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14,600 | A finite group is supersolvable if and only if every maximal chain of subgroups has the same length. This is important to those interested in the lattice of subgroups of a group, and is sometimes called the Jordan–Dedekind chain condition. By Baum's theorem, every supersolvable finite group has a DFT algorithm running ... | Supersolvable group | 0.815051 |
14,601 | The child borrows the memory management unit setup from the parent and memory pages are shared among the parent and child process with no copying done, and in particular with no copy-on-write semantics; hence, if the child process makes a modification in any of the shared pages, no new page will be created and the modi... | Fork (system call) | 0.81505 |
14,602 | Instead, virtual memory pages in both processes may refer to the same pages of physical memory until one of them writes to such a page: then it is copied. This optimization is important in the common case where fork is used in conjunction with exec to execute a new program: typically, the child process performs only a ... | Fork (system call) | 0.81505 |
14,603 | Most of the approaches investigated in the past to address this problem rely on scheduling or tuning techniques that aim at overlapping communication with computation. However, this approach can lead to an improvement of at most a factor of two. Ghosting is a different technique for reducing communication, in which a p... | Communication-avoiding algorithm | 0.815049 |
14,604 | Corollary 6.2: More general results for other numerical linear algebra operations can be found in. The following proof is from. | Communication-avoiding algorithm | 0.815049 |
14,605 | Energy consumption increases by orders of magnitude as we go higher in the memory hierarchy. United States president Barack Obama cited communication-avoiding algorithms in the FY 2012 Department of Energy budget request to Congress: New Algorithm Improves Performance and Accuracy on Extreme-Scale Computing Systems. On... | Communication-avoiding algorithm | 0.815049 |
14,606 | In probability theory, the mixing time of a Markov chain is the time until the Markov chain is "close" to its steady state distribution. More precisely, a fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution π and, regardless of the initial state... | Markov chain mixing time | 0.815046 |
14,607 | In quantitative genetics, QST is a statistic intended to measure the degree of genetic differentiation among populations with regard to a quantitative trait. It was developed by Ken Spitze in 1993. Its name reflects that QST was intended to be analogous to the fixation index for a single genetic locus (FST). QST is oft... | QST (genetics) | 0.815043 |
14,608 | Gordon Plotkin and Ehud Shapiro laid the initial theoretical foundation for inductive machine learning in a logical setting. Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples. The first full first-orde... | Inductive Logic Programming | 0.815039 |
14,609 | Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP sys... | Inductive Logic Programming | 0.815039 |
14,610 | Scalar particles (neutral atoms) described by the Klein–Gordon equation can be accelerated by gravitational waves (e.g. those emitted from black hole mergers.) The physical basis for macromolecular bioactivity — molecular recognition — the protein-protein and protein-DNA interaction, is poorly understood. Such interact... | Resonant interaction | 0.815037 |
14,611 | Resonant interaction between acoustic waves and soliton internal waves have been proposed as the source of these anomalies. In astrophysics, non-linear resonant interactions between warping and oscillations in the relativistically spinning accretion disk around a black hole have been proposed as the origin of observed ... | Resonant interaction | 0.815037 |
14,612 | The resonant interactions of Rossby waves have been observed to have a connection to Diophantine equations, normally considered to be a topic in number theory. Constructive methods for solving Diophantine equations appearing in the context of the resonant wave interactions of various types (including Rossby waves) have... | Resonant interaction | 0.815037 |
14,613 | Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; inst... | Resonant interaction | 0.815037 |
14,614 | In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields... | Resonant interaction | 0.815037 |
14,615 | To select these top four life science contestants for this international competition, all member countries host Biology Olympiad competitions in typically 3-5 consecutively more difficult national competition rounds. As a consequence, this leads to a trickle-down effect, engaging more than 1 million students worldwide ... | International Biology Olympiad | 0.815036 |
