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31,400 | Since Cram is an impartial game, the Sprague–Grundy theorem indicates that in the normal version any Cram position is equivalent to a nim-heap of a given size, also called the Grundy value. Some values can be found in Winning Ways for your Mathematical Plays, in particular the 2 × n board, whose value is 0 if n is even... | Cram (game) | 0.80445 |
31,401 | : 196, 202 Neural networks, by contrast, are considered to be better suited to generate decisions in uncertain domains, since they can be taught to weigh the factors considered by judicial decision makers from case data. Yet, they do not provide an explanation for the conclusions they reach. Split_up, with a view to ov... | Split Up (expert system) | 0.804449 |
31,402 | Split Up is an intelligent decision support system, which makes predictions about the distribution of marital property following divorce in Australia. It is designed to assist judges, registrars of the Family Court of Australia, mediators and lawyers. Split Up operates as a hybrid system, combining rule – based reasoni... | Split Up (expert system) | 0.804449 |
31,403 | The backing of an argument supports the validity of the warrant. In the legal domain, this is typically a reference to a statute or a precedent. Here, a neural network (or rules), produce a conclusion from the data of an argument and the data, warrant and backing are reproduced to generate an explanation. | Split Up (expert system) | 0.804449 |
31,404 | The court may further look at each party's financial resources and future needs under section 75(2)of the Family Law Act 1975. These needs can include factors such as the inability to gain employment, the continued care of a child under 18 years of age or medical expenses. This means that different judges may and will ... | Split Up (expert system) | 0.804449 |
31,405 | It is trained by repeatedly exposing it to examples of the problem and learning the significance (weights) of the input nodes. : 196 The neural network used by Split_up is said to generalise well if the output of the network is correct (or nearly correct) for examples not seen during training, which classifies it as an... | Split Up (expert system) | 0.804449 |
31,406 | Hence the inputs to the neural network are contributions, future needs and wealth, and the output the percentage split predicted. On each arc there is a statistical weight. Using back propagation the neural network learns the necessary pattern to recognize the prediction. | Split Up (expert system) | 0.804449 |
31,407 | The output signal of a processing element depends on the input to the processing element, i.e. each input is gated by a weighting factor that determines the amount of influence that the input will have on the output. The strength of the weighting factors is adjusted autonomously by the processing element as the data is... | Split Up (expert system) | 0.804449 |
31,408 | Twenty one solid arcs represent inferences performed with the use of rule sets. For example, the level of wealth of a marriage is determined by a rule, which uses the common pool value. By contrast, the fourteen dashed arcs establish inferences performed with the use of neural networks. | Split Up (expert system) | 0.804449 |
31,409 | In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices. | Random recursive tree | 0.804448 |
31,410 | The dream of a complex, deterministic molecular nanotechnology remains elusive. Since the mid-1990s, thousands of surface scientists and thin film technocrats have latched on to the nanotechnology bandwagon and redefined their disciplines as nanotechnology. This has caused much confusion in the field and has spawned th... | Molecular Nanotechnology | 0.804446 |
31,411 | A breakthrough in MNT is needed which proceeds from the simple atomic ensembles which can be built with, e.g., an STM to complex MNT systems via a process of design evolution. A handicap in this process is the difficulty of seeing and manipulation at the nanoscale compared to the macroscale which makes deterministic se... | Molecular Nanotechnology | 0.804446 |
31,412 | Molecular nanotechnology (MNT) is a technology based on the ability to build structures to complex, atomic specifications by means of mechanosynthesis. This is distinct from nanoscale materials. Based on Richard Feynman's vision of miniature factories using nanomachines to build complex products (including additional n... | Molecular Nanotechnology | 0.804446 |
31,413 | Similar ideas are advocated in the Foresight Guidelines on Molecular Nanotechnology, and a map of the 137-dimensional replicator design space recently published by Freitas and Merkle provides numerous proposed methods by which replicators could, in principle, be safely controlled by good design. However, the concept of... | Molecular Nanotechnology | 0.804446 |
