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1,300 | Gauge block wringing: What is the mechanism that allows gauge blocks to be wrung together?Fractional Hall effect: What mechanism explains the existence of the u = 5/2 state in the fractional quantum Hall effect? Does it describe quasiparticles with non-Abelian fractional statistics? Liquid crystals: Can the nematic to ... | Open problems in physics | 0.839823 |
1,301 | Are there other theories of quantum gravity other than string theory that admit a holographic description? Problem of time: In quantum mechanics, time is a classical background parameter and the flow of time is universal and absolute. In general relativity time is one component of four-dimensional spacetime, and the fl... | Open problems in physics | 0.839823 |
1,302 | The cosmic censorship hypothesis and the chronology protection conjecture: Can singularities not hidden behind an event horizon, known as "naked singularities", arise from realistic initial conditions, or is it possible to prove some version of the "cosmic censorship hypothesis" of Roger Penrose which proposes that thi... | Open problems in physics | 0.839823 |
1,303 | Black holes, black hole information paradox, and black hole radiation: Do black holes produce thermal radiation, as expected on theoretical grounds? Does this radiation contain information about their inner structure, as suggested by gauge–gravity duality, or not, as implied by Hawking's original calculation? If not, a... | Open problems in physics | 0.839823 |
1,304 | Quantum gravity: Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)? Is spacetime fundamentally continuous or discrete? Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spaceti... | Open problems in physics | 0.839823 |
1,305 | Do gluons form a dense system called colour glass condensate? What are the signatures and evidences for the Balitsky–Fadin–Kuarev–Lipatov, Balitsky–Kovchegov, Catani–Ciafaloni–Fiorani–Marchesini evolution equations? Nuclei and nuclear astrophysics: Why is there a lack of convergence in estimates of the mean lifetime of... | Open problems in physics | 0.839823 |
1,306 | What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime? How does this elucidate the proper interpretation of the fundamental nature of quantum physics? Quantum mind: Does quantum mechanical phenomena, such as entanglement and superposition, play an important part in... | Open problems in physics | 0.839823 |
1,307 | Locality: Are there non-local phenomena in quantum physics? If they exist, are non-local phenomena limited to the entanglement revealed in the violations of the Bell inequalities, or can information and conserved quantities also move in a non-local way? Under what circumstances are non-local phenomena observed? | Open problems in physics | 0.839823 |
1,308 | Interpretation of quantum mechanics: How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse or quantum decoherence, give rise to the reality we perceive? Another way of stating this question regards the measurement problem: What constitutes a "... | Open problems in physics | 0.839823 |
1,309 | Theory of everything: Is there a singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe? Dimensionless physical constants: At the present time, the values of various dimensionless physical constants cannot be calculated; they can... | Open problems in physics | 0.839823 |
1,310 | The following is a list of notable unsolved problems grouped into broad areas of physics.Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a ... | Open problems in physics | 0.839823 |
1,311 | Shape of the universe: What is the 3-manifold of comoving space, i.e., of a comoving spatial section of the universe, informally called the "shape" of the universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. The cosmic inflation h... | Open problems in physics | 0.839823 |
1,312 | Or are most native conformations thermodynamically unstable, but kinetically trapped in metastable states? What keeps the high density of proteins present inside cells from precipitating? Quantum biology: Can coherence be maintained in biological systems at timeframes long enough to be functionally important? Are there... | Open problems in physics | 0.839823 |
1,313 | The injection problem: Fermi acceleration is thought to be the primary mechanism that accelerates astrophysical particles to high energy. However, it is unclear what mechanism causes those particles to initially have energies high enough for Fermi acceleration to work on them. Alfvénic turbulence: In the solar wind and... | Open problems in physics | 0.839823 |
