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21,700 | A basic (early) result in digital topology says that 2D binary images require the alternative use of 4- or 8-adjacency or "pixel connectivity" (for "object" or "non-object" pixels) to ensure the basic topological duality of separation and connectedness. This alternative use corresponds to open or closed sets in the 2D ... | Combinatorial manifold | 0.810032 |
21,701 | In order to design a distributed metaheuristic, we must take several decisions. Among them, a chief decision is to determine the migration policy: topology (logical links between the islands), migration rate (number of individuals that undergo migration in every exchange), migration frequency (number of steps in every ... | Parallel metaheuristic | 0.81003 |
21,702 | Among the most widely known types of structured metaheuristics, the distributed (or coarse grain) and cellular (or fine grain) algorithms are very popular optimization procedures. In the case of distributed ones, the population is partitioned in a set of subpopulations (islands) in which isolated serial algorithms are ... | Parallel metaheuristic | 0.81003 |
21,703 | Iteratively, the probabilistic application of variation operators on selected individuals guides the population to tentative solutions of higher quality. The most well-known metaheuristic families based on the manipulation of a population of solutions are evolutionary algorithms (EAs), ant colony optimization (ACO), pa... | Parallel metaheuristic | 0.81003 |
21,704 | Parallel metaheuristic is a class of techniques that are capable of reducing both the numerical effort and the run time of a metaheuristic. To this end, concepts and technologies from the field of parallelism in computer science are used to enhance and even completely modify the behavior of existing metaheuristics. Jus... | Parallel metaheuristic | 0.81003 |
21,705 | Metaheuristics for solving optimization problems could be viewed as walks through neighborhoods tracing search trajectories through the solution domains of the problem at hands: Algorithm: Sequential trajectory-based general pseudo-code Generate(s(0)); // Initial solution t := 0; // Numerical step while not Termination... | Parallel metaheuristic | 0.81003 |
21,706 | Thus, metaheuristics usually allow to meet the resolution delays imposed in the industrial field as well as they allow to study general problem classes instead that particular problem instances. In general, many of the best performing techniques in precision and effort to solve complex and real-world problems are metah... | Parallel metaheuristic | 0.81003 |
21,707 | In practice, optimization (and searching, and learning) problems are often NP-hard, complex, and time-consuming. Two major approaches are traditionally used to tackle these problems: exact methods and metaheuristics. Exact methods allow to find exact solutions but are often impractical as they are extremely time-consum... | Parallel metaheuristic | 0.81003 |
21,708 | Although written at a graduate level, the main prerequisites for reading the book are linear algebra and general topology, both at an undergraduate level.In a review of the first edition of the book, Werner Fenchel calls it "a remarkable achievement", "a wealth of material", "well organized and presented in a lucid sty... | Convex Polytopes | 0.81003 |
21,709 | Chapter 18 studies arrangements of hyperplanes and their dual relation to the combinatorial structure of zonotopes. A concluding chapter, chapter 19, also includes material on the symmetries of polytopes.Exercises throughout the book make it usable as a textbook, and provide additional links to recent research, and the... | Convex Polytopes | 0.81003 |
21,710 | It also touches on the multisets of face sizes that can be realized as polyhedra (Eberhard's theorem) and on the combinatorial types of polyhedra that can have inscribed spheres or circumscribed spheres.Chapter 14 concerns relations analogous to the Dehn–Sommerville equations for sums of angles of polytopes, and uses s... | Convex Polytopes | 0.81003 |
21,711 | Chapter 12 studies the question of when a skeleton uniquely determines the higher-dimensional combinatorial structure of its polytope. Chapter 13 provides a complete answer to this theorem for three-dimensional convex polytopes via Steinitz's theorem, which characterizes the graphs of convex polyhedra combinatorially a... | Convex Polytopes | 0.81003 |