31,414 | Molecularassembler.com. Retrieved 2010-09-05. by Robert Freitas and Ralph Merkle. Nanotechnology: Molecular Speculations on Global Abundance Edited by BC Crandall (ISBN 0-262-53137-2) offers interesting ideas for MNT applications. | Molecular Nanotechnology | 0.804446 |
31,415 | Unbounding the Future: the Nanotechnology Revolution and . Unbounding the Future is an easy-to-read book that introduces the ideas of molecular nanotechnology in a not-too-technical way. Other notable works in the same vein are Nanomedicine Vol. | Molecular Nanotechnology | 0.804446 |
31,416 | The primary technical reference work on this topic is Nanosystems: Molecular Machinery, Manufacturing, and Computation, an in-depth, physics-based analysis of a particular class of potential nanomachines and molecular manufacturing systems, with extensive analyses of their feasibility and performance. Nanosystems is cl... | Molecular Nanotechnology | 0.804446 |
31,417 | In the novel "Prey" by Michael Crichton, self replicating nanobots create autonomous nano-swarms with predatory behaviors. The protagonist must stop the swarm before it evolves into a grey goo plague. In the films Avengers Infinity War and Avengers Endgame Tony Stark's Iron Man suit was constructed using nanotechnology... | Molecular Nanotechnology | 0.804446 |
31,418 | (They are similar to the creatures in Star Trek: The Next Generation episode "Evolution", which featured "nanites" taking over the Enterprise.) The Nanites made their first appearance in season 8. Based on the concept of nanotechnology, their comical deus ex machina activities included such diverse tasks as instant rep... | Molecular Nanotechnology | 0.804446 |
31,419 | In The Diamond Age by Neal Stephenson, diamond can be built directly out of carbon atoms. All sorts of devices from dust-size detection devices to giant diamond zeppelins are constructed atom by atom using only carbon, oxygen, nitrogen and chlorine atoms. In the novel Tomorrow by Andrew Saltzman (ISBN 1-4243-1027-X), a... | Molecular Nanotechnology | 0.804446 |
31,420 | In 2006, U.S. National Academy of Sciences released the report of a study of molecular manufacturing as part of a longer report, A Matter of Size: Triennial Review of the National Nanotechnology Initiative The study committee reviewed the technical content of Nanosystems, and in its conclusion states that no current th... | Molecular Nanotechnology | 0.804446 |
31,421 | In 2004 Richard Jones wrote Soft Machines (nanotechnology and life), a book for lay audiences published by Oxford University. In this book he describes radical nanotechnology (as advocated by Drexler) as a deterministic/mechanistic idea of nano engineered machines that does not take into account the nanoscale challenge... | Molecular Nanotechnology | 0.804446 |
31,422 | Another proposed application of molecular nanotechnology is "utility fog" — in which a cloud of networked microscopic robots (simpler than assemblers) would change its shape and properties to form macroscopic objects and tools in accordance with software commands. Rather than modify the current practices of consuming m... | Molecular Nanotechnology | 0.804446 |
31,423 | They challenged the relevance of Smalley's arguments to the more specific proposals advanced in Nanosystems. Also, Smalley argued that nearly all of modern chemistry involves reactions that take place in a solvent (usually water), because the small molecules of a solvent contribute many things, such as lowering binding... | Molecular Nanotechnology | 0.804446 |
31,424 | Several researchers, including Nobel Prize winner Dr. Richard Smalley (1943–2005), attacked the notion of universal assemblers, leading to a rebuttal from Drexler and colleagues, and eventually to an exchange of letters. Smalley argued that chemistry is extremely complicated, reactions are hard to control, and that a u... | Molecular Nanotechnology | 0.804446 |
31,425 | The objective is a pervasive change in manufacturing, a change that will leave virtually no product untouched. Economic progress and military readiness in the 21st Century will depend fundamentally on maintaining a competitive position in nanotechnology. Despite the current early developmental status of nanotechnology ... | Molecular Nanotechnology | 0.804446 |
31,426 | Molecular surgical tools, guided by molecular computers and injected into the blood stream could find and destroy cancer cells or invading bacteria, unclog arteries, or provide oxygen when the circulation is impaired. Nanotechnology will replace our entire manufacturing base with a new, radically more precise, radicall... | Molecular Nanotechnology | 0.804446 |
31,427 | Nanotechnology (or molecular nanotechnology to refer more specifically to the goals discussed here) will let us continue the historical trends in manufacturing right up to the fundamental limits imposed by physical law. It will let us make remarkably powerful molecular computers. It will let us make materials over fift... | Molecular Nanotechnology | 0.804446 |
