link stack. The e5500 core is the first 64-bit Power ISA core designed solely by Freescale and was introduced at Freescale Technology Forum in June 2010.
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The case is not truly analogous with the > plot of a novel, because the plot is part of the work itself. The user > interface is not part of the work itself. One could permute all the letters > and other codes in the command names, and it would still work in the same > way, and all that would be lost is a modest mnemonic advantage. To approach > the problem in this way may at least be consistent with the distinction > between idea and expression that finds its way into the Software Directive, > but, of course, it draws the line between idea and expression in a > particular place which some would say lies too far on the side of > expression.
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For the expression A-B, the right operand must be evaluated and pushed immediately prior to the Minus step. Without stack permutation or hardware multithreading, relatively little useful code can be put in between while waiting for the Load B to finish. Stack machines can work around the memory delay by either having a deep out-of-order execution pipeline covering many instructions at once, or more likely, they can permute the stack such that they can work on other workloads while the load completes, or they can interlace the execution of different program threads, as in the Unisys A9 system. Today's increasingly parallel computational loads suggests, however, this might not be the disadvantage it's been made out to be in the past.
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The 26-fullerene graph has D_{3h} prismatic symmetry, the same group of symmetries as the triangular prism. This symmetry group has 12 elements; it has six symmetries that arbitrarily permute the three hexagonal faces of the graph and preserve the orientation of its planar embedding, and another six orientation-reversing symmetries. The number of fullerenes with a given even number of vertices grows quickly in the number of vertices; 26 is the largest number of vertices for which the fullerene structure is unique. The only two smaller fullerenes are the graph of the regular dodecahedron (a fullerene with 20 vertices) and the graph of the truncated hexagonal trapezohedron (a 24-vertex fullerene), which are the two types of cells in the Weaire–Phelan structure.
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Permutatude is a portmanteau of permute and attitude, though it also calls to mind other words such as mute (as in being silent) and mutation (as in an act or modification in form and/or structure). The first published definition for permutatude occurs in the 1992 catalog from Nalls' solo exhibition, Permutatude, at Phillippe Staib Gallery in New York City: A world capable of being changed; a transformation or rapid evolution of attitude of individuals on a large scale allowing a reordering to take place; revolt by the once silent masses against constituted authority; majority will; a sudden necessary modification in the global community ‘permitting’ rapid change to take place; exercise of authority by the masses, the natural instincts of democracy.Nalls, G. (1992). Permutatude: Adjust to the great evolutionary forces of change.
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If we systematically and consistently reorder the three items in each triple (that is, permute the three columns in the array form), another orthogonal array (and, thus, another Latin square) is obtained. For example, we can replace each triple (r,c,s) by (c,r,s) which corresponds to transposing the square (reflecting about its main diagonal), or we could replace each triple (r,c,s) by (c,s,r), which is a more complicated operation. Altogether there are 6 possibilities including "do nothing", giving us 6 Latin squares called the conjugates (also parastrophes) of the original square. Finally, we can combine these two equivalence operations: two Latin squares are said to be paratopic, also main class isotopic, if one of them is isotopic to a conjugate of the other.
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In keeping with the "load/store" model of the PowerPC's RISC design, the vector registers, like the scalar registers, can only be loaded from and stored to memory. However, VMX/AltiVec provides a much more complete set of "horizontal" operations that work across all the elements of a vector; the allowable combinations of data type and operations are much more complete. Thirty-two 128-bit vector registers are provided, compared to eight for SSE and SSE2 (extended to 16 in x86-64), and most VMX/AltiVec instructions take three register operands compared to only two register/register or register/memory operands on IA-32. VMX/AltiVec is also unique in its support for a flexible vector permute instruction, in which each byte of a resulting vector value can be taken from any byte of either of two other vectors, parametrized by yet another vector.
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The PowerPC 970FX used a 90 nm manufacturing process and has a maximum power rating of 11 watts at 149 degrees Fahrenheit (65 °C) while clocked at 1 GHz and a maximum of 48 watts at 2 GHz. The PowerPC 970's pipeline was lengthened from 9 stages to 16 - 21 stages for the PowerPC 970 FX. It has 10 functional units - 2 Fixed-Point Units, 2 Load/Store Units, 2 Floating Point Units, 1 Branch Unit, 1 SIMD ALU unit, 1 SIMD Permute unit, and 1 Condition Register. It supports up to 215 instructions in-flight: 16 in the Instruction Fetch Unit, 67 in the Instruction Decode Unit, 100 in the Functional Units, and 32 in the Store Queue. It has 64 KBytes of directly mapped Instruction Cache and 32 KBytes of D-Cache. Apple released their 970FX-powered machines throughout 2004: the Xserve G5 in January, the Power Mac G5 in June, and the iMac G5 in August.
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Assume by induction that after the initial iteration of the loop, the remaining iterations permute the first n − 1 elements according to a cycle of length n − 1 (those remaining iterations are just Sattolo's algorithm applied to those first n − 1 elements). This means that tracing the initial element to its new position p, then the element originally at position p to its new position, and so forth, one only gets back to the initial position after having visited all other positions. Suppose the initial iteration swapped the final element with the one at (non-final) position k, and that the subsequent permutation of first n − 1 elements then moved it to position l; we compare the permutation π of all n elements with that remaining permutation σ of the first n − 1 elements. Tracing successive positions as just mentioned, there is no difference between π and σ until arriving at position k.
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