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11,700 | The first use of analytic ideas in number theory actually goes back to Euler (1730s), who used formal power series and non-rigorous (or implicit) limiting arguments. The use of complex analysis in number theory comes later: the work of Bernhard Riemann (1859) on the zeta function is the canonical starting point; Jacobi... | Combinatorial number theory | 0.817696 |
11,701 | Starting early in the nineteenth century, the following developments gradually took place: The rise to self-consciousness of number theory (or higher arithmetic) as a field of study. The development of much of modern mathematics necessary for basic modern number theory: complex analysis, group theory, Galois theory—acc... | Combinatorial number theory | 0.817696 |
11,702 | By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating-point arithmetic.) The use of the ter... | Combinatorial number theory | 0.817696 |
11,703 | Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers... | Combinatorial number theory | 0.817696 |
11,704 | Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."... | Combinatorial number theory | 0.817696 |
11,705 | The Korean Biology Olympiad (KBO) is a biology olympiad held by Korean Biology Educational Society. The top four finalists become eligible to join the International Biology Olympiad. | Korean Biology Olympiad | 0.817695 |
11,706 | Many templates and tools for decision capturing exist, both in agile communities (e.g., M. Nygard's architecture decision records) and in software engineering and architecture design methods (e.g., see table layouts suggested by IBM UMF and by Tyree and Akerman from CapitalOne. G. Fairbanks included decision rationale ... | Architectural decision | 0.817695 |
11,707 | In software engineering and software architecture design, architectural decisions are design decisions that address architecturally significant requirements; they are perceived as hard to make and/or costly to change. | Architectural decision | 0.817695 |
11,708 | The Ahlswede–Daykin inequality (Ahlswede & Daykin 1978), also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It is a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the pro... | Four functions inequality | 0.817694 |
11,709 | Computational methods have been developed to predict the immunogenicity of peptides and proteins, which are particularly useful in designing therapeutic antibodies, assessing likely virulence of mutations in viral coat particles, and validation of proposed peptide-based drug treatments. Early techniques relied mainly o... | Immune function | 0.817691 |
11,710 | In robot kinematics, forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters.The kinematics equations of the robot are used in robotics, computer games, and animation. The reverse process, that computes the joi... | Forward kinematics | 0.817687 |
11,711 | The kinematics equations of a serial chain of n links, with joint parameters θi are given by = 0 T n = ∏ i = 1 n i − 1 T i ( θ i ) , {\displaystyle ={}^{0}T_{n}=\prod _{i=1}^{n}{}^{i-1}T_{i}(\theta _{i}),} where i − 1 T i ( θ i ) {\displaystyle {}^{i-1}T_{i}(\theta _{i})} is the transformation matrix from the frame of... | Forward kinematics | 0.817687 |
11,712 | One of the most commonly reported effect size statistics for rANOVA is partial eta-squared (ηp2). It is also common to use the multivariate η2 when the assumption of sphericity has been violated, and the multivariate test statistic is reported. A third effect size statistic that is reported is the generalized η2, which... | Repeated measures design | 0.817681 |
11,713 | In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or ... | Intervening variable | 0.817679 |
11,714 | The bioinorganic chemistry of the alkali metal ions has been extensively reviewed. Solid state crystal structures have been determined for many complexes of alkali metal ions in small peptides, nucleic acid constituents, carbohydrates and ionophore complexes.Lithium naturally only occurs in traces in biological systems... | Group 1 element | 0.817679 |
11,715 | Its biochemistry, the way it is handled by the human body and studies using rats and goats suggest that it is an essential trace element, although the natural biological function of lithium in humans has yet to be identified.Sodium and potassium occur in all known biological systems, generally functioning as electrolyt... | Group 1 element | 0.817679 |
