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2,500 | Also, as scientists understand more about the role of this noncoding DNA (often referred to as junk DNA), it will become more important to have a complete genome sequence as a background to understanding the genetics and biology of any given organism. In many ways genome projects do not confine themselves to only deter... | Genome project | 0.834096 |
2,501 | Since the 1980s, molecular biology and bioinformatics have created the need for DNA annotation. DNA annotation or genome annotation is the process of identifying attaching biological information to sequences , and particularly in identifying the locations of genes and determining what those genes do. | Genome project | 0.834096 |
2,502 | In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and polypropylene. The catalyst was one of the first major departures from metallocene-based catalysts and ushered in much innovation in the development of new plastics. | Constrained geometry complex | 0.834093 |
2,503 | In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. We use these notations for the ... | Parallelogram equality | 0.834067 |
2,504 | Measurements are often expressed as a size relative to a theoretically perfect part that has its geometry defined in a print or computer model. A print is a blueprint illustrating the defined geometry of a part and its features. Each feature can have a size, a distance from other features, and an allowed tolerance set ... | Dimensional metrology | 0.834053 |
2,505 | The Coulomb failure criterion requires that the Coulomb stress exceeds a value σf defined by the shear stress τB, normal stress σB, pore pressure p, and coefficient of friction μ of a failure plane, such that It is also often assumed that changes in pore fluid pressure induced by changes in stress are proportional to t... | Coulomb stress transfer | 0.834026 |
2,506 | Vaxign, an even more comprehensive program, was created in 2008. Vaxign is web-based and completely public-access.Though Vaxign has been found to be extremely accurate and efficient, some scientists still utilize the online software RANKPEP for the peptide bonding predictions. Both Vaxign and RANKPEP employ PSSMs (Posi... | Reverse vaccinology | 0.834012 |
2,507 | Attempts at reverse vaccinology first began with Meningococcus B (MenB). Meningococcus B caused over 50% of meningococcal meningitis, and scientists had been unable to create a successful vaccine for the pathogen because of the bacterium's unique structure. This bacterium's polysaccharide shell is identical to that of ... | Reverse vaccinology | 0.834012 |
2,508 | Reverse vaccinology is an improvement of vaccinology that employs bioinformatics and reverse pharmacology practices, pioneered by Rino Rappuoli and first used against Serogroup B meningococcus. Since then, it has been used on several other bacterial vaccines. | Reverse vaccinology | 0.834012 |
2,509 | Reverse vaccinology has caused an increased focus on pathogenic biology. Reverse vaccinology led to the discovery of pili in gram-positive pathogens such as A streptococcus, B streptococcus, and pneumococcus. Previously, all gram-positive bacteria were thought to not have any pili. Reverse vaccinology also led to the d... | Reverse vaccinology | 0.834012 |
2,510 | The basic idea behind reverse vaccinology is that an entire pathogenic genome can be screened using bioinformatics approaches to find genes. Some traits that the genes are monitored for, may indicate antigenicity and include genes that code for proteins with extracellular localization, signal peptides & B cell epitopes... | Reverse vaccinology | 0.834012 |
2,511 | Atomic unit systems are based (in part) on the Planck constant. The physical meaning of the Planck constant could suggest some basic features of our physical world. The Planck constant is one of the smallest constants used in physics. | Planck's constant | 0.834002 |
2,512 | Thus there is no value of the action as classically defined. Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics. Classical physics cannot explain either quantization of energy or the lack of classical particle motion. In ma... | Planck's constant | 0.834002 |
2,513 | Classification, including pattern and sequence recognition, novelty detection and sequential decision making. Data processing, including filtering, clustering, blind source separation and compression. Robotics, including directing manipulators and prostheses. | Neural net | 0.833991 |
2,514 | Using artificial neural networks requires an understanding of their characteristics. Choice of model: This depends on the data representation and the application. Overly complex models are slow learning. Learning algorithm: Numerous trade-offs exist between learning algorithms. | Neural net | 0.833991 |
