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14,300 | Stoic physics refers to the natural philosophy of the Stoic philosophers of ancient Greece and Rome which they used to explain the natural processes at work in the universe. To the Stoics, the cosmos is a single pantheistic god, one which is rational and creative, and which is the basis of everything which exists. Noth... | Stoic physics | 0.815336 |
14,301 | Plato had defined being as "that which has the power to act or be acted upon," and for the Stoics this meant that all action proceeds by bodily contact; every form of causation is reduced to the efficient cause, which implies the communication of motion from one body to another. Only Body exists. The Stoics did recogni... | Stoic physics | 0.815335 |
14,302 | In pursuing their physics the Stoics wanted to create a picture of the world which would be completely coherent. Stoic physics can be described in terms of (a) monism, (b) materialism, and (c) dynamism. | Stoic physics | 0.815335 |
14,303 | If ψ {\displaystyle \psi } is a class function on H {\displaystyle H} and φ {\displaystyle \varphi } is a class function on G , {\displaystyle G,} then we have: Ind ( ψ ⋅ Res φ ) = ( Ind ψ ) ⋅ φ . {\displaystyle {\text{Ind}}(\psi \cdot {\text{Res}}\varphi )=({\text{Ind}}\psi )\cdot \varphi .} Theorem. | Representation theory of finite groups | 0.815332 |
14,304 | {\displaystyle V.} Theorem. An irreducible representation V {\displaystyle V} is one and only one of the following: (i) complex: χ V {\displaystyle \chi _{V}} is not real-valued and there exists no G {\displaystyle G} –invariant nondegenerate bilinear form on V . | Representation theory of finite groups | 0.815332 |
14,305 | 89-93,185-189 Echterhoff, Siegfried; Deitmar, Anton: Principles of harmonic analysis Springer-Verlag 2009, ISBN 978-0-387-85468-7, p. 127-150 Lang, Serge: Algebra Springer-Verlag, New York 2002, ISBN 0-387-95385-X, p. 663-729 Sengupta, Ambar (2012). | Representation theory of finite groups | 0.815332 |
14,306 | Bonnafé, Cedric (2010). Representations of SL2(Fq). Algebra and Applications. Vol. | Representation theory of finite groups | 0.815332 |
14,307 | However, the group algebra provides no helpful information in the case of infinite groups, because the continuity condition gets lost during the construction. Instead the convolution algebra L 1 ( G ) {\displaystyle L^{1}(G)} takes its place. Most properties of representations of finite groups can be transferred with a... | Representation theory of finite groups | 0.815332 |
14,308 | Since π ( g ) − 1 = π ( g − 1 ) , {\displaystyle \pi (g)^{-1}=\pi (g^{-1}),} we can do without the last requirement. In the following, we will consider in particular representations of compact groups in Hilbert spaces. Just as with finite groups, we can define the group algebra and the convolution algebra. | Representation theory of finite groups | 0.815332 |
14,309 | A topological group is a group together with a topology with respect to which the group composition and the inversion are continuous. Such a group is called compact, if any cover of G , {\displaystyle G,} which is open in the topology, has a finite subcover. Closed subgroups of a compact group are compact again. Let G ... | Representation theory of finite groups | 0.815332 |
14,310 | The irreducible representation corresponding to such a partition (or Young tableau) is called a Specht module. Representations of different symmetric groups are related: any representation of S n × S m {\displaystyle S_{n}\times S_{m}} yields a representation of S n + m {\displaystyle S_{n+m}} by induction, and vice ve... | Representation theory of finite groups | 0.815332 |
14,311 | The representation is called an irreducible representation, if these two are the only subrepresentations. Some authors also call these representations simple, given that they are precisely the simple modules over the group algebra C {\displaystyle \mathbb {C} } . | Representation theory of finite groups | 0.815332 |
14,312 | The elementary subgroups H arising in Brauer's theorem have a richer representation theory than cyclic groups, they at least have the property that any irreducible representation for such H is induced by a one-dimensional representation of a (necessarily also elementary) subgroup K ⊂ H {\displaystyle K\subset H} . (Thi... | Representation theory of finite groups | 0.815332 |
