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8,500 | Of the three types (flavors) of neutrinos known in the Standard Model of particle physics, the Sun produces only electron neutrinos. When neutrino detectors became sensitive enough to measure the flow of electron neutrinos from the Sun, the number detected was much lower than predicted. In various experiments, the numb... | Solar neutrino problem | 0.821266 |
8,501 | The model gives a detailed account of the Sun's internal operation. In 2002, Ray Davis and Masatoshi Koshiba won part of the Nobel Prize in Physics for experimental work which found the number of solar neutrinos to be around a third of the number predicted by the standard solar model.In recognition of the firm evidence... | Solar neutrino problem | 0.821266 |
8,502 | In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension. Typically, the poten... | Step potential | 0.821265 |
8,503 | The relativistic calculation of a free particle colliding with a step potential can be obtained using relativistic quantum mechanics. For the case of 1/2 fermions, like electrons and neutrinos, the solutions of the Dirac equation for high energy barriers produce transmission and reflection coefficients that are not bou... | Step potential | 0.821265 |
8,504 | Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 1.70 fm (1.70×10−15 m) for hydrogen (the diameter of a single proton) to abo... | Atomic nuclei | 0.821264 |
8,505 | In the rare case of a hypernucleus, a third baryon called a hyperon, containing one or more strange quarks and/or other unusual quark(s), can also share the wave function. However, this type of nucleus is extremely unstable and not found on Earth except in high-energy physics experiments. The neutron has a positively c... | Atomic nuclei | 0.821264 |
8,506 | Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, generating predictions from theory is much more difficult than for most other areas of particle physics. This is due to two reasons: In principle, the physics within a nucleus can be derived ent... | Atomic nuclei | 0.821264 |
8,507 | Paraboloidal coordinates can be useful for solving certain partial differential equations. For instance, the Laplace equation and Helmholtz equation are both separable in paraboloidal coordinates. Hence, the coordinates can be used to solve these equations in geometries with paraboloidal symmetry, i.e. with boundary co... | Paraboloidal coordinates | 0.821263 |
8,508 | A more modern approach to word recognition has been based on recent research on neuron functioning. The visual aspects of a word, such as horizontal and vertical lines or curves, are thought to activate word-recognizing receptors. From those receptors, neural signals are sent to either excite or inhibit connections to ... | Word recognition | 0.821262 |
8,509 | Serif fonts, i.e.: fonts with small appendages at the end of strokes, hinder lexical access. Word recognition is quicker with sans-serif fonts by an average of 8 ms. These fonts have significantly more inter-letter spacing, and studies have shown that responses to words with increased inter-letter spacing were faster, ... | Word recognition | 0.821262 |
8,510 | Introduction to the Theory of Computation (ISBN 0-534-95097-3) is a textbook in theoretical computer science, written by Michael Sipser and first published by PWS Publishing in 1997. | Introduction to the Theory of Computation | 0.82126 |
8,511 | The science of chemistry began to develop with the work of Robert Boyle, the discoverer of gas, and Antoine Lavoisier, who developed the theory of the Conservation of mass. The discovery of the chemical elements and atomic theory began to systematize this science, and researchers developed a fundamental understanding o... | Natural science | 0.821259 |
8,512 | Most chemical processes can be studied directly in a laboratory, using a series of (often well-tested) techniques for manipulating materials, as well as an understanding of the underlying processes. Chemistry is often called "the central science" because of its role in connecting the other natural sciences. Early exper... | Natural science | 0.821259 |
8,513 | Constituting the scientific study of matter at the atomic and molecular scale, chemistry deals primarily with collections of atoms, such as gases, molecules, crystals, and metals. The composition, statistical properties, transformations, and reactions of these materials are studied. Chemistry also involves understandin... | Natural science | 0.821259 |