14,616 | The International Biology Olympiad (IBO) is a biological olympiad for pre-university students under the age 20, and is one of the most well-known International Science Olympiads. The first IBO was held in Czechoslovakia in 1990, and it has since been held annually. The competition have gradually expanded to include mor... | International Biology Olympiad | 0.815036 |
14,617 | Finally, they had to propose a professional poster or presentation about an outstanding, innovative idea that can determine biology's future and solve a critical global issue. Every performance was evaluated by noble professors of Japan in life science. Altogether, 53 countries and 202 contestants participated in the I... | International Biology Olympiad | 0.815036 |
14,618 | In the face of the threat of the International Science Olympiads' cancellation due to the COVID-19 pandemic (the International Physics Olympiad was officially canceled), the IBO 2020 was the first in the International Science Olympiads that was claimed by the host (Japan) to be held entirely virtually with a guaranteed... | International Biology Olympiad | 0.815036 |
14,619 | The Chemical Engineer is a monthly chemical engineering technical and news magazine published by the Institution of Chemical Engineers (IChemE). It has technical articles of interest to practitioners and educators, and also addresses current events in world of chemical engineering including research, international busi... | The Chemical Engineer | 0.815036 |
14,620 | To describe the real spin representations, one must know how the spin group sits inside its Clifford algebra. The pin group, Pinp,q is the set of invertible elements in Clp,q that can be written as a product of unit vectors: Comparing with the above concrete realizations of the Clifford algebras, the pin group correspo... | Clifford multiplication | 0.815035 |
14,621 | Given a vector space V, one can construct the exterior algebra ⋀V, whose definition is independent of any quadratic form on V. It turns out that if K does not have characteristic 2 then there is a natural isomorphism between ⋀V and Cl(V, Q) considered as vector spaces (and there exists an isomorphism in characteristic ... | Clifford multiplication | 0.815035 |
14,622 | In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected wi... | Clifford multiplication | 0.815035 |
14,623 | For the same reasons, the irreducible representations of the spin coincide with the irreducible representations of Clp,q. To classify the pin representations, one need only appeal to the classification of Clifford algebras. To find the spin representations (which are representations of the even subalgebra), one can fir... | Clifford multiplication | 0.815035 |
14,624 | Recall that the tensor algebra T(V) has a natural filtration: F0 ⊂ F1 ⊂ F2 ⊂ ⋯, where Fk contains sums of tensors with order ≤ k. Projecting this down to the Clifford algebra gives a filtration on Cl(V, Q). The associated graded algebra is naturally isomorphic to the exterior algebra ⋀V. Since the associated graded alg... | Clifford multiplication | 0.815035 |
14,625 | Clifford multiplication together with the distinguished subspace is strictly richer than the exterior product since it makes use of the extra information provided by Q. The Clifford algebra is a filtered algebra, the associated graded algebra is the exterior algebra. More precisely, Clifford algebras may be thought of ... | Clifford multiplication | 0.815035 |
14,626 | Clifford algebras are closely related to exterior algebras. Indeed, if Q = 0 then the Clifford algebra Cl(V, Q) is just the exterior algebra ⋀V. For nonzero Q there exists a canonical linear isomorphism between ⋀V and Cl(V, Q) whenever the ground field K does not have characteristic two. That is, they are naturally iso... | Clifford multiplication | 0.815035 |
14,627 | Cl0,1(R) is a two-dimensional algebra generated by e1 that squares to −1, and is algebra-isomorphic to C, the field of complex numbers. Cl0,2(R) is a four-dimensional algebra spanned by {1, e1, e2, e1e2}. The latter three elements all square to −1 and anticommute, and so the algebra is isomorphic to the quaternions H. ... | Clifford multiplication | 0.815035 |
14,628 | A standard basis {e1, ..., en} for Rp,q consists of n = p + q mutually orthogonal vectors, p of which square to +1 and q of which square to −1. Of such a basis, the algebra Clp,q(R) will therefore have p vectors that square to +1 and q vectors that square to −1. A few low-dimensional cases are: Cl0,0(R) is naturally is... | Clifford multiplication | 0.815035 |