14,313 | Brauer's induction theorem asserts that φ {\displaystyle \varphi } is surjective, provided that X is the family of all elementary subgroups. Here a group H is elementary if there is some prime p such that H is the direct product of a cyclic group of order prime to p {\displaystyle p} and a p {\displaystyle p} –group. I... | Representation theory of finite groups | 0.815332 |
14,314 | Since R ( G ) {\displaystyle {\mathcal {R}}(G)} is finitely generated as a group, the first point can be rephrased as follows: For each character χ {\displaystyle \chi } of G , {\displaystyle G,} there exist virtual characters χ H ∈ R ( H ) , H ∈ X {\displaystyle \chi _{H}\in {\mathcal {R}}(H),\,H\in X} and an integer ... | Representation theory of finite groups | 0.815332 |
14,315 | Induction theorems relate the representation ring of a given finite group G to representation rings of a family X consisting of some subsets H of G. More precisely, for such a collection of subgroups, the induction functor yields a map φ: Ind: ⨁ H ∈ X R ( H ) → R ( G ) {\displaystyle \varphi :{\text{Ind}}:\bigoplus _{H... | Representation theory of finite groups | 0.815332 |
14,316 | We obtain the canonical decomposition by combining all the isomorphic irreducible subrepresentations: ρ 1 := η ⊕ τ {\displaystyle \rho _{1}:=\eta \oplus \tau } is the τ {\displaystyle \tau } -isotype of ρ {\displaystyle \rho } and consequently the canonical decomposition is given by ρ = ρ 1 ⊕ 1 , C 5 = C ( e 1 , e 2 , ... | Representation theory of finite groups | 0.815332 |
14,317 | Then the complement W 0 {\displaystyle W^{0}} of W {\displaystyle W} exists in V {\displaystyle V} and is G {\displaystyle G} -invariant.A subrepresentation and its complement determine a representation uniquely. The following theorem will be presented in a more general way, as it provides a very beautiful result about... | Representation theory of finite groups | 0.815332 |
14,318 | In order to understand representations more easily, a decomposition of the representation space into the direct sum of simpler subrepresentations would be desirable. This can be achieved for finite groups as we will see in the following results. More detailed explanations and proofs may be found in and . Theorem. | Representation theory of finite groups | 0.815332 |
14,319 | In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory. Point-free geometry was first formulated in Whitehead (1919, 1920), not as a th... | Point-free geometry | 0.815332 |
14,320 | If the force F is derivable from a potential (conservative), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields: where A and B are the beginning and end of the path along which the work was done. The power at any point along the curve C is the ... | Power (physics) | 0.815331 |
14,321 | The result gives a partial differential equation for the diffusive field and a series of boundary conditions at the interface, which should correspond to the sharp interface model and whose comparison with it provides the values of the parameters of the phase-field model. Whereas such expansions were in early phase-fie... | Phase-field model | 0.815328 |
14,322 | Multidimensional Turing machine: For example, a model by Schönhage uses the four head-movement commands { North, South, East, West }. Single-tape, multi-head Turing machine: In an undecidability proof of the "problem of tag", Minsky and Shepherdson and Sturgis described machines with a single tape that could read along... | Turing machine equivalents | 0.815323 |
14,323 | Systems biomedicine, also called systems biomedical science, is the application of systems biology to the understanding and modulation of developmental and pathological processes in humans, and in animal and cellular models. Whereas systems biology aims at modeling exhaustive networks of interactions (with the long-ter... | Systems biomedicine | 0.815314 |
14,324 | If this is the case then the two bodies are called quasi-identical. This happens for instance if the bodies are mirror-symmetric with respect to the contact plane and have the same elastic constants. Classical solutions based on the half-space approach are: Hertz solved the contact problem in the absence of friction, f... | Frictional contact mechanics | 0.815313 |
