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78,600 | In the context of the development of field theory, the fact that a function could be written to give the force per unit mass, charge, or current for each point in space was just a mathematical construct. It was seen as untenable on metaphysical grounds that a force be exerted across empty space, and hence these force l... | History of the philosophy of field theory | 0.785693 |
78,601 | The idea of motion may not be applied to it." Hence it was made clear that in the case of electromagnetism there is no underlying material through which the forces must propagate. In these cases there can be no distinction made between the effects of a field arising through a potential and the effects of an "action at ... | History of the philosophy of field theory | 0.785693 |
78,602 | Field theory, the study of dynamical fields in physics, was originally a mathematical formulation of Newtonian mechanics. The success of Newtonian physics since the publication of Isaac Newton's Principia in 1687 provided a framework with which to investigate the motion and forces associated with electricity and magnet... | History of the philosophy of field theory | 0.785693 |
78,603 | Field theory had its origins in the 18th century in a mathematical formulation of Newtonian mechanics, but it was seen as deficient as it implied action at a distance. In 1852, Michael Faraday treated the magnetic field as a physical object, reasoning about lines of force. James Clerk Maxwell used Faraday's conceptuali... | History of the philosophy of field theory | 0.785693 |
78,604 | In molecular biology, glycoside hydrolase family 25 is a family of glycoside hydrolases. Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside h... | Glycoside hydrolase family 25 | 0.785691 |
78,605 | In computer science, the clique problem is the computational problem of finding a maximum clique, or all cliques, in a given graph. It is NP-complete, one of Karp's 21 NP-complete problems. It is also fixed-parameter intractable, and hard to approximate. Nevertheless, many algorithms for computing cliques have been dev... | Clique (graph theory) | 0.78569 |
78,606 | Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the gr... | Clique (graph theory) | 0.78569 |
78,607 | In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G {\displaystyle G} is an induced subgraph of G {\displaystyle G} that is complete. Cliques are one of the basic concept... | Clique (graph theory) | 0.78569 |
78,608 | The American Institute of Chemists Gold Medal is the highest award of the American Institute of Chemists and has been awarded since 1926.It is presented annually to a person who has most encouraged the science of chemistry or the profession of chemist or chemical engineer in the United States of America, giving "exempl... | American Institute of Chemists Gold Medal | 0.785689 |
78,609 | The unique conditions lead to flora and fauna that differ from both whitewater and clearwater rivers. The classification of Amazonian rivers into black, clear, and whitewater was first proposed by Alfred Russel Wallace in 1853 based on water colour, but the types were more clearly defined by chemistry and physics by Ha... | Tannin-stained waters | 0.785689 |
78,610 | A blackwater river is a type of river with a slow-moving channel flowing through forested swamps or wetlands. Most major blackwater rivers are in the Amazon Basin and the Southern United States. The term is used in fluvial studies, geology, geography, ecology, and biology. Not all dark rivers are blackwater in that tec... | Tannin-stained waters | 0.785689 |
78,611 | Source transformation is the process of simplifying a circuit solution, especially with mixed sources, by transforming voltage sources into current sources, and vice versa, using Thévenin's theorem and Norton's theorem respectively. | Source transformation | 0.785687 |
78,612 | However, this means that source transformation is bound by the same conditions as Thevenin's theorem and Norton's theorem; namely that the load behaves linearly, and does not contain dependent voltage or current sources. Source transformations are used to exploit the equivalence of a real current source and a real volt... | Source transformation | 0.785687 |
78,613 | Performing a source transformation consists of using Ohm's law to take an existing voltage source in series with a resistance, and replacing it with a current source in parallel with the same resistance, or vice versa. The transformed sources are considered identical and can be substituted for one another in a circuit.... | Source transformation | 0.785687 |
