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22,500 | This is because these studies are thought to overlook the vast majority of deleterious mutations for which the overall effect on viability is too small in magnitude to be observed by way of such assays. Higher Ud values (>1) that are more in line with current scientific consensus regarding the estimation of this parame... | Mutation accumulation experiments | 0.80936 |
22,501 | A mutation accumulation experiment conducted by Ruth Shaw and colleagues serves as a good example of a typical MA experiment: the group sought to measure the effects of spontaneous mutations on the reproductive traits of Arabidopsis thaliana. A.thaliana is an ideal candidate for a MA experiment because it is capable of... | Mutation accumulation experiments | 0.80936 |
22,502 | Facebook, and other similar social media platforms, have been able to figure out how to use artificial intelligence and machine learning, or more specifically weak AI, to predict how people will react to being show certain images. Weak artificial intelligence systems have been able to identify what users will identify ... | Narrow AI | 0.809353 |
22,503 | Autocorrection for typing, speech recognition for speech to text programs, and vast expansions in the data science fields are just to name a few. As much as weak and some strong AI is slowly starting to help out societies, they are also starting to hurt it as well. AI had already unfairly put people in jail, discrimina... | Narrow AI | 0.809353 |
22,504 | Another issue with weak artificial intelligence currently, is that behavior that it follows can become inconsistent. Patterns could become difficulty to come up with one consistent system that worked every time. Simple artificial intelligence programs have already worked their way into our society and we just might not... | Narrow AI | 0.809353 |
22,505 | John Wallis algebrised this method; he wrote in his Arithmetica Infinitorum (1656) some series which are equivalent to what is now called the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress: quadratures for some algebraic curves and spirals. Christiaan Huygens suc... | Quadrature (mathematics) | 0.809348 |
22,506 | In mathematics, quadrature is a historical term for the process of determining area. This term is still used in the context of differential equations, where "solving an equation by quadrature" or "reduction to quadrature" means expressing its solution in terms of integrals. Quadrature problems served as one of the main... | Quadrature (mathematics) | 0.809348 |
22,507 | As such, the Gödel sentence can be written in the language of arithmetic with a simple syntactic form. In particular, it can be expressed as a formula in the language of arithmetic consisting of a number of leading universal quantifiers followed by a quantifier-free body (these formulas are at level Π 1 0 {\displaystyl... | First incompleteness theorem | 0.809347 |
22,508 | To prove the first incompleteness theorem, Gödel demonstrated that the notion of provability within a system could be expressed purely in terms of arithmetical functions that operate on Gödel numbers of sentences of the system. Therefore, the system, which can prove certain facts about numbers, can also indirectly prov... | First incompleteness theorem | 0.809347 |
22,509 | The closure of the stable shells predicts unusually stable configurations, analogous to the noble group of nearly-inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element. Similarly, the distance from shell-closure ... | Nuclear model | 0.809347 |
22,510 | A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting ... | Nuclear model | 0.809347 |
22,511 | The Monitoring through many eyes project collates thousands of underwater images of the Great Barrier Reef and provides an interface for elicitation of reef health indicators.The National Oceanic and Atmospheric Administration (NOAA) also offers opportunities for volunteer participation. By taking measurements in The U... | Citizen scientists | 0.809347 |
22,512 | One of the largest citizen science games is Eyewire, a brain-mapping puzzle game developed at the Massachusetts Institute of Technology that now has over 200,000 players. Another example is Quantum Moves, a game developed by the Center for Driven Community Research at Aarhus University, which uses online community effo... | Citizen scientists | 0.809347 |