14,629 | The Clifford algebra on Rp,q is denoted Clp,q(R). The symbol Cln(R) means either Cln,0(R) or Cl0,n(R) depending on whether the author prefers positive-definite or negative-definite spaces. | Clifford multiplication | 0.815035 |
14,630 | Clifford algebras are also sometimes referred to as geometric algebras, most often over the real numbers. Every nondegenerate quadratic form on a finite-dimensional real vector space is equivalent to the standard diagonal form: where n = p + q is the dimension of the vector space. The pair of integers (p, q) is called ... | Clifford multiplication | 0.815035 |
14,631 | One of the principal applications of the exterior algebra is in differential geometry where it is used to define the bundle of differential forms on a smooth manifold. In the case of a (pseudo-)Riemannian manifold, the tangent spaces come equipped with a natural quadratic form induced by the metric. Thus, one can defin... | Clifford multiplication | 0.815035 |
14,632 | One can also study Clifford algebras on complex vector spaces. Every nondegenerate quadratic form on a complex vector space of dimension n is equivalent to the standard diagonal form Thus, for each dimension n, up to isomorphism there is only one Clifford algebra of a complex vector space with a nondegenerate quadratic... | Clifford multiplication | 0.815035 |
14,633 | In this section, Hamilton's quaternions are constructed as the even subalgebra of the Clifford algebra Cl3,0(R). Let the vector space V be real three-dimensional space R3, and the quadratic form be the usual quadratic form. Then, for v, w in R3 we have the bilinear form (or scalar product) Now introduce the Clifford pr... | Clifford multiplication | 0.815035 |
14,634 | As a vector space, the dimension of the cycle space of a graph with n {\displaystyle n} vertices, m {\displaystyle m} edges, and c {\displaystyle c} connected components is m − n + c {\displaystyle m-n+c} . This number can be interpreted topologically as the first Betti number of the graph. In graph theory, it is known... | Cycle space | 0.815035 |
14,635 | In planar graphs, colorings with k {\displaystyle k} distinct colors are dual to nowhere-zero flows over the ring Z k {\displaystyle \mathbb {Z} _{k}} of integers modulo k {\displaystyle k} . In this duality, the difference between the colors of two adjacent regions is represented by a flow value across the edge separa... | Cycle space | 0.815035 |
14,636 | In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree subgraphs. This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dimension of this space is the circuit rank of the graph. The same space can al... | Cycle space | 0.815035 |
14,637 | Applying this fact separately to the neighborhoods of each vertex shows that the symmetric difference operator preserves the property of being Eulerian. A family of sets closed under the symmetric difference operation can be described algebraically as a vector space over the two-element finite field Z 2 {\displaystyle ... | Cycle space | 0.815035 |
14,638 | If one applies any set operation such as union or intersection of sets to two spanning subgraphs of a given graph, the result will again be a subgraph. In this way, the edge space of an arbitrary graph can be interpreted as a Boolean algebra. The cycle space, also, has an algebraic structure, but a more restrictive one... | Cycle space | 0.815035 |
14,639 | By Veblen's theorem, every Eulerian subgraph of a given graph can be decomposed into simple cycles, subgraphs in which all vertices have degree zero or two and in which the degree-two vertices form a connected set. Therefore, it is always possible to find a basis in which the basis elements are themselves all simple cy... | Cycle space | 0.815035 |
14,640 | An undirected graph may be viewed as a simplicial complex with its vertices as zero-dimensional simplices and the edges as one-dimensional simplices. The chain complex of this topological space consists of its edge space and vertex space (the Boolean algebra of sets of vertices), connected by a boundary operator that m... | Cycle space | 0.815035 |
14,641 | Though it can be implemented more efficiently using modular exponentiation, when large values of m are involved this is most efficiently computed with the Montgomery reduction method. This algorithm itself requires a modular inverse mod m, which is what was to be calculated in the first place. Without the Montgomery me... | Discrete inverse | 0.815034 |
