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32,800 | Intel's TSX/TSX-NI specification describes how the transactional memory is exposed to programmers, but withholds details on the actual transactional memory implementation. Intel specifies in its developer's and optimization manuals that Haswell maintains both read-sets and write-sets at the granularity of a cache line,... | Transactional Synchronization Extensions | 0.803723 |
32,801 | In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps: The initial, "prediction" step, starts from a function fitted to ... | Predictor-corrector method | 0.803722 |
32,802 | If the field has a parallel gradient, a particle with a finite Larmor radius will also experience a force in the direction away from the larger magnetic field. This effect is known as the magnetic mirror. While it is closely related to guiding center drifts in its physics and mathematics, it is nevertheless considered ... | Grad-B drift | 0.803722 |
32,803 | kilobase (kb) A unit of nucleic acid length equal to 1,000 bases in single-stranded molecules or 1,000 base pairs in duplex molecules such as double-stranded DNA. kinetochore A disc-shaped protein complex which assembles around the centromere of a chromosome during prometaphase of mitosis and meiosis, where it function... | Glossary of gene expression terms | 0.80372 |
32,804 | forward genetics forward mutation frameshift mutation A type of mutation in a nucleic acid sequence caused by the insertion or deletion of a number of nucleotides that is not divisible by three. Because of the triplet nature by which nucleotides code for amino acids, a mutation of this sort causes a shift in the readin... | Glossary of gene expression terms | 0.80372 |
32,805 | genetically modified organism (GMO) Any organism whose genetic material has been altered using genetic engineering techniques, particularly in a way that does not occur naturally by mating or by natural genetic recombination. genetics The field of biology that studies genes, genetic variation, and heredity in living or... | Glossary of gene expression terms | 0.80372 |
32,806 | The direct, deliberate manipulation of an organism's genetic material using any of a variety of biotechnology methods, including the insertion or removal of genes, the transfer of genes within and between species, the mutation of existing sequences, and the construction of novel sequences using artificial gene synthesi... | Glossary of gene expression terms | 0.80372 |
32,807 | The mutation responsible may occur spontaneously during embryonic development or may be inherited from one or both parents, in which case the genetic disorder is also classified as a hereditary disorder. Though the abnormality itself is present before birth, the actual disease it causes may not develop until much later... | Glossary of gene expression terms | 0.80372 |
32,808 | Gene Expression Omnibus (GEO) A database of high-throughput functional genomics and gene expression data derived from experimental chips and next-generation sequencing and managed by the National Center for Biotechnology Information. gene fusion The union, either by natural mutation or by recombinant laboratory techniq... | Glossary of gene expression terms | 0.80372 |
32,809 | G banding Also Giemsa banding or G-banding. A technique used in cytogenetics to produce a visible karyotype by staining the condensed chromosomes with Giemsa stain. The staining produces consistent and identifiable patterns of dark and light "bands" in regions of chromatin, which allows specific chromosomes to be easil... | Glossary of gene expression terms | 0.80372 |
32,810 | The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Although the definition of heat implicitly means the transfer of energ... | Heat energy | 0.803717 |
32,811 | For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy ΔU of the system is equal to the amount of heat Q supplied to the system minus the amount of thermodynamic work W done by system on its surroundings. The forego... | Heat energy | 0.803717 |
32,812 | In March 2017, the European Patent Office (EPO) announced its intention to allow claims for editing all types of cells to Max-Planck Institute in Berlin, University of California, and University of Vienna, and in August 2017, the EPO announced its intention to allow CRISPR claims in a patent application that MilliporeS... | CRISPR-Cas9 gene editing | 0.803717 |
32,813 | In 2017, Doudna and Charpentier were awarded the Japan Prize in Tokyo, Japan for their revolutionary invention of CRISPR-Cas9. In 2016, Charpentier, Doudna, and Zhang won the Tang Prize in Biopharmaceutical Science. In 2020, Charpentier and Doudna were awarded the Nobel Prize in Chemistry, the first such prize for an a... | CRISPR-Cas9 gene editing | 0.803717 |