22,513 | This includes supporting, organization and dissemination of personal DNA (genetic) testing. Like amateur astronomy, citizen scientists encouraged by volunteer organizations like the International Society of Genetic Genealogy have provided valuable information and research to the professional scientific community.With u... | Citizen scientists | 0.809347 |
22,514 | Scientist Joshua Pearce has advocated for the creation of open-source hardware based scientific equipment that both citizen scientists and professional scientists, which can be replicated by digital manufacturing techniques such as 3D printing. Multiple studies have shown this approach radically reduces scientific equi... | Citizen scientists | 0.809347 |
22,515 | Newer technologies have increased the options for citizen science. Citizen scientists can build and operate their own instruments to gather data for their own experiments or as part of a larger project. Examples include amateur radio, amateur astronomy, Six Sigma Projects, and Maker activities. | Citizen scientists | 0.809347 |
22,516 | In the research paper "Can citizen science enhance public understanding of science?" by Bonney et al. 2016, statistics which analyse the economic worth of citizen science are used, drawn from two papers: i) Sauermann and Franzoni 2015, and ii)Theobald et al. 2015. In "Crowd science user contribution patterns and their ... | Citizen scientists | 0.809347 |
22,517 | Premultiplied alpha A variation of a bitmap image or alpha blending calculation in which the RGB color values are assumed to be already multiplied by an alpha channel, to reduce computations during Alpha blending; uses the blend operation: dst *= (1 - alpha) + src; capable of mixing alpha blending with additive blendin... | Vertex buffer | 0.809346 |
22,518 | Photometry Science of measuring light in terms of human perception. Photon mapping Photorealistic rendering algorithm based on tracing rays from the camera as well as light sources, able to simulate effects such as caustics. Physically based rendering (PBR) Rendering algorithms based on physics simulation of light, inc... | Vertex buffer | 0.809346 |
22,519 | Mathematically, this is stated like so: k B T = h 2 2 m λ 2 < h 2 2 m d 2 {\displaystyle k_{B}T={\frac {h^{2}}{2m\lambda ^{2}}}<{\frac {h^{2}}{2md^{2}}}} It is easy to see how the above definition relates to the particle density, n. We can write k B T < h 2 2 m n 2 3 {\displaystyle k_{B}T<{\frac {h^{2}}{2m}}n^{\frac {2... | Quantum fluids | 0.809343 |
22,520 | Quantum mechanical effects become significant for physics in the range of the de Broglie wavelength. For condensed matter, this is when the de Broglie wavelength of a particle is greater than the spacing between the particles in the lattice that comprises the matter. The de Broglie wavelength associated with a massive ... | Quantum fluids | 0.809343 |
22,521 | In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem. | Pascal's simplex | 0.809341 |
22,522 | Under Tannaka–Krein duality, every fusion category arises as the representations of a weak Hopf algebra. | Fusion category | 0.80934 |
22,523 | In mathematics, a fusion category is a category that is rigid, semisimple, k {\displaystyle k} -linear, monoidal and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field k {\displaystyle k} is algebraically closed, then the latter is equivalent to H o ... | Fusion category | 0.80934 |
22,524 | In plasma physics, plasma confinement refers to the act of maintaining a plasma in a discrete volume. Confining plasma is required in order to achieve fusion power. There are two major approaches to confinement: magnetic confinement and inertial confinement. | Plasma containment | 0.80934 |
22,525 | The Mach–Zehnder interferometer (MZI) illustrates the concepts of superposition and interference with linear algebra in dimension 2, rather than differential equations. It can be seen as a simplified version of the double-slit experiment, but it is of interest in its own right, for example in the delayed choice quantum... | Quantum system | 0.809333 |
22,526 | In physical chemistry, when referring to surface processes, saturation denotes the degree at which a binding site is fully occupied. For example, base saturation refers to the fraction of exchangeable cations that are base cations. == References == | Coordinative unsaturation | 0.809333 |
22,527 | In 1961 Gottlieb became the first director of the renamed Princeton Plasma Physics Laboratory. 1951–1961: Lyman Spitzer, director of Project Matterhorn 1961–1980: Melvin B. Gottlieb 1981–1990: Harold Fürth 1991–1996: Ronald C. Davidson 1997 (January–July): John A. Schmidt, interim director 1997–2008: Robert J. Goldston... | Princeton Plasma Physics Laboratory | 0.809331 |
