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8,100 | The Faculty of Electrical Engineering represents a complex, modernly organized teaching and scientific institution. Within its teaching activities, the Faculty organizes and realizes undergraduate, specialist, postgraduate and doctoral studies. | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,101 | Undergraduate academic studies at the Faculty are organized through two study groups: Energy and Automatics Electronics, Telecommunications and ComputersUndergraduate applied studies are organized through the Applied Computer Sciences study group. | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,102 | Among the most notable alumni and members of the academic staff of the Faculty of Electrical Engineering are: Milica Pejanović-Đurišić - politician, former Minister of Defence of Montenegro. Momir Đurović - former president of the Montenegrin Academy of Sciences and Arts Ljubiša Stanković - former Rector (2003-2008) an... | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,103 | The University of Montenegro Faculty of Electrical Engineering (Montenegrin: Elektrotehnički fakultet Univerziteta Crne Gore Електротехнички факултет Универзитета Црне Горе) is one of the educational institutions of the University of Montenegro. Its main building is located in Podgorica, at the University campus. | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,104 | Studies of Electrical Engineering were established in 1961, and two years later the Technical Faculty with the Department for Electrical Engineering was established in Podgorica. It was a part of the University of Belgrade until April 29, 1974, when the Agreement on Association into the University of Titograd (today's ... | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,105 | Postgraduate specialist and master academic studies are organized through two study groups: Applied Computer Sciences Energy and Automatics, with the course of studies Electrical Engineering Systems, Industrial Electrical Engineering and Automatics Electronics, Telecommunications and Computers, with the course of studi... | University of Montenegro Faculty of Electrical Engineering | 0.821863 |
8,106 | First proposed by Kneller and Hawig in 1991, the exchange spring magnet utilizes the epitaxy between hard and soft magnetic materials: the hard material helps retain the soft material's anisotropy, which increases its coercivity.The magnetic hysteresis loop of an exchange spring magnet theoretically takes on a shape re... | Exchange spring magnet | 0.821862 |
8,107 | Additionally, the volume fraction of the soft phase needs to be as large as possible in order to achieve a high magnetization saturation. One viable material geometry is to fabricate a magnet by embedding hard particles inside a soft matrix. That way, the soft matrix material occupies the largest volume fraction while ... | Exchange spring magnet | 0.821862 |
8,108 | Radio astronomy has led to substantial increases in astronomical knowledge, particularly with the discovery of several classes of new objects, including pulsars, quasars and radio galaxies. This is because radio astronomy allows us to see things that are not detectable in optical astronomy. Such objects represent some ... | Microwave astronomy | 0.821849 |
8,109 | A binary block code consists of a set of codewords, each of which is a string of 0s and 1s, all the same length. When each pair of codewords has large Hamming distance, it can be used as an error-correcting code. A block code can also be described as a family of sets, by describing each codeword as the set of positions... | Family of sets | 0.821847 |
8,110 | Any family of subsets of a set S {\displaystyle S} is itself a subset of the power set ℘ ( S ) {\displaystyle \wp (S)} if it has no repeated members. Any family of sets without repetitions is a subclass of the proper class of all sets (the universe). Hall's marriage theorem, due to Philip Hall, gives necessary and suff... | Family of sets | 0.821847 |
8,111 | A Sperner family is a set family in which none of the sets contains any of the others. Sperner's theorem bounds the maximum size of a Sperner family. A Helly family is a set family such that any minimal subfamily with empty intersection has bounded size. Helly's theorem states that convex sets in Euclidean spaces of bo... | Family of sets | 0.821847 |
8,112 | Radiative flux, also known as radiative flux density or radiation flux (or sometimes power flux density), is the amount of power radiated through a given area, in the form of photons or other elementary particles, typically measured in W/m2. It is used in astronomy to determine the magnitude and spectral class of a sta... | Radiative flux | 0.821841 |
8,113 | Given a group G and a commutative ring R, one can construct RG, known as the group algebra; it is an R-module equipped with a multiplication. A group is the same as a category with a single object in which all morphisms are isomorphisms (where the elements of the group correspond to the morphisms of the category), so t... | Category algebra | 0.82184 |