32,814 | In 2012 Jennifer Doudna, Emmanuelle Charpentier, Martin Jínek, Krzysztof Chyliński, Ines Fonfara and Michael Hauer published their finding that CRISPR-Cas9 could be programmed with RNA to edit genomic DNA, now considered one of the most significant discoveries in the history of biology. | CRISPR-Cas9 gene editing | 0.803717 |
32,815 | The development of the technique earned Jennifer Doudna and Emmanuelle Charpentier the Nobel Prize in Chemistry in 2020. The third researcher group that shared the Kavli Prize for the same discovery, led by Virginijus Šikšnys, was not awarded the Nobel prize.Working like genetic scissors, the Cas9 nuclease opens both s... | CRISPR-Cas9 gene editing | 0.803717 |
32,816 | CRISPR gene editing (pronounced "crisper") is a genetic engineering technique in molecular biology by which the genomes of living organisms may be modified. It is based on a simplified version of the bacterial CRISPR-Cas9 antiviral defense system. By delivering the Cas9 nuclease complexed with a synthetic guide RNA (gR... | CRISPR-Cas9 gene editing | 0.803717 |
32,817 | As of March 2015, multiple groups had announced ongoing research with the intention of laying the foundations for applying CRISPR to human embryos for human germline engineering, including labs in the US, China, and the UK, as well as US biotechnology company OvaScience. Scientists, including a CRISPR co-discoverer, ur... | CRISPR-Cas9 gene editing | 0.803717 |
32,818 | CRISPRs are much easier to design because the process requires synthesizing only a short RNA sequence, a procedure that is already widely used for many other molecular biology techniques (e.g. creating oligonucleotide primers).Whereas methods such as RNA interference (RNAi) do not fully suppress gene function, CRISPR, ... | CRISPR-Cas9 gene editing | 0.803717 |
32,819 | The coherent potential approximation (or CPA) is a method, in physics, of finding the Green's function of an effective medium. It is a useful concept in understanding how sound waves scatter in a material which displays spatial inhomogeneity. One version of the CPA is an extension to random materials of the muffin-tin ... | Coherent potential approximation | 0.803717 |
32,820 | Scientists can easily manipulate and combine genes within the bacteria to create novel or disrupted proteins and observe the effect this has on various molecular systems. Researchers have combined the genes from bacteria and archaea, leading to insights on how these two diverged in the past. In the field of synthetic b... | Genetically Modified Organism | 0.803716 |
32,821 | Once a gene is isolated it can be stored inside the bacteria, providing an unlimited supply for research. A large number of custom plasmids make manipulating DNA extracted from bacteria relatively easy.Their ease of use has made them great tools for scientists looking to study gene function and evolution. The simplest ... | Genetically Modified Organism | 0.803716 |
32,822 | The United States Department of Agriculture (USDA) considers GMOs to be plants or animals with heritable changes introduced by genetic engineering or traditional methods, while GEO specifically refers to organisms with genes introduced, eliminated, or rearranged using molecular biology, particularly recombinant DNA tec... | Genetically Modified Organism | 0.803716 |
32,823 | Let S be a set equipped with one or several methods for producing elements of S from other elements of S. A subset X of S is said to be closed under these methods, if, when all input elements are in X, then all possible results are also in X. Sometimes, one may also say that X has the closure property. The main propert... | Closure (mathematics) | 0.803716 |
32,824 | The radical of an ideal in a commutative ring. In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset. In formal languages, the Kleene closure of a language can be described as the set of strings that can be made by concatenating zero or more strings from that language. In g... | Closure (mathematics) | 0.803716 |
32,825 | In matroid theory, the closure of X is the largest superset of X that has the same rank as X. The transitive closure of a set. The algebraic closure of a field. The integral closure of an integral domain in a field that contains it. | Closure (mathematics) | 0.803716 |
32,826 | The Cartagena Protocol on Biosafety used the synonym living modified organism (LMO) in 2000 and defined it as "any living organism that possesses a novel combination of genetic material obtained through the use of modern biotechnology." Modern biotechnology is further defined as "In vitro nucleic acid techniques, inclu... | Genetically Modified Organism | 0.803716 |