14,325 | First of all, there is the deformation of the separate bodies in reaction to loads applied on their surfaces. This is the subject of general continuum mechanics. It depends largely on the geometry of the bodies and on their (constitutive) material behavior (e.g. elastic vs. plastic response, homogeneous vs. layered str... | Frictional contact mechanics | 0.815313 |
14,326 | With respect to sliding, the classical solutions are due to C. Cattaneo (1938) and R.D. Mindlin (1949), who considered the tangential shifting of a sphere on a plane (see below).In the 1950s, interest in the rolling contact of railway wheels grew. In 1958, Kenneth L. Johnson presented an approximate approach for the 3D... | Frictional contact mechanics | 0.815313 |
14,327 | Formally the semantics of the generalized selection is defined as follows: σ φ ( R ) = { t: t ∈ R , φ ( t ) } {\displaystyle \sigma _{\varphi }(R)=\{\ t:t\in R,\ \varphi (t)\ \}} The result of the selection is only defined if the attribute names that it mentions are in the header of the relation that it operates upon. ... | Selection (relational algebra) | 0.815307 |
14,328 | The structural flexibility of this protein together with its susceptibility to modification in the cell leads to misfolding and aggregation. Genetics, oxidative and nitrative stress as well as mitochondrial impairment impact the structural flexibility of the unstructured α-synuclein protein and associated disease mecha... | Intrinsically disordered proteins | 0.815307 |
14,329 | In molecular biology, an intrinsically disordered protein (IDP) is a protein that lacks a fixed or ordered three-dimensional structure, typically in the absence of its macromolecular interaction partners, such as other proteins or RNA. IDPs range from fully unstructured to partially structured and include random coil, ... | Intrinsically disordered proteins | 0.815307 |
14,330 | Logic programming Prolog Constraint programming Artificial intelligence Genetic programming Machine learning Artificial life Evolution Metaprogramming | Inferential programming | 0.815305 |
14,331 | In early model theory, quantifier elimination was used to demonstrate that various theories possess properties like decidability and completeness. A common technique was to show first that a theory admits elimination of quantifiers and thereafter prove decidability or completeness by considering only the quantifier-fre... | Quantifier elimination | 0.815302 |
14,332 | Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement " ∃ x {\displaystyle \exists x} such that … {\displaystyle \ldots } " can be viewed as a question "When is there an x {\displaystyle x} such that … {\displ... | Quantifier elimination | 0.815302 |
14,333 | The multidimensional Szemerédi theorem states that for any fixed finite subset S ⊆ Z d {\displaystyle S\subseteq \mathbb {Z} ^{d}} , and for every ε > 0 {\displaystyle \varepsilon >0} , there exists a positive integer N ( S , ε ) {\displaystyle N(S,\varepsilon )} such that for any N ≥ N ( S , ε ) {\displaystyle N\geq N... | Corners theorem | 0.815302 |
14,334 | In arithmetic combinatorics, the corners theorem states that for every ε > 0 {\displaystyle \varepsilon >0} , for large enough N {\displaystyle N} , any set of at least ε N 2 {\displaystyle \varepsilon N^{2}} points in the N × N {\displaystyle N\times N} grid { 1 , … , N } 2 {\displaystyle \{1,\ldots ,N\}^{2}} contains... | Corners theorem | 0.815302 |
14,335 | A corner in Z d {\displaystyle \mathbb {Z} ^{d}} is a set of points of the form { a } ∪ { a + h e i: 1 ≤ i ≤ d } {\displaystyle \{a\}\cup \{a+he_{i}:1\leq i\leq d\}} , where e 1 , … , e d {\displaystyle e_{1},\ldots ,e_{d}} is the standard basis of R d {\displaystyle \mathbb {R} ^{d}} , and h ≠ 0 {\displaystyle h\neq 0... | Corners theorem | 0.815302 |
14,336 | In turn, one can also derive ordinary functions of one variable from a binary function. Given any element x ∈ X {\displaystyle x\in X} , there is a function f x {\displaystyle f^{x}} , or f ( x , ⋅ ) {\displaystyle f(x,\cdot )} , from Y {\displaystyle Y} to Z {\displaystyle Z} , given by f x ( y ) = f ( x , y ) {\displ... | Binary function | 0.8153 |