8,114 | In other words, RC consists of formal linear combinations (which are finite sums) of the form ∑ a i f i {\displaystyle \sum a_{i}f_{i}} , where fi are morphisms of C, and ai are elements of the ring R. Define a multiplication operation on RC as follows, using the composition operation in the category: ∑ a i f i ∑ b j g... | Category algebra | 0.82184 |
8,115 | The definition used for incidence algebras assumes that the category C is locally finite (see below), is dual to the above definition, and defines a different object. This isn't a useful assumption for groups, as a group that is locally finite as a category is finite. A locally finite category is one where every morphi... | Category algebra | 0.82184 |
8,116 | The computation core performs in silico docking to generate rank-ordered lists of predicted substrates for targeted enzymes using both experimentally determined and/or homology modeled protein structures. The microbiology core examines in vivo functions using genetic techniques and metabolomics to complement in vitro f... | Enzyme Function Initiative | 0.821838 |
8,117 | The bioinformatics core contributes bioinformatic analysis by collecting and curating complete sequence data sets, generating sequence similarity networks, and classification of superfamily members into subgroups and families for subsequent annotation transfer and evaluation as targets for functional characterization. ... | Enzyme Function Initiative | 0.821838 |
8,118 | The Enzyme Function Initiative (EFI) is a large-scale collaborative project aiming to develop and disseminate a robust strategy to determine enzyme function through an integrated sequence–structure-based approach. The project was funded in May 2010 by the National Institute of General Medical Sciences as a Glue Grant w... | Enzyme Function Initiative | 0.821838 |
8,119 | The EFI is developing an integrated sequence-structure based strategy for functional assignment by predicting the substrate specificities of unknown members of mechanistically diverse enzyme superfamilies. The approach leverages conserved features within a given superfamily such as known chemistry, identity of active s... | Enzyme Function Initiative | 0.821838 |
8,120 | The mass of a current T {\displaystyle T} is then defined as The mass of a current represents the weighted area of the generalized surface. A current such that M(T) < ∞ is representable by integration of a regular Borel measure by a version of the Riesz representation theorem. | Integral current | 0.82183 |
8,121 | Integration over a compact rectifiable oriented submanifold M (with boundary) of dimension m defines an m-current, denoted by ] {\displaystyle ]}: If the boundary ∂M of M is rectifiable, then it too defines a current by integration, and by virtue of Stokes' theorem one has: This relates the exterior derivative d with ... | Integral current | 0.82183 |
8,122 | In mathematics, more particularly in functional analysis, differential topology, and geometric measure theory, a k-current in the sense of Georges de Rham is a functional on the space of compactly supported differential k-forms, on a smooth manifold M. Currents formally behave like Schwartz distributions on a space of ... | Integral current | 0.82183 |
8,123 | The space of currents is naturally endowed with the weak-* topology, which will be further simply called weak convergence. A sequence T k {\displaystyle T_{k}} of currents, converges to a current T {\displaystyle T} if It is possible to define several norms on subspaces of the space of all currents. One such norm is th... | Integral current | 0.821829 |
8,124 | In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds to a potential which is zero everywhere, except at a single point, where it takes an infinite value. This can be used to simulate situations where a p... | Delta potential barrier (QM) | 0.821818 |
8,125 | (1)(2) This model of circadian rhythm generation also has implications for the study of circadian “evolutionary biology”. Given the simplicity of cyanobacteria and of this circadian system, it may be safe to assume that eukaryotic circadian oscillators are derived from a system similar to that present in cyanobacterium... | Cyanobacterial clock proteins | 0.821818 |
8,126 | In molecular biology, the cyanobacterial clock proteins are the main circadian regulator in cyanobacteria. The cyanobacterial clock proteins comprise three proteins: KaiA, KaiB and KaiC. The kaiABC complex may act as a promoter-nonspecific transcription regulator that represses transcription, possibly by acting on the ... | Cyanobacterial clock proteins | 0.821818 |