32,827 | There are examples of crops that fit this definition, but are not normally considered GMOs. For example, the grain crop triticale was fully developed in a laboratory in 1930 using various techniques to alter its genome.Genetically engineered organism (GEO) can be considered a more precise term compared to GMO when desc... | Genetically Modified Organism | 0.803716 |
32,828 | This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently: The algebraic sum of currents in a network of conductors meeting... | Kirchhoff's circuit laws | 0.803715 |
32,829 | Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Cl... | Kirchhoff's circuit laws | 0.803715 |
32,830 | A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an... | Transition density | 0.803714 |
32,831 | Markovian systems appear extensively in thermodynamics and statistical mechanics, whenever probabilities are used to represent unknown or unmodelled details of the system, if it can be assumed that the dynamics are time-invariant, and that no relevant history need be considered which is not already included in the stat... | Transition density | 0.803714 |
32,832 | In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. | Reflected light | 0.803714 |
32,833 | Processor design is a subfield of computer science and computer engineering (fabrication) that deals with creating a processor, a key component of computer hardware. The design process involves choosing an instruction set and a certain execution paradigm (e.g. VLIW or RISC) and results in a microarchitecture, which mig... | Processor design | 0.803713 |
32,834 | ShangMi 3 (SM3) is a cryptographic hash function used in the Chinese National Standard. It was published by the National Cryptography Administration (Chinese: 国家密码管理局) on 2010-12-17 as "GM/T 0004-2012: SM3 cryptographic hash algorithm".SM3 is used for implementing digital signatures, message authentication codes, and p... | SM3 (hash function) | 0.803712 |
32,835 | The duality between the symmetric group and the partition algebra generalizes the original Schur-Weyl duality between the general linear group and the symmetric group. There are other generalizations. In the relevant tensor product spaces, we write V n {\displaystyle V_{n}} for an irreducible n {\displaystyle n} -dimen... | Partition algebra | 0.80371 |
32,836 | Subalgebras of the partition algebra can be defined by the following properties: Whether they are planar i.e. whether lines may cross in diagrams. Whether subsets are allowed to have any size 1 , 2 , … , 2 k {\displaystyle 1,2,\dots ,2k} , or size 1 , 2 {\displaystyle 1,2} , or only size 2 {\displaystyle 2} . Whether w... | Partition algebra | 0.80371 |
32,837 | Let n ≥ 2 k {\displaystyle n\geq 2k} be integer. Let us take V {\displaystyle V} to be the natural permutation representation of the symmetric group S n {\displaystyle S_{n}} . This n {\displaystyle n} -dimensional representation is a sum of two irreducible representations: the standard and trivial representations, V =... | Partition algebra | 0.80371 |
32,838 | Assume n ∈ N ∗ {\displaystyle n\in \mathbb {N} ^{*}} . For V {\displaystyle V} a n {\displaystyle n} -dimensional vector space with basis v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} , there is a natural action of the partition algebra P k ( n ) {\displaystyle P_{k}(n)} on the vector space V ⊗ k {\displaystyle V^{\... | Partition algebra | 0.80371 |
32,839 | The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. Its subalgebras include diagram algebras such as the Brauer algebra, the Temperley–Lieb algebra, or the group algebra of the symmetric group. Representations of the partition algebra... | Partition algebra | 0.80371 |
32,840 | The partition algebra P k ( n ) {\displaystyle P_{k}(n)} is generated by 3 k − 2 {\displaystyle 3k-2} elements of the type These generators obey relations that include s i 2 = 1 , s i s i + 1 s i = s i + 1 s i s i + 1 , p i 2 = n p i , b i 2 = b i , p i b i p i = p i {\displaystyle s_{i}^{2}=1\quad ,\quad s_{i}s_{i+1}s... | Partition algebra | 0.80371 |
32,841 | The partition algebra P k ( n ) {\displaystyle P_{k}(n)} is an associative algebra. It has a multiplicative identity The partition algebra P k ( n ) {\displaystyle P_{k}(n)} is semisimple for n ∈ C − { 0 , 1 , … , 2 k − 2 } {\displaystyle n\in \mathbb {C} -\{0,1,\dots ,2k-2\}} . For any two n , n ′ {\displaystyle n,n'}... | Partition algebra | 0.80371 |