22,528 | In 1950, John Wheeler was setting up a secret H-bomb research lab at Princeton University. Lyman Spitzer, Jr., an avid mountaineer, was aware of this program and suggested the name "Project Matterhorn".Spitzer, a professor of astronomy, had for many years been involved in the study of very hot rarefied gases in interst... | Princeton Plasma Physics Laboratory | 0.809331 |
22,529 | Matterhorn ultimately ended its involvement in the bomb field in 1954, becoming entirely devoted to the fusion power field. In 1958, this magnetic fusion research was declassified following the United Nations International Conference on the Peaceful Uses of Atomic Energy. This generated an influx of graduate students e... | Princeton Plasma Physics Laboratory | 0.809331 |
22,530 | DOE Scientific Simulation Initiative U.S. MHD Working Group Field Reversed Configuration (FRC) Theory Consortium Tokamak Physics Design and Analysis Codes TRANSP Code National Transport Code Collaboration (NTCC) Modules Library | Princeton Plasma Physics Laboratory | 0.809331 |
22,531 | The focus of this program changed from H-bombs to fusion power in 1951, when Lyman Spitzer developed the stellarator concept and was granted funding from the Atomic Energy Commission to study the concept. This led to a series of machines in the 1950s and 1960s. In 1961, after declassification, Project Matterhorn was re... | Princeton Plasma Physics Laboratory | 0.809331 |
22,532 | Princeton Plasma Physics Laboratory (PPPL) is a United States Department of Energy national laboratory for plasma physics and nuclear fusion science. Its primary mission is research into and development of fusion as an energy source. It is known in particular for the development of the stellarator and tokamak designs, ... | Princeton Plasma Physics Laboratory | 0.809331 |
22,533 | The PPPL physicist Richard Hawryluk served as ITER Deputy Director-General from 2011 to 2013. In 2022, PPPL staff developed with researchers from other national labs and universities over several months an US ITER research plan during the joint Fusion Energy Sciences Research Needs Workshop.Staff are applying knowledge... | Princeton Plasma Physics Laboratory | 0.809331 |
22,534 | Furthermore, the polarization is compatible with the algebraic structure on A , {\displaystyle A,} so that where Sym ⋅ V ∗ {\displaystyle \operatorname {Sym} ^{\cdot }V^{*}} is the full symmetric algebra over V ∗ . {\displaystyle V^{*}.} | Polarization formula | 0.80933 |
22,535 | In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by e... | Polarization formula | 0.80933 |
22,536 | Many DUFs are highly conserved, indicating an important role in biology. However, many such DUFs are not essential, hence their biological role often remains unknown. For instance, DUF143 is present in most bacteria and eukaryotic genomes. | Domain of unknown function | 0.809327 |
22,537 | In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense... | Pseudo inverse | 0.809327 |
22,538 | ISBN 978-0-521-38632-6. Nakamura, Yoshihiko (1991). Advanced Robotics: Redundancy and Optimization. | Pseudo inverse | 0.809327 |
22,539 | In September or October 2014, Newlink formed a steering committee among the interested parties, including PHAC, the NIH, and the WHO, to plan the clinical development of the vaccine.In October 2014, Newlink Genetics began a Phase I clinical trial of rVSV-ZEBOV on healthy human subjects to evaluate the immune response, ... | RVSV-ZEBOV vaccine | 0.809323 |
22,540 | In 2005, a single intramuscular injection of the EBOV or MARV vaccine was found to induce completely protective immune responses in nonhuman primates (crab-eating macaques) against corresponding infections with the otherwise typically lethal EBOV or MARV.In 2010, PHAC licensed the intellectual property on the vaccine t... | RVSV-ZEBOV vaccine | 0.809323 |
22,541 | It consists of rice-derived recombinant human serum albumin and live attenuated recombinant vesicular stomatitis virus (VSV), which has been genetically engineered to express the main glycoprotein from the Zaire ebolavirus so as to provoke a neutralizing immune response to the Ebola virus.The vaccine was approved for m... | RVSV-ZEBOV vaccine | 0.809323 |
22,542 | System appreciation is an activity often included in the maintenance phase of software engineering projects. Key deliverables from this phase include documentation that describes what the system does in terms of its functional features, and how it achieves those features in terms of its architecture and design. Softwar... | System appreciation | 0.809323 |