1,314 | Plasma physics and fusion power: Fusion energy may potentially provide power from an abundant resource (e.g. hydrogen) without the type of radioactive waste that fission energy currently produces. However, can ionized gases (plasma) be confined long enough and at a high enough temperature to create fusion power? What i... | Open problems in physics | 0.839823 |
1,315 | However, there are also long-duration GRBs that show evidence against an associated supernova, such as the Swift event GRB 060614. Solar neutrino problem (1968–2001): Solved by a new understanding of neutrino physics, requiring a modification of the Standard Model of particle physics—specifically, neutrino oscillation.... | Open problems in physics | 0.839823 |
1,316 | The Board of Genomics England includes a number of notable scientists: Sir John Chisholm (Executive Chair), former chair of the UK Medical Research Council Professor Sir Mark Caulfield (Chief Scientist), Queen Mary University of London Professor Sir John Bell, University of Oxford Dame Sally Davies (Non-executive Direc... | Genomics England | 0.839823 |
1,317 | Genomics England was formally established as a company on 17 April 2013 and was formally launched on 5 July 2013 as part of the celebrations for the 65th Birthday of the UK's National Health Service In August 2014, the Wellcome Trust announced that it was investing £27 million in a genome-sequencing hub for Genomics En... | Genomics England | 0.839823 |
1,318 | Genomics England is a British company set up and owned by the United Kingdom Department of Health and Social Care to run the 100,000 Genomes Project. The project aimed in 2014 to sequence 100,000 genomes from NHS patients with a rare disease and their families, and patients with cancer. An infectious disease strand is ... | Genomics England | 0.839823 |
1,319 | Inner product space: an F vector space V with a definite bilinear form V × V → F. Bialgebra: an associative algebra with a compatible coalgebra structure. Lie bialgebra: a Lie algebra with a compatible bialgebra structure. Hopf algebra: a bialgebra with a connection axiom (antipode). Clifford algebra: an associative Z ... | Outline of algebraic structures | 0.839789 |
1,320 | Lie coalgebra: a vector space with a "comultiplication" defined dually to that of Lie algebras. Graded algebra: a graded vector space with an algebra structure compatible with the grading. The idea is that if the grades of two elements a and b are known, then the grade of ab is known, and so the location of the product... | Outline of algebraic structures | 0.839789 |
1,321 | Lie algebra: a special type of nonassociative algebra whose product satisfies the Jacobi identity. Jordan algebra: a special type of nonassociative algebra whose product satisfies the Jordan identity. Coalgebra: a vector space with a "comultiplication" defined dually to that of associative algebras. | Outline of algebraic structures | 0.839789 |
1,322 | Associative algebra: an algebra over a ring such that the multiplication is associative. Nonassociative algebra: a module over a commutative ring, equipped with a ring multiplication operation that is not necessarily associative. Often associativity is replaced with a different identity, such as alternation, the Jacobi... | Outline of algebraic structures | 0.839789 |
1,323 | This includes distributivity over addition and linearity with respect to multiplication by elements of R. Algebra over a field: This is a ring which is also a vector space over a field. Multiplication is usually assumed to be associative. The theory is especially well developed. | Outline of algebraic structures | 0.839789 |
1,324 | These structures are defined over two sets, a ring R and an R-module M equipped with an operation called multiplication. This can be viewed as a system with five binary operations: two operations on R, two on M and one involving both R and M. Many of these structures are hybrid structures of the previously mentioned on... | Outline of algebraic structures | 0.839789 |
1,325 | Boolean algebra: a complemented distributive lattice. Either of meet or join can be defined in terms of the other and complementation. This can be shown to be equivalent with the ring-like structure of the same name above. Heyting algebra: a bounded distributive lattice with an added binary operation, relative pseudo-c... | Outline of algebraic structures | 0.839789 |
1,326 | The following module-like structures have the common feature of having two sets, A and B, so that there is a binary operation from A×A into A and another operation from A×B into A. Modules, counting the ring operations, have at least three binary operations. Group with operators: a group G with a set Ω and a binary ope... | Outline of algebraic structures | 0.839789 |
1,327 | Most structures appearing on this page will be common ones which most authors agree on. Other web lists of algebraic structures, organized more or less alphabetically, include Jipsen and PlanetMath. These lists mention many structures not included below, and may present more information about some structures than is pr... | Outline of algebraic structures | 0.839789 |