11,716 | A product of countably infinite copies of the discrete space { 0 , 1 } {\displaystyle \{0,1\}} is homeomorphic to the Cantor set; and in fact uniformly homeomorphic to the Cantor set if we use the product uniformity on the product. Such a homeomorphism is given by using ternary notation of numbers. (See Cantor space.) ... | Discrete space | 0.817679 |
11,717 | A discrete structure is often used as the "default structure" on a set that doesn't carry any other natural topology, uniformity, or metric; discrete structures can often be used as "extreme" examples to test particular suppositions. For example, any group can be considered as a topological group by giving it the discr... | Discrete space | 0.817679 |
11,718 | In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open i... | Discrete space | 0.817679 |
11,719 | In some ways, the opposite of the discrete topology is the trivial topology (also called the indiscrete topology), which has the fewest possible open sets (just the empty set and the space itself). Where the discrete topology is initial or free, the indiscrete topology is final or cofree: every function from a topologi... | Discrete space | 0.817679 |
11,720 | Because Presburger arithmetic is decidable, automatic theorem provers for Presburger arithmetic exist. For example, the Coq proof assistant system features the tactic omega for Presburger arithmetic and the Isabelle proof assistant contains a verified quantifier elimination procedure by Nipkow (2010). The double expone... | Presburger arithmetic | 0.817678 |
11,721 | Fischer and Rabin also proved that for any reasonable axiomatization (defined precisely in their paper), there exist theorems of length n which have doubly exponential length proofs. Intuitively, this suggests there are computational limits on what can be proven by computer programs. Fischer and Rabin's work also impli... | Presburger arithmetic | 0.817678 |
11,722 | Presburger-definable relations admit another characterization: by Muchnik's theorem. It is more complicated to state, but led to the proof of the two former characterizations. Before Muchnik's theorem can be stated, some additional definitions must be introduced. Let R ⊆ N d {\displaystyle R\subseteq \mathbb {N} ^{d}} ... | Presburger arithmetic | 0.817678 |
11,723 | Mojżesz Presburger proved Presburger arithmetic to be: consistent: There is no statement in Presburger arithmetic which can be deduced from the axioms such that its negation can also be deduced. complete: For each statement in the language of Presburger arithmetic, either it is possible to deduce it from the axioms or ... | Presburger arithmetic | 0.817678 |
11,724 | By the Cobham–Semenov theorem, a relation is Presburger-definable if and only if it is definable in Büchi arithmetic of base k {\displaystyle k} for all k ≥ 2 {\displaystyle k\geq 2} . A relation definable in Büchi arithmetic of base k {\displaystyle k} and k ′ {\displaystyle k'} for k {\displaystyle k} and k ′ {\displ... | Presburger arithmetic | 0.817678 |
11,725 | The Min-RVLS problem is important in machine learning and linear discriminant analysis. Given a set of positive and negative examples, it is required to minimize the number of features that are required to correctly classify them. The problem is known as the minimum feature set problem. An algorithm that approximates M... | Minimum relevant variables in linear system | 0.817677 |
11,726 | MINimum Relevant Variables in Linear System (Min-RVLS) is a problem in mathematical optimization. Given a linear program, it is required to find a feasible solution in which the number of non-zero variables is as small as possible. The problem is known to be NP-hard and even hard to approximate. | Minimum relevant variables in linear system | 0.817677 |
11,727 | Reflecting the billiard: Consider a square with side lcm ( a , b ) {\displaystyle \operatorname {lcm} (a,b)} . By displaying multiple copies of the original rectangle (with mirror symmetry) we can visualise the arithmetic billiard path as a diagonal of that square. In other words, we can think of reflecting the recta... | Arithmetic billiards | 0.817676 |
11,728 | Importantly, it also has the potential to break down the artificial barriers between medical microbiology and environmental microbiology. It is hoped that the HMP will not only identify new ways to determine health and predisposition to diseases but also define the parameters needed to design, implement and monitor str... | Human Microbiome Project | 0.817675 |
11,729 | Prior to the HMP launch, it was often reported in popular media and scientific literature that there are about 10 times as many microbial cells and 100 times as many microbial genes in the human body as there are human cells; this figure was based on estimates that the human microbiome includes around 100 trillion bact... | Human Microbiome Project | 0.817675 |