31,428 | According to Chris Phoenix a "So-called grey goo could only be the product of a deliberate and difficult engineering process, not an accident". With the advent of nano-biotech, a different scenario called green goo has been forwarded. Here, the malignant substance is not nanobots but rather self-replicating biological ... | Molecular Nanotechnology | 0.804446 |
31,429 | International institutions dedicated specifically to nanotechnology (perhaps analogously to the International Atomic Energy Agency IAEA) or general arms control may also be designed. One may also jointly make differential technological progress on defensive technologies, a policy that players should usually favour. The... | Molecular Nanotechnology | 0.804446 |
31,430 | Additionally, molecular manufacturing could be used to cheaply produce highly advanced, durable weapons, which is an area of special concern regarding the impact of nanotechnology. Being equipped with compact computers and motors these could be increasingly autonomous and have a large range of capabilities.According to... | Molecular Nanotechnology | 0.804446 |
31,431 | Molecular manufacturing is a potential future subfield of nanotechnology that would make it possible to build complex structures at atomic precision. Molecular manufacturing requires significant advances in nanotechnology, but once achieved could produce highly advanced products at low costs and in large quantities in ... | Molecular Nanotechnology | 0.804446 |
31,432 | A radiant barrier reduces the radiant heat transfer from the underside of the roof to the other surfaces in the attic. Some studies show that radiant barriers can reduce cooling costs 5% to 10% when used in a warm, sunny climate. The reduced heat gain may even allow for a smaller air conditioning system. In cool climat... | Radiant barrier | 0.804443 |
31,433 | MFA is complementary to the other core industrial ecology methods life cycle assessment (LCA) and input-output (I/O) models. Some overlaps between the different methods exist as they all share the system approach and to some extent the mass balance principle. The methods mainly differ in purpose, scope, and data requir... | Substance flow analysis | 0.804442 |
31,434 | MFA is an important tool to study the circular economy and to devise material flow management. Since the 1990s, the number of publications related to material flow analysis has grown steadily. Peer-reviewed journals that publish MFA-related work include the Journal of Industrial Ecology, Ecological Economics, Environme... | Substance flow analysis | 0.804442 |
31,435 | Material flow analysis (MFA), also referred to as substance flow analysis (SFA), is an analytical method to quantify flows and stocks of materials or substances in a well-defined system. MFA is an important tool to study the bio-physical aspects of human activity on different spatial and temporal scales. It is consider... | Substance flow analysis | 0.804442 |
31,436 | In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped-geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-d... | Warp factor | 0.804441 |
31,437 | A key theorem in this area states that any convex body in E n {\displaystyle E^{n}} can be determined by parallel, coplanar X-rays in a set of four directions whose slopes have a transcendental cross ratio. | Geometric tomography | 0.804437 |
31,438 | The examples forming a Boolean algebra have special properties treated in the article on residuated Boolean algebras. In natural language residuated lattices formalize the logic of "and" when used with its noncommutative meaning of "and then." Setting x = bet, y = win, z = rich, we can read x•y ≤ z as "bet and then win... | Residuated lattice | 0.804435 |
31,439 | When X is empty the algebra is the degenerate Boolean algebra in which 0 = 1 = I. The residuated lattice of all languages on Σ is commutative just when Σ has at most one letter. It is finite just when Σ is empty, consisting of the two languages 0 (the empty language {}) and the monoid unit I = {ε} = 1. | Residuated lattice | 0.804435 |
31,440 | Had we chosen ≤ and ≥ instead of < and >, ≥\≤ and ≤/≥ would have been the same because ≤•≥ = ≥•≤, both of which always hold between all x and y (since x≤1≥y and x≥0≤y). The Boolean algebra 2Σ* of all formal languages over an alphabet (set) Σ forms a residuated lattice whose monoid multiplication is language concatenati... | Residuated lattice | 0.804435 |
31,441 | A more general class of examples is given by the Boolean algebra of all binary relations on a set X, namely the power set of X2, made a residuated lattice by taking the monoid multiplication • to be composition of relations and the monoid unit to be the identity relation I on X consisting of all pairs (x,x) for x in X.... | Residuated lattice | 0.804435 |