1,328 | Algebraic structures are so numerous today that this article will inevitably be incomplete. In addition to this, there are sometimes multiple names for the same structure, and sometimes one name will be defined by disagreeing axioms by different authors. | Outline of algebraic structures | 0.839789 |
1,329 | From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called nonvarieties, are sometimes included among the algebraic structures by tradition. Concrete examples of ... | Outline of algebraic structures | 0.839789 |
1,330 | In mathematics, there are many types of algebraic structures which are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates... | Outline of algebraic structures | 0.839789 |
1,331 | There are many examples of mathematical structures where algebraic structure exists alongside non-algebraic structure. Topological vector spaces are vector spaces with a compatible topology. Lie groups: These are topological manifolds that also carry a compatible group structure. Ordered groups, ordered rings and order... | Outline of algebraic structures | 0.839789 |
1,332 | Robinson arithmetic with an axiom schema of induction. Most ring and field axioms bearing on the properties of addition and multiplication are theorems of Peano arithmetic or of proper extensions thereof.Lattice-like structures have two binary operations called meet and join, connected by the absorption law. Latticoid:... | Outline of algebraic structures | 0.839789 |
1,333 | Kleene algebras: a semiring with idempotent addition and a unary operation, the Kleene star, satisfying additional properties. *-algebra or *-ring: a ring with an additional unary operation (*) known as an involution, satisfying additional properties. Arithmetic: addition and multiplication on an infinite set, with an ... | Outline of algebraic structures | 0.839789 |
1,334 | In full generality, an algebraic structure may use any number of sets and any number of axioms in its definition. The most commonly studied structures, however, usually involve only one or two sets and one or two binary operations. The structures below are organized by how many sets are involved, and how many binary op... | Outline of algebraic structures | 0.839789 |
1,335 | Universal algebra studies algebraic structures abstractly, rather than specific types of structures. Varieties Category theory studies interrelationships between different structures, algebraic and non-algebraic. To study a non-algebraic object, it is often useful to use category theory to relate the object to an algeb... | Outline of algebraic structures | 0.839789 |
1,336 | Algebraic structures appear in most branches of mathematics, and one can encounter them in many different ways. Beginning study: In American universities, groups, vector spaces and fields are generally the first structures encountered in subjects such as linear algebra. They are usually introduced as sets with certain ... | Outline of algebraic structures | 0.839789 |
1,337 | Lie algebras Inner product spaces Kac–Moody algebra The quaternions and more generally geometric algebrasIn Mathematical logic: Boolean algebras are both rings and lattices, under their two operations. Heyting algebras are a special example of boolean algebras. Peano arithmetic Boundary algebra MV-algebraIn Computer sc... | Outline of algebraic structures | 0.839789 |
1,338 | Some algebraic structures find uses in disciplines outside of abstract algebra. The following is meant to demonstrate some specific applications in other fields. In Physics: Lie groups are used extensively in physics. A few well-known ones include the orthogonal groups and the unitary groups. | Outline of algebraic structures | 0.839789 |
1,339 | Set: a degenerate algebraic structure S having no operations. Pointed set: S has one or more distinguished elements, often 0, 1, or both. Unary system: S and a single unary operation over S. Pointed unary system: a unary system with S a pointed set. | Outline of algebraic structures | 0.839789 |