11,730 | In indexed (ISAM) files a specified section of each record is defined as a key which can be used to look up specific records. In direct access (BDAM) files, the application program has to specify the relative block number, the relative track and record (TTR) or the actual physical location (MBBCCHHR) in a Direct-access... | Multiprogramming with a Variable number of Tasks | 0.817668 |
11,731 | Relative Record Datasets (RRDS) are a replacement for direct access (BDAM) datasets, allowing applications to access a record by specifying a relative record number. Unlike ESDS and KSDS, RRDS does not support variable-length records.These VSAM formats became the basis of IBM's database management systems, IMS/VS and D... | Multiprogramming with a Variable number of Tasks | 0.817668 |
11,732 | Spherical nucleic acids (SNAs) are nanostructures that consist of a densely packed, highly oriented arrangement of linear nucleic acids in a three-dimensional, spherical geometry. This novel three-dimensional architecture is responsible for many of the SNA's novel chemical, biological, and physical properties that make... | Spherical nucleic acids | 0.817667 |
11,733 | Directional interactions and valency have been used to direct the formation of new lattice symmetries with protein cores that are difficult to access with inorganic particles. DNA origami frameworks borrowed from the structural DNA nanotechnology community have also been applied as cages for inorganic nanoparticle core... | Spherical nucleic acids | 0.817667 |
11,734 | For example, when using atomic or ionic building blocks in the construction of materials, the crystal structure, symmetry, and spacing are fixed by atomic radii and electronegativity. However, in the nanoparticle-based system, crystal structure can be tuned independent of the nanoparticle size and composition by simply... | Spherical nucleic acids | 0.817667 |
11,735 | SNAs have been utilized to develop an entire new field of materials science – one that focuses on using SNAs as synthetically programmable building blocks for the construction of colloidal crystals (Fig. 7). In 2011, a landmark paper was published in Science that defines a set of design rules for making superlattice st... | Spherical nucleic acids | 0.817667 |
11,736 | Another paper has discussed SmartFlare applicability in early equine conceptuses, equine dermal fibroblast cells, and trophoblastic vesicles, finding that SmartFlares may only be applicable for certain uses. Aptamer nanoflares have also been developed to bind to molecular targets other than intracellular mRNA. Aptamers... | Spherical nucleic acids | 0.817667 |
11,737 | Nanosphere was one of the first nanotechnology-based biotechnology firms to go public in late 2007. It burnt through over $412.5 million since inception before being sold for $58M in 2016 to Luminex. The FDA-cleared Verigene system is now sold by Luminex with accompanying FDA-cleared panel assays for bloodstream, respi... | Spherical nucleic acids | 0.817666 |
11,738 | The Physics Instructional Association (PIRA) is an American association of physics education professionals and enthusiasts. Members are physics teachers, physics administrators, physics educational support staff and physics students. Interests cover all aspects of physics education with an emphasis on demonstrations, l... | Physics Instructional Resource Association | 0.817666 |
11,739 | PIRA holds annual meetings during the summer meeting of the American Association of Physics Teachers. It is sponsored by the Apparatus Committee and annually hosts the Lecture Demonstration Workshop. PIRA assists or hosts the Physics Demonstrations Show at each summer meeting when the hosting institution requests. | Physics Instructional Resource Association | 0.817666 |
11,740 | PIRA has continually updated the Demonstration Bibliography since its inception in the 1980s. It is based on a unique numbering system called the Demonstration Classification Scheme (DCS). The scheme originated from the demonstrations catalog used at the University of Minnesota. PIRA has also generated a subset of this... | Physics Instructional Resource Association | 0.817666 |
11,741 | The training is typically completed at a clinical site rather than a college.The core curriculum in medical technology generally comprises 20 credits in clinical chemistry, 20 credits in hematology, and 20 credits in clinical microbiology. During clinical rotations, the student experiences hands-on learning in each dis... | Medical technologist | 0.817664 |