8,127 | Soft computing is a set of algorithms, including neural networks, fuzzy logic, and evolutionary algorithms. These algorithms are tolerant of imprecision, uncertainty, partial truth and approximation. It is contrasted with hard computing: algorithms which find provably correct and optimal solutions to problems. | Soft computing | 0.821817 |
8,128 | In Baghdad the first pharmacies, or drug stores, were established in 754, under the Abbasid Caliphate during the Islamic Golden Age. By the 9th century, these pharmacies were state-regulated.The advances made in the Middle East in botany and chemistry led medicine in medieval Islam substantially to develop pharmacology... | Pharmaceutical science | 0.821817 |
8,129 | An establishment in which pharmacy (in the first sense) is practiced is called a pharmacy (this term is more common in the United States) or chemists (which is more common in Great Britain, though pharmacy is also used). In the United States and Canada, drugstores commonly sell medicines, as well as miscellaneous items... | Pharmaceutical science | 0.821817 |
8,130 | Encyclopedic content and bibliographic materials related to physics, mathematics and mathematical physics are developed by PlanetPhysics. The site, launched in 2005, uses similar software (Noosphere), but a significantly different moderation model with emphasis on current research in physics and peer review. Additional... | PlanetMath | 0.82181 |
8,131 | The site is supervised by the Content Committee. Its basic mission is to maintain the integrity and quality of the mathematical content and organization of PlanetMath. As defined in its Charter, the tasks of the Committee include: Developing/maintaining the standards for PlanetMath content Improving individual PlanetMa... | PlanetMath | 0.82181 |
8,132 | A game can be balanced dynamically by a gamemaster who observes players and adjusts the game in response to their actions, emotional state, etc., or even proactively changes the direction of the game to create certain experiences. Although gamemasters have historically been humans, some videogames now feature artificia... | Game difficulty | 0.821804 |
8,133 | In the theory of elliptic partial differential equations, one demonstrates the existence of a weak solution of a differential equation with reasonable ease using some functional analysis arguments. However, the weak solution exhibited lies in a space of functions with fewer derivatives than one would desire; for exampl... | Free boundary problem | 0.821792 |
8,134 | In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function u {\displaystyle u} and an unknown domain Ω {\displaystyle \Omega } . The segment Γ {\displaystyle \Gamma } of the boundary of Ω {\displaystyle \Omega } which is not known at the outset of t... | Free boundary problem | 0.821792 |
8,135 | Inclusion is a partial order: Explicitly, this means that inclusion ⊆ , {\displaystyle \,\subseteq ,\,} which is a binary operation, has the following three properties: Reflexivity: L ⊆ L {\textstyle L\subseteq L} Antisymmetry: ( L ⊆ R and R ⊆ L ) if and only if L = R {\textstyle (L\subseteq R{\text{ and }}R\subseteq L... | List of set identities and relations | 0.821785 |
8,136 | {\displaystyle {\mathcal {S}}_{0}.} Then the algebra generated by S {\displaystyle {\mathcal {S}}} is the set Φ S {\displaystyle \Phi _{\mathcal {S}}} consisting of all possible finite unions of sets in S 1 . {\displaystyle {\mathcal {S}}_{1}.} | List of set identities and relations | 0.821785 |
8,137 | It is called the algebra generated by S {\displaystyle {\mathcal {S}}} and it will be denote it by Φ S . {\displaystyle \Phi _{\mathcal {S}}.} This algebra can be constructed as follows: If S = ∅ {\displaystyle {\mathcal {S}}=\varnothing } then Φ S = { ∅ , X } {\displaystyle \Phi _{\mathcal {S}}=\{\varnothing ,X\}} and... | List of set identities and relations | 0.821785 |
8,138 | Every algebra of sets is also a ring of sets and a π-system. Algebra generated by a family of sets Given any family S {\displaystyle {\mathcal {S}}} of subsets of X , {\displaystyle X,} there is a unique smallest algebra of sets in X {\displaystyle X} containing S . {\displaystyle {\mathcal {S}}.} | List of set identities and relations | 0.821785 |
8,139 | Algebra of sets A family Φ {\displaystyle \Phi } of subsets of a set X {\displaystyle X} is said to be an algebra of sets if ∅ ∈ Φ {\displaystyle \varnothing \in \Phi } and for all L , R ∈ Φ , {\displaystyle L,R\in \Phi ,} all three of the sets X ∖ R , L ∩ R , {\displaystyle X\setminus R,\,L\cap R,} and L ∪ R {\display... | List of set identities and relations | 0.821785 |
8,140 | algebra on X {\displaystyle X} is a non-empty family of subsets of X {\displaystyle X} that contains the empty set, forms a π−system, and is also closed under complementation with respect to X . {\displaystyle X.} σ-algebra on X {\displaystyle X} is an algebra on X {\displaystyle X} that is closed under countable union... | List of set identities and relations | 0.821785 |