14,337 | A binary operation is a binary function where the sets X, Y, and Z are all equal; binary operations are often used to define algebraic structures. In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f x and fy are all linear transf... | Binary function | 0.815299 |
14,338 | Any set of data can be represented by a string of symbols from a finite (say, binary) alphabet. is based on the following insight: any regularity in a given set of data can be used to compress the data, i.e. to describe it using fewer symbols than needed to describe the data literally. (Grünwald, 2004) Based on this, i... | Minimum description length | 0.815298 |
14,339 | Statistical MDL learning is very strongly connected to probability theory and statistics through the correspondence between codes and probability distributions mentioned above. This has led some researchers to view MDL as equivalent to Bayesian inference: code length of model and data together in MDL correspond respect... | Minimum description length | 0.815298 |
14,340 | MDL has its origins mostly in information theory and has been further developed within the general fields of statistics, theoretical computer science and machine learning, and more narrowly computational learning theory. Historically, there are different, yet interrelated, usages of the definite noun phrase "the minimu... | Minimum description length | 0.815298 |
14,341 | MDL applies in machine learning when algorithms (machines) generate descriptions. Learning occurs when an algorithm generates a shorter description of the same data set. The theoretic minimum description length of a data set, called its Kolmogorov complexity, cannot, however, be computed. That is to say, even if by ran... | Minimum description length | 0.815298 |
14,342 | Surface power density is an important factor in comparison of industrial energy sources. The concept was popularised by geographer Vaclav Smil. The term is usually shortened to "power density" in the relevant literature, which can lead to confusion with homonymous or related terms. Measured in W/m2 it describes the amo... | Surface power density | 0.815297 |
14,343 | In physics and engineering, surface power density is power per unit area. | Surface power density | 0.815297 |
14,344 | Synthetic biology is a field that aims to engineer cells with "novel biological functions." Such cells are usually used to create larger systems (e.g., biofilms) which can be "programmed" utilizing synthetic gene networks such as genetic toggle switches, to change their color, shape, etc. Such bioinspired approaches to... | Programmable matter | 0.815293 |
14,345 | 3. Reducing the environmental footprint by reusing the same modules in many different solutions. Self-reconfiguring modular robotics enjoys a vibrant and active research community. | Programmable matter | 0.815293 |
14,346 | The CAM-8 architecture is an example hardware realization of this model. This function is also known as "digital referenced areas" (DRA) in some forms of self-replicating machine science.In the early 1990s, there was a significant amount of work in reconfigurable modular robotics with a philosophy similar to programmab... | Programmable matter | 0.815293 |
14,347 | Self-reconfiguring modular robotics is a field of robotics in which a group of basic robot modules work together to dynamically form shapes and create behaviours suitable for many tasks, similar to programmable matter. SRCMR aims to offer significant improvement to many kinds of objects or systems by introducing many n... | Programmable matter | 0.815293 |
14,348 | At the nanoscale end of the spectrum there are a tremendous number of different bases for programmable matter, ranging from shape changing molecules to quantum dots. Quantum dots are in fact often referred to as artificial atoms. In the micrometer to sub-millimeter range examples include MEMS-based units, cells created... | Programmable matter | 0.815293 |
14,349 | There are many proposed implementations of programmable matter. Scale is one key differentiator between different forms of programmable matter. At one end of the spectrum reconfigurable modular robotics pursues a form of programmable matter where the individual units are in the centimeter size range. | Programmable matter | 0.815293 |