21,712 | The book has 19 chapters. After two chapters introducing background material in linear algebra, topology, and convex geometry, two more chapters provide basic definitions of polyhedra, in their two dual versions (intersections of half-spaces and convex hulls of finite point sets), introduce Schlegel diagrams, and provi... | Convex Polytopes | 0.81003 |
21,713 | In 1997, a physics student demonstrating the Leidenfrost effect by holding liquid nitrogen in his mouth accidentally swallowed the substance, resulting in near-fatal injuries. This was apparently the first case in medical literature of liquid nitrogen ingestion. | Liquid nitrogen | 0.81003 |
21,714 | Liquid nitrogen is a compact and readily transported source of dry nitrogen gas, as it does not require pressurization. Further, its ability to maintain temperatures far below the freezing point of water makes it extremely useful in a wide range of applications, primarily as an open-cycle refrigerant, including: in cry... | Liquid nitrogen | 0.81003 |
21,715 | Furthermore, morphisms that preserve all joins are equivalently characterized as the lower adjoint part of a unique Galois connection. For any pair of preorders P and Q, these are given by pairs of monotone functions f and g such that f ( x ) ≤ y ⟺ x ≤ g ( y ) {\displaystyle f(x)\leq y\iff x\leq g(y)} where f is called... | Complete lattices | 0.810026 |
21,716 | The lattice of all transitive relations on a set. The lattice of all sub-multisets of a multiset. The lattice of all equivalence relations on a set; the equivalence relation ~ is considered to be smaller (or "finer") than ≈ if x~y always implies x≈y. The lattice of self-adjoint projections (also known as orthogonal pro... | Complete lattices | 0.810026 |
21,717 | The infimum is given by the intersection of convex sets and the supremum by the convex hull of the union. The topologies on a set, ordered by inclusion. The infimum is given by the intersection of topologies, and the supremum by the topology generated by the union of topologies. | Complete lattices | 0.810026 |
21,718 | Indeed, a totally ordered set (with its order topology) is compact as a topological space if it is complete as a lattice. The non-negative integers, ordered by divisibility. The least element of this lattice is the number 1, since it divides any other number. | Complete lattices | 0.810026 |
21,719 | Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra. Complete lattices must not be confused with complete partial orders (cpos), which constitute a strictly more general class of partially or... | Complete lattices | 0.810026 |
21,720 | In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear alg... | Linear combination | 0.810021 |
21,721 | An important application of linear combinations is to wave functions in quantum mechanics. | Linear combination | 0.810021 |
21,722 | ISBN 978-0-321-98238-4. Strang, Gilbert (2016). Introduction to Linear Algebra (5th ed.). Wellesley Cambridge Press. ISBN 978-0-9802327-7-6. | Linear combination | 0.810021 |
21,723 | (2016). Linear Algebra and its Applications (5th ed.). Pearson. | Linear combination | 0.810021 |
21,724 | Katznelson, Yitzhak; Katznelson, Yonatan R. (2008). A (Terse) Introduction to Linear Algebra. | Linear combination | 0.810021 |
21,725 | Axler, Sheldon Jay (2015). Linear Algebra Done Right (3rd ed.). Springer. ISBN 978-3-319-11079-0. | Linear combination | 0.810021 |
21,726 | (E)-Stilbene, commonly known as trans-stilbene, is an organic compound represented by the condensed structural formula C6H5CH=CHC6H5. Classified as a diarylethene, it features a central ethylene moiety with one phenyl group substituent on each end of the carbon–carbon double bond. It has an (E) stereochemistry, meaning... | (E)-Stilbene | 0.810021 |
21,727 | The Journal of Statistical Mechanics: Theory and Experiment is a peer-reviewed scientific journal published by the International School for Advanced Studies and IOP Publishing. The journal is targeted to scientists interested in different aspects of statistical physics. The editor-in-chief is Marc Mézard (CNRS, Univers... | Journal of Statistical Mechanics: Theory and Experiment | 0.810021 |
21,728 | The MPA is one of several Max Planck Institutes that specialize in astronomy and astrophysics. Others are the Max Planck Institute for Extraterrestrial Physics in Garching (located next-door to the MPA), the Max Planck Institute for Astronomy in Heidelberg, the Max Planck Institute for Radio Astronomy in Bonn, the Max ... | Max Planck Institute for Astrophysics | 0.810018 |
