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79,000 | The convolution theorem states that F { f ∗ g } = F { f } ⋅ F { g } {\displaystyle {\mathcal {F}}\{f*g\}={\mathcal {F}}\{f\}\cdot {\mathcal {F}}\{g\}} where F { f } {\displaystyle {\mathcal {F}}\{f\}} denotes the Fourier transform of f {\displaystyle f} . | Convolution kernel | 0.785549 |
79,001 | The convolution defines a product on the linear space of integrable functions. This product satisfies the following algebraic properties, which formally mean that the space of integrable functions with the product given by convolution is a commutative associative algebra without identity (Strichartz 1994, §3.3). Other ... | Convolution kernel | 0.785549 |
79,002 | In Smoothed-particle hydrodynamics, simulations of fluid dynamics are calculated using particles, each with surrounding kernels. For any given particle i {\displaystyle i} , some physical quantity A i {\displaystyle A_{i}} is calculated as a convolution of A j {\displaystyle A_{j}} with a weighting function, where j {\... | Convolution kernel | 0.785549 |
79,003 | In structural reliability, the reliability index can be defined based on the convolution theorem. The definition of reliability index for limit state functions with nonnormal distributions can be established corresponding to the joint distribution function. In fact, the joint distribution function can be obtained using... | Convolution kernel | 0.785549 |
79,004 | In probability theory, the probability distribution of the sum of two independent random variables is the convolution of their individual distributions. In kernel density estimation, a distribution is estimated from sample points by convolution with a kernel, such as an isotropic Gaussian. In radiotherapy treatment pla... | Convolution kernel | 0.785549 |
79,005 | The impulse response function provides that factor as a function of the elapsed time since each input value occurred. In physics, wherever there is a linear system with a "superposition principle", a convolution operation makes an appearance. For instance, in spectroscopy line broadening due to the Doppler effect on it... | Convolution kernel | 0.785549 |
79,006 | The convolution of two signals is the filtering of one through the other. In electrical engineering, the convolution of one function (the input signal) with a second function (the impulse response) gives the output of a linear time-invariant system (LTI). At any given moment, the output is an accumulated effect of all ... | Convolution kernel | 0.785549 |
79,007 | In digital data processing In analytical chemistry, Savitzky–Golay smoothing filters are used for the analysis of spectroscopic data. They can improve signal-to-noise ratio with minimal distortion of the spectra In statistics, a weighted moving average is a convolution. In acoustics, reverberation is the convolution of... | Convolution kernel | 0.785549 |
79,008 | Convolution and related operations are found in many applications in science, engineering and mathematics. Convolutional neural networks apply multiple cascaded convolution kernels with applications in machine vision and artificial intelligence. Though these are actually cross-correlations rather than convolutions in m... | Convolution kernel | 0.785549 |
79,009 | One of the first technical records concerning carbon nanofibers is probably a patent dated 1889 on synthesis of filamentous carbon by Hughes and Chambers. They utilized a methane/hydrogen gaseous mixture and grew carbon filaments through gas pyrolysis and subsequent carbon deposition and filament growth. The true appre... | Carbon nanofibers | 0.785548 |
79,010 | Cells that are impaled by nanostructures can express the delivered gene(s). For electrode materials Oil spill remediation Oil spill remediation: The process for the manufacture of a carbon-carbon-composite material comprises the steps of treating a carbonaceous carrier material with a metal-containing catalyst material... | Carbon nanofibers | 0.785548 |
79,011 | Composite materials Scanning probe microscopy tips Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans the specimen. Carrier material for various catalysts in petrochemistry In vertically-aligned arrays, a platform for gene delivery. (See Impalefecti... | Carbon nanofibers | 0.785548 |
79,012 | Reporter genes can also be expressed by induction during growth. In these cases, trans-acting elements, such as transcription factors are used to express the reporter gene.Reporter gene assay have been increasingly used in high throughput screening (HTS) to identify small molecule inhibitors and activators of protein t... | Reporter gene | 0.785547 |
79,013 | In molecular biology, a reporter gene (often simply reporter) is a gene that researchers attach to a regulatory sequence of another gene of interest in bacteria, cell culture, animals or plants. Such genes are called reporters because the characteristics they confer on organisms expressing them are easily identified an... | Reporter gene | 0.785547 |