8,141 | The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes, Error detecting and error correcting codes, in 1950. Hamming weight analysis of bits is used in several disciplines including information theory, coding theory, and cryptography.It is used in telec... | Hamming cube | 0.821783 |
8,142 | In 1760 Lagrange extended Euler's results on the calculus of variations involving integrals in one variable to two variables. He had in mind the following problem: Given a closed curve in E3, find a surface having the curve as boundary with minimal area. Such a surface is called a minimal surface. In 1776 Jean Baptiste... | Shape operator | 0.821776 |
8,143 | This invariant is easy to compute combinatorially in terms of the number of vertices, edges, and faces of the triangles in the decomposition, also called a triangulation. This interaction between analysis and topology was the forerunner of many later results in geometry, culminating in the Atiyah-Singer index theorem. ... | Shape operator | 0.821776 |
8,144 | His formula showed that the Gaussian curvature could be calculated near a point as the limit of area over angle excess for geodesic triangles shrinking to the point. Since any closed surface can be decomposed up into geodesic triangles, the formula could also be used to compute the integral of the curvature over the wh... | Shape operator | 0.821776 |
8,145 | On a sphere or a hyperboloid, the area of a geodesic triangle, i.e. a triangle all the sides of which are geodesics, is proportional to the difference of the sum of the interior angles and π. The constant of proportionality is just the Gaussian curvature, a constant for these surfaces. For the torus, the difference is ... | Shape operator | 0.821776 |
8,146 | Given any two local parametrizations f: V → U and f ′: V ′→ U ′ of a regular surface, the composition f −1 ∘ f ′ is necessarily smooth as a map between open subsets of ℝ2. This shows that any regular surface naturally has the structure of a smooth manifold, with a smooth atlas being given by the inverses of local param... | Shape operator | 0.821776 |
8,147 | The homeomorphisms appearing in the first definition are known as local parametrizations or local coordinate systems or local charts on S. The equivalence of the first two definitions asserts that, around any point on a regular surface, there always exist local parametrizations of the form (u, v) ↦ (h(u, v), u, v), (u,... | Shape operator | 0.821776 |
8,148 | The American Naturalist The Biological Bulletin Freshwater Science International Journal of Plant Sciences The Journal of Geology Physiological and Biochemical Zoology The Quarterly Review of Biology | Freshwater Science | 0.821775 |
8,149 | In mathematics, specifically in topology, a pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition relies on the notion of a measured foliation introduced by William Thurston, who also coined the term "pseudo-A... | Measured foliation | 0.821767 |
8,150 | These algorithms all include distributed parallel versions that integrate with Apache Hadoop and Spark.Deeplearning4j is open-source software released under Apache License 2.0, developed mainly by a machine learning group headquartered in San Francisco. It is supported commercially by the startup Skymind, which bundles... | Deeplearning4j | 0.821766 |
8,151 | Eclipse Deeplearning4j is a programming library written in Java for the Java virtual machine (JVM). It is a framework with wide support for deep learning algorithms. Deeplearning4j includes implementations of the restricted Boltzmann machine, deep belief net, deep autoencoder, stacked denoising autoencoder and recursiv... | Deeplearning4j | 0.821766 |
8,152 | What a Web server is to the Internet, a model server is to AI. Where a Web server receives an HTTP request and returns data about a Web site, a model server receives data, and returns a decision or prediction about that data: e.g. sent an image, a model server might return a label for that image, identifying faces or a... | Deeplearning4j | 0.821766 |
8,153 | Deeplearning4j serves machine-learning models for inference in production using the free developer edition of SKIL, the Skymind Intelligence Layer. A model server serves the parametric machine-learning models that makes decisions about data. It is used for the inference stage of a machine-learning workflow, after data ... | Deeplearning4j | 0.821766 |
8,154 | Deeplearning4j is as fast as Caffe for non-trivial image recognition tasks using multiple GPUs. For programmers unfamiliar with HPC on the JVM, there are several parameters that must be adjusted to optimize neural network training time. These include setting the heap space, the garbage collection algorithm, employing o... | Deeplearning4j | 0.821766 |
8,155 | Deeplearning4j includes an n-dimensional array class using ND4J that allows scientific computing in Java and Scala, similar to the functions that NumPy provides to Python. It's effectively based on a library for linear algebra and matrix manipulation in a production environment. | Deeplearning4j | 0.821766 |