14,350 | John Flinders Petrie was a lifelong friend of Coxeter and had a remarkable ability to visualise four-dimensional geometry. He and Coxeter had worked together on many mathematical problems. His direct contribution to the fifty nine icosahedra was the exquisite set of three-dimensional drawings which provide much of the ... | The Fifty-Nine Icosahedra | 0.815291 |
14,351 | In statistical physics, a Coulomb gas is a many-body system of charged particles interacting under the electrostatic force. It is named after Charles-Augustin de Coulomb, as the force by which the particles interact is also known as the Coulomb force. The system can be defined in any number of dimensions. | Coulomb gas | 0.815289 |
14,352 | While the three-dimensional Coulomb gas is the most experimentally realistic, the best understood is the two-dimensional Coulomb gas. The two-dimensional Coulomb gas is known to be equivalent to the continuum XY model of magnets and the sine-Gordon model (upon taking certain limits) in a physical sense, in that physica... | Coulomb gas | 0.815289 |
14,353 | Computers use base 2 counting (0s and 1s), also known as Boolean algebra. Counting can also be in the form of finger counting, especially when counting small numbers. This is often used by children to facilitate counting and simple mathematical operations. | Inclusive counting | 0.815288 |
14,354 | Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n} for any natural number n; these are called infinite sets, while those sets for which such a bijection does exist (for some n) are called finite sets. Infinite sets cannot be counted in the usual sense; for one thing, the ... | Inclusive counting | 0.815288 |
14,355 | In mathematics, the essence of counting a set and finding a result n, is that it establishes a one-to-one correspondence (or bijection) of the set with the subset of positive integers {1, 2, ..., n}. A fundamental fact, which can be proved by mathematical induction, is that no bijection can exist between {1, 2, ..., n}... | Inclusive counting | 0.815288 |
14,356 | Studia Mathematica is a triannual peer-reviewed scientific journal of mathematics published by the Polish Academy of Sciences. Papers are written in English, French, German, or Russian, primarily covering functional analysis, abstract methods of mathematical analysis, and probability theory. The editor-in-chief is Adam... | Studia Mathematica | 0.815288 |
14,357 | First used in theoretical physics, the MD method gained popularity in materials science soon afterward, and since the 1970s is also common in biochemistry and biophysics. MD is frequently used to refine 3-dimensional structures of proteins and other macromolecules based on experimental constraints from X-ray crystallog... | Molecular Dynamics | 0.815285 |
14,358 | The second one treats the nuclei, which are much heavier than electrons, as point particles that follow classical Newtonian dynamics. In classical molecular dynamics, the effect of the electrons is approximated as one potential energy surface, usually representing the ground state. When finer levels of detail are neede... | Molecular Dynamics | 0.815285 |
14,359 | A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a force field and in materials physics as an interatomic potential. Potentials may be defined at ... | Molecular Dynamics | 0.815285 |
14,360 | Chemistry force fields commonly employ preset bonding arrangements (an exception being ab initio dynamics), and thus are unable to model the process of chemical bond breaking and reactions explicitly. On the other hand, many of the potentials used in physics, such as those based on the bond order formalism can describe... | Molecular Dynamics | 0.815285 |
14,361 | Empirical potentials used in chemistry are frequently called force fields, while those used in materials physics are called interatomic potentials. Most force fields in chemistry are empirical and consist of a summation of bonded forces associated with chemical bonds, bond angles, and bond dihedrals, and non-bonded for... | Molecular Dynamics | 0.815285 |
14,362 | When coarse-graining is done at higher levels, the accuracy of the dynamic description may be less reliable. But very coarse-grained models have been used successfully to examine a wide range of questions in structural biology, liquid crystal organization, and polymer glasses. Examples of applications of coarse-grainin... | Molecular Dynamics | 0.815285 |