14,642 | As an alternative to the extended Euclidean algorithm, Euler's theorem may be used to compute modular inverses.According to Euler's theorem, if a is coprime to m, that is, gcd(a, m) = 1, then a ϕ ( m ) ≡ 1 ( mod m ) , {\displaystyle a^{\phi (m)}\equiv 1{\pmod {m}},} where ϕ {\displaystyle \phi } is Euler's totient func... | Discrete inverse | 0.815034 |
14,643 | As with the analogous operation on the real numbers, a fundamental use of this operation is in solving, when possible, linear congruences of the form a x ≡ b ( mod m ) . {\displaystyle ax\equiv b{\pmod {m}}.} Finding modular multiplicative inverses also has practical applications in the field of cryptography, e.g. publ... | Discrete inverse | 0.815033 |
14,644 | Protein structure prediction is the prediction of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of a protein's tertiary structure from its primary structure. It is one of the most important goals pursued by bioinformatics and theoretical chemistry. Protein structure p... | Systems biology modeling | 0.815033 |
14,645 | In mathematics, the base change theorems relate the direct image and the inverse image of sheaves. More precisely, they are about the base change map, given by the following natural transformation of sheaves: g ∗ ( R r f ∗ F ) → R r f ∗ ′ ( g ′ ∗ F ) {\displaystyle g^{*}(R^{r}f_{*}{\mathcal {F}})\to R^{r}f'_{*}(g'^{*}{... | Base change theorems | 0.815031 |
14,646 | Machine learning and AI depend on the development of novel algorithms, software and hardware technologies. As such, Meta AI's systems research teams studies computer languages, compilers, and hardware applications. | Meta AI | 0.81503 |
14,647 | Artificial intelligence communication requires a machine to understand natural language and to generate language that is natural. Meta AI seeks to improve these technologies to improve safe communication regardless of what language the user might speak. Thus, a central task involves the generalization of natural langua... | Meta AI | 0.81503 |
14,648 | Meta AI's computer vision research aims to extract information about the environment from digital images and videos. One example of computer vision technology developed by AI is panoptic segmentation, which recognizes objects in the foreground but also classifies the scenes in the background. Meta AI seeks to improve V... | Meta AI | 0.81503 |
14,649 | Meta AI studies the mathematical and theoretical foundations of artificial intelligence. Meta AI has publications in learning theory, optimization, and signal processing. | Meta AI | 0.81503 |
14,650 | FAIR released Torch deep-learning modules as well as PyTorch in 2017, an open-source machine learning framework, which was subsequently used in several deep learning technologies, such as Tesla's autopilot and Uber's Pyro. Also in 2017, FAIR discontinued a research project once AI bots developed a language that was uni... | Meta AI | 0.81503 |
14,651 | In 2018, FAIR was placed 25th in the AI Research Rankings 2019, which ranked the top global organizations leading AI research. FAIR quickly rose to eighth position in 2019, and maintained eighth position in the 2020 rank. FAIR had approximately 200 staff in 2018, and had the goal to double that number by 2020.FAIR's in... | Meta AI | 0.81503 |
14,652 | FAIR opened a research center in Paris, France in 2015, and subsequently launched smaller satellite research labs in Seattle, Pittsburgh, Tel Aviv, Montreal and London. In 2016, FAIR partnered with Google, Amazon, IBM, and Microsoft in creating the Partnership on Artificial Intelligence to Benefit People and Society, a... | Meta AI | 0.81503 |
14,653 | Working with NYU's Center for Data Science, FAIR's initial goal was to research data science, machine learning, and artificial intelligence and to "understand intelligence, to discover its fundamental principles, and to make machines significantly more intelligent". Research at FAIR pioneered the technology that led to... | Meta AI | 0.81503 |
14,654 | Meta AI started as Facebook Artificial Intelligence Research (FAIR) with locations in the Menlo Park, California, headquarters, London, United Kingdom, and a new laboratory in Manhattan. FAIR was officially announced in September, 2013. FAIR was directed by New York University's Yann LeCun, a deep learning Professor an... | Meta AI | 0.81503 |
14,655 | Meta AI is an artificial intelligence laboratory that belongs to Meta Platforms Inc. (formerly known as Facebook, Inc.) Meta AI intends to develop various forms of artificial intelligence, improving augmented and artificial reality technologies. Meta AI is an academic research laboratory focused on generating knowledge... | Meta AI | 0.81503 |