8,156 | Deeplearning4j includes a vector space modeling and topic modeling toolkit, implemented in Java and integrating with parallel GPUs for performance. It is designed to handle large text sets. Deeplearning4j includes implementations of term frequency–inverse document frequency (tf–idf), deep learning, and Mikolov's word2v... | Deeplearning4j | 0.821766 |
8,157 | Deeplearning4j can be used via multiple API languages including Java, Scala, Python, Clojure and Kotlin. Its Scala API is called ScalNet. Keras serves as its Python API. And its Clojure wrapper is known as DL4CLJ. The core languages performing the large-scale mathematical operations necessary for deep learning are C, C... | Deeplearning4j | 0.821766 |
8,158 | Real-world use cases for Deeplearning4j include network intrusion detection and cybersecurity, fraud detection for the financial sector, anomaly detection in industries such as manufacturing, recommender systems in e-commerce and advertising, and image recognition. Deeplearning4j has integrated with other machine-learn... | Deeplearning4j | 0.821766 |
8,159 | The CERN Axion Solar Telescope (CAST) is an experiment in astroparticle physics to search for axions originating from the Sun. The experiment, sited at CERN in Switzerland, was commissioned in 1999 and came online in 2002 with the first data-taking run starting in May 2003. The successful detection of solar axions woul... | CAST experiment | 0.821754 |
8,160 | CAST experiment began with the goal of devising new methods and implementing novel technologies for the detection of solar axions. Owing to the inter-disciplinary and interrelated field of axion studies, dark matter, dark energy, and axion-like exotic particles, the new collaborations at CAST have broadened their resea... | CAST experiment | 0.821754 |
8,161 | In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture of confocal ellipses and hyperbolas, any ellipse intersects any hyperbola ortho... | Confocal quadrics | 0.821753 |
8,162 | Hence | P 11 P 22 | = | P 12 P 21 | {\displaystyle |P_{11}P_{22}|=|P_{12}P_{21}|} The proof of the statement for confocal parabolas is a simple calculation. Ivory even proved the 3-dimensional version of his theorem (s. Blaschke, p. 111): For a 3-dimensional rectangular cuboid formed by confocal quadrics the diagonals ... | Confocal quadrics | 0.821753 |
8,163 | The standard form of a continuous optimization problem is where f: ℝn → ℝ is the objective function to be minimized over the n-variable vector x, gi(x) ≤ 0 are called inequality constraints hj(x) = 0 are called equality constraints, and m ≥ 0 and p ≥ 0.If m = p = 0, the problem is an unconstrained optimization problem.... | Optimal solution | 0.821752 |
8,164 | In mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is kno... | Optimal solution | 0.821752 |
8,165 | The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided—not even if we want to use them just for proving derivability of tautologies. This basic diversity among the various calcul... | Judgment (mathematical logic) | 0.82175 |
8,166 | Judgments are used in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well (thus, hypotheses and conclusions of proofs are judgments). A characteristic feature of the variants of Hilbert-sty... | Judgment (mathematical logic) | 0.82175 |
8,167 | The function Φ x: I ( x ) → X {\displaystyle \Phi _{x}:I(x)\to X} is called the flow through x and its graph is called the trajectory through x. The set γ x ≡ { Φ ( t , x ): t ∈ I ( x ) } {\displaystyle \gamma _{x}\equiv \{\Phi (t,x):t\in I(x)\}} is called the orbit through x. Note that the orbit through x is the image... | Dynamic systems | 0.821747 |
8,168 | In the 2006 film Stranger than Fiction, the main character, Harold Crick, is able to perform rapid arithmetic at the request of his co-workers. In the 2007 sitcom The Big Bang Theory, the main character, Sheldon Cooper, calculates numbers and solutions in his head for his theoretical physics research. In the 2008 show ... | Mental calculator | 0.821745 |
8,169 | In the 1988 movie Rain Man, Raymond Babbitt, who has savant syndrome, can mentally calculate large numbers, amongst other abilities. Andrew Jackson "Slipstick" Libby is a calculating prodigy in Robert A. Heinlein's Sci-Fi story Methuselah's Children. In the USA Network legal drama Suits, the main character, Mike Ross, ... | Mental calculator | 0.821745 |
8,170 | His interpretation does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it intends simply to interpret the wave function. It does not propose to lead to actual results that differ from ortho... | Ensemble Interpretation | 0.821741 |
8,171 | The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system.The advocates of the ensemble interpretation of quantum mechanics claim that it is mini... | Ensemble Interpretation | 0.821741 |