2,515 | Successive adjustments will cause the neural network to produce output that is increasingly similar to the target output. After a sufficient number of these adjustments, the training can be terminated based on certain criteria. | Neural net | 0.833991 |
2,516 | Neural networks learn (or are trained) by processing examples, each of which contains a known "input" and "result", forming probability-weighted associations between the two, which are stored within the data structure of the net itself. The training of a neural network from a given example is usually conducted by deter... | Neural net | 0.833991 |
2,517 | Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset, and use the results as feedback to teach the NAS networ... | Neural net | 0.833991 |
2,518 | The solution to a linear Volterra integral equation of the first kind, given by the equation:can be described by the following uniqueness and existence theorem. Recall that the Volterra integral operator V: C ( I ) → C ( I ) {\displaystyle {\mathcal {V}}:C(I)\to C(I)} , can be defined as follows:where t ∈ I = {\displa... | Integral equations | 0.833972 |
2,519 | Linear: An integral equation is linear if the unknown function u(x) and its integrals appear linear in the equation. Hence, an example of a linear equation would be:As a note on naming convention: i) u(x) is called the unknown function, ii) f(x) is called a known function, iii) K(x,t) is a function of two variables and... | Integral equations | 0.833972 |
2,520 | In the following section, we give an example of how to convert an initial value problem (IVP) into an integral equation. There are multiple motivations for doing so, among them being that integral equations can often be more readily solvable and are more suitable for proving existence and uniqueness theorems.The follow... | Integral equations | 0.833972 |
2,521 | Space charges can also occur within solid or liquid dielectrics that are stressed by high electric fields. Trapped space charges within solid dielectrics are often a contributing factor leading to dielectric failure within high voltage power cables and capacitors. In semiconductor physics, space charge layers that are ... | Space charge | 0.833969 |
2,522 | In chemistry, specific rotation () is a property of a chiral chemical compound. : 244 It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution. : 2–65 Compounds which rotate the plane of pol... | Specific rotation | 0.833953 |
2,523 | The CRC Handbook of Chemistry and Physics defines specific rotation as: For an optically active substance, defined by θλ = α/γl, where α is the angle through which plane polarized light is rotated by a solution of mass concentration γ and path length l. Here θ is the Celsius temperature and λ the wavelength of the ligh... | Specific rotation | 0.833953 |
2,524 | With increasing levels of variable renewable energy (wind and solar energy) in the grid, it has become more challenging to match supply and demand. Storage plays an increasing role in bridging that gap. There are four types of energy storage technologies, each in varying states of technology readiness: batteries (elect... | Electricity | 0.833949 |
2,525 | These charges and holes are understood in terms of quantum physics. The building material is most often a crystalline semiconductor.Solid-state electronics came into its own with the emergence of transistor technology. The first working transistor, a germanium-based point-contact transistor, was invented by John Bardee... | Electricity | 0.833949 |
2,526 | Einstein was awarded the Nobel Prize in Physics in 1921 for "his discovery of the law of the photoelectric effect". The photoelectric effect is also employed in photocells such as can be found in solar panels. The first solid-state device was the "cat's-whisker detector" first used in the 1900s in radio receivers. | Electricity | 0.833949 |
2,527 | Michael Faraday invented the electric motor in 1821, and Georg Ohm mathematically analysed the electrical circuit in 1827. Electricity and magnetism (and light) were definitively linked by James Clerk Maxwell, in particular in his "On Physical Lines of Force" in 1861 and 1862.: 148 While the early 19th century had seen... | Electricity | 0.833949 |
2,528 | Electromagnetic waves were analysed theoretically by James Clerk Maxwell in 1864. Maxwell developed a set of equations that could unambiguously describe the interrelationship between electric field, magnetic field, electric charge, and electric current. He could moreover prove that in a vacuum such a wave would travel ... | Electricity | 0.833949 |
2,529 | The problem of determining whether a formula in propositional logic is satisfiable is decidable, and is known as the Boolean satisfiability problem, or SAT. In general, the problem of determining whether a sentence of first-order logic is satisfiable is not decidable. In universal algebra, equational theory, and automa... | Satisfiability problem | 0.833915 |