21,729 | Focusing on theoretical investigations, the MPA covers a wide range of topics in astrophysics. These include: Cosmology, in particular galaxy formation and evolution, reionization, and the cosmic microwave background; High-energy astronomy and astrophysics, including supermassive black holes, galaxy clusters, active ga... | Max Planck Institute for Astrophysics | 0.810018 |
21,730 | The Max Planck Society was founded on 26 February 1948. It effectively replaced the Kaiser Wilhelm Society for the Advancement of Science, which was dissolved after World War II. The society is named after Max Planck, one of the founders of quantum theory. The MPA was founded as the Max Planck Institute for Physics and... | Max Planck Institute for Astrophysics | 0.810018 |
21,731 | The Max Planck Institute for Astrophysics (MPA) is a research institute located in Garching, just north of Munich, Bavaria, Germany. It is one of many scientific research institutes belonging to the Max Planck Society. The MPA is widely considered to be one of the leading institutions in the world for theoretical astro... | Max Planck Institute for Astrophysics | 0.810018 |
21,732 | The International Max Planck Research School (IMPRS) for Astrophysics is a graduate program offering a PhD in astrophysics. The school is a cooperation with the Ludwig Maximilian University of Munich and Technical University Munich. | Max Planck Institute for Astrophysics | 0.810018 |
21,733 | For a route to become a feasible successor, its RD must be smaller than the FD of the successor. If this feasibility condition is met, there is no way that adding this route to the routing table could cause a loop. If all the successor routes to a destination fail, the feasible successor becomes the successor and is im... | Diffusing Update Algorithm | 0.810017 |
21,734 | The primary path is usually the path with the lowest metric to reach the destination, and the redundant path is the path with the second lowest cost (if it meets the feasibility condition). There may be multiple successors and multiple feasible successors. Both successors and feasible successors are maintained in the t... | Diffusing Update Algorithm | 0.810017 |
21,735 | "Passive" routes are stable and can be used for data transmission. "Active" routes are being recalculated, and/or not available.Routing table contains the best route(s) to a destination (in terms of the lowest "metric"). These routes are the successors from the topology table.DUAL evaluates the data received from other... | Diffusing Update Algorithm | 0.810017 |
21,736 | This information is received from neighboring routers contained in the Neighbor table. The primary (successor) and secondary (feasible successor) routes to a destination will be determined with the information in the topology table. Among other things, each entry in the topology table contains the following:"FD (Feasib... | Diffusing Update Algorithm | 0.810017 |
21,737 | The full name of the algorithm is DUAL finite-state machine (DUAL FSM). EIGRP is responsible for the routing within an autonomous system, and DUAL responds to changes in the routing topology and dynamically adjusts the routing tables of the router automatically. EIGRP uses a feasibility condition to ensure that only lo... | Diffusing Update Algorithm | 0.810017 |
21,738 | This is achieved through "Hello" packets. If a "Hello" packet is not received from a neighbor for a specified time period, the router is assumed down and removed from the neighbor table. Topology table contains the metric (cost information) of all routes to any destination within the autonomous system. | Diffusing Update Algorithm | 0.810017 |
21,739 | In physics, a homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition: L X g a b = 2 c g a b {\displaystyle {\mathcal {L}}_{X}g_{ab}=2cg_{ab}} where c is a real constant. Homothetic vector fields find application in the study of singularities i... | Homothetic vector field | 0.810016 |
21,740 | A comparator system, or simply comparator, in the fields of biophysics, biology, and neurology is a particular organisation of neurons. Comparators, as their name suggests, compare several inputs of internal or external information, and are important to the field of neural learning. In biological systems, comparators h... | Comparator system | 0.810015 |
21,741 | In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x2 + y2 + 10z2 with integral values for x, y and z. Srinivasa Ramanujan considered this expression in a footnote in a paper published in 1916 and briefly discussed the representability of integers in this form. Aft... | Ramanujan's ternary quadratic form | 0.810013 |