8,514 | The idea of fields contrasted with the Newtonian construct of gravitation as simply "action at a distance", or the attraction of objects with nothing in the space between them to intervene. James Clerk Maxwell in the 19th century unified these discoveries in a coherent theory of electrodynamics. Using mathematical equa... | Natural science | 0.821259 |
8,515 | Newton, an English mathematician, and physicist was the seminal figure in the scientific revolution. Drawing on advances made in astronomy by Copernicus, Brahe, and Kepler, Newton derived the universal law of gravitation and laws of motion. These laws applied both on earth and in outer space, uniting two spheres of the... | Natural science | 0.821259 |
8,516 | According to Cohen, "the emancipation of science from an overarching entity called 'natural philosophy is one defining characteristic of the Scientific Revolution." Other historians of science, including Edward Grant, contend that the scientific revolution that blossomed in the 17th, 18th, and 19th centuries occurred w... | Natural science | 0.821259 |
8,517 | The titles of Galileo's work Two New Sciences and Johannes Kepler's New Astronomy underscored the atmosphere of change that took hold in the 17th century as Aristotle was dismissed in favor of novel methods of inquiry into the natural world. Bacon was instrumental in popularizing this change; he argued that people shou... | Natural science | 0.821259 |
8,518 | There is considerable overlap with physics and in some areas of earth science. There are also interdisciplinary fields such as astrophysics, planetary sciences, and cosmology, along with allied disciplines such as space physics and astrochemistry. While the origins of the study of celestial features and phenomena can b... | Natural science | 0.821259 |
8,519 | It is concerned with the evolution, physics, chemistry, meteorology, geology, and motion of celestial objects, as well as the formation and development of the universe. Astronomy includes the examination, study, and modeling of stars, planets, comets. Most of the information used by astronomers is gathered by remote ob... | Natural science | 0.821259 |
8,520 | There are two types of astronomy: observational astronomy and theoretical astronomy. Observational astronomy is focused on acquiring and analyzing data, mainly using basic principles of physics while Theoretical astronomy is oriented towards the development of computer or analytical models to describe astronomical obje... | Natural science | 0.821259 |
8,521 | That includes objects we can see with our naked eyes. Astronomy is one of the oldest sciences. Astronomers of early civilizations performed methodical observations of the night sky, and astronomical artifacts have been found from much earlier periods. | Natural science | 0.821259 |
8,522 | Astronomy is a natural science that studies celestial objects and phenomena. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Astronomy is the study of everything in the universe beyond Earth's atmosphere. | Natural science | 0.821259 |
8,523 | Some key developments in biology were the discovery of genetics, evolution through natural selection, the germ theory of disease, and the application of the techniques of chemistry and physics at the level of the cell or organic molecule. Modern biology is divided into subdisciplines by the type of organism and by the ... | Natural science | 0.821259 |
8,524 | The biological fields of botany, zoology, and medicine date back to early periods of civilization, while microbiology was introduced in the 17th century with the invention of the microscope. However, it was not until the 19th century that biology became a unified science. Once scientists discovered commonalities betwee... | Natural science | 0.821259 |
8,525 | This field encompasses a diverse set of disciplines that examines phenomena related to living organisms. The scale of study can range from sub-component biophysics up to complex ecologies. Biology is concerned with the characteristics, classification and behaviors of organisms, as well as how species were formed and th... | Natural science | 0.821259 |