31,442 | One difference in usage is that B need not be an ideal of R: it may just be a subset. Boolean algebras and Heyting algebras are commutative residuated lattices in which x•y = x∧y (whence the unit I is the top element 1 of the algebra) and both residuals x\y and y/x are the same operation, namely implication x → y. The ... | Residuated lattice | 0.804435 |
31,443 | One of the original motivations for the study of residuated lattices was the lattice of (two-sided) ideals of a ring. Given a ring R, the ideals of R, denoted Id(R), forms a complete lattice with set intersection acting as the meet operation and "ideal addition" acting as the join operation. The monoid operation • is g... | Residuated lattice | 0.804435 |
31,444 | This necessary distributivity of • over ∨ does not in general entail distributivity of ∧ over ∨, that is, a residuated lattice need not be a distributive lattice. However distributivity of ∧ over ∨ is entailed when • and ∧ are the same operation, a special case of residuated lattices called a Heyting algebra. Alternati... | Residuated lattice | 0.804435 |
31,445 | More precisely, for a given x in L, the unary operations x• and x\ are respectively the lower and upper adjoints of a Galois connection on L, and dually for the two functions •y and /y. By the same reasoning that applies to any Galois connection, we have yet another definition of the residuals, namely, x•(x\y) ≤ y ≤ x\... | Residuated lattice | 0.804435 |
31,446 | In mathematics, a residuated lattice is an algebraic structure L = (L, ≤, •, I) such that (i) (L, ≤) is a lattice. (ii) (L, •, I) is a monoid. (iii) For all z there exists for every x a greatest y, and for every y a greatest x, such that x•y ≤ z (the residuation properties).In (iii), the "greatest y", being a function ... | Residuated lattice | 0.804435 |
31,447 | In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z and z/y, loosely analogous to division or implication, when x•y is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, ... | Residuated lattice | 0.804435 |
31,448 | The essential idea behind relational quantum mechanics, following the precedent of special relativity, is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observ... | Interpretations of quantum mechanics | 0.804434 |
31,449 | These approaches have been described as a revival of immaterialism. Interpretations where quantum mechanics is said to describe an observer's knowledge of the world, rather than the world itself. This approach has some similarity with Bohr's thinking. | Interpretations of quantum mechanics | 0.804434 |
31,450 | The point where two particles appear to "become entangled" is simply a point where each particle is being influenced by events that occur to the other particle in the future. Not all advocates of time-symmetric causality favour modifying the unitary dynamics of standard quantum mechanics. Thus a leading exponent of the... | Interpretations of quantum mechanics | 0.804434 |
31,451 | Time-symmetric interpretations of quantum mechanics were first suggested by Walter Schottky in 1921. Several theories have been proposed which modify the equations of quantum mechanics to be symmetric with respect to time reversal. (See Wheeler–Feynman time-symmetric theory.) This creates retrocausality: events in the ... | Interpretations of quantum mechanics | 0.804434 |
31,452 | The many-worlds interpretation is an interpretation of quantum mechanics in which a universal wavefunction obeys the same deterministic, reversible laws at all times; in particular there is no (indeterministic and irreversible) wavefunction collapse associated with measurement. The phenomena associated with measurement... | Interpretations of quantum mechanics | 0.804434 |
31,453 | In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place of the Laplace operator. The discrete Poisson equation is frequently used in numerical analysis as a stand-in for the continuous Poisson equation, although it is al... | Discrete Poisson equation | 0.804433 |
31,454 | This potential is then used for a second Schrödinger equation containing only the 36 coordinates of the nuclei. So, taking the most optimistic estimate for the complexity, instead of a large equation requiring at least 162 2 = 26 244 {\displaystyle 162^{2}=26\,244} hypothetical calculation steps, a series of smaller ca... | Born–Oppenheimer approximation | 0.804431 |
31,455 | An AO depends visibly on the coordinates of an electron, but the nuclear coordinates are not explicit in the MO. However, upon change of geometry, i.e., change of R {\displaystyle \mathbf {R} } , the LCAO coefficients obtain different values and we see corresponding changes in the functional form of the MO χ k {\displa... | Born–Oppenheimer approximation | 0.804431 |
31,456 | In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are... | Born–Oppenheimer approximation | 0.804431 |
31,457 | In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere. | Equidimensionality | 0.80443 |