1,340 | We can identify APS as a subalgebra of the spacetime algebra (STA) C ℓ 1 , 3 ( R ) {\displaystyle C\ell _{1,3}(\mathbb {R} )} , defining σ k = γ k γ 0 {\displaystyle \sigma _{k}=\gamma _{k}\gamma _{0}} and I = γ 0 γ 1 γ 2 γ 3 {\displaystyle I=\gamma _{0}\gamma _{1}\gamma _{2}\gamma _{3}} . The γ μ {\displaystyle \gamma... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,341 | It is of algebraic convenience that the geometric product is invertible, while the inner and outer products are not. As such, powerful techniques such as Green's functions can be used. | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,342 | This formulation uses the algebra that spacetime generates through the introduction of a distributive, associative (but not commutative) product called the geometric product. Elements and operations of the algebra can generally be associated with geometric meaning. The members of the algebra may be decomposed by grade ... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,343 | In free space, where ε = ε0 and μ = μ0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. In what follows, cgs-Gaussian units, not SI units are used. (To convert to SI, see here.) The electric and magnetic fields are now jointly ... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,344 | In advanced classical mechanics it is often useful, and in quantum mechanics frequently essential, to express Maxwell's equations in a potential formulation involving the electric potential (also called scalar potential) φ, and the magnetic potential (a vector potential) A. For example, the analysis of radio antennas m... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,345 | Analogous to the tensor formulation, two objects, one for the electromagnetic field and one for the current density, are introduced. In geometric algebra (GA) these are multivectors. | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,346 | In quantum mechanics, the connection itself is used to define the dynamics of the system. This formulation allows a natural description of the Aharonov–Bohm effect. In this experiment, a static magnetic field runs through a long magnetic wire (e.g., an iron wire magnetized longitudinally). | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,347 | These basis vectors share the algebra of the Pauli matrices, but are usually not equated with them, as they are different objects with different interpretations. After defining the derivative Maxwell's equations are reduced to the single equation In three dimensions, the derivative has a special structure allowing the ... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,348 | In the Algebra of physical space (APS), also known as the Clifford algebra C ℓ 3 , 0 ( R ) {\displaystyle C\ell _{3,0}(\mathbb {R} )} , the field and current are represented by multivectors. The field multivector, known as the Riemann–Silberstein vector, is and the current multivector is using an orthonormal basis { σ ... | Mathematical descriptions of the electromagnetic field | 0.839781 |
1,349 | While being a certified CIT may help in obtaining a chemistry related job, it is not typically required to do chemistry work. All work performed by an CIT must still be checked and certified by a P.Chem. == References == | Chemist in Training | 0.839766 |
1,350 | A licensed CIT is certified to work in a chemistry profession. Upon completing a certain amount of work experience under the supervision of a Licensed Professional Chemist (P.Chem.) as determined by a licensing board, a CIT is then eligible to gain experience by supervision from a P.Chem. | Chemist in Training | 0.839766 |
1,351 | If we have a field extension F/K, which is to say a bigger field F that contains K, then there is a natural way to construct an algebra over F from any algebra over K. It is the same construction one uses to make a vector space over a bigger field, namely the tensor product V F := V ⊗ K F {\displaystyle V_{F}:=V\otimes... | Algebra over a field | 0.839749 |
1,352 | Given K-algebras A and B, a K-algebra homomorphism is a K-linear map f: A → B such that f(xy) = f(x) f(y) for all x, y in A. The space of all K-algebra homomorphisms between A and B is frequently written as H o m K -alg ( A , B ) . {\displaystyle \mathbf {Hom} _{K{\text{-alg}}}(A,B).} A K-algebra isomorphism is a bijec... | Algebra over a field | 0.839749 |
1,353 | For example, the theory of Gröbner bases was introduced by Bruno Buchberger for ideals in a polynomial ring R = K over a field. The construction of the unital zero algebra over a free R-module allows extending this theory as a Gröbner basis theory for submodules of a free module. This extension allows, for computing a ... | Algebra over a field | 0.839749 |
1,354 | If e1, ... ed is a basis of V, the unital zero algebra is the quotient of the polynomial ring K by the ideal generated by the EiEj for every pair (i, j). An example of unital zero algebra is the algebra of dual numbers, the unital zero R-algebra built from a one dimensional real vector space. These unital zero algebras... | Algebra over a field | 0.839749 |
1,355 | An algebra is called zero algebra if uv = 0 for all u, v in the algebra, not to be confused with the algebra with one element. It is inherently non-unital (except in the case of only one element), associative and commutative. One may define a unital zero algebra by taking the direct sum of modules of a field (or more g... | Algebra over a field | 0.839749 |