8,526 | A key factor was Galileo's introduction of the telescope to examine the night sky in more detail. The mathematical treatment of astronomy began with Newton's development of celestial mechanics and the laws of gravitation, although it was triggered by earlier work of astronomers such as Kepler. By the 19th century, astr... | Natural science | 0.821259 |
8,527 | There is also a subset of cross-disciplinary fields that have strong currents that run counter to specialization by the nature of the problems that they address. Put another way: In some fields of integrative application, specialists in more than one field are a key part of the most dialog. Such integrative fields, for... | Natural science | 0.821259 |
8,528 | Oceanography is sub-categorized into more specialized cross-disciplines, such as physical oceanography and marine biology. As the marine ecosystem is very large and diverse, marine biology is further divided into many subfields, including specializations in particular species. | Natural science | 0.821259 |
8,529 | The distinctions between the natural science disciplines are not always sharp, and they share many cross-discipline fields. Physics plays a significant role in the other natural sciences, as represented by astrophysics, geophysics, chemical physics and biophysics. Likewise chemistry is represented by such fields as bio... | Natural science | 0.821259 |
8,530 | Planetary science or planetology, is the scientific study of planets, which include terrestrial planets like the Earth, and other types of planets, such as gas giants other celestial bodies, such as moons, asteroids, and comets. This largely includes the Solar System, but recently has started to expand to exoplanets, p... | Natural science | 0.821259 |
8,531 | Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatability of findings are used to try to ensure the validity of scientific advance... | Natural science | 0.821259 |
8,532 | If m is the number of bits needed to express any number in the set and n is the size of the set then m / n < 1 {\displaystyle m/n<1} tends to have many solutions and m / n > 1 {\displaystyle m/n>1} tends to have few or no solutions. As n and m get larger, the probability of a perfect partition goes to 1 or 0 respective... | Partition problem | 0.821258 |
8,533 | In practice, problems of arbitrary size can be solved by CKK if the numbers have at most 12 significant digits. CKK can also run as an anytime algorithm: it finds the KK solution first, and then finds progressively better solutions as time allows (possibly requiring exponential time to reach optimality, for the worst i... | Partition problem | 0.821258 |
8,534 | In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-com... | Partition problem | 0.821258 |
8,535 | To see this, suppose that such a rule satisfies IIA. Since majority preferences are respected, the society prefers A to B (two votes for A > B and one for B > A), B to C, and C to A. Thus a cycle is generated, which contradicts the assumption that social preference is transitive. So, what Arrow's theorem really shows i... | Arrow's impossibility theorem | 0.821256 |
8,536 | Although Arrow's theorem is a mathematical result, it is often expressed in a non-mathematical way with a statement such as no voting method is fair, every ranked voting method is flawed, or the only voting method that is not flawed is a dictatorship. These statements are simplifications of Arrow's result which are not... | Arrow's impossibility theorem | 0.821256 |
8,537 | This gives considerable opportunity for weaker teams to win, thus adding interest and tension throughout the tournament. This means that the person controlling the order by which the choices are paired (the agenda maker) has great control over the outcome. In any case, when viewing the entire voting process as one game... | Arrow's impossibility theorem | 0.821256 |
8,538 | The IIA property might not be satisfied in human decision-making of realistic complexity because the scalar preference ranking is effectively derived from the weighting—not usually explicit—of a vector of attributes (one book dealing with the Arrow theorem invites the reader to consider the related problem of creating ... | Arrow's impossibility theorem | 0.821256 |