78,614 | The transformation can be derived from the uniqueness theorem. In the present context, it implies that a black box with two terminals must have a unique well-defined relation between its voltage and current. It is readily to verify that the above transformation indeed gives the same V-I curve, and therefore the transfo... | Source transformation | 0.785687 |
78,615 | Despite this shared topology, the protein families do not share enough sequence similarity to confidently infer common ancestry. Pannexins are similar to innexins and are usually considered a sub-group, but they do not participate in the formation of gap junctions and the channels have seven subunits.Vinnexins, viral h... | Innexin | 0.785687 |
78,616 | The many self-organizing phenomena in physics include phase transitions and spontaneous symmetry breaking such as spontaneous magnetization and crystal growth in classical physics, and the laser, superconductivity and Bose–Einstein condensation in quantum physics. It is found in self-organized criticality in dynamical ... | Self organisation | 0.785685 |
78,617 | In his 1995 conference paper "Cosmology as a problem in critical phenomena" Lee Smolin said that several cosmological objects or phenomena, such as spiral galaxies, galaxy formation processes in general, early structure formation, quantum gravity and the large scale structure of the universe might be the result of or h... | Self organisation | 0.785685 |
78,618 | Self-organization in biology can be observed in spontaneous folding of proteins and other biomacromolecules, self-assembly of lipid bilayer membranes, pattern formation and morphogenesis in developmental biology, the coordination of human movement, eusocial behaviour in insects (bees, ants, termites) and mammals, and f... | Self organisation | 0.785685 |
78,619 | Phenomena from mathematics and computer science such as cellular automata, random graphs, and some instances of evolutionary computation and artificial life exhibit features of self-organization. In swarm robotics, self-organization is used to produce emergent behavior. In particular the theory of random graphs has bee... | Self organisation | 0.785685 |
78,620 | The virtue of their idea is that it resolves what they perceive as a "clash of doctrines" about the nature of time in physics. Most physicists would agree that there is neither empirical evidence to support their view, nor is there a mathematical necessity for it. There is no "clash of doctrines." | Self organisation | 0.785685 |
78,621 | Heinz Pagels, in a 1985 review of Ilya Prigogine and Isabelle Stengers's book Order Out of Chaos in Physics Today, appeals to authority: Most scientists would agree with the critical view expressed in Problems of Biological Physics (Springer Verlag, 1981) by the biophysicist L. A. Blumenfeld, when he wrote: "The meanin... | Self organisation | 0.785685 |
78,622 | Optimization algorithms can be considered self-organizing because they aim to find the optimal solution to a problem. If the solution is considered as a state of the iterative system, the optimal solution is the selected, converged structure of the system. Self-organizing networks include small-world networks self-stab... | Self organisation | 0.785685 |
78,623 | {\displaystyle F(x)-F(a)=\int _{a}^{x}F'(t)\,dt.} Conversely, the Lebesgue differentiation theorem continues to hold for the Henstock–Kurzweil integral: if f is Henstock–Kurzweil integrable on , and F ( x ) = ∫ a x f ( t ) d t , {\displaystyle F(x)=\int _{a}^{x}f(t)\,dt,} then F′(x) = f(x) almost everywhere in (in par... | Henstock integral | 0.785685 |
78,624 | If F is differentiable everywhere (or with countably many exceptions), the derivative F′ is Henstock–Kurzweil integrable, and its indefinite Henstock–Kurzweil integral is F. (Note that F′ need not be Lebesgue integrable.) In other words, we obtain a simpler and more satisfactory version of the second fundamental theore... | Henstock integral | 0.785685 |
78,625 | For example, if f is bounded with compact support, the following are equivalent: f is Henstock–Kurzweil integrable, f is Lebesgue integrable, f is Lebesgue measurable.In general, every Henstock–Kurzweil integrable function is measurable, and f is Lebesgue integrable if and only if both f and |f| are Henstock–Kurzweil i... | Henstock integral | 0.785685 |
78,626 | The important Hake's theorem states that ∫ a b f ( x ) d x = lim c → b − ∫ a c f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx=\lim _{c\to b^{-}}\int _{a}^{c}f(x)\,dx} whenever either side of the equation exists, and likewise symmetrically for the lower integration bound. This means that if f is "improperly Henstock–K... | Henstock integral | 0.785685 |