1,356 | {\displaystyle (k,a)\mapsto \eta (k)a.} Given two such associative unital K-algebras A and B, a unital K-algebra homomorphism f: A → B is a ring homomorphism that commutes with the scalar multiplication defined by η, which one may write as f ( k a ) = k f ( a ) {\displaystyle f(ka)=kf(a)} for all k ∈ K {\displaystyle k... | Algebra over a field | 0.839749 |
1,357 | The definition of an associative K-algebra with unit is also frequently given in an alternative way. In this case, an algebra over a field K is a ring A together with a ring homomorphism η: K → Z ( A ) , {\displaystyle \eta \colon K\to Z(A),} where Z(A) is the center of A. Since η is a ring homomorphism, then one must ... | Algebra over a field | 0.839749 |
1,358 | Let K be a field, and let A be a vector space over K equipped with an additional binary operation from A × A to A, denoted here by · (that is, if x and y are any two elements of A, then x · y is an element of A that is called the product of x and y). Then A is an algebra over K if the following identities hold for all ... | Algebra over a field | 0.839749 |
1,359 | The test had 50 multiple choice questions that were to be answered in one hour. All questions had five answer choices. Students received 1 point for every correct answer, lost ¼ of a point for each incorrect answer, and received 0 points for questions left blank. The questions covered a broad range of topics. Approxima... | SAT Subject Test in Mathematics Level 1 | 0.839734 |
1,360 | The SAT Subject Test in Mathematics Level 2 covered more advanced content. Generally you need to have completed a semester of a pre-calculus class with a solid “B” or better to feel comfortable on the Math 1, whereas the content of the Math 2 test extends through Algebra II and basic trigonometry, precalculus, and basi... | SAT Subject Test in Mathematics Level 1 | 0.839734 |
1,361 | The SAT Subject Test in Mathematics Level 1 (formerly known as Math I or MathIC (the "C" representing the use of a calculator)) was the name of a one-hour multiple choice test given on algebra, geometry, basic trigonometry, algebraic functions, elementary statistics and basic foundations of calculus by The College Boar... | SAT Subject Test in Mathematics Level 1 | 0.839734 |
1,362 | The College Board suggested as preparation for the test three years of mathematics, including two years of algebra, and one year of geometry. | SAT Subject Test in Mathematics Level 1 | 0.839734 |
1,363 | For that reason, the construction of this inverse operation in modern algebra is often discarded in favor of introducing the concept of inverse elements (as sketched under § Addition), where subtraction is regarded as adding the additive inverse of the subtrahend to the minuend, that is, a − b = a + (−b). The immediate... | Arithmetical operations | 0.839727 |
1,364 | Elementary arithmetic is typically taught at the primary or secondary school levels and is governed by local educational standards. In the United States and Canada, there has been debate about the content and methods used to teach elementary arithmetic. One issue has been the use of calculators versus manual computatio... | Elementary arithmetic | 0.839705 |
1,365 | The asterisk notation is most commonly used in computer programming languages. In algebra, the multiplication symbol may be omitted; for example, xy represents x multiplied by y. The order in which two numbers are multiplied does not affect the result. This is known as the commutative property of multiplication. | Elementary arithmetic | 0.839705 |
1,366 | A few things should be considered when improving the accuracy of the decision tree classifier. The following are some possible optimizations to consider when looking to make sure the decision tree model produced makes the correct decision or classification. Note that these things are not the only things to consider but... | Decision trees | 0.839698 |
1,367 | Some graphing calculators have a computer algebra system (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions, performing operations such as factor, expand, and simplify. In addition, they can give answers in exact form without numerical approxim... | Graphing Calculators | 0.839654 |
1,368 | The book is aimed at students, written for a general audience, and does not require any background in mathematics beyond high school algebra. However, many of its chapters include exercises, making it suitable for teaching high school or undergraduate-level courses using it. It is also suitable for readers interested i... | The Mathematics of Games and Gambling | 0.83962 |