21,742 | As of 2006, the academy consisted of 90 members. The academy organizes the International Congress of Quantum Chemistry every three years. The academy awards a medal to a young member of the scientific community who has distinguished themselves by a pioneering and important contribution. The award has been made every ye... | International Academy of Quantum Molecular Science | 0.810013 |
21,743 | This was later raised to 30, and then to 35. There is no limit on the number of members over 65 years of age. The members are "chosen among the scientists of all countries who have distinguished themselves by the value of their scientific work, their role of pioneer or leader of a school in the broad field of quantum c... | International Academy of Quantum Molecular Science | 0.810013 |
21,744 | The International Academy of Quantum Molecular Science (IAQMS) is an international scientific learned society covering all applications of quantum theory to chemistry and chemical physics. It was created in Menton in 1967. The founding members were Raymond Daudel, Per-Olov Löwdin, Robert G. Parr, John Pople and Bernard... | International Academy of Quantum Molecular Science | 0.810013 |
21,745 | This holds in particular for ions on lattice sites of polar symmetry, which are the crystallographic point groups C1, C1h, Cn or Cnv, n = 2, 3, 4 or 6. A thorough analysis of the bonding geometry was recently carried out for pyrite-type compounds, where monovalent chalcogen ions reside on C3 lattice sites. It was found... | Ionic radii | 0.810012 |
21,746 | Arthur Brown and Wesley L. Harris (January 2018). "A Vehicle Design and Optimization Model for On-Demand Aviation" (PDF). Massachusetts Institute of Technology. | Personal Air Vehicle | 0.81001 |
21,747 | This makes it easy for the automatizer to learn appropriate, rarely changing memories across long intervals. In turn, this helps the automatizer to make many of its once unpredictable inputs predictable, such that the chunker can focus on the remaining unpredictable events.A generative model partially overcame the vani... | Recurrent neural network | 0.810008 |
21,748 | Gated recurrent units (GRUs) are a gating mechanism in recurrent neural networks introduced in 2014. They are used in the full form and several simplified variants. Their performance on polyphonic music modeling and speech signal modeling was found to be similar to that of long short-term memory. They have fewer parame... | Recurrent neural network | 0.810008 |
21,749 | Microsoft Cognitive Toolkit MXNet: an open-source deep learning framework used to train and deploy deep neural networks. PyTorch: Tensors and Dynamic neural networks in Python with GPU acceleration. TensorFlow: Apache 2.0-licensed Theano-like library with support for CPU, GPU and Google's proprietary TPU, mobile Theano... | Recurrent neural network | 0.810008 |
21,750 | Deeplearning4j: Deep learning in Java and Scala on multi-GPU-enabled Spark. Flux: includes interfaces for RNNs, including GRUs and LSTMs, written in Julia. Keras: High-level API, providing a wrapper to many other deep learning libraries. | Recurrent neural network | 0.810008 |
21,751 | A special case of recursive neural networks is the RNN whose structure corresponds to a linear chain. Recursive neural networks have been applied to natural language processing. The Recursive Neural Tensor Network uses a tensor-based composition function for all nodes in the tree. | Recurrent neural network | 0.810008 |
21,752 | A recursive neural network is created by applying the same set of weights recursively over a differentiable graph-like structure by traversing the structure in topological order. Such networks are typically also trained by the reverse mode of automatic differentiation. They can process distributed representations of st... | Recurrent neural network | 0.810008 |
21,753 | Additional stored states and the storage under direct control by the network can be added to both infinite-impulse and finite-impulse networks. The storage can also be replaced by another network or graph if that incorporates time delays or has feedback loops. Such controlled states are referred to as gated state or ga... | Recurrent neural network | 0.810008 |
21,754 | The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic gra... | Recurrent neural network | 0.810008 |