31,458 | An affine algebraic variety whose coordinate ring is a Cohen–Macaulay ring is equidimensional. == References == | Equidimensionality | 0.80443 |
31,459 | Design of anti-terrorism systems Linguistic analysis, including grammar induction and other aspects of Natural language processing (NLP) such as word-sense disambiguation. | List of genetic algorithm applications | 0.804429 |
31,460 | Clustering, using genetic algorithms to optimize a wide range of different fit-functions. Multidimensional systems Multimodal Optimization Multiple criteria production scheduling Multiple population topologies and interchange methodologies Mutation testing Parallelization of GAs/GPs including use of hierarchical decomp... | List of genetic algorithm applications | 0.804429 |
31,461 | Bioinformatics Multiple Sequence Alignment Bioinformatics: RNA structure prediction Bioinformatics: Motif Discovery Biology and computational chemistry Building phylogenetic trees. Gene expression profiling analysis. Medicine: Clinical decision support in ophthalmology and oncology Computational Neuroscience: finding v... | List of genetic algorithm applications | 0.804429 |
31,462 | Satellite communication scheduling for the NASA Deep Space Network was shown to benefit from genetic algorithms. Learning robot behavior using genetic algorithms Image processing: Dense pixel matching Learning fuzzy rule base using genetic algorithms Molecular structure optimization (chemistry) Optimisation of data com... | List of genetic algorithm applications | 0.804429 |
31,463 | Distributed computer network topologies Electronic circuit design, known as evolvable hardware Feature selection for Machine Learning Feynman-Kac models File allocation for a distributed system Filtering and signal processing Finding hardware bugs. Game theory equilibrium resolution Genetic Algorithm for Rule Set Produ... | List of genetic algorithm applications | 0.804429 |
31,464 | Bayesian inference links to particle methods in Bayesian statistics and hidden Markov chain models Artificial creativity Chemical kinetics (gas and solid phases) Calculation of bound states and local-density approximations Code-breaking, using the GA to search large solution spaces of ciphers for the one correct decryp... | List of genetic algorithm applications | 0.804429 |
31,465 | Audio watermark insertion/detection Airlines revenue management Automated design of mechatronic systems using bond graphs and genetic programming (NSF) Automated design of industrial equipment using catalogs of exemplar lever patterns Automated design, including research on composite material design and multi-objective... | List of genetic algorithm applications | 0.804429 |
31,466 | Optimization of beam dynamics in accelerator physics. Design of particle accelerator beamlines | List of genetic algorithm applications | 0.804429 |
31,467 | Neural Networks; particularly recurrent neural networks Training artificial neural networks when pre-classified training examples are not readily obtainable (neuroevolution) | List of genetic algorithm applications | 0.804429 |
31,468 | A mini-seminar has also been taught at Swarthmore College.Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice. "Similar approaches can also be found in the teaching of ethics to computer science students, where the term "embedded ethics" has established... | Ethics in mathematics | 0.804429 |
31,469 | Priority and attribution of mathematical discovery are important to professional practice, even as some theorems bear the name of the person making the conjecture rather than finding the proof. Folk theorems, or mathematical folklore cannot be attributed to an individual, and may not have an agreed proof, despite being... | Ethics in mathematics | 0.804429 |
31,470 | Mathematicians have a professional responsibility to support the ethical use of mathematics in practice, both to sustain the reputation of the profession and to protect society from the impacts of unethical behavior. For example, mathematics is extensively applied in the use of Big Data in Artificial Intelligence appli... | Ethics in mathematics | 0.804429 |
31,471 | Ethics and mathematics both appear to rely on reasoning from intuition, unlike empirical sciences which rely fundamentally on observations and experiments. That has been suggested as a reason in support of objectivity or moral realism in ethics, since arguments against objectivity in ethics are paralleled by arguments ... | Ethics in mathematics | 0.804429 |
31,472 | Financial mathematicsReal options valuation Portfolio optimization Genetic algorithm in economics Representing rational agents in economic models such as the cobweb model the same, in Agent-based computational economics generally, and in artificial financial markets | List of genetic algorithm applications | 0.804429 |