14,656 | In the February 23, 2022, live event Inside the Lab: Building for the Metaverse with AI, the Meta AI team discussed the major advancements in research and development in artificial intelligence. One such tool is the BuilderBot, which allows users to generate virtual worlds by using voice commands. Other tools include t... | Meta AI | 0.81503 |
14,657 | Simulating the geodynamo by computer requires numerically solving a set of nonlinear partial differential equations for the magnetohydrodynamics (MHD) of the Earth's interior. Simulation of the MHD equations is performed on a 3D grid of points and the fineness of the grid, which in part determines the realism of the so... | Terrestrial magnetism | 0.815028 |
14,658 | The C–Pb bond in tetramethyllead is 222 pm long with a dissociation energy of 49 kcal/mol (204 kJ/mol). For comparison the C–Sn bond in tetramethyltin is 214 pm long with dissociation energy 71 kcal/mol (297 kJ/mol). The dominance of Pb(IV) in organolead chemistry is remarkable because inorganic lead compounds tend to ... | Organolead compound | 0.815027 |
14,659 | Organolead chemistry is the scientific study of the synthesis and properties of organolead compounds, which are organometallic compounds containing a chemical bond between carbon and lead. The first organolead compound was hexaethyldilead (Pb2(C2H5)6), first synthesized in 1858. Sharing the same group with carbon, lead... | Organolead compound | 0.815027 |
14,660 | Artificial selection, also known as selective breeding, is imposed by an outside entity, typically humans, in order to increase the frequency of desired traits. The principles of population genetics apply similarly to all types of selection, though in fact each may produce distinct effects due to clustering of genes wi... | Molecular Evolution | 0.815022 |
14,661 | The history of molecular evolution starts in the early 20th century with comparative biochemistry, and the use of "fingerprinting" methods such as immune assays, gel electrophoresis, and paper chromatography in the 1950s to explore homologous proteins. The field of molecular evolution came into its own in the 1960s and... | Molecular Evolution | 0.815022 |
14,662 | Molecular evolution is the process of change in the sequence composition of cellular molecules such as DNA, RNA, and proteins across generations. The field of molecular evolution uses principles of evolutionary biology and population genetics to explain patterns in these changes. Major topics in molecular evolution con... | Molecular Evolution | 0.815022 |
14,663 | In spectral graph theory, an eigenvalue of a graph is defined as an eigenvalue of the graph's adjacency matrix A {\displaystyle A} , or (increasingly) of the graph's Laplacian matrix due to its discrete Laplace operator, which is either D − A {\displaystyle D-A} (sometimes called the combinatorial Laplacian) or I − D −... | Spectral properties | 0.815019 |
14,664 | In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by λ {\displaystyle \lambda } , is the multiplying factor. Geometricall... | Spectral properties | 0.815019 |
14,665 | ML Fairness, short for Machine Learning Fairness, is an initiative by Google to implement fairness as a part of their machine learning techniques. The campaign is presented as a means to stop political bias in artificial intelligence. == References == | ML Fairness | 0.815014 |
14,666 | Some organisms can detect magnetic fields, a phenomenon known as magnetoception. Some materials in living things are ferromagnetic, though it is unclear if the magnetic properties serve a special function or are merely a byproduct of containing iron. For instance, chitons, a type of marine mollusk, produce magnetite to... | Magnetic attraction | 0.815014 |
14,667 | However, in its generalizations such as noncommutative field theory and quantum gravity—string theory in particular—it is expected that interrelations between UV and IR physics start to emerge. In many cases, these interrelations, UV/IR mixing, may be demonstrated explicitly. Longer, technical description can be found ... | UV/IR mixing | 0.815008 |
14,668 | In theoretical physics, it is usually possible to organize physical phenomena according to the energy scale or distance scale. The theory of renormalization group is based on this paradigm. The short-distance, ultraviolet (UV) physics does not directly affect qualitative features of the long-distance, infrared (IR) phy... | UV/IR mixing | 0.815008 |
14,669 | In general, the decision version of the knapsack problem (Can a value of at least V be achieved under a restriction of a certain capacity W?) is NP-complete. Thus, a given solution can be verified to in polynomial time while no algorithm can identify a solution efficiently. The optimization knapsack problem is NP-hard ... | Quadratic knapsack problem | 0.815005 |