78,627 | It took a while to understand that the Perron and Denjoy integrals are actually identical. Later, in 1957, the Czech mathematician Jaroslav Kurzweil discovered a new definition of this integral elegantly similar in nature to Riemann's original definition which he named the gauge integral. Ralph Henstock independently i... | Henstock integral | 0.785685 |
78,628 | Roller coaster design is another important aspect that requires a working knowledge of basic physics to enhance ride comfort and avoid harmful strain to the rider. Ride designers must carefully analyze the movement a ride subjects its riders to, ensuring it is within a reasonable tolerance. The human body needs suffici... | Roller coasters | 0.785682 |
78,629 | In molecular biology, a downstream promoter element (DPE) is a core promoter element. Like all core promoters, the DPE plays an important role in the initiation of gene transcription by RNA polymerase II. The DPE was first described by T. W. Burke and James T. Kadonaga in Drosophila melanogaster at the University of Ca... | Downstream promoter element | 0.785681 |
78,630 | This then provides three sterile neutrinos which are perfectly consistent with current neutrino oscillation data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies. Because the left-right symmetry is spontaneously broken, left-right models predict domain wall... | Chiral symmetry | 0.78568 |
78,631 | In theoretical physics, the electroweak model breaks parity maximally. All its fermions are chiral Weyl fermions, which means that the charged weak gauge bosons W+ and W− only couple to left-handed quarks and leptons.Some theorists found this objectionable, and so conjectured a GUT extension of the weak force which has... | Chiral symmetry | 0.78568 |
78,632 | Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a vector theory, since both chiralities of all quarks appear in the theory, and couple to gluons in the same way. The electroweak theory, developed in the m... | Chiral symmetry | 0.78568 |
78,633 | On the other hand, if the gene is expressed at low levels, the organism may produce less of the enzyme and exhibit a different trait.Gene expression is regulated at various levels and thus each level can affect certain phenotypes, including transcriptional and post-transcriptional regulation. Changes in the levels of g... | Behavioral phenotype | 0.78568 |
78,634 | Very few properties of rutherfordium or its compounds have been measured; this is due to its extremely limited and expensive production and the fact that rutherfordium (and its parents) decays very quickly. A few singular chemistry-related properties have been measured, but properties of rutherfordium metal remain unkn... | Rutherfordium | 0.785679 |
78,635 | Early work on the study of the chemistry of rutherfordium focused on gas thermochromatography and measurement of relative deposition temperature adsorption curves. The initial work was carried out at Dubna in an attempt to reaffirm their discovery of the element. Recent work is more reliable regarding the identificatio... | Rutherfordium | 0.785679 |
78,636 | The TWG responded by saying that this was not the case and having assessed each point raised by the American group said that they found no reason to alter their conclusion regarding priority of discovery. The IUPAC finally used the name suggested by the American team (rutherfordium).The International Union of Pure and ... | Rutherfordium | 0.785679 |
78,637 | As a consequence of the initial competing claims of discovery, an element naming controversy arose. Since the Soviets claimed to have first detected the new element they suggested the name kurchatovium (Ku) in honor of Igor Kurchatov (1903–1960), former head of Soviet nuclear research. This name had been used in books ... | Rutherfordium | 0.785679 |
78,638 | It is in period 7 and is a group 4 element. Chemistry experiments have confirmed that rutherfordium behaves as the heavier homolog to hafnium in group 4. | Rutherfordium | 0.785679 |
78,639 | In 1992, the IUPAC/IUPAP Transfermium Working Group (TWG) assessed the claims of discovery and concluded that both teams provided contemporaneous evidence to the synthesis of element 104 and that credit should be shared between the two groups.The American group wrote a scathing response to the findings of the TWG, stat... | Rutherfordium | 0.785679 |
78,640 | Some of its properties were determined by gas-phase experiments and aqueous chemistry. The oxidation state +4 is the only stable state for the latter two elements and therefore rutherfordium should also exhibit a stable +4 state. In addition, rutherfordium is also expected to be able to form a less stable +3 state. | Rutherfordium | 0.785679 |