21,755 | A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some ... | Recurrent neural network | 0.810008 |
21,756 | A multiple timescales recurrent neural network (MTRNN) is a neural-based computational model that can simulate the functional hierarchy of the brain through self-organization that depends on spatial connection between neurons and on distinct types of neuron activities, each with distinct time properties. With such vari... | Recurrent neural network | 0.810008 |
21,757 | Neural Turing machines (NTMs) are a method of extending recurrent neural networks by coupling them to external memory resources which they can interact with by attentional processes. The combined system is analogous to a Turing machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be effi... | Recurrent neural network | 0.810008 |
21,758 | Long short-term memory (LSTM) networks were invented by Hochreiter and Schmidhuber in 1997 and set accuracy records in multiple applications domains.Around 2007, LSTM started to revolutionize speech recognition, outperforming traditional models in certain speech applications. In 2009, a Connectionist Temporal Classific... | Recurrent neural network | 0.810008 |
21,759 | Long short-term memory (LSTM) is a deep learning system that avoids the vanishing gradient problem. LSTM is normally augmented by recurrent gates called "forget gates". LSTM prevents backpropagated errors from vanishing or exploding. | Recurrent neural network | 0.810008 |
21,760 | The Moon has been suggested as a testbed for new technology to protect sites in the Solar System, and astronauts, from forward and back contamination. Currently, the Moon has no contamination restrictions because it is considered to be "not of interest" for prebiotic chemistry and origins of life. Analysis of the conta... | Forward contamination | 0.810006 |
21,761 | SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionles... | Derived SI unit | 0.810006 |
21,762 | The family of all normal distributions can be thought of as a 2-dimensional parametric space parametrized by the expected value μ and the variance σ2 ≥ 0. Equipped with the Riemannian metric given by the Fisher information matrix, it is a statistical manifold with a geometry modeled on hyperbolic space. A way of pictur... | Statistical manifold | 0.810004 |
21,763 | Let X be an orientable manifold, and let ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} be a measure on X. Equivalently, let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space on Ω = X {\displaystyle \Omega =X} , with sigma algebra F = Σ {\displaystyle {\mathcal {F}}=\Sigma } and probabilit... | Statistical manifold | 0.810004 |
21,764 | In mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a metric on these manifolds. Following this definition, the log-likelihood function i... | Statistical manifold | 0.810004 |
21,765 | {\displaystyle \{p_{x},p_{y}\}_{DB}=-{\frac {qB}{4c}}.} Therefore, the correct implementation of canonical quantization dictates the commutation relations, = − i ℏ c q B {\displaystyle =-i{\frac {\hbar c}{qB}}} = = i ℏ 2 {\displaystyle ==i{\frac {\hbar }{2}}} with the cross terms vanishing, and = − i ℏ q B 4 c . {\... | Dirac bracket | 0.810004 |
21,766 | Xeno nucleic acids (XNA) are synthetic nucleic acid analogues that have a different sugar backbone than the natural nucleic acids DNA and RNA. As of 2011, at least six types of synthetic sugars have been shown to form nucleic acid backbones that can store and retrieve genetic information. Research is now being done to ... | Xeno Nucleic Acid | 0.809999 |
21,767 | XNA exhibits a variety of structural chemical changes relative to its natural counterparts. Types of synthetic XNA created so far include: 1,5-anhydrohexitol nucleic acid (HNA) Cyclohexene nucleic acid (CeNA) Threose nucleic acid (TNA) Glycol nucleic acid (GNA) Locked nucleic acid (Locked nucleic acid) Peptide nucleic ... | Xeno Nucleic Acid | 0.809999 |
21,768 | Shannon was born in Petoskey, Michigan in 1916 and grew up in Gaylord, Michigan. He is well known for founding digital circuit design theory in 1937, when—as a 21-year-old master's degree student at MIT—he wrote his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numeric... | A Mind at Play | 0.809996 |
21,769 | To any group ring or Hopf algebra is associated its representation ring or "Green ring". The representation ring's additive group is the free abelian group whose basis are the indecomposable modules and whose addition corresponds to the direct sum. Expressing a module in terms of the basis is finding an indecomposable ... | Ring (mathematics) | 0.809993 |