2,530 | This concept is closely related to the consistency of a theory, and in fact is equivalent to consistency for first-order logic, a result known as Gödel's completeness theorem. The negation of satisfiability is unsatisfiability, and the negation of validity is invalidity. These four concepts are related to each other in... | Satisfiability problem | 0.833915 |
2,531 | The Clausius theorem (1854) states that in a cyclic process ∮ δ Q T surr ≤ 0. {\displaystyle \oint {\frac {\delta Q}{T_{\text{surr}}}}\leq 0.} The equality holds in the reversible case and the strict inequality holds in the irreversible case, with Tsurr as the temperature of the heat bath (surroundings) here. The rever... | Kelvin–Planck statement | 0.833905 |
2,532 | For non-equilibrium situations in general, it may be useful to consider statistical mechanical definitions of other quantities that may be conveniently called 'entropy', but they should not be confused or conflated with thermodynamic entropy properly defined for the second law. These other quantities indeed belong to s... | Kelvin–Planck statement | 0.833905 |
2,533 | The second law of thermodynamics is a physical law that is not symmetric to reversal of the time direction. This does not conflict with symmetries observed in the fundamental laws of physics (particularly CPT symmetry) since the second law applies statistically on time-asymmetric boundary conditions. The second law has... | Kelvin–Planck statement | 0.833905 |
2,534 | Its first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that the efficiency of conversion of heat to work in a heat engine has an upper limit. The first rigorous definition of the seco... | Kelvin–Planck statement | 0.833905 |
2,535 | For open systems (also allowing exchange of matter): d S d t = Q ˙ T + S ˙ + S ˙ i {\displaystyle {\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}+{\dot {S}}_{i}} with S ˙ i ≥ 0 {\displaystyle {\dot {S}}_{i}\geq 0} Here S ˙ {\displaystyle {\dot {S}}} is the flow of entropy into the system associated with the flow of m... | Kelvin–Planck statement | 0.833905 |
2,536 | The expression of the second law for closed systems (so, allowing heat exchange and moving boundaries, but not exchange of matter) is: d S d t = Q ˙ T + S ˙ i {\displaystyle {\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}_{i}} with S ˙ i ≥ 0 {\displaystyle {\dot {S}}_{i}\geq 0} Here Q ˙ {\displaystyle {\dot {Q}}} is ... | Kelvin–Planck statement | 0.833905 |
2,537 | In 1865, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form: ∫ δ Q T = − N {\displaystyle \int {\frac {\delta Q}{T}}=-N} where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations... | Kelvin–Planck statement | 0.833905 |
2,538 | For an arbitrary heat engine, the efficiency is: where Wn is the net work done by the engine per cycle, qH > 0 is the heat added to the engine from a hot reservoir, and qC = - |qC| < 0 is waste heat given off to a cold reservoir from the engine. Thus the efficiency depends only on the ratio |qC| / |qH|. Carnot's theore... | Kelvin–Planck statement | 0.833905 |
2,539 | Second law analysis is valuable in scientific and engineering analysis in that it provides a number of benefits over energy analysis alone, including the basis for determining energy quality (exergy content), understanding fundamental physical phenomena, and improving performance evaluation and optimization. As a resul... | Kelvin–Planck statement | 0.833905 |
2,540 | The book's use of cgs units rather than SI units was also mentioned as problematic. The review continues by saying "espite the criticism, this text is very beautifully written and gives a well-structured and clear insight into the topic" and that it has "become some sort of standard" and "can be recommended to any stud... | Electricity and Magnetism (book) | 0.833865 |
2,541 | In a review of Andrew Zangwill's Electrodynamics in Physics Today, Roy Schwitters states that he encourages undergraduates to get the third edition of this book In 2013, in Physics Today, Jermey N. A. Mathews called it one of five books that stood out, remarking that "learly, Purcell's E&M matures slowly. "In 2012, a r... | Electricity and Magnetism (book) | 0.833865 |
2,542 | The reviewer notes that the main problems with the book are the restrictions of the Berkeley Physics Series and the lack of references to wave phenomena. According to the review the issues were fixed in the new edition and the "result is spectacular".In 1999, Norman Foster Ramsey Jr. wrote, in his obituary for Purcell,... | Electricity and Magnetism (book) | 0.833865 |
2,543 | In 1999, it was noted by Norman Foster Ramsey Jr. that the book was widely adopted and has many foreign translations.The 1965 edition, now supposed to be freely available due to a condition of the federal grant, was originally published as a volume of the Berkeley Physics Course. (See below for more on the legal situat... | Electricity and Magnetism (book) | 0.833865 |