1,369 | The book has seven chapters. Its first gives a survey of the history of gambling games in western culture, including brief biographies of two famous gamblers, Gerolamo Cardano and Fyodor Dostoevsky, and a review of the games of chance found in Dostoevsky's novel The Gambler. The next four chapters introduce the basic c... | The Mathematics of Games and Gambling | 0.83962 |
1,370 | The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006. | The Mathematics of Games and Gambling | 0.83962 |
1,371 | Chemistry sets may have been the first American toys marketed toward parents with the goal of "improving" children for success in later life. The target market for chemistry sets was almost exclusively boys, deemed "young men of science." However, during the 1950s, Gilbert introduced a set targeting girls. | Chemistry set | 0.839619 |
1,372 | Robert Treat Johnson, noting the number of chemistry students at Yale whose interest in the science began with a chemistry set, argued the production of chemistry sets was a "patriotic duty. "Toy companies promoted chemistry sets through advertising campaigns, the "Chemcraft Chemist Club" and its accompanying "Chemcraf... | Chemistry set | 0.839619 |
1,373 | Alfred Carlton Gilbert earned money by performing magic tricks while a medical student at Yale. He and John Petrie formed the Mysto Manufacturing Company (later the A. C. Gilbert Company) in 1909, and began selling boxed magic sets. By 1917, they sold chemistry sets, which they produced through World War II, in spite o... | Chemistry set | 0.839619 |
1,374 | Beginning in the early 1900s, modern chemistry sets targeted younger people with the intention to popularize chemistry. In the United States, Porter Chemical Company and the A. C. Gilbert Company produced the best known sets. Although Porter and Gilbert were the largest American producers of chemistry sets, other manuf... | Chemistry set | 0.839619 |
1,375 | A chemistry set is an educational toy allowing the user (typically a teenager) to perform simple chemistry experiments. | Chemistry set | 0.839619 |
1,376 | Typical contents found in chemistry sets, including equipment and chemicals, might include: | Chemistry set | 0.839618 |
1,377 | Primarily used for training druggists and medical students, they could also be carried and used in the field.Scientific kits also attracted well-educated members of the upper class who enjoyed experimenting and demonstrating their results. James Woodhouse of Philadelphia presented a Young Chemist's Pocket Companion (17... | Chemistry set | 0.839618 |
1,378 | The forerunners of the chemistry set were 17th century books on "natural magick", "which all excellent wise men do admit and embrace, and worship with great applause; neither is there any thing more highly esteemed, or better thought of, by men of learning." Authors such as Giambattista della Porta included chemical ma... | Chemistry set | 0.839618 |
1,379 | The experiments described in the instruction manual typically require a number of chemicals not shipped with the chemistry set, because they are common household chemicals: Acetic acid (in vinegar) Ammonium carbonate ("baker's ammonia" or "salts of hartshorn") Citric acid (in lemons) Ethanol (in denatured alcohol) Sodi... | Chemistry set | 0.839618 |
1,380 | They sold the set in an attractive pink box, but the set identified girls as "laboratory assistants" or "lab technicians," not scientists.In 1971, a Johnny Horizon Environmental Test Kit was licensed by the U. S. Department of the Interior and produced by Parker Brothers. It included four air pollution tests and six wa... | Chemistry set | 0.839618 |
1,381 | Around the 1960s, safety concerns began to limit the range of materials and experiments available in chemistry sets. In the United States, the Federal Hazardous Substances Labeling Act of 1960, the Toy Safety Act of 1969, the Consumer Product Safety Commission, established in 1972, and the Toxic Substances Control Act ... | Chemistry set | 0.839618 |
1,382 | In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition. Commutative diagrams play the role i... | Mathematical diagram | 0.839593 |
1,383 | For very short interatomic separations, important in radiation material science, the interactions can be described quite accurately with screened Coulomb potentials which have the general form V ( r i j ) = 1 4 π ε 0 Z 1 Z 2 e 2 r i j φ ( r / a ) {\displaystyle V(r_{ij})={1 \over 4\pi \varepsilon _{0}}{Z_{1}Z_{2}e^{2} ... | Interatomic potential | 0.83957 |
1,384 | The arguably simplest widely used interatomic interaction model is the Lennard-Jones potential V L J ( r ) = 4 ε {\displaystyle V_{\mathrm {LJ} }(r)=4\varepsilon \left} where ε {\displaystyle \textstyle \varepsilon } is the depth of the potential well and σ {\displaystyle \textstyle \sigma } is the distance at which t... | Interatomic potential | 0.83957 |