78,641 | Rutherfordium is expected to have the electron configuration 5f14 6d2 7s2 and therefore behave as the heavier homologue of hafnium in group 4 of the periodic table. It should therefore readily form a hydrated Rf4+ ion in strong acid solution and should readily form complexes in hydrochloric acid, hydrobromic or hydrofl... | Rutherfordium | 0.785679 |
78,642 | The chemical properties of rutherfordium are characterized only partly. They compare well with the other group 4 elements, even though some calculations had indicated that the element might show significantly different properties due to relativistic effects. In the 1960s, small amounts of rutherfordium were produced at... | Rutherfordium | 0.785679 |
78,643 | Note that it is acceptable that the green grouping overlaps with the red one. In the same way, the blue grouping gives the term BCD. The solutions of each grouping are combined: the normal form of the circuit is A C ¯ + A B ¯ + B C D ¯ {\displaystyle A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}} . Thus the Karna... | Veitch chart | 0.785679 |
78,644 | Once the Karnaugh map has been constructed and the adjacent 1s linked by rectangular and square boxes, the algebraic minterms can be found by examining which variables stay the same within each box. For the red grouping: A is the same and is equal to 1 throughout the box, therefore it should be included in the algebrai... | Veitch chart | 0.785679 |
78,645 | The design of vacuum pumps evolved over time in the van Musschenbroek workshop. The first produced vacuum pump in the workshop was a request by Burchard de Volder, a professor of physics at the Leiden University. The pump was constructed in 1675 and was based on a design by Robert Hooke. This instrument never became a ... | Van Musschenbroek vacuum pump | 0.785678 |
78,646 | Johann Bernoulli taught physics at University of Groningen between 1695 and 1705. He acquired the 1698 van Musschenbroek vacuum pump from the Musschenbroek workshop in early 1698 along with other instruments expecting "not to do anything important" and only to "amuse our students with mathematico-physical experiments".... | Van Musschenbroek vacuum pump | 0.785678 |
78,647 | Metathesis has been a powerful tool in the coupling of olefins for several decades. The ability to rearrange carbon-carbon double bonds has provided great utility in all aspects of organic chemistry. Cossy et al. report a simple synthesis to form substituted five and six membered lactones from the cross metathesis of a... | Tandem catalysis | 0.785677 |
78,648 | The Mori–Zwanzig formalism, named after the physicists Hajime Mori and Robert Zwanzig, is a method of statistical physics. It allows the splitting of the dynamics of a system into a relevant and an irrelevant part using projection operators, which helps to find closed equations of motion for the relevant part. It is us... | Mori-Zwanzig formalism | 0.785675 |
78,649 | In Galois geometry over a Galois field GF(q) a line has q + 1 points, where ∞ = (1,0). In this line four points form a harmonic tetrad when two harmonically separate the others. The condition ( c , d ; a , b ) = − 1 , equivalently 2 ( c d + a b ) = ( c + d ) ( a + b ) , {\displaystyle (c,d;a,b)=-1,\ {\text{ equivalentl... | Projective harmonic conjugate | 0.785673 |
78,650 | In the case where the conic is a circle, on the extended diameters of the circle, harmonic conjugates with respect to the circle are inverses in a circle. This fact follows from one of Smogorzhevsky's theorems: If circles k and q are mutually orthogonal, then a straight line passing through the center of k and intersec... | Projective harmonic conjugate | 0.785673 |
78,651 | For instance, Abraham H. Taub reviewed Mathematical Cosmology and Extragalactic Astronomy, saying The chronometric theory as described in this book is not a theory concerning the nature of the universe nor the behaviour of objects in it. Rather it ignores the effect of gravitational forces on these objects, postulates ... | Chronometric cosmology | 0.785671 |
78,652 | He was elected to the National Academy of Sciences in 1973. In 1983 Victor Guillemin edited a festschrift dedicated to Irving Segal. Physics Today published a review of Introduction to Algebraic and Constructive Quantum Field Theory (1992), which Segal coauthored.Segal died in Lexington, Massachusetts, on August 30, 19... | Chronometric cosmology | 0.785671 |
78,653 | Irving Ezra Segal (1918–1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for his developments in quantum field theory and in functional and harmonic analysis,... | Chronometric cosmology | 0.785671 |