21,770 | The set of natural numbers N {\displaystyle \mathbb {N} } with the usual operations is not a ring, since ( N , + ) {\displaystyle (\mathbb {N} ,+)} is not even a group (not all the elements are invertible with respect to addition – for instance, there is no natural number which can be added to 3 to get 0 as a result). ... | Ring (mathematics) | 0.809993 |
21,771 | A nilpotent element in a nonzero ring is necessarily a zero divisor. An idempotent e {\displaystyle e} is an element such that e2 = e. One example of an idempotent element is a projection in linear algebra. | Ring (mathematics) | 0.809993 |
21,772 | However, in the current state of particle physics, the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. For example, at low temperatures, fermions show superfluidity for uncharged particles and superconductivity for charged particle... | Half-integer spin | 0.809993 |
21,773 | In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin-statistics relation is, in fact, a spin statistics-quantum number relation.As a consequence of the Pauli exclusion principle, only ... | Half-integer spin | 0.809993 |
21,774 | Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons. In contrast, particles with half-integer spin are fermions. | Half-integer spin | 0.809993 |
21,775 | In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these, such ... | Half-integer spin | 0.809993 |
21,776 | Expressed using notation used in geometric algebra, the unnormalized results of the Gram–Schmidt process can be expressed as which is equivalent to the expression using the proj {\displaystyle \operatorname {proj} } operator defined above. The results can equivalently be expressed as which is closely related to the exp... | Gram-Schmidt theorem | 0.809992 |
21,777 | In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product. The Gram–Schmidt process takes a finite, line... | Gram-Schmidt theorem | 0.809992 |
21,778 | Laser diffraction analysis is based on the observation that the angle of the light diffracted by a particle is inversely proportional to its size. Strictly speaking, the laser diffraction equivalent diameter is the diameter of a sphere yielding, on the same detector geometry, the same diffraction pattern as the particl... | Equivalent spherical diameter | 0.809991 |
21,779 | NWChem is an ab initio computational chemistry software package which includes quantum chemical and molecular dynamics functionality. It was designed to run on high-performance parallel supercomputers as well as conventional workstation clusters. It aims to be scalable both in its ability to treat large problems effici... | NWChem | 0.809986 |
21,780 | Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for ... | Gradient descent | 0.809978 |
21,781 | In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, b... | Gradient descent | 0.809978 |
21,782 | In organic chemistry, a tricarbonate is a compound containing the divalent −O−C(=O)−O−C(=O)−O−C(=O)−O− functional group, which consists of three carbonate groups linked in a chain by sharing of oxygen oxygen atoms. These compounds can be viewed as derivatives of a hypothetical tricarbonic acid, HO−C(=O)−O−C(=O)−O−C(=O)... | Tricarbonate | 0.809976 |
21,783 | Subsequently, several advancements both in DGS type, geometry, and cross-polar performance have been achieved. Yet another idea of patch-DGS integration has advanced the microstrip antenna array design. The issue of mutual coupling among the array elements can be reduced by integrating simple DGS- first reported in 200... | Defected ground structure | 0.809974 |
21,784 | In organic chemistry, a Schiff base (named after Hugo Schiff) is a compound with the general structure R1R2C=NR3 (R3 = alkyl or aryl, but not hydrogen). They can be considered a sub-class of imines, being either secondary ketimines or secondary aldimines depending on their structure. Anil refers to a common subset of S... | Schiff bases | 0.809973 |
21,785 | In the influential textbooks of Grünbaum and Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoid the endless repetition of the word "convex", and that the discussion should throughout be under... | Convex polyhedron | 0.809973 |
21,786 | Affine space Affine geometry Affine hull | Affine combination | 0.80997 |