32,842 | The uniform block permutation algebra U k {\displaystyle U_{k}} is generated by subsets with as many top elements as bottom elements. It is generated by s i , b i {\displaystyle s_{i},b_{i}} .An algebra with a half-integer index k + 1 2 {\displaystyle k+{\frac {1}{2}}} is defined from partitions of 2 k + 2 {\displaysty... | Partition algebra | 0.80371 |
32,843 | In addition to the eight subalgebras described above, other subalgebras have been defined: The totally propagating partition subalgebra prop P k {\displaystyle {\text{prop}}P_{k}} is generated by diagrams whose blocks all propagate, i.e. partitions whose subsets all contain top and bottom elements. These diagrams from ... | Partition algebra | 0.80371 |
32,844 | A partition of 2 k {\displaystyle 2k} elements labelled 1 , 1 ¯ , 2 , 2 ¯ , … , k , k ¯ {\displaystyle 1,{\bar {1}},2,{\bar {2}},\dots ,k,{\bar {k}}} is represented as a diagram, with lines connecting elements in the same subset. In the following example, the subset { 1 ¯ , 4 ¯ , 5 ¯ , 6 } {\displaystyle \{{\bar {1}},{... | Partition algebra | 0.80371 |
32,845 | For example, a standard module of the Temperley–Lieb algebra is parametrized by an integer 0 ≤ ℓ ≤ k {\displaystyle 0\leq \ell \leq k} with ℓ ≡ k mod 2 {\displaystyle \ell \equiv k{\bmod {2}}} , and a basis is simply given by a set of partitions. The following table lists the irreducible representations of the partitio... | Partition algebra | 0.80371 |
32,846 | Representations of non-planar subalgebras have similar structures as representations of the partition algebra. For example, the Brauer-Specht modules of the Brauer algebra are built from Specht modules, and certain sets of partitions. In the case of the planar subalgebras, planarity prevents nontrivial permutations, an... | Partition algebra | 0.80371 |
32,847 | In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other. This method ... | Single linkage clustering | 0.803708 |
32,848 | The modern solid and hashed wedges were introduced in the 1940s by Giulio Natta to represent the structure of high polymers, and extensively popularised in the 1959 textbook Organic Chemistry by Donald J. Cram and George S. Hammond.Skeletal formulae can depict cis and trans isomers of alkenes. Wavy single bonds are the... | Skeletal structure | 0.803706 |
32,849 | An obsolescent depiction of hydrogen stereochemistry that used to be common in steroid chemistry is the use of a filled circle centered on a vertex (sometimes called H-dot/H-dash/H-circle, respectively) for an upward pointing hydrogen atom and two hash marks next to vertex or a hollow circle for a downward pointing hyd... | Skeletal structure | 0.803706 |
32,850 | Stereochemistry is conveniently denoted in skeletal formulae: The relevant chemical bonds can be depicted in several ways: Solid lines represent bonds in the plane of the paper or screen. Solid wedges represent bonds that point out of the plane of the paper or screen, towards the observer. Hashed wedges or dashed lines... | Skeletal structure | 0.803706 |
32,851 | Headquartered in Adelaide, the company has over 150 staff based across operational offices in: Melbourne; Brisbane; Perth; and Chişinău, Moldova.The company develops advanced planning and scheduling business optimisation software, which helps manage complex operations using artificial intelligence. Most of the products... | SolveIT Software | 0.803706 |
32,852 | The company was set up in 2005 by four academics who were also experienced business people, all recent immigrants to Australia. The team was headed by ex-Ernst & Young consultant Matthew Michalewicz, who had moved to Adelaide in 2004 after selling his last company, NuTech Solutions. The other three partners were Zbigni... | SolveIT Software | 0.803706 |
32,853 | The multielectron catalytic chemistry involved in making carbon-based fuels (such as methanol) from reduction of carbon dioxide is challenging; a feasible alternative is hydrogen production from protons, though use of water as the source of electrons (as plants do) requires mastering the multielectron oxidation of two ... | Solar technology | 0.803706 |
32,854 | The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by H ^ {\displaystyle {\hat {H}}} , where... | Hamiltonian (quantum mechanics) | 0.803704 |
32,855 | In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system'... | Hamiltonian (quantum mechanics) | 0.803704 |
32,856 | Combining these yields the form used in the Schrödinger equation: which allows to apply the Hamiltonian to systems described by a wave function Ψ ( r , t ) {\displaystyle \Psi (\mathbf {r} ,t)} . This is the approach commonly taken in introductory treatments of quantum mechanics, using the formalism of Schrödinger's wa... | Hamiltonian (quantum mechanics) | 0.803704 |