78,654 | It has been suggested that at least some of these "Lenard rays" were actually X-rays.In 1889, Ukrainian-born Ivan Puluj, a lecturer in experimental physics at the Prague Polytechnic who since 1877 had been constructing various designs of gas-filled tubes to investigate their properties, published a paper on how sealed ... | X rays | 0.785668 |
78,655 | When Stanford University physics professor Fernando Sanford created his "electric photography", he also unknowingly generated and detected X-rays. From 1886 to 1888, he had studied in the Hermann von Helmholtz laboratory in Berlin, where he became familiar with the cathode rays generated in vacuum tubes when a voltage ... | X rays | 0.785668 |
78,656 | Other notable uses of X-rays include: X-ray crystallography in which the pattern produced by the diffraction of X-rays through the closely spaced lattice of atoms in a crystal is recorded and then analysed to reveal the nature of that lattice. A related technique, fiber diffraction, was used by Rosalind Franklin to dis... | X rays | 0.785668 |
78,657 | In organic chemistry, 1β-Methylseleno-N-acetyl-D-galactosamine is an amino sugar containing selenium. It is found in urine, as a disposal metabolite for selenium. | 1β-Methylseleno-N-acetyl-D-galactosamine | 0.785667 |
78,658 | He theorized correctly that the explanation of the light emission was in the new science of quantum mechanics, speculating that it was the inverse of the photoelectric effect discovered by Albert Einstein in 1905. He wrote to Einstein about it, but did not receive a reply. | Cat's-whisker detector | 0.785667 |
78,659 | His technology was dubbed "Crystodyne" by science publisher Hugo Gernsback one of the few people in the West who paid attention to it. After ten years he abandoned research into this technology and it was forgotten.The negative resistance diode was rediscovered with the invention of the tunnel diode in 1957, for which ... | Cat's-whisker detector | 0.785667 |
78,660 | Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposit... | Proof by exhaustion | 0.785667 |
78,661 | One of the main weaknesses of the disposable soma theory is that it does not postulate any specific cellular mechanisms to which an organism shifts energy to somatic repair over reproduction. Instead, it only offers an evolutionary perspective on why aging may occur due to reproduction. Therefore, parts of it are rathe... | Disposable soma theory of aging | 0.785666 |
78,662 | This idea allows one to analyze the properties of partial differential equations with methods of differential geometry. For instance, we can apply the Cartan–Kähler_theorem to a system of partial differential equations by writing down the associated exterior differential system. We can frequently apply Cartan's equival... | Differential ideal | 0.785664 |
78,663 | In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior differentiation d, meaning that for any form α in I, the exterior derivative d... | Differential ideal | 0.785664 |
78,664 | A free body should also be distinguished from a freely falling body. In Newtonian physics, the latter term refers to a body which is falling under pure gravity with all other forces being zero. In Einstein's general theory of relativity, where gravity becomes curvature of spacetime, a freely falling body is subject to ... | Free body | 0.785663 |
78,665 | A frame grabber is an electronic device that captures (i.e., "grabs") individual, digital still frames from an analog video signal or a digital video stream. It is usually employed as a component of a computer vision system, in which video frames are captured in digital form and then displayed, stored, transmitted, ana... | Frame grabbing | 0.785661 |
78,666 | Actor: Rigging and animation of digital characters using skeletons, as well as dynamics tools for physics simulations of object interactions. Included inverse kinematics and weighted / rigid skinning. Matter: Creation of materials and rendering images for output. Standard features included 2D and 3D textures, field ren... | Softimage 3D | 0.78566 |
78,667 | Bernd Sturmfels, Professor of Mathematics and Computer Science at Berkeley, and Josephine Yu classified six-point metrics using T-theory. | T-theory | 0.785658 |
78,668 | T-theory is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces. | T-theory | 0.785658 |
78,669 | A classical modular form of weight k can be thought of roughly as a function f from pairs (E,ω) of a complex elliptic curve with a holomorphic 1-form ω to complex numbers, such that f(E,λω) = λ−kf(E,ω), and satisfying some additional conditions such as being holomorphic in some sense. Katz's definition of a p-adic modu... | P-adic modular form | 0.785658 |