21,787 | This concept is fundamental in Euclidean geometry and affine geometry, because the set of all affine combinations of a set of points forms the smallest subspace containing the points, exactly as the linear combinations of a set of vectors form their linear span. The affine combinations commute with any affine transform... | Affine combination | 0.80997 |
21,788 | SOAP is a multi-pass assembler, that is, it processes the source program more than once in order to generate the object program. The first version of SOAP was succeeded by SOAP II in 1957, which supported additional hardware features such as index registers and magnetic core memory, SOAP IIA in 1958, SOAP 2L, SOAP 2L T... | Symbolic Optimal Assembly Program | 0.809963 |
21,789 | Each instruction contains the address of the next instruction to execute; instead of a sequential array of instructions the memory appears to be a linked list. SOAP optimizes by placing instructions to be executed sequentially in locations around the drum such that the next instruction is available as soon as possible ... | Symbolic Optimal Assembly Program | 0.809963 |
21,790 | In computational chemistry a chicken wire model or chicken wire surface plot is a way to visualize molecular models by drawing the polygon mesh of their surface (defined e.g. as the van der Waals radius or a certain electron density). == References == | Chicken wire (chemistry) | 0.809957 |
21,791 | In chemistry the term chicken wire is used in different contexts. Most of them relate to the similarity of the regular hexagonal (honeycomb-like) patterns found in certain chemical compounds to the mesh structure commonly seen in real chicken wire. | Chicken wire (chemistry) | 0.809957 |
21,792 | It is an old joke in chemistry to draw a polycyclic hexagonal chemical structure and call this fictional compound chickenwire. By adding one or two simple chemical groups to this skeleton, the compound can then be named following the official chemical naming convention. Examples are: 1,2-Dimethyl-chickenwire in a carto... | Chicken wire (chemistry) | 0.809957 |
21,793 | More generally, if an algebraic object represents a geometric object, but is expressed in terms of a particular basis, then it is necessary to, when the basis is changed, also change the representation. Physicists will often call this representation of a geometric object a tensor if it transforms under a sequence of li... | Relative tensor | 0.809957 |
21,794 | In physics and related fields, it is often useful to work with the components of an algebraic object rather than the object itself. An example would be decomposing a vector into a sum of basis vectors weighted by some coefficients such as where v → {\displaystyle {\vec {v}}} is a vector in 3-dimensional Euclidean space... | Relative tensor | 0.809957 |
21,795 | Ultimately however, Aristotle's aim was to perfect a theory of forms, rather than to reject it. Although Aristotle strongly rejected the independent existence Plato attributed to forms, his metaphysics do agree with Plato's a priori considerations quite often. For example, Aristotle argues that changeless, eternal subs... | Predicate dualism | 0.809956 |
21,796 | Bodies were seen as biological organisms to be studied in their constituent parts (materialism) by means of anatomy, physiology, biochemistry and physics (reductionism). The mind-body dualism remained the biomedical paradigm and model for the following three centuries.Substance dualism is a philosophical position compa... | Predicate dualism | 0.809956 |
21,797 | When present in large numbers, giant kelp forms kelp forests that are home to many marine species that depend upon the kelp directly for food and shelter, or indirectly as a hunting ground for prey. Both the large size of the kelp and the large number of individuals significantly alter the availability of light, the fl... | Macrocystis pyrifera | 0.809955 |
21,798 | Cancer immunology has been given so much importance that the data related to it is growing rapidly. Protein–protein interaction networks provide valuable information on tumorigenesis in humans. Cancer proteins exhibit a network topology that is different from normal proteins in the human interactome. | Computational immunology | 0.809954 |
21,799 | Artificial neural network (ANN), a computer model was used to study peptide binding to human TAP and its relationship with MHC class I binding. The affinity of HLA-binding peptides for TAP was found to differ according to the HLA supertype concerned using this method. This research could have important implications for... | Computational immunology | 0.809954 |
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