8,539 | In that sense, the approach is qualitatively different from the earlier one in voting theory, in which rules were investigated one by one. One can therefore say that the contemporary paradigm of social choice theory started from this theorem.The practical consequences of the theorem are debatable. Arrow has said: "Most... | Arrow's impossibility theorem | 0.821256 |
8,540 | There is no "dictator": no single voter possesses the power to always determine the group's preference.Cardinal voting electoral systems are not covered by the theorem, as they convey more information than rank orders. Gibbard's theorem and the Duggan–Schwartz theorem show that strategic voting remains a problem. The a... | Arrow's impossibility theorem | 0.821256 |
8,541 | Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide... | Arrow's impossibility theorem | 0.821256 |
8,542 | Other rated electoral system which pass certain generalizations of Arrow's criteria include approval voting and majority judgment. Note that Arrow's theorem does not apply to single-winner methods such as these, but Gibbard's theorem still does: no non-defective electoral system is fully strategy-free, so the informal ... | Arrow's impossibility theorem | 0.821256 |
8,543 | Arrow originally rejected cardinal utility as a meaningful tool for expressing social welfare, and so focused his theorem on preference rankings, but later stated that a cardinal score system with three or four classes "is probably the best".Arrow's framework assumes that individual and social preferences are "ordering... | Arrow's impossibility theorem | 0.821256 |
8,544 | Plant ontology (PO) is a collection of ontologies developed by the Plant Ontology Consortium. These ontologies describe anatomical structures and growth and developmental stages across Viridiplantae. The PO is intended for multiple applications, including genetics, genomics, phenomics, and development, taxonomy and sys... | Plant ontology | 0.82124 |
8,545 | During the 1980s, Yahli Lorch and Roger Kornberg showed that a nucleosome on a core promoter prevents the initiation of transcription in vitro, and Michael Grunstein demonstrated that histones repress transcription in vivo, leading to the idea of the nucleosome as a general gene repressor. Relief from repression is bel... | Histone modification | 0.821239 |
8,546 | Their paper became a citation classic. Paul T'so and James Bonner had called together a World Congress on Histone Chemistry and Biology in 1964, in which it became clear that there was no consensus on the number of kinds of histone and that no one knew how they would compare when isolated from different organisms. Bonn... | Histone modification | 0.821239 |
8,547 | The addition of one, two, or many methyl groups to lysine has little effect on the chemistry of the histone; methylation leaves the charge of the lysine intact and adds a minimal number of atoms so steric interactions are mostly unaffected. However, proteins containing Tudor, chromo or PHD domains, amongst others, can ... | Histone modification | 0.821239 |
8,548 | The representable relation algebras, forming the class RRA, are those relation algebras isomorphic to some relation algebra consisting of binary relations on some set, and closed under the intended interpretation of the RA operations. It is easily shown, e.g. using the method of pseudoelementary classes, that RRA is a ... | Relation algebra | 0.821238 |
8,549 | (N.B. The Boolean algebra fragment of RA is complete and decidable.) | Relation algebra | 0.821238 |
8,550 | Hence RA is, in effect, a way of algebraizing nearly all mathematics, while dispensing with FOL and its connectives, quantifiers, turnstiles, and modus ponens. Because RA can express Peano arithmetic and set theory, Gödel's incompleteness theorems apply to it; RA is incomplete, incompletable, and undecidable. | Relation algebra | 0.821238 |
8,551 | The metamathematics of RA are discussed at length in Tarski and Givant (1987), and more briefly in Givant (2006). RA consists entirely of equations manipulated using nothing more than uniform replacement and the substitution of equals for equals. Both rules are wholly familiar from school mathematics and from abstract ... | Relation algebra | 0.821238 |
8,552 | The following table shows how many of the usual properties of binary relations can be expressed as succinct RA equalities or inequalities. Below, an inequality of the form A ≤ B is shorthand for the Boolean equation A∨B = B. The most complete set of results of this nature is Chapter C of Carnap (1958), where the notati... | Relation algebra | 0.821238 |