22,543 | Ringel's motivation was in trying to solve a variation of total coloring for planar graphs, in which one simultaneously colors the vertices and faces of a planar graph in such a way that no two adjacent vertices have the same color, no two adjacent faces have the same color, and no vertex and face that are adjacent to ... | 1-planar graph | 0.809323 |
22,544 | However, 1-planar graphs that are not optimal 1-planar may not be map graphs.1-planar graphs have been generalized to k-planar graphs, graphs for which each edge is crossed at most k times (0-planar graphs are exactly the planar graphs). Ringel defined the local crossing number of G to be the least non-negative integer... | 1-planar graph | 0.809323 |
22,545 | It is NP-complete to test whether a given graph is 1-planar, and it remains NP-complete even for the graphs formed from planar graphs by adding a single edge and for graphs of bounded bandwidth. The problem is fixed-parameter tractable when parameterized by cyclomatic number or by tree-depth, so it may be solved in pol... | 1-planar graph | 0.809323 |
22,546 | In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point, where it crosses a single additional edge. If a 1-planar graph, one of the most natural generalizations of planar graphs, is drawn that way, the drawing is calle... | 1-planar graph | 0.809323 |
22,547 | In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group SL ( n , R ) ⋉ R n . {\displaystyle {\mbox{SL}}(n,\mathbb {R} )\ltimes \mathbb {R} ^{n}.} In the ... | Affine geometry of curves | 0.80932 |
22,548 | In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In g... | Area | 0.809317 |
22,549 | Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient ... | Area | 0.809317 |
22,550 | There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. | Area | 0.809317 |
22,551 | Another approach for a coordinate triangle is to use calculus to find the area. A simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points: i + b 2 − 1 {\displaystyle i+{\frac {b}{2}}-1} , where i is the number of grid po... | Area | 0.809317 |
22,552 | The development of integral calculus in the late 17th century provided tools that could subsequently be used for computing more complicated areas, such as the area of an ellipse and the surface areas of various curved three-dimensional objects. | Area | 0.809317 |
22,553 | In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at infinitesimal distances. | UV divergence | 0.809316 |
22,554 | Various techniques and tools are used in solid geometry. Among them, analytic geometry and vector techniques have a major impact by allowing the systematic use of linear equations and matrix algebra, which are important for higher dimensions. | Three-dimensional figure | 0.809314 |
22,555 | A major application of solid geometry and stereometry is in 3D computer graphics. | Three-dimensional figure | 0.809314 |
22,556 | Ships which activate hyperdrive close to a star are likely to disappear without a trace. This effect is regarded as a limitation based on the laws of physics. In Niven's novel Ringworld's Children the Ringworld itself is converted into a gigantic Quantum II hyperdrive and launched into hyperspace while within its star'... | Known Space | 0.809313 |
22,557 | The Ringworld is an artificial world structure with three million times the surface area of Earth, built in the shape of a giant ring circling its sun, a million miles wide and with a diameter of 186 million miles. It was built by the Pak, who either abandoned it, or more likely died out much as the Earth Pak did, due ... | Known Space | 0.809313 |
22,558 | As the Reynolds number increases, the continuous turbulent-flow moves closer to the inlet and the intermittency in between increases, until the flow becomes fully turbulent at ReD > 2900. This result is generalized to non-circular channels using the hydraulic diameter, allowing a transition Reynolds number to be calcul... | Reynolds Number | 0.809311 |
22,559 | In order for two flows to be similar, they must have the same geometry and equal Reynolds and Euler numbers. When comparing fluid behavior at corresponding points in a model and a full-scale flow, the following holds: R e m = R e , E u m = E u , {\displaystyle {\begin{aligned}\mathrm {Re} _{\text{m}}&=\mathrm {Re} ,\\\... | Reynolds Number | 0.80931 |
22,560 | SBE-UIET conducted these events in 2019-20: Induction Program 2k19 Induction Programme 2k19 was organised for the freshers on 30 August. Several games such as ball wars and biology charades were there for the students to know each other along with song and dance performances. Our president addressed the students and ta... | Society for Biological Engineering (UIET) | 0.80931 |