32,857 | As of 2015 the laboratory is headed by Andy Parker and the Cavendish Professor of Physics is Sir Richard Friend. | Theory of Condensed Matter | 0.803704 |
32,858 | The Cavendish Laboratory was initially located on the New Museums Site, Free School Lane, in the centre of Cambridge. It is named after British chemist and physicist Henry Cavendish for contributions to science and his relative William Cavendish, 7th Duke of Devonshire, who served as chancellor of the university and do... | Theory of Condensed Matter | 0.803704 |
32,859 | The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the School of Physical Sciences. The laboratory was opened in 1874 on the New Museums Site as a laboratory for experimental physics and is named after the British chemist and physicist Henry Cavendish. The laboratory ha... | Theory of Condensed Matter | 0.803704 |
32,860 | All were impressed by the new DNA model, especially Brenner who subsequently worked with Crick at Cambridge in the Cavendish Laboratory and the new Laboratory of Molecular Biology. According to the late Dr. Beryl Oughton, later Rimmer, they all travelled together in two cars once Dorothy Hodgkin announced to them that ... | Theory of Condensed Matter | 0.803704 |
32,861 | The Cambridge University undergraduate newspaper Varsity also ran its own short article on the discovery on Saturday 30 May 1953. Bragg's original announcement of the discovery at a Solvay Conference on proteins in Belgium on 8 April 1953 went unreported by the British press. Sydney Brenner, Jack Dunitz, Dorothy Hodgki... | Theory of Condensed Matter | 0.803704 |
32,862 | The Cavendish Laboratory has had an important influence on biology, mainly through the application of X-ray crystallography to the study of structures of biological molecules. Francis Crick already worked in the Medical Research Council Unit, headed by Max Perutz and housed in the Cavendish Laboratory, when James Watso... | Theory of Condensed Matter | 0.803704 |
32,863 | Several important early physics discoveries were made here, including the discovery of the electron by J.J. Thomson (1897) the Townsend discharge by John Sealy Townsend, and the development of the cloud chamber by C.T.R. Wilson. Ernest Rutherford became Director of the Cavendish Laboratory in 1919. Under his leadership... | Theory of Condensed Matter | 0.803704 |
32,864 | Physical Chemistry (originally the department of Colloid Science led by Eric Rideal) had left the old Cavendish site, subsequently locating as the Department of Physical Chemistry (under RG Norrish) in the then new chemistry building with the Department of Chemistry (led by Lord Todd) in Lensfield Road: both chemistry ... | Theory of Condensed Matter | 0.803704 |
32,865 | If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, Newton (1687) showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the me... | Geodesic polygon area | 0.803702 |
32,866 | The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a strai... | Geodesic polygon area | 0.803702 |
32,867 | For this reason, geodesics on simple surfaces such as ellipsoids of revolution or triaxial ellipsoids are frequently used as "test cases" for exploring new methods. Examples include: the development of elliptic integrals (Legendre 1811) and elliptic functions (Weierstrass 1861); the development of differential geometry... | Geodesic polygon area | 0.803702 |
32,868 | The direct and inverse geodesic problems no longer play the central role in geodesy that they once did. Instead of solving adjustment of geodetic networks as a two-dimensional problem in spheroidal trigonometry, these problems are now solved by three-dimensional methods (Vincenty & Bowring 1978). Nevertheless, terrestr... | Geodesic polygon area | 0.803702 |
32,869 | {\big (}1-\Phi (x_{i}^{\operatorname {T} }\beta ){\big )}{\bigg )}} The estimator β ^ {\displaystyle {\hat {\beta }}} which maximizes this function will be consistent, asymptotically normal and efficient provided that E {\displaystyle \operatorname {E} } exists and is not singular. It can be shown that this log-like... | Probit model | 0.8037 |
32,870 | Then let F: X × Y → R ∪ { + ∞ } {\displaystyle F:X\times Y\to \mathbb {R} \cup \{+\infty \}} be a perturbation function such that F ( x , 0 ) = f ( x ) {\displaystyle F(x,0)=f(x)} . The duality gap is the difference given by inf x ∈ X − sup y ∗ ∈ Y ∗ {\displaystyle \inf _{x\in X}-\sup _{y^{*}\in Y^{*}}} where F ∗ {\d... | Duality gap | 0.803699 |
32,871 | In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If d ∗ {\displaystyle d^{*}} is the optimal dual value and p ∗ {\displaystyle p^{*}} is the optimal primal value then the duality gap is equal to p ∗ − d ∗ {\displaystyle p^{*}-d^{*}} . This value i... | Duality gap | 0.803699 |