11,742 | In the United States, a medical laboratory scientist (MLS), medical technologist (MT), or a clinical laboratory scientist (CLS) typically earns a bachelor's degree in medical laboratory science, clinical laboratory science, or medical technology. Other routes include attaining a degree in biomedical science or in a lif... | Medical technologist | 0.817664 |
11,743 | A particular application of the ladder operator concept is found in the quantum mechanical treatment of angular momentum. For a general angular momentum vector, J, with components, Jx, Jy and Jz one defines the two ladder operators, J+ and J–, where i is the imaginary unit. The commutation relation between the cartesia... | Raising operator | 0.817662 |
11,744 | P C P ( p o l y , 0 ) {\displaystyle {\mathsf {PCP}}({\mathsf {poly}},0)} , the class of polynomial-time machines with access to polynomially many random bits is co-RP. Arora and Safra's first major result was that PCP(log, log) = NP; put another way, if the verifier in the NP protocol is constrained to choose only O (... | Interactive proof systems | 0.817652 |
11,745 | Not only can interactive proof systems solve problems not believed to be in NP, but under assumptions about the existence of one-way functions, a prover can convince the verifier of the solution without ever giving the verifier information about the solution. This is important when the verifier cannot be trusted with t... | Interactive proof systems | 0.817652 |
11,746 | This restriction means that functions in FP are a module (generated by the built-in functions) over the algebra of functional forms, and are thus algebraically tractable. For instance, the general question of equality of two functions is equivalent to the halting problem, and is undecidable, but equality of two functio... | Function-level programming | 0.817643 |
11,747 | In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming. In his 1977 Turing Award lecture, Backus set forth what he considered to be the need to switch to... | Function-level programming | 0.817643 |
11,748 | The function-level approach offers the possibility of making the set of programs a mathematical space by emphasizing the algebraic properties of the program-forming operations over the space of programs. Another potential advantage of the function-level view is the ability to use only strict functions and thereby have ... | Function-level programming | 0.817643 |
11,749 | In the function-level style of programming, a program is built directly from programs that are given at the outset, by combining them with program-forming operations or functionals. Thus, in contrast with the value-level approach that applies the given programs to values to form a succession of values culminating in th... | Function-level programming | 0.817643 |
11,750 | Before developing his implicit order approach, Bohm had proposed a hidden variable theory of quantum physics (see Bohm interpretation). According to Bohm, a key motivation for doing so had been purely to show the possibility of such theories. On this, Bohm 1980, p. 81 said, "... it should be kept in mind that before th... | Implicate and explicate order | 0.817643 |
11,751 | A key motivation for Bohm in proposing a new notion of order was the well-known incompatibility of quantum theory with relativity theory. Bohm 1980, p. xv summarised the state of affairs he perceived to exist: ...in relativity, movement is continuous, causally determinate and well defined, while in quantum mechanics it... | Implicate and explicate order | 0.817643 |
11,752 | Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different frameworks for understanding the same phenomenon or aspect of reality. In particular, the concepts were developed in order to explain... | Implicate and explicate order | 0.817643 |
11,753 | The word mechatronics was registered as trademark by the company in Japan with the registration number of "46-32714" in 1971. The company later released the right to use the word to the public, and the word began being used globally. Currently the word is translated into many languages and is considered an essential te... | Mechatronics | 0.817641 |
11,754 | Mechatronics engineering also called mechatronics, is an interdisciplinary branch of engineering that focuses on the integration of mechanical, electrical and electronic engineering systems, and also includes a combination of robotics, electronics, computer science, telecommunications, systems, control, and product eng... | Mechatronics | 0.817641 |