14,363 | Semi-empirical potentials make use of the matrix representation from quantum mechanics. However, the values of the matrix elements are found through empirical formulae that estimate the degree of overlap of specific atomic orbitals. The matrix is then diagonalized to determine the occupancy of the different atomic orbi... | Molecular Dynamics | 0.815285 |
14,364 | Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are... | Molecular Dynamics | 0.815285 |
14,365 | {\displaystyle V(t)={\dot {X}}(t).} The potential energy function U ( X ) {\displaystyle U(X)} of the system is a function of the particle coordinates X {\displaystyle X} . It is referred to simply as the potential in physics, or the force field in chemistry. | Molecular Dynamics | 0.815285 |
14,366 | In the microcanonical ensemble, the system is isolated from changes in moles (N), volume (V), and energy (E). It corresponds to an adiabatic process with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved. For a ... | Molecular Dynamics | 0.815285 |
14,367 | ESCAPE is being designed and built by several institutions, led by Principal Investigator Kevin France at the Laboratory for Atmospheric and Space Physics (LASP), a research institute at University of Colorado Boulder. LASP is responsible for the overall project, instrument design, instrument integration, mission opera... | Extreme-ultraviolet Stellar Characterization for Atmospheric Physics and Evolution | 0.815284 |
14,368 | The Extreme-ultraviolet Stellar Characterization for Atmospheric Physics and Evolution (ESCAPE) mission aims to find environments beyond Earth's solar system that might host planets with thick atmospheres to support life.The long-term stability of exoplanetary atmospheres depends critically on the extreme-ultraviolet (... | Extreme-ultraviolet Stellar Characterization for Atmospheric Physics and Evolution | 0.815284 |
14,369 | The expected running time of Welzl’s algorithm is O ( ( d + 1 ) ( d + 1 ) ! n ) {\displaystyle O((d+1)(d+1)!n)} , which again reduces to O ( n ) {\displaystyle O(n)} for any fixed dimension d {\displaystyle d} . The paper provides experimental results demonstrating its practicality in higher dimensions. A more recent d... | Bounding sphere | 0.815283 |
14,370 | Each one had a regular stepped line separating metals from nonmetals. Merck and Company prepared a handout form of Deming's 18-column table, in 1928, which was widely circulated in American schools. By the 1930s Deming's table was appearing in handbooks and encyclopaedias of chemistry. It was also distributed for many ... | Dividing line between metals and nonmetals | 0.815283 |
14,371 | References to a dividing line between metals and nonmetals appear in the literature as far back as at least 1869. In 1891, Walker published a periodic 'tabulation' with a diagonal straight line drawn between the metals and the nonmetals. In 1906, Alexander Smith published a periodic table with a zigzag line separating ... | Dividing line between metals and nonmetals | 0.815283 |
14,372 | Performance optimization of programs or operating systems often involves reducing the number of page faults. Two primary focuses of the optimization are reducing overall memory usage and improving memory locality. To reduce the page faults, developers must use an appropriate page replacement algorithm that maximizes th... | Page fault | 0.815283 |
14,373 | In set theory, the random algebra or random real algebra is the Boolean algebra of Borel sets of the unit interval modulo the ideal of measure zero sets. It is used in random forcing to add random reals to a model of set theory. The random algebra was studied by John von Neumann in 1935 (in work later published as Neum... | Random algebra | 0.815279 |
14,374 | A large number of studied regulatory systems come from developmental biology. Examples include: The colinearity of the Hox gene cluster with their nested antero-posterior patterning Pattern generation of the hand (digits - interdigits): the gradient of sonic hedgehog (secreted inducing factor) from the zone of polarizi... | Gene control | 0.815278 |
14,375 | (See Epigenetics of cocaine addiction for some details.) Chronic nicotine intake in mice alters brain cell epigenetic control of gene expression through acetylation of histones. This increases expression in the brain of the protein FosB, important in addiction. | Gene control | 0.815278 |