8,172 | The state function is not taken to be physically real, or be a literal summation of states. The wave function, is taken to be an abstract statistical function, only applicable to the statistics of repeated preparation procedures. The ket does not directly apply to a single particle detection, but only the statistical r... | Ensemble Interpretation | 0.821741 |
8,173 | This gives a clear and utterly non-mysterious physical or direct explanation instead of the debated concept of wave function "collapse". It is presented in terms of quantum mechanics by other present day writers also, for example, Van Vliet. For those who prefer physical clarity rather than mysterianism, this is an adv... | Ensemble Interpretation | 0.821741 |
8,174 | "The second motivation for an ensemble interpretation is the intuition that because quantum mechanics is inherently probabilistic, it only needs to make sense as a theory of ensembles. Whether or not probabilities can be given a sensible meaning for individual systems, this motivation is not compelling. For a theory ou... | Ensemble Interpretation | 0.821741 |
8,175 | Leslie Ballentine promoted the ensemble interpretation in his book Quantum Mechanics, A Modern Development. In it, he described what he called the "Watched Pot Experiment". His argument was that, under certain circumstances, a repeatedly measured system, such as an unstable nucleus, would be prevented from decaying by ... | Ensemble Interpretation | 0.821741 |
8,176 | In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group G and a positive integer n, one asks for the smallest value of k such that every sequence of elements of G of size k contains n terms that sum to 0. The... | Zero-sum problem | 0.82174 |
8,177 | (Indeed, the lower bound is easy to see: the multiset containing n − 1 copies of 0 and n − 1 copies of 1 contains no n-subset summing to a multiple of n.) This result is known as the Erdős–Ginzburg–Ziv theorem after its discoverers. It may also be deduced from the Cauchy–Davenport theorem.More general results than this... | Zero-sum problem | 0.82174 |
8,178 | As a polynomial in X, φn has coefficients that are polynomials over Q {\displaystyle \mathbb {Q} } in j(τ). On the conjugate lattices, the modular group acts as PGL(2, Z/nZ). It follows that φn has Galois group isomorphic to PGL(2, Z/nZ) over Q ( J ( τ ) ) {\displaystyle \mathbb {Q} (\mathrm {J} (\tau ))} . Use of Hilb... | Inverse Galois theory | 0.821739 |
8,179 | Line or stick – atomic nuclei are not represented, just the bonds as sticks or lines. As in 2D molecular structures of this type, atoms are implied at each vertex.Electron density plot – shows the electron density determined either crystallographically or using quantum mechanics rather than distinct atoms or bonds.Ball... | Molecular structures | 0.821739 |
8,180 | This criterion can for example be used to show that all the symmetric groups are realizable. Much detailed work has been carried out on the question, which is in no sense solved in general. Some of this is based on constructing G geometrically as a Galois covering of the projective line: in algebraic terms, starting wi... | Inverse Galois theory | 0.821739 |
8,181 | There is a great deal of detailed information in particular cases. It is known that every finite group is realizable over any function field in one variable over the complex numbers C {\displaystyle \mathbb {C} } , and more generally over function fields in one variable over any algebraically closed field of characteri... | Inverse Galois theory | 0.821739 |
8,182 | The first definition of the term bioinformatics was coined by Paulien Hogeweg and Ben Hesper in 1970, to refer to the study of information processes in biotic systems. This definition placed bioinformatics as a field parallel to biochemistry (the study of chemical processes in biological systems).Bioinformatics and com... | Genetic informatics | 0.821737 |
8,183 | In genomics, annotation refers to the process of marking the stop and start regions of genes and other biological features in a sequenced DNA sequence. Many genomes are too large to be annotated by hand. As the rate of sequencing exceeds the rate of genome annotation, genome annotation has become the new bottleneck in ... | Genetic informatics | 0.821737 |
8,184 | Session leaders represented numerous branches of the FDA and NIH Institutes and Centers, non-profit entities including the Human Variome Project and the European Federation for Medical Informatics, and research institutions including Stanford, the New York Genome Center, and the George Washington University. It was dec... | Genetic informatics | 0.821737 |
8,185 | In 2014, the US Food and Drug Administration sponsored a conference held at the National Institutes of Health Bethesda Campus to discuss reproducibility in bioinformatics. Over the next three years, a consortium of stakeholders met regularly to discuss what would become BioCompute paradigm. These stakeholders included ... | Genetic informatics | 0.821737 |