14,670 | As one might expect, QKP has a wide range of applications including telecommunication, transportation network, computer science and economics. In fact, Witzgall first discussed QKP when selecting sites for satellite stations in order to maximize the global traffic with respect to a budget constraint. Similar model appl... | Quadratic knapsack problem | 0.815005 |
14,671 | Quadknap is an exact branch-and-bound algorithm proposed by Caprara et al., where upper bounds are computed by considering a Lagrangian relaxation which approximate a difficult problem by a simpler problem and penalizes violations of constraints using Lagrange multiplier to impost a cost on violations. Quadknap release... | Quadratic knapsack problem | 0.815005 |
14,672 | We need to make P a positive semi-definite matrix in order to reformulate a convex function. In this case, we modify the objective function to be p T x + x T P x + ∑ i = 1 n ( ∑ j = 1 , j ≠ i n | P i j | ) ( x i 2 − x i ) {\displaystyle p^{T}x+x^{T}Px+\sum _{i=1}^{n}\left(\sum _{j=1,j\neq i}^{n}|P_{ij}|\right)(x_{i}^{2... | Quadratic knapsack problem | 0.815005 |
14,673 | Informally, a function is concave if the line segment connecting two points on the graph lies above or on the graph, while a function is convex if below or on the graph. Thus, by rewriting the objective function into an equivalent convex function, we can reformulate the program to be convex, which can be solved using o... | Quadratic knapsack problem | 0.815005 |
14,674 | Computational scientists are typically researchers at academic universities, national labs, or tech companies.One of the tasks of a computational scientist is to analyze large amounts of data, often from astrophysics or related fields, as these can often generate huge amounts of data. Computational scientists often hav... | Computational scientist | 0.815005 |
14,675 | A computational scientist is a person skilled in scientific computing. This person is usually a scientist, a statistician, an applied mathematician, or an engineer who applies high-performance computing and sometimes cloud computing in different ways to advance the state-of-the-art in their respective applied disciplin... | Computational scientist | 0.815005 |
14,676 | Dalvit, Diego; Milonni, Peter; Roberts, David; Da Rosa, Felipe (2011). Dalvit, Diego; Milonni, Peter W.; Roberts, David; da Rosa, Felipe (eds.). Casimir Physics. | Casimir vacuum | 0.815002 |
14,677 | "New developments in the Casimir effect". Physics Reports. 353 (1–3): 1–205. | Casimir vacuum | 0.815002 |
14,678 | In this case, it should be understood that additional physics has to be taken into account. In particular, at extremely large frequencies (above the plasma frequency), metals become transparent to photons (such as X-rays), and dielectrics show a frequency-dependent cutoff as well. This frequency dependence acts as a na... | Casimir vacuum | 0.815002 |
14,679 | The set of associations among a collection of items in memory is equivalent to the links between nodes in a network, where each node corresponds to a unique item in memory. Indeed, neural networks and semantic networks may be characterized as associative models of cognition. However, associations are often more clearly... | Semantic memory | 0.815 |
14,680 | Positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) allow cognitive neuroscientists to explore different hypotheses concerning the neural network organization of semantic memory. By using these neuroimaging techniques researchers can observe the brain activity of participants while they ... | Semantic memory | 0.815 |
14,681 | This solution gives the circuit voltages and currents when the circuit is in DC steady state. Such a circuit is represented by a system of differential equations. The solution to these equations usually contain a time varying or transient part as well as constant or steady state part. | Direct current circuit | 0.814999 |
14,682 | In molecular biology, open reading frames (ORFs) are defined as spans of DNA sequence between the start and stop codons. Usually, this is considered within a studied region of a prokaryotic DNA sequence, where only one of the six possible reading frames will be "open" (the "reading", however, refers to the RNA produced... | Open reading frame | 0.814998 |
14,683 | Many terms in the Hamiltonians of atomic or molecular systems involve the scalar product of angular momentum operators. An example is the magnetic dipole term in the hyperfine Hamiltonian, where I is the nuclear spin. The angular momentum algebra can often be simplified by recasting it in the spherical basis. Using the... | Ladder operators | 0.814997 |