79,014 | The Warburg–Christian method is an ultraviolet spectroscopic protein and nucleic acid assay method based on the absorbance of UV light at 260 nm and 280 nm wavelengths. Proteins generally absorb light at 280 nanometers due to the presence of tryptophan and tyrosine. Nucleic acids absorb more at 260 nm, primarily due to... | Warburg–Christian method | 0.785547 |
79,015 | In computer science, a canonical LR parser or LR(1) parser is an LR(k) parser for k=1, i.e. with a single lookahead terminal. The special attribute of this parser is that any LR(k) grammar with k>1 can be transformed into an LR(1) grammar. However, back-substitutions are required to reduce k and as back-substitutions i... | Canonical LR parser | 0.785545 |
79,016 | That makes simple rules such as X → yrequiring a great many artificial rules that essentially enumerate the combinations of all the possible states and lookahead terminals that can follow. A similar problem appears for implementing non-lookahead rules such as A1 → A Bwhere all the possible lookaheads must be enumerated... | Canonical LR parser | 0.785545 |
79,017 | The lexicographic order on the image of this map induces a group order on Z n . {\displaystyle \mathbb {Z} ^{n}.} Robbiano's theorem is that every group order may be obtained in this way. More precisely, given a group order on Z n , {\displaystyle \mathbb {Z} ^{n},} there exist an integer s ≤ n {\displaystyle s\leq n} ... | Colexicographic order | 0.785543 |
79,018 | In hydrology the distribution of long duration river discharge or rainfall, e.g. monthly and yearly totals, is often thought to be practically normal according to the central limit theorem. The blue picture, made with CumFreq, illustrates an example of fitting the normal distribution to ranked October rainfalls showing... | Normally distributed | 0.785542 |
79,019 | I can only recognize the occurrence of the normal curve – the Laplacian curve of errors – as a very abnormal phenomenon. It is roughly approximated to in certain distributions; for this reason, and on account for its beautiful simplicity, we may, perhaps, use it as a first approximation, particularly in theoretical inv... | Normally distributed | 0.785542 |
79,020 | Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observation... | Normally distributed | 0.785542 |
79,021 | In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left... | Normally distributed | 0.785542 |
79,022 | Intrusive ultramafic rocks are often found in large, layered ultramafic intrusions where differentiated rock types often occur in layers. Such cumulate rock types do not represent the chemistry of the magma from which they crystallized. The ultramafic intrusives include the dunites, peridotites and pyroxenites. Other r... | Ultramafic rock | 0.78554 |
79,023 | However, the application of SRM is not limited to VLJ pilots. This training applies to all single-pilot flights in general aviation (GA). In the United States, GA accounts for 96% of aircraft, 60% of flight hours. It also accounts for 94% of fatal aviation accidents, Airline and military aviation estimates of the numbe... | Single pilot resource management | 0.785538 |
79,024 | Two ecological paradigms deal with the problem. The first paradigm predominates in what may be called “classical” ecology. It assumes that niche space is largely saturated with individuals and species, leading to strong competition. Niches are restricted because “neighbouring” species, i.e., species with similar ecolog... | Ecological niche | 0.785537 |
79,025 | However, as a result of pressure from, and interactions with, other organisms (i.e. inter-specific competition) species are usually forced to occupy a niche that is narrower than this, and to which they are mostly highly adapted; this is termed the realized niche. Hutchinson used the idea of competition for resources a... | Ecological niche | 0.785537 |
79,026 | For such a bell-shaped distribution, the position, width and form of the niche correspond to the mean, standard deviation and the actual distribution itself. One advantage in using statistics is illustrated in the figure, where it is clear that for the narrower distributions (top) there is no competition for prey betwe... | Ecological niche | 0.785537 |
79,027 | His work inspired many others to develop models to explain how many and how similar coexisting species could be within a given community, and led to the concepts of 'niche breadth' (the variety of resources or habitats used by a given species), 'niche partitioning' (resource differentiation by coexisting species), and ... | Ecological niche | 0.785537 |