11,755 | Mechanical modeling calls for modeling and simulating physical complex phenomena in the scope of a multi-scale and multi-physical approach. This implies to implement and to manage modeling and optimization methods and tools, which are integrated in a systemic approach. The specialty is aimed for students in mechanics w... | Mechatronics | 0.817641 |
11,756 | Mechanical engineering is an important part of mechatronics engineering. It includes the study of mechanical nature of how an object works. Mechanical elements refer to mechanical structure, mechanism, thermo-fluid, and hydraulic aspects of a mechatronics system. The study of thermodynamics, dynamics, fluid mechanics, ... | Mechatronics | 0.817641 |
11,757 | Automation and programmed logical controls Power and driving electronics Modern and digital control systems Robotics systems Mechatronics systems Automated control Computer applications for mechatronics Calculus Electrical circuits Systems Dynamics Dynamics and vibrations Artificial Intelligence Engineering Mathematics... | Mechatronics | 0.817641 |
11,758 | In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors (PE), the square difference between the fitted values implied by the predictive function g ^ {\displa... | Prediction error | 0.817639 |
11,759 | Momentum of each particle has stabilized and is again a good quantum number a long time after the collision. Theorem: A necessary and sufficient condition for the q j {\displaystyle q_{j}} to be good is that O {\displaystyle O} commutes with the Hamiltonian H {\displaystyle H} . A proof of this theorem is given below. ... | Good quantum number | 0.817633 |
11,760 | In quantum mechanics, given a particular Hamiltonian H {\displaystyle H} and an operator O {\displaystyle O} with corresponding eigenvalues and eigenvectors given by O | q j ⟩ = q j | q j ⟩ {\displaystyle O|q_{j}\rangle =q_{j}|q_{j}\rangle } , the q j {\displaystyle q_{j}} are said to be good quantum numbers if every e... | Good quantum number | 0.817633 |
11,761 | And then, if any number of subsequent measurements of A {\displaystyle A} are made, they are bound to yield the same result. In this case, a (weaker) statement of conservation holds: Using the Ehrenfest Theorem, = 0 {\textstyle =0} doesn't explicitly depend on time: d d t ⟨ A ⟩ = ⟨ ∂ A ∂ t ⟩ + 1 i ℏ ⟨ ⟩ = 0 {\display... | Good quantum number | 0.817633 |
11,762 | Now, if the system is in one of the common eigenstates of the operator A {\displaystyle A} (and H {\displaystyle H} too), then the system remains in this eigenstate as time progresses. Any measurement of the quantity A {\displaystyle A} will give us the eigenvalue (or the good quantum number) associated with the eigens... | Good quantum number | 0.817633 |
11,763 | The Ehrenfest Theorem gives the rate of change of the expectation value of operators. It reads as follows: d d t ⟨ A ( t ) ⟩ = ⟨ ∂ A ( t ) ∂ t ⟩ + 1 i ℏ ⟨ ⟩ {\displaystyle {\frac {d}{dt}}\langle A(t)\rangle =\left\langle {\frac {\partial A(t)}{\partial t}}\right\rangle +{\frac {1}{i\hbar }}\langle \rangle } Commonly o... | Good quantum number | 0.817633 |
11,764 | In non-relativistic treatment, l {\displaystyle l} and s {\displaystyle s} are good quantum numbers but in relativistic quantum mechanics they are no longer good quantum numbers as L {\displaystyle L} and S {\displaystyle S} do not commute with H {\displaystyle H} (in Dirac theory). J = L + S {\displaystyle J=L+S} is a... | Good quantum number | 0.817633 |
11,765 | In classical mechanics, the total time derivative of a physical quantity A {\displaystyle A} is given as: d A d t = ∂ A ∂ t + { A , H } {\displaystyle {\frac {dA}{dt}}={\frac {\partial A}{\partial t}}+\{A,H\}} where the curly braces refer to Poisson bracket of A {\displaystyle A} and H {\displaystyle H} . This bears a ... | Good quantum number | 0.817633 |
11,766 | In particle physics, secondary emission is a phenomenon where primary incident particles of sufficient energy, when hitting a surface or passing through some material, induce the emission of secondary particles. The term often refers to the emission of electrons when charged particles like electrons or ions in a vacuum... | Secondary electron emission | 0.81763 |
11,767 | This is a list of algebraic number theory topics. | List of algebraic number theory topics | 0.817624 |