2,544 | Copyright © 1963, 1964, 1965 by Education Development Center, Inc. (successor by merger to Education Services Incorporated).... Education Development Center, Inc., Newton, Massachusetts ... The copyright owner will give permission for the use of the original work in the English language after January 1, 1975. For condi... | Electricity and Magnetism (book) | 0.833865 |
2,545 | Because it was funded by the National Science Foundation, the original editions of the Berkeley Physics Series contained notices on their copyright pages stating that the books were to be available royalty-free after five years. The copyright page of the original 1965 edition of Electricity and Magnetism includes a not... | Electricity and Magnetism (book) | 0.833865 |
2,546 | Solutions Manual to Accompany Electricity and Magnetism: Berkeley Physics Course, Volume 2, First Edition. McGraw-Hill. Purcell, Edward M. | Electricity and Magnetism (book) | 0.833865 |
2,547 | Solutions Manual to Accompany Electricity and Magnetism: Berkeley Physics Course, Volume 2, Second Edition. McGraw-Hill. Purcell, Edward M.; Morin, David J. | Electricity and Magnetism (book) | 0.833865 |
2,548 | In physics and engineering, Davenport chained rotations are three chained intrinsic rotations about body-fixed specific axes. Euler rotations and Tait–Bryan rotations are particular cases of the Davenport general rotation decomposition. The angles of rotation are called Davenport angles because the general problem of d... | Euler rotations | 0.833857 |
2,549 | A common optimization is to put the unsorted elements of the buckets back in the original array first, then run insertion sort over the complete array; because insertion sort's runtime is based on how far each element is from its final position, the number of comparisons remains relatively small, and the memory hierarc... | Bucket sorting | 0.833856 |
2,550 | The foundation which the subject is built on is D'Alembert's principle. This principle states that infinitesimal virtual work done by a force across reversible displacements is zero, which is the work done by a force consistent with ideal constraints of the system. The idea of a constraint is useful - since this limits... | Analytical mechanics | 0.833853 |
2,551 | Lagrangian field theoryGeneralized coordinates apply to discrete particles. For N scalar fields φi(r, t) where i = 1, 2, ... N, the Lagrangian density is a function of these fields and their space and time derivatives, and possibly the space and time coordinates themselves: and the Euler–Lagrange equations have an anal... | Analytical mechanics | 0.833853 |
2,552 | In the three-body problem, parameters can also be assigned specific values; however, the solution at these assigned values or a collection of such solutions does not reveal the mathematical structure of the problem. As in many other problems, the mathematical structure can be elucidated only by examining the differenti... | Analytical mechanics | 0.833853 |
2,553 | A problem is regarded as solved when the particles coordinates at time t are expressed as simple functions of t and of parameters defining the initial positions and velocities. However, 'simple function' is not a well-defined concept: nowadays, a function f(t) is not regarded as a formal expression in t (elementary fun... | Analytical mechanics | 0.833853 |
2,554 | Given a fundamental and universal quantity called action, the principle that this action be stationary under small variation of some other mechanical quantity generates the required set of differential equations. The statement of the principle does not require any special coordinate system, and all results are expresse... | Analytical mechanics | 0.833853 |
2,555 | The goal of mechanical theory is to solve mechanical problems, such as arise in physics and engineering. Starting from a physical system—such as a mechanism or a star system—a mathematical model is developed in the form of a differential equation. The model can be solved numerically or analytically to determine the mot... | Analytical mechanics | 0.833853 |
2,556 | "Momentum space" also refers to "k-space"; the set of all wave vectors (given by De Broglie relations) as used in quantum mechanics and theory of waves: this is not referred to in this context. Phase space The set of all positions and momenta form the phase space; P = C × M = { ( q , p ) ∈ R 2 N } , {\displaystyle {\ma... | Analytical mechanics | 0.833853 |
2,557 | The term "path" or "trajectory" refers to the time evolution of the system as a path through configuration space C {\displaystyle {\mathcal {C}}} , in other words q(t) tracing out a path in C {\displaystyle {\mathcal {C}}} . The path for which action is least is the path taken by the system. From this principle, all eq... | Analytical mechanics | 0.833853 |