79,028 | The applications of the spin angular momentum of light are undistinguishable from the innumerable applications of the light polarization and will not be discussed here. The possible applications of the orbital angular momentum of light are instead currently the subject of research. In particular, the following applicat... | Angular momentum of light | 0.785537 |
79,029 | One commonly used expression for the total angular momentum of an electromagnetic field is the following one, in which there is no explicit distinction between the two forms of rotation: where E {\displaystyle \mathbf {E} } and B {\displaystyle \mathbf {B} } are the electric and magnetic fields, respectively, ϵ 0 {\dis... | Angular momentum of light | 0.785537 |
79,030 | Nitrosonium octafluoroxenate(VI) is a chemical compound of xenon with nitrogen, oxygen, and fluorine, having formula (NO)2XeF8. It is an ionic compound containing well-separated nitrosonium cations (NO+) and octafluoroxenate(VI) anions (XeF2−8). The molecular geometry of the octafluoroxenate(VI) ion is square antiprism... | Nitrosonium octafluoroxenate(VI) | 0.785536 |
79,031 | Doody, Burghardt & Dinets consider several ways of assessing and classifying animal sociality and state that "Porges’ dichotomy is incorrect. While many mammals (particularly humans) may show more complex social behavior than reptiles, there is considerable overlap in social tendencies between the two groups. The label... | Polyvagal theory | 0.785535 |
79,032 | According to polyvagal theory, this effect has been observed and demonstrated by adaptive reactivity dependent on the neural circuits' phylogenetical development. Polyvagal theory claims that human facial expressions are associated with, or reflect, physical reactions, such as cardiac and digestive changes.Porges argue... | Polyvagal theory | 0.785535 |
79,033 | Polyvagal theory (poly- "many" + vagal "wandering" or "PVT") is a collection of proposed evolutionary, neuroscientific, and psychological constructs pertaining to the role of the vagus nerve in emotion regulation, social connection and fear response. PVT was introduced in 1994 by Stephen Porges. There is consensus amon... | Polyvagal theory | 0.785535 |
79,034 | In mathematics, Kōmura's theorem is a result on the differentiability of absolutely continuous Banach space-valued functions, and is a substantial generalization of Lebesgue's theorem on the differentiability of the indefinite integral, which is that Φ: → R given by Φ ( t ) = ∫ 0 t φ ( s ) d s , {\displaystyle \Phi (t... | Kōmura's theorem | 0.785535 |
79,035 | Data Analysis Tools: These tools are motivated by the fact that particle physics experiments and simulations often create large datasets, e.g. see references. Software Libraries: Many software libraries are used for particle physics computations. Also important are packages that simulate particle physics interactions u... | Computational particle physics | 0.785533 |
79,036 | Computer algebra: Many of the computer algebra languages were developed initially to help particle physics calculations: Reduce, Mathematica, Schoonschip, Form, GiNaC. Data Grid: The largest planned use of the grid systems will be for the analysis of the LHC - produced data. Large software packages have been developed ... | Computational particle physics | 0.785533 |
79,037 | Computational particle physics refers to the methods and computing tools developed in and used by particle physics research. Like computational chemistry or computational biology, it is, for particle physics both a specific branch and an interdisciplinary field relying on computer science, theoretical and experimental ... | Computational particle physics | 0.785533 |
79,038 | Particle physics played a role in the early history of the internet; the World-Wide Web was created by Tim Berners-Lee when working at CERN in 1991. | Computational particle physics | 0.785533 |
79,039 | Following this change of paradigma, the library GiNaC was developed. The GiNac library allows symbolic calculations in C++. Code generation for computer algebra can also be used in this area. | Computational particle physics | 0.785533 |
79,040 | In addition, also a few dedicated programs appeared, an example relevant to particle physics is the program FORM by J. Vermaseren as a (portable) successor to SCHOONSHIP. More recently issues of the maintainability of large projects became more and more important and the overall programming paradigma changed from proce... | Computational particle physics | 0.785533 |
79,041 | Also the program MACSYMA deserves to be mentioned explicitly, since it triggered important development with regard to algorithms. In the 1980s new computer algebra systems started to be written in C. This enabled the better exploitation of the resources of the computer (compared to the interpreted language LISP) and at... | Computational particle physics | 0.785533 |