11,768 | These topics are basic to the field, either as prototypical examples, or as basic objects of study. Algebraic number field Gaussian integer, Gaussian rational Quadratic field Cyclotomic field Cubic field Biquadratic field Quadratic reciprocity Ideal class group Dirichlet's unit theorem Discriminant of an algebraic numb... | List of algebraic number theory topics | 0.817624 |
11,769 | Fermat's Last Theorem Class number problem for imaginary quadratic fields Stark–Heegner theorem Heegner number Langlands program | List of algebraic number theory topics | 0.817624 |
11,770 | Different ideal Dedekind domain Splitting of prime ideals in Galois extensions Decomposition group Inertia group Frobenius automorphism Chebotarev's density theorem Totally real field Local field p-adic number p-adic analysis Adele ring Idele group Idele class group Adelic algebraic group Global field Hasse principle H... | List of algebraic number theory topics | 0.817624 |
11,771 | Class field theory Abelian extension Kronecker–Weber theorem Hilbert class field Takagi existence theorem Hasse norm theorem Artin reciprocity Local class field theory | List of algebraic number theory topics | 0.817624 |
11,772 | Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg formula Hasse–Weil zeta function | List of algebraic number theory topics | 0.817624 |
11,773 | Iwasawa theory Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem Euler system p-adic L-function | List of algebraic number theory topics | 0.817624 |
11,774 | Hence, dead-end elimination is a mirror image of dynamic programming, in which "good" combinations are identified and explored further. Although the method itself is general, it has been developed and applied mainly to the problems of predicting and designing the structures of proteins. It closely related to the notion... | Dead-end elimination | 0.817624 |
11,775 | The above two criteria are normally applied iteratively until convergence, defined as the point at which no more rotamers or pairs can be eliminated. Since this is normally a reduction in the sample space by many orders of magnitude, simple enumeration will suffice to determine the minimum within this pared-down set. G... | Dead-end elimination | 0.817624 |
11,776 | More powerful and more general criteria have been introduced that improve both the efficiency and the eliminating power of the method for both prediction and design applications. One example is a refinement of the singles elimination criterion known as the Goldstein criterion, which arises from fairly straightforward a... | Dead-end elimination | 0.817624 |
11,777 | In organometallic chemistry, a coordinatively unsaturated complex has fewer than 18 valence electrons and thus is susceptible to oxidative addition or coordination of an additional ligand. Unsaturation is characteristic of many catalysts. The opposite of coordinatively unsaturated is coordinatively saturated. Complexes... | Coordinatively saturated | 0.817619 |
11,778 | Reduced phase space quantization constraints are solved first then quantized. This approach was considered for some time to be impossible as it seems to require first finding the general solution to Einstein's equations. However, with use of ideas involved in Dittrich's approximation scheme (built on ideas of Rovelli) ... | Problem of time | 0.817595 |
11,779 | This new interpretation solves the problems of the use of environmental decoherence as a solution to the problem of measurement in quantum mechanics by invoking fundamental limitations, due to the quantum mechanical nature of clocks, in the process of measurement in quantum mechanics. These limitations are very natural... | Problem of time | 0.817595 |
11,780 | The way out is addressed in a way similar to the Page–Wooters approach. The idea is to pick one of the physical variables to be a clock and asks relational questions. These ideas, where the clock is also quantum mechanical, have actually led to a new interpretation of quantum mechanics — the Montevideo interpretation o... | Problem of time | 0.817595 |
11,781 | Motivated by the Immirzi ambiguity in loop quantum gravity and the near conformal invariance of the standard model of elementary particles, Charles Wang and co-workers have argued that the problem of time may be related to an underlying scale invariance of gravity-matter systems. Scale invariance has also been proposed... | Problem of time | 0.817595 |
11,782 | In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative. This problem raises the question of what time... | Problem of time | 0.817595 |