2,558 | Symmetry transformations in classical space and timeEach transformation can be described by an operator (i.e. function acting on the position r or momentum p variables to change them). The following are the cases when the operator does not change r or p, i.e. symmetries. where R(n̂, θ) is the rotation matrix about an a... | Analytical mechanics | 0.833853 |
2,559 | The Hamiltonian density H {\displaystyle {\mathcal {H}}} is defined by analogy with mechanics: The equations of motion are: where the variational derivative must be used instead of merely partial derivatives. For N fields, these Hamiltonian field equations are a set of 2N first order partial differential equations, whi... | Analytical mechanics | 0.833853 |
2,560 | The student's score was based entirely on his or her performance in answering the multiple-choice questions. The questions covered a broad range of topics in general biology. There were more specific questions related respectively on ecological concepts (such as population studies and general Ecology) on the E test and... | SAT Subject Test in Biology E/M | 0.833816 |
2,561 | The average for Molecular is 630 while Ecological is 591.On January 19 2021, the College Board discontinued all SAT Subject tests, including the SAT Subject Test in Biology E/M. This was effective immediately in the United States, and the tests were to be phased out by the following summer for international students. T... | SAT Subject Test in Biology E/M | 0.833816 |
2,562 | Of all SAT subject tests, the Biology E/M test was the only SAT II that allowed the test taker a choice between the ecological or molecular tests. A set of 60 questions was taken by all test takers for Biology and a choice of 20 questions was allowed between either the E or M tests. This test was graded on a scale betw... | SAT Subject Test in Biology E/M | 0.833816 |
2,563 | The SAT Subject Test in Biology was the name of a one-hour multiple choice test given on biology by the College Board. A student chose whether to take the test depending upon college entrance requirements for the schools in which the student is planning to apply. Until 1994, the SAT Subject Tests were known as Achievem... | SAT Subject Test in Biology E/M | 0.833816 |
2,564 | The College Board suggested a year-long course in biology at the college preparatory level, as well as a one-year course in algebra, and lab experience as preparation for the test. The test required understanding of biological data and concepts, science-related terms, and the ability to effectively synthesize and inter... | SAT Subject Test in Biology E/M | 0.833816 |
2,565 | In more intuitive terms, a member of Ω {\displaystyle \Omega } is a possible outcome, a member of F {\displaystyle {\mathcal {F}}} is a measurable subset of possible outcomes, the function P {\displaystyle P} gives the probability of each such measurable subset, E {\displaystyle E} represents the set of values that the... | Random variables | 0.833811 |
2,566 | The most formal, axiomatic definition of a random variable involves measure theory. Continuous random variables are defined in terms of sets of numbers, along with functions that map such sets to probabilities. Because of various difficulties (e.g. the Banach–Tarski paradox) that arise if such sets are insufficiently c... | Random variables | 0.833811 |
2,567 | {\displaystyle \{\omega :X(\omega )\leq r\}\in {\mathcal {F}}\qquad \forall r\in \mathbb {R} .} This definition is a special case of the above because the set { ( − ∞ , r ]: r ∈ R } {\displaystyle \{(-\infty ,r]:r\in \mathbb {R} \}} generates the Borel σ-algebra on the set of real numbers, and it suffices to check meas... | Random variables | 0.833811 |
2,568 | Applying classical methods of machine learning to the study of quantum systems is the focus of an emergent area of physics research. A basic example of this is quantum state tomography, where a quantum state is learned from measurement. Other examples include learning Hamiltonians, learning quantum phase transitions, a... | Machine learning in physics | 0.83381 |
2,569 | Variational circuits are a family of algorithms which utilize training based on circuit parameters and an objective function. Variational circuits are generally composed of a classical device communicating input parameters (random or pre-trained parameters) into a quantum device, along with a classical Mathematical opt... | Machine learning in physics | 0.83381 |
2,570 | A deep learning system was reported to learn intuitive physics from visual data (of virtual 3D environments) based on an unpublished approach inspired by studies of visual cognition in infants. Other researchers have developed a machine learning algorithm that could discover sets of basic variables of various physical ... | Machine learning in physics | 0.83381 |