79,042 | An exception to the LISP-based programs was SCHOONSHIP, written in assembler language by Martinus J. G. Veltman and specially designed for applications in particle physics. The use of assembler code lead to an incredible fast program (compared to the interpreted programs at that time) and allowed the calculation of mor... | Computational particle physics | 0.785533 |
79,043 | LISP is an interpreted language and, as the name already indicates, designed for the manipulation of lists. Its importance for symbolic computer programs in the early days has been compared to the importance of FORTRAN for numerical programs in the same period. Already in this first period, the program REDUCE had some ... | Computational particle physics | 0.785533 |
79,044 | Note: This section contains an excerpt from 'Computer Algebra in Particle Physics' by Stefan Weinzierl Particle physics is an important field of application for computer algebra and exploits the capabilities of Computer Algebra Systems (CAS). This leads to valuable feed-back for the development of CAS. Looking at the h... | Computational particle physics | 0.785533 |
79,045 | The group 6, chalcogen, and noble gas hexafluorides are colourless, but the other hexafluorides have colours ranging from white, through yellow, orange, red, brown, and grey, to black. The molecular geometry of binary hexafluorides is generally octahedral, although some derivatives are distorted from Oh symmetry. For t... | MF6 | 0.785533 |
79,046 | A locally convex topological vector space has a bounded neighborhood of zero if and only if its topology can be defined by a single seminorm. The polar of a bounded set is an absolutely convex and absorbing set. Using the definition of uniformly bounded sets given below, Mackey's countability condition can be restated ... | Bounded set (topological vector space) | 0.785533 |
79,047 | An algebraic proof, based on the variational interpretation of eigenvalues, has been published in Magnus' Matrix Differential Calculus with Applications in Statistics and Econometrics. From the geometric point of view, B'AB can be considered as the orthogonal projection of A onto the linear subspace spanned by B, so th... | Poincaré separation theorem | 0.785533 |
79,048 | In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The ... | Poincaré separation theorem | 0.785532 |
79,049 | Consider a monochromatic point source at P0, which illuminates an aperture in a screen. The intensity of the wave emitted by a point source falls off as the inverse square of the distance traveled, so the amplitude falls off as the inverse of the distance. The complex amplitude of the disturbance at a distance r {\disp... | Kirchhoff's diffraction formula | 0.785531 |
79,050 | In this geometry, the observation point P is located in the volume enclosed by the two spheres so the Fresnel-Kirchhoff diffraction formula is applied on the two spheres. (The surface normal on these integral surfaces are, say again, toward the enclosed volume in the diffraction formula above.) In the formula applicati... | Kirchhoff's diffraction formula | 0.785531 |
79,051 | As a result, the angle ( n , r ) = 0 {\displaystyle (n,r)=0} and the angle ( n , s ) {\displaystyle (n,s)} is related with the angle χ {\displaystyle \chi } (the angle as defined in Huygens–Fresnel principle) as The complex amplitude of the wavefront at r0 is given by So, the diffraction formula becomes where the integ... | Kirchhoff's diffraction formula | 0.785531 |
79,052 | Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an a... | Kirchhoff's diffraction formula | 0.785531 |
79,053 | Kirchhoff's diffraction formula (also called Fresnel–Kirchhoff diffraction formula) approximates light intensity and phase in optical diffraction: light fields in the boundary regions of shadows. The approximation can be used to model light propagation in a wide range of configurations, either analytically or using num... | Kirchhoff's diffraction formula | 0.785531 |
79,054 | Living polymerization, however, produces only one type of tacticity per catalyst. While the specific tacticity can be controlled by altering the type of catalyst used, creating a block copolymer requires that the polymerization be terminated, the catalyst destroyed, and that the chain re-propagate using another catalys... | Chain shuttling polymerization | 0.78553 |
79,055 | Olefin polymers (such as polypropylene and polyethylene) have seen widespread use in the plastics industry in the past 50 years. A way to enhance the properties of these olefin polymers was first discovered by the scientists Karl Ziegler and Giulio Natta. Ziegler discovered the original Titanium based catalyst essentia... | Chain shuttling polymerization | 0.78553 |