22,561 | Emphasis was also be given on understanding the current growth and future prospects of biotechnology in India. Goonj 2019- Bio-Riddles and Pictionary were organised on the 1st day of the fest and Crime Scene Investigation (CSI) on the 2nd day of the fest. Winners were awarded accordingly. | Society for Biological Engineering (UIET) | 0.80931 |
22,562 | SBE UIET offers membership to Biotechnology undergraduates and postgraduates, B.Sc. graduates and postgraduates and research scholars studying in tricity of Chandigarh, Mohali and Panchkula every year. SBE UIET board for a particular year is selected on the basis of several in-person and telephonic interviews. SBE UIET... | Society for Biological Engineering (UIET) | 0.80931 |
22,563 | During this event Assistant Controller of Patent & Designs, Patent Office, Ministry of Industry & Commerce, Government of India Dr Usha Rao deliberated upon the patent laws and IPR issues related to Biotechnology. The second talk by Senior Scientific Officer (Env) & Incharge (PIC), Punjab State Council for Science & Te... | Society for Biological Engineering (UIET) | 0.80931 |
22,564 | SBE UIET conducted several events in 2016-17 and there are many more yet to organize. Some of them are: Bio-cAMP 2016: The IPR Cell of Centre for Industry Institute Partnership Programme (CIIPP) of Panjab University (PU) in collaboration with Cell for IPR Promotion & Management (CIPAM), department of Industrial Policy ... | Society for Biological Engineering (UIET) | 0.80931 |
22,565 | The Society for Biological Engineering (SBE), an American Institute of Chemical Engineers Technological Community, is a professional organization of Biological engineers and scientists in the field of Biotechnology. Its area of working generally focuses on Bioprocessing, Biomedical and Biomolecular engineering. | Society for Biological Engineering (UIET) | 0.80931 |
22,566 | Society for Biological Engineering Students Chapter at UIET, Panjab University (SBE UIET) is professional organisation for Biotechnology students of engineering and sciences running under the department of Biotechnology, University Institute of Engineering and Technology, Panjab University, located in Chandigarh, India... | Society for Biological Engineering (UIET) | 0.80931 |
22,567 | SBE-UIET conducted several events during 2018-19: 1-day industrial trip to Central Research Institute, Kasauli, Himachal Pradesh, India on 5 October 2018. Bio-cAMP 2018: To promote quality research in the field of Biotechnology by acquainting the students to the latest in the field of Biotechnology, a national symposiu... | Society for Biological Engineering (UIET) | 0.80931 |
22,568 | In general, DNA repair enzymes complete the Okazaki fragments through a variety of means, including: base pair excision and 5' to 3' exonuclease activity that removes the chemically unstable ribonucleotides from the lagging duplex and replaces them with stable deoxynucleotides. This process is referred to as 'maturatio... | Replisome | 0.809309 |
22,569 | The replisome is a system in which various factors work together to solve the structural and chemical challenges of DNA replication. Chromosome size and structure varies between organisms, but since DNA molecules are the reservoir of genetic information for all forms of life, many replication challenges and solutions a... | Replisome | 0.809309 |
22,570 | Clamp loader is a generic term that refers to replication factors called gamma (bacteria) or RFC (eukaryotes). The combination of template DNA and primer RNA is referred to as 'A-form DNA' and it is thought that clamp loading replication proteins (helical heteropentamers) want to associate with A-form DNA because of it... | Replisome | 0.809309 |
22,571 | The chemistry of each mismatch varies, and so does the behaviour of the replicative polymerase with respect to its mismatch sensing activity. The replication of bacteriophage T4 DNA upon infection of E. coli is a well-studied DNA replication system. During the period of exponential DNA increase at 37°C, the rate of elo... | Replisome | 0.809309 |
22,572 | Base pair errors distort the polymerase active site for between 4 and 6 nucleotides, which means, depending on the type of mismatch, there are up to six chances for error correction. The error sensing and error correction features, combined with the inherent accuracy that arises from the structure and chemistry of repl... | Replisome | 0.809309 |