78,670 | The Brauer–Suzuki theorem shows that the groups whose Sylow 2-subgroups are generalized quaternion cannot be simple. Another terminology reserves the name "generalized quaternion group" for a dicyclic group of order a power of 2, which admits the presentation ⟨ x , y ∣ x 2 m = y 4 = 1 , x 2 m − 1 = y 2 , y − 1 x y = x ... | Generalized quaternion group | 0.785656 |
78,671 | }}D^{k}} be the inverse operator, the coefficients a k {\displaystyle a_{k}} being those of the usual reciprocal of a formal power series, so that T p n ( x ) = x n . {\displaystyle Tp_{n}(x)=x^{n}.\,} In the conventions of the umbral calculus, one often treats this formal power series T {\displaystyle T} as representi... | Appell sequence | 0.785656 |
78,672 | Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure (yield). Dependi... | Material failure theory | 0.785656 |
78,673 | In materials science, material failure is the loss of load carrying capacity of a material unit. This definition introduces to the fact that material failure can be examined in different scales, from microscopic, to macroscopic. In structural problems, where the structural response may be beyond the initiation of nonli... | Material failure theory | 0.785656 |
78,674 | Virtuoso Universal Server is a middleware and database engine hybrid that combines the functionality of a traditional relational database management system (RDBMS), object–relational database (ORDBMS), virtual database, RDF, XML, free-text, web application server and file server functionality in a single system. Rather... | Virtuoso Universal Server | 0.785652 |
78,675 | Relational database management system List of relational database management systems Comparison of object–relational database management systems Comparison of relational database management systems | Virtuoso Universal Server | 0.785652 |
78,676 | RapidMind developed a stream programming package for the PS3.On January 3, 2007, Dr. Frank Mueller, Associate Professor of Computer Science at North Carolina State University, clustered 8 PS3s. Mueller commented that the 256 MB of system RAM is a limitation for this particular application, and considered attempting to ... | PS3 cluster | 0.785652 |
78,677 | The latest report stated that Folding@Home has passed the 5 native petaFLOP mark, of which 767 teraFLOPS were supplied by PlayStation 3 clients.The Computational Biochemistry and Biophysics Lab in Barcelona has launched a distributed computing project called PS3GRID. This project was expected to run sixteen times faste... | PS3 cluster | 0.785652 |
78,678 | In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931, and developed a... | Continued fraction factorization | 0.785651 |
78,679 | The Jiles–Atherton model is implemented in JAmodel, a MATLAB/OCTAVE toolbox. It uses the Runge-Kutta algorithm for solving ordinary differential equations. JAmodel is open-source is under MIT license.The two most important computational problems connected with the Jiles–Atherton model were identified: numerical integra... | Jiles–Atherton model | 0.78565 |
78,680 | There is a unique complex Lie algebra of type E8, corresponding to a complex group of complex dimension 248. The complex Lie group E8 of complex dimension 248 can be considered as a simple real Lie group of real dimension 496. This is simply connected, has maximal compact subgroup the compact form (see below) of E8, an... | E8 Lie algebra | 0.785649 |
78,681 | By means of a Chevalley basis for the Lie algebra, one can define E8 as a linear algebraic group over the integers and, consequently, over any commutative ring and in particular over any field: this defines the so-called split (sometimes also known as “untwisted”) form of E8. Over an algebraically closed field, this is... | E8 Lie algebra | 0.785649 |
78,682 | The compact real form of E8 is the isometry group of the 128-dimensional exceptional compact Riemannian symmetric space EVIII (in Cartan's classification). It is known informally as the "octooctonionic projective plane" because it can be built using an algebra that is the tensor product of the octonions with themselves... | E8 Lie algebra | 0.785649 |
78,683 | One can construct the (compact form of the) E8 group as the automorphism group of the corresponding e8 Lie algebra. This algebra has a 120-dimensional subalgebra so(16) generated by Jij as well as 128 new generators Qa that transform as a Weyl–Majorana spinor of spin(16). These statements determine the commutators = δ... | E8 Lie algebra | 0.785649 |
78,684 | In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras... | E8 Lie algebra | 0.785649 |