8,553 | :a\in A\}} ), and the identity by the singleton subset { e } {\displaystyle \{e\}} . There is a relation algebra homomorphism embedding 2 G {\displaystyle 2^{G}} in 2 G × G {\displaystyle 2^{G\times G}} which sends each subset A ⊂ G {\displaystyle A\subset G} to the relation R A = { ( g , h ) ∈ G × G: h ∈ A g } {\displ... | Relation algebra | 0.821238 |
8,554 | The previous section says more about the relevant metamathematics. Let G be a group. Then the power set 2 G {\displaystyle 2^{G}} is a relation algebra with the obvious Boolean algebra operations, composition given by the product of group subsets, the converse by the inverse subset ( A − 1 = { a − 1: a ∈ A } {\displays... | Relation algebra | 0.821238 |
8,555 | While 2E is not a subalgebra of 2 X 2 when E ≠ X 2 (since in that case it does not contain the relation X 2, the top element 1 being E instead of X 2), it is nevertheless turned into a relation algebra using the same definitions of the operations. Its importance resides in the definition of a representable relation alg... | Relation algebra | 0.821238 |
8,556 | Any Boolean algebra can be turned into a RA by interpreting conjunction as composition (the monoid multiplication •), i.e. x • y is defined as x∧y. This interpretation requires that converse interpret identity (ў = y), and that both residuals y \ x and x /y interpret the conditional y → x (i.e., ¬y ∨ x). The motivating... | Relation algebra | 0.821238 |
8,557 | An RA is a Q-relation algebra (QRA) if, in addition to B1-B10, there exist some A and B such that (Tarski and Givant 1987: §8.4): Q0: A˘ • A ≤ I Q1: B˘ • B ≤ I Q2: A˘ • B = 1Essentially these axioms imply that the universe has a (non-surjective) pairing relation whose projections are A and B. It is a theorem that every... | Relation algebra | 0.821238 |
8,558 | Hence a relation algebra can equally well be defined as an algebraic structure (L, ∧, ∨, −, 0, 1, •, I, ◁ , ▷). The advantage of this signature over the usual one is that a relation algebra can then be defined in full simply as a residuated Boolean algebra for which I ◁ x is an involution, that is, I ◁ (I ◁ x) = x. The... | Relation algebra | 0.821238 |
8,559 | A relation algebra (L, ∧, ∨, −, 0, 1, •, I, ˘) is an algebraic structure equipped with the Boolean operations of conjunction x∧y, disjunction x∨y, and negation x−, the Boolean constants 0 and 1, the relational operations of composition x•y and converse x˘, and the relational constant I, such that these operations and c... | Relation algebra | 0.821238 |
8,560 | The axioms B1-B10 below are adapted from Givant (2006: 283), and were first set out by Tarski in 1948.L is a Boolean algebra under binary disjunction, ∨, and unary complementation ()−: B1: A ∨ B = B ∨ A B2: A ∨ (B ∨ C) = (A ∨ B) ∨ C B3: (A− ∨ B)− ∨ (A− ∨ B−)− = AThis axiomatization of Boolean algebra is due to Huntingt... | Relation algebra | 0.821238 |
8,561 | RelMICS / Relational Methods in Computer Science maintained by Wolfram Kahl Carsten Sinz: ARA / An Automatic Theorem Prover for Relation Algebras Stef Joosten, Relation Algebra as programming language using the Ampersand compiler, Journal of Logical and Algebraic Methods in Programming, Volume 100, April 2018, Pages 11... | Relation algebra | 0.821238 |
8,562 | In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X2, with R•S interpreted ... | Relation algebra | 0.821238 |
8,563 | Indeed, a greedy algorithm finds the k-combination corresponding to N: take ck maximal with ( c k k ) ≤ N {\displaystyle {\tbinom {c_{k}}{k}}\leq N} , then take ck−1 maximal with ( c k − 1 k − 1 ) ≤ N − ( c k k ) {\displaystyle {\tbinom {c_{k-1}}{k-1}}\leq N-{\tbinom {c_{k}}{k}}} , and so forth. Finding the number N, u... | Combinatorial number system | 0.821237 |
8,564 | For systems that obey the generalized mass action law the semi-detailed balance condition is sufficient for the dissipation inequality d F / d t ≥ 0 {\displaystyle dF/dt\geq 0} (for the Helmholtz free energy under isothermal isochoric conditions and for the dissipation inequalities under other classical conditions for ... | Detailed balance equations | 0.821235 |