2,571 | The ability to experimentally control and prepare increasingly complex quantum systems brings with it a growing need to turn large and noisy data sets into meaningful information. This is a problem that has already been studied extensively in the classical setting, and consequently, many existing machine learning techn... | Machine learning in physics | 0.83381 |
2,572 | Quantum machine learning can also be applied to dramatically accelerate the prediction of quantum properties of molecules and materials. This can be helpful for the computational design of new molecules or materials. Some examples include Interpolating interatomic potentials; Inferring molecular atomization energies th... | Machine learning in physics | 0.83381 |
2,573 | Machine learning techniques can be used to find a better manifold of integration for path integrals in order to avoid the sign problem. | Machine learning in physics | 0.83381 |
2,574 | Physics is an open access online publication containing commentaries on the best of the peer-reviewed research published in the journals of the American Physical Society. The editor-in-chief of Physics is Matteo Rini. It highlights papers in Physical Review Letters and the Physical Review family of journals. The magazi... | APS Physics | 0.833799 |
2,575 | Physics contains three types of commentaries on research papers: journalistic articles ("Focus"), in depth pieces written by active researchers ("Viewpoints"), and short summaries of a research paper ("Synopsis") written by editorial staff. Readers get free access to the underlying research papers on which the commenta... | APS Physics | 0.833799 |
2,576 | The chapters in the book each cover an algorithm. Search engine indexing PageRank Public-key cryptography Forward error correction Pattern recognition Data compression Database Digital signature | 9 Algorithms That Changed the Future | 0.83379 |
2,577 | One reviewer said the book is written in a clear and simple style.A reviewer for New York Journal of Books suggested that this book would be a good complement to an introductory college-level computer science course.Another reviewer called the book "a valuable addition to the popular computing literature". | 9 Algorithms That Changed the Future | 0.83379 |
2,578 | It is also possible that binding site and gate are attached to a single subunit. In order to develop these ideas, double electron-electron resonance (DEER) and rapid fixing techniques can show these mechanistic movements.A 2007 study suggests that because of the various and complex regulatory properties in addition to ... | Cyclic nucleotide-gated ion channel | 0.833787 |
2,579 | In the knapsack problem, we are given n {\displaystyle n} items with weight w i {\displaystyle w_{i}} and value v i {\displaystyle v_{i}} , along with a maximum weight capacity of a knapsack W {\displaystyle W} . The goal is to solve the following optimization problem; informally, what's the best way to fit the items i... | Pseudo-polynomial time | 0.833769 |
2,580 | Variation and Evolution in Plants is a book written by G. Ledyard Stebbins, published in 1950. It is one of the key publications embodying the modern synthesis of evolution and genetics, as the first comprehensive publication to discuss the relationship between genetics and natural selection in plants. The book has bee... | Variation and Evolution in Plants | 0.833763 |
2,581 | The book is based on the Jesup Lectures that Stebbins delivered at Columbia University in October and November 1946 and is a synthesis of his ideas and the then current research on the evolution of seed plants in terms of genetics. | Variation and Evolution in Plants | 0.833763 |
2,582 | The 643-page book cites more than 1,250 references and was the longest of the four books associated with the modern evolutionary synthesis. The other key works of the modern synthesis, whose publication also followed their authors' Jesup lectures, are Theodosius Dobzhansky's Genetics and the Origin of Species, Ernst Ma... | Variation and Evolution in Plants | 0.833763 |
2,583 | In Lie theory and related areas of mathematics, a lattice in a locally compact group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of Rn, this amounts to the usual geometric notion of a lattice as a periodic subset of points, and both the... | Arithmetic lattice | 0.833722 |
2,584 | For nilpotent groups the theory simplifies much from the general case, and stays similar to the case of Abelian groups. All lattices in a nilpotent Lie group are uniform, and if N {\displaystyle N} is a connected simply connected nilpotent Lie group (equivalently it does not contain a nontrivial compact subgroup) then ... | Arithmetic lattice | 0.833722 |
2,585 | The property known as (T) was introduced by Kazhdan to study the algebraic structure lattices in certain Lie groups when the classical, more geometric methods failed or at least were not as efficient. The fundamental result when studying lattices is the following: A lattice in a locally compact group has property (T) i... | Arithmetic lattice | 0.833721 |