78,685 | In differential geometry, Loewner's torus inequality is an inequality due to Charles Loewner. It relates the systole and the area of an arbitrary Riemannian metric on the 2-torus. | Loewner's torus inequality | 0.785649 |
78,686 | Then the expected value E(X 2) of X 2 expresses the total area of the given metric. Meanwhile, the expected value E(X) of X can be related to the systole by using Fubini's theorem. The variance of X can then be thought of as the isosystolic defect, analogous to the isoperimetric defect of Bonnesen's inequality. This ap... | Loewner's torus inequality | 0.785649 |
78,687 | In the ancient Egyptian calendar, the date of the annual flooding of the Nile was predicted by observing the heliacal rising of a star. Indeed, the belief in a strong association between the events on the earth and in the heavens led to the development of astrology.The first recorded conflict between religious orthodox... | Astronomy and religion | 0.785648 |
78,688 | Astronomy has been a favorite and significant component of mythology and religion throughout history. Astronomy and cosmology are parts of the myths of many cultures and religion around the world. Astronomy and religion have long been closely intertwined, particularly during the early history of astronomy. Archaeologic... | Astronomy and religion | 0.785648 |
78,689 | Isaac Newton was a Catholic. After coming to the conclusion that the Holy Trinity could not exist due to the fact that Jesus couldn't be equal to God, Newton chose to not become a minister. He still believed in the Bible so much so that the idea of going against the first commandment was worse than walking away from Ca... | Astronomy and religion | 0.785648 |
78,690 | While the GAN game has a unique global equilibrium point when both the generator and discriminator have access to their entire strategy sets, the equilibrium is no longer guaranteed when they have a restricted strategy set.In practice, the generator has access only to measures of form μ Z ∘ G θ − 1 {\displaystyle \mu _... | Generative Adversarial Network | 0.785646 |
78,691 | This section provides some of the mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra. As a result, a more rigorous definition of the GAN game would make the following changes:Each probability space ( Ω , B , μ re... | Generative Adversarial Network | 0.785646 |
78,692 | The two time-scale update rule (TTUR) is proposed to make GAN convergence more stable by making the learning rate of the generator lower than that of the discriminator. The authors argued that the generator should move slower than the discriminator, so that it does not "drive the discriminator steadily into new regions... | Generative Adversarial Network | 0.785646 |
78,693 | The generator and encoder are on one team, and the discriminator on the other team. The generator's strategies are functions G: Ω Z → Ω X {\displaystyle G:\Omega _{Z}\to \Omega _{X}} , and the encoder's strategies are functions E: Ω X → Ω Z {\displaystyle E:\Omega _{X}\to \Omega _{Z}} . The discriminator's strategies a... | Generative Adversarial Network | 0.785646 |
78,694 | Typically, the generator is seeded with randomized input that is sampled from a predefined latent space (e.g. a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the gener... | Generative Adversarial Network | 0.785646 |
78,695 | Adversarial machine learning has other uses besides generative modeling and can be applied to models other than neural networks. In control theory, adversarial learning based on neural networks was used in 2006 to train robust controllers in a game theoretic sense, by alternating the iterations between a minimizer poli... | Generative Adversarial Network | 0.785646 |
78,696 | In 1991, Juergen Schmidhuber published generative and adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model with stochasticity that models a probability distribution over output patterns. The... | Generative Adversarial Network | 0.785646 |
78,697 | GANs can improve astronomical images and simulate gravitational lensing for dark matter research. They were used in 2019 to successfully model the distribution of dark matter in a particular direction in space and to predict the gravitational lensing that will occur.GANs have been proposed as a fast and accurate way of... | Generative Adversarial Network | 0.785646 |
78,698 | Artificial intelligence art for video uses AI to generate video from text as Text-to-Video model | Generative Adversarial Network | 0.785646 |
78,699 | For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, full... | Generative Adversarial Network | 0.785646 |
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