8,565 | For any reaction mechanism and a given positive equilibrium a cone of possible velocities for the systems with detailed balance is defined for any non-equilibrium state N Q D B ( N ) = c o n e { γ r s g n ( w r + ( N ) − w r − ( N ) ) | r = 1 , … , m } , {\displaystyle \mathbf {Q} _{\rm {DB}}(N)={\rm {cone}}\{\gamma _{... | Detailed balance equations | 0.821235 |
8,566 | For a Markov transition matrix and a stationary distribution, the detailed balance equations may not be valid. However, it can be shown that a unique Markov transition matrix exists which is closest according to the stationary distribution and a given norm. The closest Matrix can be computed by solving a quadratic-conv... | Detailed balance equations | 0.821235 |
8,567 | In statistics, per-comparison error rate (PCER) is the probability of a Type I error in the absence of any multiple hypothesis testing correction. This is a liberal error rate relative to the false discovery rate and family-wise error rate, in that it is always less than or equal to those rates. == References == | Per-comparison error rate | 0.821234 |
8,568 | To directly impact existing capacity to develop public health interventions in endemic Africa countries by driving collaboration and networks development and training. To expose and educate young and established scientists to the latest bioinformatics tools and techniques used in researching treatments and cures for Af... | ISCB Africa ASBCB Conference on Bioinformatics | 0.821229 |
8,569 | The ISCB Africa ASBCB Conference on Bioinformatics is a biennial academic conference on the subjects of bioinformatics and computational biology, organized by the African Society for Bioinformatics and Computational Biology (ASBCB). The conference was first held in 2007 as the "ASBCB Conference on the Bioinformatics of... | ISCB Africa ASBCB Conference on Bioinformatics | 0.821229 |
8,570 | Machine Learning is a peer-reviewed scientific journal, published since 1986. In 2001, forty editors and members of the editorial board of Machine Learning resigned in order to support the Journal of Machine Learning Research (JMLR), saying that in the era of the internet, it was detrimental for researchers to continue... | Machine Learning (journal) | 0.821229 |
8,571 | "QG/GA: a stochastic search for Progol". Machine Learning. 70 (2–3): 121–133. doi:10.1007/s10994-007-5029-3. == References == | Machine Learning (journal) | 0.821229 |
8,572 | "Inductive Process Modeling". Machine Learning. Stephen Muggleton and Alireza Tamaddoni-Nezhad (2008). | Machine Learning (journal) | 0.821229 |
8,573 | Simon Colton and Stephen Muggleton (2006). "Mathematical Applications of Inductive Logic Programming" (PDF). Machine Learning. | Machine Learning (journal) | 0.821229 |
8,574 | Machine Learning. 46: 225–254. doi:10.1023/A:1012470815092. | Machine Learning (journal) | 0.821229 |
8,575 | "Learning DFA from Simple Examples". Machine Learning. 44 (1/2): 9–35. | Machine Learning (journal) | 0.821229 |
8,576 | P. Rossmanith and T. Zeugmann (2001). "Stochastic Finite Learning of the Pattern Languages". Machine Learning. | Machine Learning (journal) | 0.821229 |
8,577 | Machine Learning. 39 (2/3): 135–168. doi:10.1023/A:1007649029923. | Machine Learning (journal) | 0.821229 |
8,578 | "Improved Boosting Algorithms Using Confidence-rated Predictions". Machine Learning. 37 (3): 297–336. | Machine Learning (journal) | 0.821229 |
8,579 | Machine Learning. 27: 1–14. Robert E. Schapire and Yoram Singer (1999). | Machine Learning (journal) | 0.821229 |
8,580 | "Clausal Discovery". Machine Learning. 26 (2/3): 99–146. | Machine Learning (journal) | 0.821229 |
8,581 | Thomas Dean and Dana Angluin and Kenneth Basye and Sean Engelson and Leslie Kaelbling and Evangelos Kokkevis and Oded Maron (1995). "Inferring Finite Automata with Stochastic Output Functions and an Application to Map Learning". Machine Learning. | Machine Learning (journal) | 0.821229 |
8,582 | Machine Learning. 14 (3): 313–320. doi:10.1007/BF00993981. | Machine Learning (journal) | 0.821229 |
8,583 | "Explorations of an Incremental, Bayesian Algorithm for Categorization". Machine Learning. 9 (4): 275–308. | Machine Learning (journal) | 0.821229 |
8,584 | J. Quinlan (1990). "Learning Logical Descriptions from Relations" (PDF). Machine Learning. | Machine Learning (journal) | 0.821229 |
8,585 | Machine Learning. 5 (2): 197–227. doi:10.1007/BF00116037. | Machine Learning (journal) | 0.821229 |