79,056 | LD50 = 25 mg/kg (mouse, i.p. ); 40 mg/kg (mouse, s.c. ); 50 mg/kg (rat, p.o.). Very toxic to aquatic organisms.Diverse data on human exposure, environmental toxicology and environmentally-related chemistry is available through the NIH Toxnet database. | Tetramethylammonium chloride | 0.78553 |
79,057 | Plant cells can inherently produce hydrostatic pressure due to a solute concentration gradient between the cytoplasm and external surroundings (osmotic potential). Further, plants can adjust this concentration through the movement of ions across the cell membrane. This then changes the shape and volume of the plant as ... | Soft robot | 0.785529 |
79,058 | Δ P {\displaystyle \Delta P} is the change in hydrostatic pressure. Δ π {\displaystyle \Delta \pi } is the change in osmotic potential.This principle has been leveraged in the creation of pressure systems for soft robotics. These systems are composed of soft resins and contain multiple fluid sacs with semi-permeable me... | Soft robot | 0.785529 |
79,059 | The cause of executive dysfunction is heterogeneous, as many neurocognitive processes are involved in the executive system and each may be compromised by a range of genetic and environmental factors. Learning and development of long-term memory play a role in the severity of executive dysfunction through dynamic intera... | Executive dysfunction | 0.785528 |
79,060 | In psychology and neuroscience, executive dysfunction, or executive function deficit, is a disruption to the efficacy of the executive functions, which is a group of cognitive processes that regulate, control, and manage other cognitive processes. Executive dysfunction can refer to both neurocognitive deficits and beha... | Executive dysfunction | 0.785528 |
79,061 | In chemistry, a hydroxy or hydroxyl group is a functional group with the chemical formula −OH and composed of one oxygen atom covalently bonded to one hydrogen atom. In organic chemistry, alcohols and carboxylic acids contain one or more hydroxy groups. Both the negatively charged anion HO−, called hydroxide, and the n... | Hydroxyl group | 0.785528 |
79,062 | The hydroxy group is pervasive in chemistry and biochemistry. Many inorganic compounds contain hydroxyl groups, including sulfuric acid, the chemical compound produced on the largest scale industrially.Hydroxy groups participate in the dehydration reactions that link simple biological molecules into long chains. The jo... | Hydroxyl group | 0.785528 |
79,063 | Reece J, Urry L, Cain M, Wasserman S, Minorsky P, Jackson R (2011). "Chapter 4&5". In Berge S, Golden B, Triglia L (eds.). Campbell Biology. | Hydroxyl group | 0.785528 |
79,064 | TSE or Tris/Saline/EDTA, is a buffer solution containing a mixture of Tris base, Sodium chloride and EDTA. In molecular biology, TSE buffers are often used in procedures involving nucleic acids. Tris-acid solutions are effective buffers for slightly basic conditions, which keep DNA deprotonated and soluble in water. Th... | TSE buffer | 0.785527 |
79,065 | In particular, Vω + ω, a particular countable level of the cumulative hierarchy, is a model of Zermelo set theory. The axiom of replacement, on the other hand, is only satisfied by Vκ for significantly larger values of κ, such as when κ is a strongly inaccessible cardinal. Friedman's theorem of 1971 showed that there i... | Borel determinacy | 0.785525 |
79,066 | The Borel determinacy theorem is of interest for its metamathematical properties as well as its consequences in descriptive set theory. Determinacy of closed sets of Aω for arbitrary A is equivalent to the axiom of choice over ZF (Kechris 1995, p. 139). When working in set-theoretical systems where the axiom of choice ... | Borel determinacy | 0.785525 |
79,067 | It was known that, using the axiom of choice, it is possible to construct a subset of {0,1}ω that is not determined (Kechris 1995, p. 139). Harvey Friedman (1971) proved that any proof that all Borel subsets of Cantor space ({0,1}ω ) were determined would require repeated use of the axiom of replacement, an axiom not t... | Borel determinacy | 0.785525 |
79,068 | In chronobiology, photoentrainment refers to the process by which an organism's biological clock, or circadian rhythm, synchronizes to daily cycles of light and dark in the environment. The mechanisms of photoentrainment differ from organism to organism. Photoentrainment plays a major role in maintaining proper timing ... | Photoentrainment (chronobiology) | 0.785524 |
79,069 | 24-hour physiological rhythms, known now as circadian rhythms, were first documented in 1729 by Jean Jacques d'Ortous de Mairan, a French astronomer who observed that mimosa plants (Mimosa pudica) would orient themselves to be toward the position of the sun despite being in a dark room. That observation spawned the fie... | Photoentrainment (chronobiology) | 0.785524 |