22,573 | Subsequently, the chemical reaction in the exonuclease unit takes over and removes nucleotides from the exposed 3' end of the growing chain. Once an error is removed, the structure and chemistry of the polymerisation unit returns to normal and DNA replication continues. Working collectively in this fashion, the polymer... | Replisome | 0.809309 |
22,574 | Although rare, incorrect base pairing polymerisation does occur during chain elongation. (The structure and chemistry of replicative polymerases mean that errors are unlikely, but they do occur.) Many replicative polymerases contain an "error correction" mechanism in the form of a 3' to 5' exonuclease domain that is ca... | Replisome | 0.809309 |
22,575 | Single-stranded DNA is highly unstable and can form hydrogen bonds with itself that are referred to as 'hairpins' (or the single strand can improperly bond to the other single strand). To counteract this instability, single-strand binding proteins (SSB in prokaryotes and Replication protein A in eukaryotes) bind to the... | Replisome | 0.809309 |
22,576 | Processivity refers to both speed and continuity of DNA replication, and high processivity is a requirement for timely replication. High processivity is in part ensured by ring-shaped proteins referred to as 'clamps' that help replicative polymerases stay associated with the leading and lagging strands. There are other... | Replisome | 0.809309 |
22,577 | In probability theory, the Mills ratio (or Mills's ratio) of a continuous random variable X {\displaystyle X} is the function m ( x ) := F ¯ ( x ) f ( x ) , {\displaystyle m(x):={\frac {{\bar {F}}(x)}{f(x)}},} where f ( x ) {\displaystyle f(x)} is the probability density function, and F ¯ ( x ) := Pr = ∫ x + ∞ f ( u )... | Inverse Mills ratio | 0.809306 |
22,578 | {\displaystyle \lambda f. (\lambda y.y\ y)\ (\lambda z.f\ (z\ z))\ .} This is possibly the simplest implementation of a fixed-point combinator in lambda calculus. | Fixed-point combinator | 0.809306 |
22,579 | For instance, they do not exist in simply typed lambda calculus. The Y combinator allows recursion to be defined as a set of rewrite rules, without requiring native recursion support in the language.In programming languages that support anonymous functions, fixed-point combinators allow the definition and use of anonym... | Fixed-point combinator | 0.809306 |
22,580 | In lambda calculus, from a computational point of view, applying a fixed-point combinator to an identity function or an idempotent function typically results in non-terminating computation. For example, we obtain ( Y λ x . | Fixed-point combinator | 0.809306 |
22,581 | In untyped lambda calculus there are terms that have the same Böhm tree as a fixed-point combinator, that is they have the same infinite extension λx.x (x (x ... )). These are called non-standard fixed-point combinators. Any fixed-point combinator is also a non-standard one, but not all non-standard fixed-point combina... | Fixed-point combinator | 0.809306 |
22,582 | In mathematics and computer science in general, a fixed point of a function is a value that is mapped to itself by the function. In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator): page 26 is a higher-order function fix {\displaystyle {\textsf {fix}}} that returns some fixed po... | Fixed-point combinator | 0.809306 |
22,583 | In System F (polymorphic lambda calculus) a polymorphic fixed-point combinator has type; ∀a. (a → a) → awhere a is a type variable. That is, fix takes a function, which maps a → a and uses it to return a value of type a. In the simply typed lambda calculus extended with recursive data types, fixed-point operators can b... | Fixed-point combinator | 0.809306 |
22,584 | Embed the graph in the plane. To prove the theorem, it is sufficient to only consider planar triangulations (because, if it holds on a triangulation, when removing nodes to return to the original graph, neither node on either side of the desired edge can be removed without reducing the minimum degree of the graph below... | Discharging method (discrete mathematics) | 0.809305 |
22,585 | In 1904, Wernicke introduced the discharging method to prove the following theorem, which was part of an attempt to prove the four color theorem. Theorem: If a planar graph has minimum degree 5, then it either has an edge with endpoints both of degree 5 or one with endpoints of degrees 5 and 6. Proof: We use V {\displa... | Discharging method (discrete mathematics) | 0.809305 |