8,186 | Tens of thousands of three-dimensional protein structures have been determined by X-ray crystallography and protein nuclear magnetic resonance spectroscopy (protein NMR) and a central question in structural bioinformatics is whether it is practical to predict possible protein–protein interactions only based on these 3D... | Genetic informatics | 0.821737 |
8,187 | Pan genomics is a concept introduced in 2005 by Tettelin and Medini. Pan genome is the complete gene repertoire of a particular monophyletic taxonomic group. Although initially applied to closely related strains of a species, it can be applied to a larger context like genus, phylum, etc. It is divided in two parts: the... | Genetic informatics | 0.821737 |
8,188 | In potential theory and optimization, polarization constants (also known as Chebyshev constants) are solutions to a max-min problem for potentials. Originally, these problems were introduced by a Japanese mathematician Makoto Ohtsuka. Recently these problems got some attention as they can help to generate random points... | Polarization constants | 0.821737 |
8,189 | There has been a tremendous advance in speed and cost reduction since the completion of the Human Genome Project, with some labs able to sequence over 100,000 billion bases each year, and a full genome can be sequenced for $1,000 or less.Computers became essential in molecular biology when protein sequences became avai... | Genetic informatics | 0.821737 |
8,190 | In the (unrealistic) limit of "pure" ionic bonding, electrons are perfectly localized on one of the two atoms in the bond. Such bonds can be understood by classical physics. The forces between the atoms are characterized by isotropic continuum electrostatic potentials. Their magnitude is in simple proportion to the cha... | Atomic bonds | 0.821736 |
8,191 | A Green's function is a fundamental solution that also satisfies a suitable condition on the boundary S of a volume V. For instance, may satisfy Now if u is any solution of the Poisson equation in V: and u assumes the boundary values g on S, then we may apply Green's identity, (a consequence of the divergence theorem) ... | Laplace's equation | 0.821728 |
8,192 | The twice continuously differentiable solutions of Laplace's equation are the harmonic functions, which are important in multiple branches of physics, notably electrostatics, gravitation, and fluid dynamics. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace's e... | Laplace's equation | 0.821728 |
8,193 | Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. Laplace's equation is also a special case of the Helmholtz equation. The general theory of solutions to Laplace's equation is known as potential theory. | Laplace's equation | 0.821728 |
8,194 | In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as or where Δ = ∇ ⋅ ∇ = ∇ 2 {\displaystyle \Delta =\nabla \cdot \nabla =\nabla ^{2}} is the Laplace operator, ∇ ⋅ {\displaystyle \nabla... | Laplace's equation | 0.821728 |
8,195 | The definition of the fundamental solution thus implies that, if the Laplacian of u is integrated over any volume that encloses the source point, then The Laplace equation is unchanged under a rotation of coordinates, and hence we can expect that a fundamental solution may be obtained among solutions that only depend u... | Laplace's equation | 0.821728 |
8,196 | This section summarizes some of the results of von Neumann (1998, Part I). These results are similar to, and were motivated by, von Neumann's work on projections in von Neumann algebras. Two elements a and b of L are called perspective, written a ∼ b, if they have a common complement. This is an equivalence relation on... | Continuous geometry | 0.821727 |
8,197 | So we can take a direct limit of P G ( F ) ⊂ P G ( F 2 ) ⊂ P G ( F 4 ) ⊂ P G ( F 8 ) ⋯ {\displaystyle PG(F)\subset PG(F^{2})\subset PG(F^{4})\subset PG(F^{8})\cdots } This has a dimension function taking values all dyadic rationals between 0 and 1. Its completion is a continuous geometry containing elements of every di... | Continuous geometry | 0.821727 |
8,198 | Finite-dimensional complex projective space, or rather its set of linear subspaces, is a continuous geometry, with dimensions taking values in the discrete set { 0 , 1 / n , 2 / n , … , 1 } {\displaystyle \{0,1/{\textit {n}}\,,2/{\textit {n}}\,,\dots ,1\}} The projections of a finite type II von Neumann algebra form a ... | Continuous geometry | 0.821727 |
8,199 | Conversely, the principal right ideals of a von Neumann regular ring form a complemented modular lattice (von Neumann 1998, Part II theorem 2.4). Suppose that R is a von Neumann regular ring and L its lattice of principal right ideals, so that L is a complemented modular lattice. Neumann showed that L is a continuous g... | Continuous geometry | 0.821727 |
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