8,586 | "Learning Quickly When Irrelevant Attributes Abound: A New Linear-threshold Algorithm" (PDF). Machine Learning. 2 (4): 285–318. | Machine Learning (journal) | 0.821229 |
8,587 | J.R. Quinlan (1986). "Induction of Decision Trees". Machine Learning. | Machine Learning (journal) | 0.821229 |
8,588 | This is a consequence of removing the axiom of the collapse of the wave packet. All possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed... | Quantum mechanical properties | 0.821225 |
8,589 | In 1935, Einstein and his collaborators Boris Podolsky and Nathan Rosen published an argument that the principle of locality implies the incompleteness of quantum mechanics, a thought experiment later termed the Einstein–Podolsky–Rosen paradox. In 1964, John Bell showed that EPR's principle of locality, together with d... | Quantum mechanical properties | 0.821225 |
8,590 | Einstein's long-running exchanges with Bohr about the meaning and status of quantum mechanics are now known as the Bohr–Einstein debates. Einstein believed that underlying quantum mechanics must be a theory that explicitly forbids action at a distance. He argued that quantum mechanics was incomplete, a theory that was ... | Quantum mechanical properties | 0.821225 |
8,591 | According to these views, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but is instead a final renunciation of the classical idea of "causality". Bohr in particular emphasized that any well-defined application of the quantum mechani... | Quantum mechanical properties | 0.821225 |
8,592 | Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics." According to Steven Weinberg, "There is now in my opinion no entirely satisfactory interpretation of quantum mechanics. "The views of Niels Bohr, Werner Heisenberg and other physicists are often grouped together as the "Cop... | Quantum mechanical properties | 0.821225 |
8,593 | Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. The arguments centre on the probabilistic nature of quantum mechanics, the difficulties with wavefunction collapse and the related measurement problem, and quantu... | Quantum mechanical properties | 0.821225 |
8,594 | In mathematics, the Zassenhaus algorithm is a method to calculate a basis for the intersection and sum of two subspaces of a vector space. It is named after Hans Zassenhaus, but no publication of this algorithm by him is known. It is used in computer algebra systems. | Zassenhaus algorithm | 0.821217 |
8,595 | For a cyclic group of order n, composition series correspond to ordered prime factorizations of n, and in fact yields a proof of the fundamental theorem of arithmetic. For example, the cyclic group C 12 {\displaystyle C_{12}} has C 1 ◃ C 2 ◃ C 6 ◃ C 12 , C 1 ◃ C 2 ◃ C 4 ◃ C 12 , {\displaystyle C_{1}\triangleleft C_{2}\... | Composition series (group theory) | 0.821217 |
8,596 | A group may have more than one composition series. However, the Jordan–Hölder theorem (named after Camille Jordan and Otto Hölder) states that any two composition series of a given group are equivalent. That is, they have the same composition length and the same composition factors, up to permutation and isomorphism. T... | Composition series (group theory) | 0.821217 |
8,597 | Language engineering involves the creation of natural language processing systems, whose cost and outputs are measurable and predictable. It is a distinct field contrasted to natural language processing and computational linguistics. A recent trend of language engineering is the use of Semantic Web technologies for the... | Language engineering | 0.821217 |
8,598 | As with P, by a slight abuse of language, one might classify function problems and search problems as being in NC. NC is known to include many problems, including Integer addition, multiplication and division; Matrix multiplication, determinant, inverse, rank; Polynomial GCD, by a reduction to linear algebra using Sylv... | NC = P problem | 0.821212 |
8,599 | Every regular language on {0,1} can be recognized by a family of branching programs of constant width and linear number of instructions (since a DFA can be converted to a branching program). BWBP denotes the class of languages recognizable by a family of branching programs of bounded width and polynomial length.Barring... | NC = P problem | 0.821212 |
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