79,070 | {\displaystyle {\begin{aligned}3{\sqrt {3}}R&\geq a+b+c\\9R^{2}&\geq a^{2}+b^{2}+c^{2}\\{\frac {27}{4}}R^{2}&\geq m_{a}^{2}+m_{b}^{2}+m_{c}^{2}.\end{aligned}}} If median m, altitude h, and internal bisector t all emanate from the same vertex of a triangle with circumradius R, then 4 R 2 h 2 ( t 2 − h 2 ) = t 4 ( m 2 − ... | Circumcenter | 0.785524 |
79,071 | By Euler's theorem in geometry, the distance between the circumcenter O and the incenter I is O I ¯ = R ( R − 2 r ) , {\displaystyle {\overline {OI}}={\sqrt {R(R-2r)}},} where r is the incircle radius and R is the circumcircle radius; hence the circumradius is at least twice the inradius (Euler's triangle inequality), ... | Circumcenter | 0.785524 |
79,072 | The angles which the circumscribed circle forms with the sides of the triangle coincide with angles at which sides meet each other. The side opposite angle α meets the circle twice: once at each end; in each case at angle α (similarly for the other two angles). This is due to the alternate segment theorem, which states... | Circumcenter | 0.785524 |
79,073 | K-14 was the most recent version of the developing process for Kodak's Kodachrome transparency film before its discontinuation (the last revision having been designated Process K-14M). It superseded previous versions of the Kodachrome process used with older films (such as K-12 for Kodachrome II and Kodachrome-X).The K... | K-14 process | 0.785524 |
79,074 | In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. T... | Elliptic complex | 0.785523 |
79,075 | We will need a particular statement from the portmanteau theorem: that convergence in distribution X n → d X {\displaystyle X_{n}{\xrightarrow {d}}X} is equivalent to E f ( X n ) → E f ( X ) {\displaystyle \mathbb {E} f(X_{n})\to \mathbb {E} f(X)} for every bounded continuous functional f.So it suffices to prove that E... | Continuous mapping theorem | 0.785522 |
79,076 | {\displaystyle \Pr {\big (}{\big |}g(X_{n})-g(X){\big |}>\varepsilon {\big )}\leq \Pr {\big (}|X_{n}-X|\geq \delta {\big )}+\Pr(X\in B_{\delta })+\Pr(X\in D_{g}).} On the right-hand side, the first term converges to zero as n → ∞ for any fixed δ, by the definition of convergence in probability of the sequence {Xn}. The... | Continuous mapping theorem | 0.785522 |
79,077 | In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The co... | Continuous mapping theorem | 0.785522 |
79,078 | When storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. Specialized computers have been made for sparse matrices, as they are common in the machine learning field. Opera... | Symmetric sparse matrix | 0.785522 |
79,079 | By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The concept of sparsity is useful in combinatorics and application areas such as network theory and numerical analysis, which typically have a low density of significant da... | Symmetric sparse matrix | 0.785522 |
79,080 | RDM Server is an embeddable, heterogeneous, client/server database management system supporting both C/C++ and SQL APIs for programming flexibility. The databases can be disk resident and/or memory resident. RDM Server implements multi-user locking, hot database backup, and a fully ACID-compliant transaction logging sy... | RDM Server | 0.785521 |
79,081 | The current standard model of cosmology, the Lambda-CDM model, uses the FLRW metric. By combining the observation data from some experiments such as WMAP and Planck with theoretical results of Ehlers–Geren–Sachs theorem and its generalization, astrophysicists now agree that the early universe is almost homogeneous and ... | Friedmann–Lemaître–Robertson–Walker metric | 0.78552 |
79,082 | Design science research, or constructive research, in contrast to explanatory science research, has academic research objectives generally of a more pragmatic nature. Research in these disciplines can be seen as a quest for understanding and improving human performance. Such renowned research institutions as the MIT Me... | Design science (methodology) | 0.78552 |
79,083 | Design science research focuses on the development and performance of (designed) artifacts with the explicit intention of improving the functional performance of the artifact. Design science research methodology is typically applied to categories of artifacts including algorithms, human/computer interfaces, design meth... | Design science (methodology) | 0.78552 |
79,084 | Since the first days of computer science, computer scientists have been doing design science research without naming it. They have developed new architectures for computers, new programming languages, new compilers, new algorithms, new data and file structures, new data models, new database management systems, and so o... | Design science (methodology) | 0.78552 |
79,085 | Those who master a body of knowledge without learning from such expertise are called "respect experts" by Kahneman, Sibony, and Sunstein. With some data, ordinary least squares (OLS) models often outperform simple heuristics. With lots of data, artificial intelligence (AI) routinely outperforms OLS. | Overconfidence effect | 0.785519 |