14,376 | Concatenate (normalized) histograms of all cells. This gives a feature vector for the entire window.The feature vector can now be processed using the Support vector machine, extreme learning machines, or some other machine learning algorithm to classify images. Such classifiers can be used for face recognition or textu... | Local binary patterns | 0.815278 |
14,377 | CMV, includes the general LBP implementation and many further extensions over LBP histogram in MATLAB. Python mahotas, an open source computer vision package which includes an implementation of LBPs. OpenCV's Cascade Classifiers support LBPs as of version 2. VLFeat, an open source computer vision library in C (with bin... | Local binary patterns | 0.815278 |
14,378 | Local binary patterns (LBP) is a type of visual descriptor used for classification in computer vision. LBP is the particular case of the Texture Spectrum model proposed in 1990. LBP was first described in 1994. It has since been found to be a powerful feature for texture classification; it has further been determined t... | Local binary patterns | 0.815278 |
14,379 | A crystal on the site Inf ( X / S ) {\displaystyle {\text{Inf}}(X/S)} is a sheaf F {\displaystyle F} of O X / S {\displaystyle O_{X/S}} modules that is rigid in the following sense: for any map f {\displaystyle f} between objects T {\displaystyle T} , T ′ {\displaystyle T'} ; of Inf ( X / S ) {\displaystyle {\text{Inf}... | Crystal (mathematics) | 0.815277 |
14,380 | They are p {\displaystyle p} -adic analogues of Q l {\displaystyle \mathbf {Q} _{l}} -adic étale sheaves, introduced by Grothendieck (1966a) and Berthelot & Ogus (1983) (though the definition of isocrystal only appears in part II of this paper by Ogus (1984)). Convergent isocrystals are a variation of isocrystals that ... | Crystal (mathematics) | 0.815277 |
14,381 | Hence, immunology is a sub-category of biology. Its origin is usually attributed to Edward Jenner, who discovered in 1796 that cowpox, or vaccinia, induced protection against human smallpox. The term immunogenetics comprises all processes of an organism, which are, on the one hand, controlled and influenced by the gene... | Immunogenetics | 0.815276 |
14,382 | The term immunogenetics is based on the two words immunology and genetics, and is defined as "a sub discipline of genetics which deals with the genetic basis of the immune response (immunity)" according to MeSH.Genetics (based on Greek γενεά geneá "descent" and γένεσις génesis "origin") is the science researching the t... | Immunogenetics | 0.815276 |
14,383 | The history of immunology and the medical study of the immune system dates back to the 19th century. The first Nobel Prize in the field of immunogenetics was awarded to Baruj Benacerraf, Jean Dausset and George Davis Snell in 1980 for discovering genetically determined cellular surface structures, which control immunol... | Immunogenetics | 0.815276 |
14,384 | Immunogenetics or immungenetics is the branch of Medical Immunology and Medical Genetics that explores the relationship between the immune system and genetics. Autoimmune diseases, such as type 1 diabetes, are complex genetic traits which result from defects in the immune system. Identification of genes defining the im... | Immunogenetics | 0.815276 |
14,385 | Since 1972, numerous H&I (histocompatibility and immunogenetics) organizations have been founded specializing in research activities on a large number of different questions in immunogenetics. Both the acceleration of and the decreasing costs for the sequencing of the genes have resulted in more intensive research of b... | Immunogenetics | 0.815276 |
14,386 | A microprotein (miP) is a small protein encoded from small open reading frames (smORFs). They are a class of protein with a single protein domain that are related to multidomain proteins. Microproteins regulate larger multidomain proteins at the post-translational level. Microproteins are analogous to microRNAs (miRNAs... | Microprotein | 0.815272 |
14,387 | The goal of the experiment is to measure exceptional events out of the billions of particle collisions in order to: Look for evidence for phenomena beyond the Standard Model of particle physics Measure and study the production and decay of heavy particles such as the Top and Bottom Quarks, and the W and Z bosons Measur... | CDF experiment | 0.815268 |