1,385 | These feature vectors are then used to directly predict the final potentials. In 2017, the first-ever MPNN model, a deep tensor neural network, was used to calculate the properties of small organic molecules. Advancements in this technology led to the development of Matlantis in 2022, which commercially applies machine... | Interatomic potential | 0.83957 |
1,386 | Atomic coordinates are sometimes transformed with atom-centered symmetry functions or pair symmetry functions before being fed into neural networks. Encoding symmetry has been pivotal in enhancing machine learning potentials by drastically constraining the neural networks' search space.Conversely, Message-Passing Neura... | Interatomic potential | 0.83957 |
1,387 | However, with continuous advancements in artificial intelligence technology, machine learning methods have become significantly more accurate, positioning machine learning as a significant player in potential fitting.Modern neural networks have revolutionized the construction of highly accurate and computationally ligh... | Interatomic potential | 0.83957 |
1,388 | Since the 1990s, machine learning programs have been employed to construct potentials, mapping atomic structures to their potential energies. Such machine learning potentials help fill the gap between highly accurate but computationally intensive simulations like density functional theory and computationally lighter, b... | Interatomic potential | 0.83957 |
1,389 | However, the accuracy of a machine-learning potential can be converged to be comparable with the underlying quantum calculations, unlike analytical models. Hence, they are in general more accurate than traditional analytical potentials, but they are correspondingly less able to extrapolate. Further, owing to the comple... | Interatomic potential | 0.83957 |
1,390 | However, more complex many-body descriptors are needed to produce highly accurate potentials. It is also possible to use a linear combination of multiple descriptors with associated machine-learning models. Potentials have been constructed using a variety of machine-learning methods, descriptors, and mappings, includin... | Interatomic potential | 0.83957 |
1,391 | E {\displaystyle E} is a machine-learning model that provides a prediction for the energy of atom i {\displaystyle i} based on the descriptor output. An accurate machine-learning potential requires both a robust descriptor and a suitable machine learning framework. The simplest descriptor is the set of interatomic dist... | Interatomic potential | 0.83957 |
1,392 | It should first be noted that non-parametric potentials are often referred to as "machine learning" potentials. While the descriptor/mapping forms of non-parametric models are closely related to machine learning in general and their complex nature make machine learning fitting optimizations almost necessary, differenti... | Interatomic potential | 0.83957 |
1,393 | Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computation... | Interatomic potential | 0.83957 |
1,394 | In most practical cases deterministic algorithms or randomized algorithms are discussed, although theoretical computer science also considers nondeterministic algorithms and other advanced models of computation. | Asymptotic time complexity | 0.839565 |
1,395 | Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To calculate means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer us... | Calculation | 0.839549 |
1,396 | Aryabhata, in the Aryabhatiya (section 2.4), has given a method for finding the square root of numbers having many digits. It was known to the ancient Greeks that square roots of positive integers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers (that is, th... | Square root | 0.839539 |
1,397 | An accurate model with relatively poor precision could be useful to study the evolutionary relationships between the structures of a set of proteins, whereas the rational drug design requires both precise and accurate models. A model that is not accurate, regardless of the degree of precision with which it was obtained... | Protein nuclear magnetic resonance | 0.839531 |
1,398 | A typical study might involve how two proteins interact with each other, possibly with a view to developing small molecules that can be used to probe the normal biology of the interaction ("chemical biology") or to provide possible leads for pharmaceutical use (drug development). Frequently, the interacting pair of pro... | Protein nuclear magnetic resonance | 0.839531 |
1,399 | This change of scale requires much higher sensitivity of detection and stability for long term measurement. In contrast to MRI, structural biology studies do not directly generate an image, but rely on complex computer calculations to generate three-dimensional molecular models. | Protein nuclear magnetic resonance | 0.839531 |
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