79,086 | A division is called an exact division (aka consensus division) if the value of piece i {\displaystyle i} is exactly w i {\displaystyle w_{i}} according to all partners, where the w i {\displaystyle w_{i}} are pre-specified weights. Suppose the sum of all weights is 1, and the value of the pie for all agents is normali... | Fair pie-cutting | 0.785519 |
79,087 | Why? Because after a rotation of 120 degrees, the sector that was previously the most valuable is now less valuable, and another sector is now the most valuable. Hence, by the intermediate value theorem, there must be a position in the rotation when partner B views two sectors as tied for largest. At this point, partne... | Fair pie-cutting | 0.785519 |
79,088 | When this equilibrium is reached, the maximum effective fitness of the population is achieved.Problem solving with evolutionary computation is realized with a cost function. If cost functions are applied to swarm optimization they are called a fitness function. Strategies like reinforcement learning and NEAT neuroevolu... | Effective fitness | 0.785518 |
79,089 | When evolutionary equations of the studied population dynamics are available, one can algorithmically compute the effective fitness of a given population. Though the perfect effective fitness model is yet to be found, it is already known to be a good framework to the better understanding of the moving of the genotype-p... | Effective fitness | 0.785518 |
79,090 | A special case of the Kneser–Tits problem asks for which fields the Whitehead group of a semisimple almost simple simply connected isotropic algebraic group is always trivial. Platonov (1969) showed that this Whitehead group is trivial for local fields K, and gave examples of fields for which it is not always trivial. ... | Kneser–Tits conjecture | 0.785518 |
79,091 | In mathematics, the Kneser–Tits problem, introduced by Tits (1964) based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple simply connected isotropic algebraic group G over a field K is trivial. The Whitehead group is the quotient of the rational points of G by the normal subgrou... | Kneser–Tits conjecture | 0.785518 |
79,092 | {\displaystyle |Q(x_{i})-f(x_{i})|<|P(x_{i})-f(x_{i})|.} When a maximum of P−f occurs at xi, then Q ( x i ) − f ( x i ) ≤ | Q ( x i ) − f ( x i ) | < | P ( x i ) − f ( x i ) | = P ( x i ) − f ( x i ) , {\displaystyle Q(x_{i})-f(x_{i})\leq |Q(x_{i})-f(x_{i})|<|P(x_{i})-f(x_{i})|=P(x_{i})-f(x_{i}),} And when a minimum of... | Approximation theory | 0.785515 |
79,093 | That such a polynomial is always optimal is asserted by the equioscillation theorem. It is possible to make contrived functions f(x) for which no such polynomial exists, but these occur rarely in practice. For example, the graphs shown to the right show the error in approximating log(x) and exp(x) for N = 4. | Approximation theory | 0.785515 |
79,094 | In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element. More precisely, if A is a finite set of generators for G then the word ... | Kuznetsov's theorem | 0.785515 |
79,095 | The discovery of PFGE can be traced back to the late 1970s and early 1980s.One of the earliest references to the use of PFGE for DNA analysis is a 1977 paper by Dr. David Burke and colleagues at the University of Colorado, where they described a method of separating DNA molecules based on their size using conventional ... | Pulsed field gel electrophoresis | 0.785515 |
79,096 | Then the estimate of the covariance function G ^ ( s , t ) {\displaystyle {\hat {G}}(s,t)} is obtained by averaging (in the dense case) or smoothing (in the sparse case) the raw covariances G i ( t i j , t i l ) = ( Y i j − μ ^ ( t i j ) ) ( Y i l − μ ^ ( t i l ) ) , j ≠ l , i = 1 , … , n . {\displaystyle G_{i}(t_{ij},... | Functional principal component analysis | 0.785513 |
79,097 | The figure below shows the three possible stereochemical pathways, assuming a chair transition state. It has been postulated that the difference in the formation of these transition states and their corresponding products is due to solvent interactions. Scanio found that changing the solvent of the reaction from dioxan... | Robinson annulation | 0.785509 |
79,098 | In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the se... | Forecast errors | 0.785509 |
79,099 | A polyphosphate is a salt or ester of polymeric oxyanions formed from tetrahedral PO4 (phosphate) structural units linked together by sharing oxygen atoms. Polyphosphates can adopt linear or a cyclic ring structures. In biology, the polyphosphate esters ADP and ATP are involved in energy storage. A variety of polyphosp... | Sodium polyphosphate | 0.785507 |
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