14,388 | Finally in February 1995, CDF had enough evidence to say that they had "discovered" the top quark. On February 24, CDF and DØ experimenters simultaneously submitted papers to Physical Review Letters describing the observation of the top quark. The two collaborations announced the discovery publicly at a seminar at Ferm... | CDF experiment | 0.815268 |
14,389 | Notice that ( W ; M 0 , M 1 ) {\displaystyle (W;M_{0},M_{1})} in the definition of S h ( X ) {\displaystyle {\mathcal {S}}^{h}(X)} resp. S s ( X ) {\displaystyle {\mathcal {S}}^{s}(X)} is an h-cobordism resp. an s-cobordism. Using the s-cobordism theorem we obtain another description for the simple structure set S s ( ... | Surgery structure set | 0.815264 |
14,390 | It is usually not the case that the general solution of an algebraic differential equation is an algebraic function: solving equations typically produces novel transcendental functions. The case of algebraic solutions is however of considerable interest; the classical Schwarz list deals with the case of the hypergeomet... | Polynomial vector field | 0.815264 |
14,391 | Algebraic differential equations are widely used in computer algebra and number theory. A simple concept is that of a polynomial vector field, in other words a vector field expressed with respect to a standard co-ordinate basis as the first partial derivatives with polynomial coefficients. This is a type of first-order... | Polynomial vector field | 0.815264 |
14,392 | In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the concept of differential algebra used. The intention is to include equations formed by means of differential operators, in which the coeff... | Polynomial vector field | 0.815264 |
14,393 | According to Gödel's first incompleteness theorem, in every formal system with computably enumerable theorems (or proofs) strong enough to contain Peano arithmetic, there are true (but unprovable) statements or theorems. This is proved by the incompressibility method; every formal system F {\displaystyle F} can be desc... | Incompressibility method | 0.815263 |
14,394 | According to an elegant Euclidean proof, there is an infinite number of prime numbers. Bernhard Riemann demonstrated that the number of primes less than a given number is connected with the 0s of the Riemann zeta function. Jacques Hadamard and Charles Jean de la Vallée-Poussin proved in 1896 that this number of primes ... | Incompressibility method | 0.815263 |
14,395 | It is easily solved by the incompressibility method, as are the coin-weighing problem, the number of covering families and expected properties; for example, at least a fraction of 1 − 1 / n {\displaystyle 1-1/n} of all transitive tournaments on n {\displaystyle n} vertices have transitive subtournaments on not more tha... | Incompressibility method | 0.815263 |
14,396 | This theorem is required in a more complicated proof, where the incompressibility argument is used a number of times to show that the number of unlabeled graphs is ∼ 2 ( n 2 ) n ! . {\displaystyle \sim {\frac {2^{n \choose 2}}{n!}}.} | Incompressibility method | 0.815263 |
14,397 | Many of the processes related to plant density can well be studied in monocultures of even-aged individuals that are sown or planted at the same time. These can be referred to as 'monostands' and are often studied in the context of agricultural, horticultural or silvicultural questions. However, they are also highly re... | Plant density | 0.815263 |
14,398 | This approach allows the system to gather information about the frequency with which various constructions occur in specific contexts. (See machine learning.) Approaches which have been used include straightforward PCFGs (probabilistic context-free grammars), maximum entropy, and neural nets. | Parsing algorithm | 0.815262 |
14,399 | Most of the more successful systems use lexical statistics (that is, they consider the identities of the words involved, as well as their part of speech). However such systems are vulnerable to overfitting and require some kind of smoothing to be effective.Parsing algorithms for natural language cannot rely on the gram... | Parsing algorithm | 0.815262 |
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