11,783 | Though classically spacetime appears to be an absolute background, general relativity reveals that spacetime is actually dynamical; gravity is a manifestation of spacetime geometry. Matter reacts with spacetime: Spacetime tells matter how to move; matter tells spacetime how to curve. Also, spacetime can interact with i... | Problem of time | 0.817595 |
11,784 | In fact, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements. Special rel... | Problem of time | 0.817595 |
11,785 | In classical mechanics, a special status is assigned to time in the sense that it is treated as a classical background parameter, external to the system itself. This special role is seen in the standard formulation of quantum mechanics. It is regarded as part of a priori given classical background with a well defined v... | Problem of time | 0.817595 |
11,786 | In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying o... | Darwinian algorithm | 0.817592 |
11,787 | It relies on a certain theorem valid for all regions of acceptability and all Gaussian distributions. The efficiency of NA relies on information theory and a certain theorem of efficiency. Its efficiency is defined as information divided by the work needed to get the information. | Darwinian algorithm | 0.817592 |
11,788 | Bacteriologic algorithms (BA) inspired by evolutionary ecology and, more particularly, bacteriologic adaptation. Evolutionary ecology is the study of living organisms in the context of their environment, with the aim of discovering how they adapt. Its basic concept is that in a heterogeneous environment, there is not o... | Darwinian algorithm | 0.817592 |
11,789 | Parallel implementations of genetic algorithms come in two flavors. Coarse-grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine-grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring ... | Darwinian algorithm | 0.817592 |
11,790 | Genetic algorithms in particular became popular through the work of John Holland in the early 1970s, and particularly his book Adaptation in Natural and Artificial Systems (1975). His work originated with studies of cellular automata, conducted by Holland and his students at the University of Michigan. Holland introduc... | Darwinian algorithm | 0.817592 |
11,791 | Many early papers are reprinted by Fogel (1998).Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game, artificial evolution only became a widely recognized optimization method as a result of the work of Ingo Rechenberg and Hans-Paul Schwefel in the 1960s and earl... | Darwinian algorithm | 0.817592 |
11,792 | From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970) and Crosby (1973). Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition, Hans-Joachim Bremerm... | Darwinian algorithm | 0.817592 |
11,793 | In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes. In 1989, Axcelis, Inc. released Evolver, the world's first commercial GA product for desktop computers. The New York Times technology writer John Markoff wrote ab... | Darwinian algorithm | 0.817592 |
11,794 | The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point. Lagrange solved this ... | Euler–Lagrange equation | 0.817592 |
11,795 | Named after René Descartes (1596–1650), French philosopher, mathematician, and scientist, whose formulation of analytic geometry gave rise to the concept of Cartesian product, which was later generalized to the notion of categorical product. | Cartesian closed | 0.817591 |
11,796 | In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or power flow of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2); kg/s3 in base SI units. It is named after its discoverer ... | Pointing vector | 0.81759 |
11,797 | Ideally, the prediction must also distinguish the hypothesis from likely alternatives; if two hypotheses make the same prediction, observing the prediction to be correct is not evidence for either one over the other. (These statements about the relative strength of evidence can be mathematically derived using Bayes' Th... | Scientific research | 0.817588 |
11,798 | Scientific methodology often directs that hypotheses be tested in controlled conditions wherever possible. This is frequently possible in certain areas, such as in the biological sciences, and more difficult in other areas, such as in astronomy. The practice of experimental control and reproducibility can have the effe... | Scientific research | 0.817588 |
11,799 | Nanothermometry is a branch of physics and engineering exploring the use of non-invasive precise thermometers working at the nanoscale. These devices have high spatial resolution (below one micrometer), where conventional methods are ineffective. | Nanothermometry | 0.817582 |
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