32,872 | Rotary actuators are used in a vast range of applications. These require actuators of all sizes, power and operating speed. These can range from zero power actuators that are only used as display devices, such as air core gauges. Others include valve actuators that operate pipeline and process valves in the petrochemic... | Rotary actuator | 0.803695 |
32,873 | A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergradu... | A Topological Picturebook | 0.803694 |
32,874 | In 2-dimensional space, a rotation can be simply described by an angle θ of rotation, but it can be also represented by the 4 entries of a rotation matrix with 2 rows and 2 columns. In 3-dimensional space, every rotation can be interpreted as a rotation by a given angle about a single fixed axis of rotation (see Euler'... | 2D computer graphics | 0.803693 |
32,875 | A rotated vector is obtained by using the matrix multiplication Rv. Since matrix multiplication has no effect on the zero vector (i.e., on the coordinates of the origin), rotation matrices can only be used to describe rotations about the origin of the coordinate system. Rotation matrices provide a simple algebraic desc... | 2D computer graphics | 0.803693 |
32,876 | In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. R = {\displaystyle R={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \\\end{bmatrix}}} rotates points in the xy-Cartesian plane counterclockwise through an angle θ about the origin of the Cartes... | 2D computer graphics | 0.803693 |
32,877 | 2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. It may refer to the branch of computer science that comprises such techniques or to the models themselves. 2D computer gr... | 2D computer graphics | 0.803693 |
32,878 | The stereochemistry of pericyclic reactions is governed by the Woodward–Hoffmann rules and that of many elimination reactions by Zaitsev's rule. Organic reactions are important in the production of pharmaceuticals. In a 2006 review, it was estimated that 20% of chemical conversions involved alkylations on nitrogen and ... | Organic reaction | 0.803692 |
32,879 | Organic chemistry has a strong tradition of naming a specific reaction to its inventor or inventors and a long list of so-called named reactions exists, conservatively estimated at 1000. A very old named reaction is the Claisen rearrangement (1912) and a recent named reaction is the Bingel reaction (1993). When the nam... | Organic reaction | 0.803691 |
32,880 | In computer science and graph theory, the term color-coding refers to an algorithmic technique which is useful in the discovery of network motifs. For example, it can be used to detect a simple path of length k in a given graph. The traditional color-coding algorithm is probabilistic, but it can be derandomized without... | Color-coding | 0.803689 |
32,881 | Recently, color-coding has attracted much attention in the field of bioinformatics. One example is the detection of signaling pathways in protein-protein interaction (PPI) networks. Another example is to discover and to count the number of motifs in PPI networks. Studying both signaling pathways and motifs allows a dee... | Color-coding | 0.803689 |
32,882 | Nuncius. Physics World. Resurrection. SIAM News.The book has also been featured online internationally, including in China. | The Turing Guide | 0.803689 |
32,883 | Biological Growth: Morphogenesis, Turing's last major scientific contribution, on the generation of complex patterns through chemical processes in biology and on the mathematics behind them, foundational in mathematical biology. Mathematics: Some of Turing's mathematical achievements, including one of his most signific... | The Turing Guide | 0.803688 |
32,884 | He made contributions to both hardware design, through the ACE computer (later implemented as the Pilot ACE) at the NPL, and software, especially at Manchester using the Manchester Baby computer, later the Manchester Mark 1 and Ferranti Mark 1. Artificial Intelligence and the Mind: Turing's pioneering and philosophical... | The Turing Guide | 0.803688 |
32,885 | The Turing Guide is divided into eight main parts, covering various aspects of Alan Turing's life and work: Biography: Biographical aspects of Alan Turing. The Universal Machine and Beyond: Turing's universal machine (now known as a Turing machine), developed while at King's College, Cambridge, which provides a theoret... | The Turing Guide | 0.803688 |