22,586 | The discharging method is a technique used to prove lemmas in structural graph theory. Discharging is most well known for its central role in the proof of the four color theorem. The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list. | Discharging method (discrete mathematics) | 0.809304 |
22,587 | ASC systems #5 and #6 were installed at TI's main plant in Austin and also used by GSI for seismic data processing. ASC #7 went to the Naval Research Lab in Washington, D.C. for plasma physics studies. | TI Advanced Scientific Computer | 0.809303 |
22,588 | The 14 chapters of the book can be grouped into two parts, with the first 2/3 of the book concerning the combinatorial properties of convex polytopes and the remainder connecting these topics to abstract algebra.The topics covered include Schlegel diagrams and Gale diagrams, irrational polytopes, point set triangulatio... | Lectures in Geometric Combinatorics | 0.809299 |
22,589 | Although originally presented as an advanced undergraduate course, the book is also suitable for graduate students and for researchers interested in beginning work in this area. It requires only an undergraduate level of background material in mathematics (particularly linear algebra), and includes exercises making it ... | Lectures in Geometric Combinatorics | 0.809299 |
22,590 | Maristella Agosti, Professor, Department of Information Engineering, University of Padova Gerhard Budin, Director of the Center of Translation Studies at the University of Vienna, Director of the Department of Corpuslinguistics and Text Technology, Austrian Academy of Sciences Jamie Callan, Professor, Language Technolo... | Information Retrieval Facility | 0.809295 |
22,591 | Plasmids, commonly used in genetic manipulation, can also be shared through horizontal gene transfer, which is especially relevant in modern medicine concerning the exchange of antibiotic-resistant plasmids.A cell's competence can be determined by its genetics, which is the case for natural competency, or it can be man... | Competence factor | 0.809295 |
22,592 | In the early 20th century, calculus was formalized using an axiomatic set theory. Lebesgue greatly improved measure theory, and introduced his own theory of integration, now known as Lebesgue integration, which proved to be a big improvement over Riemann's. Hilbert introduced Hilbert spaces to solve integral equations.... | Mathematical Analysis | 0.809294 |
22,593 | Around that time, the attempts to refine the theorems of Riemann integration led to the study of the "size" of the set of discontinuities of real functions. Also, various pathological objects, (such as nowhere continuous functions, continuous but nowhere differentiable functions, and space-filling curves), commonly kno... | Mathematical Analysis | 0.809294 |
22,594 | Thus, his definition of continuity required an infinitesimal change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the formal theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations and harmonic ana... | Mathematical Analysis | 0.809294 |
22,595 | In the 18th century, Euler introduced the notion of a mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the modern definition of continuity in 1816, but Bolzano's work did not become widely known until the 1870s. In 1821, Cauchy began to put calculus on a fir... | Mathematical Analysis | 0.809294 |
22,596 | Complex analysis (traditionally known as the "theory of functions of a complex variable") is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, applied mathematics; as well as in physics, includin... | Mathematical Analysis | 0.809294 |
22,597 | Real analysis (traditionally, the "theory of functions of a real variable") is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences... | Mathematical Analysis | 0.809294 |
22,598 | Additionally, the requirements for substitute/temporary teachers are generally not as rigorous as those for full-time professionals. The Bureau of Labor Statistics estimates that there are 1.4 million elementary school teachers, 674,000 middle school teachers, and 1 million secondary school teachers employed in the U.S... | Teaching aid | 0.809291 |
22,599 | Mathematical Models and Methods in Applied Sciences is a journal founded in 1991 and published by World Scientific. It covers: mathematical modelling of systems in the applied sciences(physics, mathematical physics, natural, and technological sciences); qualitative and quantitative analysis of mathematical physics and ... | Mathematical Models and Methods in Applied Sciences | 0.809291 |
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