2,586 | Let G {\displaystyle G} be a locally compact group and Γ {\displaystyle \Gamma } a discrete subgroup (this means that there exists a neighbourhood U {\displaystyle U} of the identity element e G {\displaystyle e_{G}} of G {\displaystyle G} such that Γ ∩ U = { e G } {\displaystyle \Gamma \cap U=\{e_{G}\}} ). Then Γ {\di... | Arithmetic lattice | 0.833721 |
2,587 | Protein & Cell is a monthly peer-reviewed open access journal covering protein and cell biology. It was established in 2010 and is published by Springer Science+Business Media. The editor-in-chief is Zihe Rao (Nankai University). According to the Journal Citation Reports, the journal has a 2018 impact factor of 7.575. | Protein & Cell | 0.833719 |
2,588 | In this case Bayes' rule isn't able to capture a mere subjective change in the probability of some critical fact. The new evidence may not have been anticipated or even be capable of being articulated after the event. It seems reasonable, as a starting position, to adopt the law of total probability and extend it to up... | Probability kinematics | 0.833717 |
2,589 | In 1961, the International Union of Pure and Applied Chemistry (IUPAC) adopted the isotope carbon-12 as the basis for atomic weights. Identification of carbon in nuclear magnetic resonance (NMR) experiments is done with the isotope 13C. Carbon-14 (14C) is a naturally occurring radioisotope, created in the upper atmosph... | Carbon atom | 0.833709 |
2,590 | Aside from basic ideas of parallel BFS, some optimization strategies can be used to speed up parallel BFS algorithm and improve the efficiency. There are already several optimizations for parallel BFS, such as direction optimization, load balancing mechanism and improved data structure and so on. | Parallel breadth-first search | 0.833705 |
2,591 | The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance, BFS is used by Dinic's algorithm to find maximum flow in a graph. Moreover, BFS is also one of the kernel algorithms... | Parallel breadth-first search | 0.833705 |
2,592 | Although the distance update is still correct with the help of synchronization, the resource is wasted. In fact, to find the vertices for the next frontier, each unvisited vertex only need to check if any its neighbor vertex is in the frontier. This is also the core idea for direction optimization. | Parallel breadth-first search | 0.833705 |
2,593 | Because there is a barrier synchronization after each layer-traversal, every processing entity must wait until the last of them finish its work. Therefore, the parallel entity which has the most neighbors decides the time consumption of this layer. With the optimization of load-balancing, the time of layer-traversal ca... | Parallel breadth-first search | 0.833705 |
2,594 | Secondly, in spite of the speedup of each layer-traversal due to parallel processing, a barrier synchronization is needed after every layer in order to completely discover all neighbor vertices in the frontier. This layer-by-layer synchronization indicates that the steps of needed communication equals the longest dista... | Parallel breadth-first search | 0.833705 |
2,595 | The axiom schemata of replacement and separation each contain infinitely many instances. Montague (1961) included a result first proved in his 1957 Ph.D. thesis: if ZFC is consistent, it is impossible to axiomatize ZFC using only finitely many axioms. On the other hand, von Neumann–Bernays–Gödel set theory (NBG) can be... | ZF set theory | 0.8337 |
2,596 | Structural induction is a proof method that is used in mathematical logic (e.g., in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction over natural numbers and can be further generalized to arbitrary Noetherian induction. Stru... | Induction on the structure | 0.8337 |
2,597 | History of oceanography – history of the branch of Earth science that studies the ocean History of paleoclimatology – history of the study of changes in climate taken on the scale of the entire history of Earth History of paleontology – history of the study of prehistoric life History of petrology – history of the bran... | Physical Sciences | 0.83369 |
2,598 | History of hydrogeology – history of the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust (commonly in aquifers). History of mineralogy – history of the study of chemistry, crystal structure, and physical (including optical) properties of minerals. ... | Physical Sciences | 0.83369 |
2,599 | History of geomorphology – history of the scientific study of landforms and the processes that shape them History of geostatistics – history of the branch of statistics focusing on spatial or spatiotemporal datasets History of geophysics – history of the physics of the Earth and its environment in space; also the study... | Physical Sciences | 0.83369 |
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