32,886 | Physiological condition or, more often "physiological conditions" is a term used in biology, biochemistry, and medicine. It refers to conditions of the external or internal milieu that may occur in nature for that organism or cell system, in contrast to artificial laboratory conditions. A temperature range of 20-40 deg... | Physiological condition | 0.803688 |
32,887 | In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. | Conductor (class field theory) | 0.803688 |
32,888 | The conductor can be defined in the same way for L/K a not necessarily abelian finite Galois extension of local fields. However, it only depends on Lab/K, the maximal abelian extension of K in L, because of the "norm limitation theorem", which states that, in this situation, N L / K ( L × ) = N L ab / K ( ( L ab ) × ) ... | Conductor (class field theory) | 0.803688 |
32,889 | If we don't allow those numbers then we can again increase the number on the right hand side of the inequality from 2√2 to √221/5, for which the numbers equivalent to 1 + 221 10 {\displaystyle {\frac {1+{\sqrt {221}}}{10}}} limits the bound. The numbers generated show how well these numbers can be approximated, this ca... | Markov constant | 0.803683 |
32,890 | (These numbers are said to be equivalent to ϕ {\displaystyle \phi } .) If we omit these numbers, just as we omitted the rational numbers in Dirichlet's theorem, then we can increase the number √5 to 2√2. Again this new bound is best possible in the new setting, but this time the number √2, and numbers equivalent to it,... | Markov constant | 0.803683 |
32,891 | Dirichlet proved in 1840 that the least readily approximable numbers are the rational numbers, in the sense that for every irrational number there exists infinitely many rational numbers approximating it to a certain degree of accuracy that only finitely many such rational approximations exist for rational numbers. Spe... | Markov constant | 0.803683 |
32,892 | Hurwitz's theorem implies that M ( α ) ≥ 5 {\displaystyle M(\alpha )\geq {\sqrt {5}}} for all α ∈ R − Q {\displaystyle \alpha \in \mathbb {R} -\mathbb {Q} } . If α = {\displaystyle \alpha =} is its continued fraction expansion then M ( α ) = lim sup k → ∞ ( + ) {\displaystyle M(\alpha )=\limsup _{k\to \infty }{(+)}}... | Markov constant | 0.803683 |
32,893 | In number theory, specifically in Diophantine approximation theory, the Markov constant M ( α ) {\displaystyle M(\alpha )} of an irrational number α {\displaystyle \alpha } is the factor for which Dirichlet's approximation theorem can be improved for α {\displaystyle \alpha } . | Markov constant | 0.803683 |
32,894 | There are many branches of engineering, each of which specializes in specific technologies and products. Typically, engineers will have deep knowledge in one area and basic knowledge in related areas. For example, mechanical engineering curricula typically include introductory courses in electrical engineering, compute... | Engineer | 0.803683 |
32,895 | Mechanical engineering cuts across most disciplines since its core essence is applied physics. Engineers also may specialize in one industry, such as motor vehicles, or in one type of technology, such as turbines or semiconductor materials.Several recent studies have investigated how engineers spend their time; that is... | Engineer | 0.803683 |
32,896 | Most engineers specialize in one or more engineering disciplines. Numerous specialties are recognized by professional societies, and each of the major branches of engineering has numerous subdivisions. Civil engineering, for example, includes structural engineering, along with transportation engineering, geotechnical e... | Engineer | 0.803683 |
32,897 | Quantum key distribution exploits certain properties of quantum physics to ensure its security. It relies on the fact that observations (or measurements) of a quantum state introduces perturbations in that state. Over many systems, these perturbations are detectable as noise by the receiver, making it possible to detec... | Key-exchange algorithm | 0.803683 |
32,898 | In Portugal, professional engineer titles and accredited engineering degrees are regulated and certified by the Ordem dos Engenheiros. In the Czech Republic, the title "engineer" (Ing.) is given to people with a (masters) degree in chemistry, technology or economics for historical and traditional reasons. In Greece, th... | Engineer | 0.803683 |
32,899 | : 48 Theorem. Let S1, S2, ..., Sm be a collection of sets such that S i 1 ∪ S i 2 ∪ ⋯ ∪ S i k {\displaystyle S_{i_{1}}\cup S_{i_{2}}\cup \dots \cup S_{i_{k}}} contains at least k elements for k = 1,2,...,m and for all k-combinations { i 1 , i 2 , … , i k {\displaystyle i_{1},i_{2},\ldots ,i_{k}} } of the integers 1,2,.... | Transversal (group theory) | 0.803681 |
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