14,684 | Digital transcriptome subtraction (DTS) is a bioinformatics method to detect the presence of novel pathogen transcripts through computational removal of the host sequences. DTS is the direct in silico analogue of the wet-lab approach representational difference analysis (RDA), and is made possible by unbiased high-thro... | Digital transcriptome subtraction | 0.814997 |
14,685 | Once a putative pathogen has been identified in the high-throughput sequencing data, it is imperative to validate the presence of pathogen in infected patients using more sensitive techniques, such as: RT-PCR and derivative methods, including 3'- and 5'-RACE to confirm the existence of pathogen mRNA. Immunohistochemist... | Digital transcriptome subtraction | 0.814997 |
14,686 | If two points lie in a plane, the line containing them lies in the plane. Unique plane assumption. Through three non-collinear points, there is exactly one plane. Intersecting planes assumption. If two different planes have a point in common, then their intersection is a line.The first three assumptions of the postulat... | Point-line-plane postulate | 0.814996 |
14,687 | The axiomatic foundation of Euclidean geometry can be dated back to the books known as Euclid's Elements (circa 300 B.C.). These five initial axioms (called postulates by the ancient Greeks) are not sufficient to establish Euclidean geometry. Many mathematicians have produced complete sets of axioms which do establish ... | Point-line-plane postulate | 0.814996 |
14,688 | In mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a "normal form" that can be computed by a finite transducer: multiplication in such a monoid is "easy", in the sense that it can be described by a rational function. | Kleene monoid | 0.814994 |
14,689 | Let f: → R be a continuous function, and suppose that f (a) < 0 and f (b) > 0. In this case, the intermediate value theorem states that f must have a root in the interval . This theorem can be proved by considering the set S = {s ∈ : f (x) < 0 for all x ≤ s} .That is, S is the initial segment of that takes negative v... | Dedekind completeness | 0.814994 |
14,690 | Published protocols are sorted into the following categories: Biochemistry Cell and tissue culture Cell biology and developmental biology (includes detection of apoptosis and others) Computational biology and theoretical biology (includes bioinformatics) Genetic analysis (includes classical genetics, reverse genetics, ... | Nature Protocols | 0.814984 |
14,691 | This choice of parameters gives the vertices the positions of Jessen's icosahedron; they are different from the regular icosahedron, for which the ratio of d {\displaystyle d} and l {\displaystyle l} would be the golden ratio, rather than 2. However both sets of coordinates lie along a continuous family of positions ra... | Tensegrity | 0.814984 |
14,692 | Biotensegrity, a term coined by Dr. Stephen Levin, is an extended theoretical application of tensegrity principles to biological structures. Biological structures such as muscles, bones, fascia, ligaments and tendons, or rigid and elastic cell membranes, are made strong by the unison of tensioned and compressed parts. ... | Tensegrity | 0.814984 |
14,693 | Tensegrity structures are based on the combination of a few simple design patterns: members loaded in either pure compression or pure tension, which means that the structure will only fail if the cables yield or the rods buckle. This enables the material properties and cross-sectional geometry of each member to be opti... | Tensegrity | 0.814984 |
14,694 | Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers. Some of the main breakthroughs include: convolutional neural networks that have proven particularly succ... | Artificial Neural Network | 0.814983 |
14,695 | ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter ... | Artificial Neural Network | 0.814983 |
14,696 | This behavior is referred to as the spectral bias, or frequency principle, of neural networks. This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions. | Artificial Neural Network | 0.814983 |
14,697 | A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections followi... | Artificial Neural Network | 0.814983 |
14,698 | Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some meth... | Artificial Neural Network | 0.814983 |
14,699 | As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attem... | Artificial Neural Network | 0.814983 |
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