31,473 | This theorem suggests the following mechanism: Ask each agent i {\displaystyle i} to report their valuation v i {\displaystyle v_{i}} Based on the answer and the known distribution functions F i , f i {\displaystyle F_{i},f_{i}} , compute w i {\displaystyle w_{i}} . Compute an allocation x that maximizes the virtual su... | Bayesian-optimal mechanism | 0.804426 |
31,474 | Define the virtual surplus of an allocation x {\displaystyle x} as: S ∗ ( x ) = ∑ i x i ⋅ w i ( v i ) − c ( x ) {\displaystyle S^{*}(x)=\sum _{i}x_{i}\cdot w_{i}(v_{i})-c(x)} Note that the virtual surplus is usually smaller than the actual surplus. A key theorem of Myerson says that:: 336 The expected profit of any tru... | Bayesian-optimal mechanism | 0.804426 |
31,475 | In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.Importance of the sampling frame is stressed by Jessen and Salant and Dillman. In many practical situat... | Sampling frame | 0.804425 |
31,476 | Much of the mathematics behind information theory with events of different probabilities were developed for the field of thermodynamics by Ludwig Boltzmann and J. Willard Gibbs. Connections between information-theoretic entropy and thermodynamic entropy, including the important contributions by Rolf Landauer in the 196... | Information Theory | 0.804421 |
31,477 | Another useful concept is mutual information defined on two random variables, which describes the measure of information in common between those variables, which can be used to describe their correlation. The former quantity is a property of the probability distribution of a random variable and gives a limit on the rat... | Information Theory | 0.804421 |
31,478 | Information theory is based on probability theory and statistics, where quantified information is usually described in terms of bits. Information theory often concerns itself with measures of information of the distributions associated with random variables. One of the most important measures is called entropy, which f... | Information Theory | 0.804421 |
31,479 | Another interpretation of the metric tensor, also considered by Gauss, is that it provides a way in which to compute the length of tangent vectors to the surface, as well as the angle between two tangent vectors. In contemporary terms, the metric tensor allows one to compute the dot product(non-euclidean geometry) of t... | Relativistic metric | 0.804418 |
31,480 | In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a... | Relativistic metric | 0.804418 |
31,481 | In statistics, identifiability is a property which a model must satisfy for precise inference to be possible. A model is identifiable if it is theoretically possible to learn the true values of this model's underlying parameters after obtaining an infinite number of observations from it. Mathematically, this is equival... | Identifiability condition | 0.804416 |
31,482 | These agents must follow the same receptive topology as others, which means that they do not fit between the receptive sites without bending. Mivacurium for example has a molecular length of 3.6 nm when stretched out, far from the 2 to 2.1 nm optimum. Mivacurium, atracurium, and doxacurium have greater N-N distance and... | Depolarizing blocking agent | 0.804415 |
31,483 | Spatial variability occurs when a quantity that is measured at different spatial locations exhibits values that differ across the locations. Spatial variability can be assessed using spatial descriptive statistics such as the range. Let us suppose that the Rev' z(x) is perfectly known at any point x within the field un... | Spatial variability | 0.804415 |
31,484 | Uncertainty is closely related to the amount of spatial variability, but it is also strongly dependent upon sampling.Geostatistical analyses have been strictly performed to study the spatial variability of pesticide sorption and degradation in the field. Webster and Oliver provided a description of geostatistical techn... | Spatial variability | 0.804415 |
31,485 | {{cite book}}: CS1 maint: location missing publisher (link) Webster, R (2007). Geostatistics for environmental scientists. Chichester Hoboken, NJ: Wiley. | Spatial variability | 0.804415 |
31,486 | Price, OR; Walker, A; Wood, M; Oliver, MA (2001). "Using geostatistics to evaluate spatial variation in pesticideysoil interactions". In Walker A. | Spatial variability | 0.804415 |
31,487 | Isaaks, E.H., Srivastava R.M. : Applied Geostatistics. 1989 Fortin, Marie-Josee, Dale, Mark. : Spatial Analysis A Guide for Ecologists. | Spatial variability | 0.804415 |
31,488 | Quantitative genetics is a statistical framework mainly concerned with modeling the evolution of continuous characters. Under this framework, correlation between traits could be the result of two processes: 1) natural selection acting simultaneously on several traits ensuring that they are inherited together (i.e. link... | Developmental constraint | 0.804413 |
31,489 | In evolutionary biology, developmental bias refers to the production against or towards certain ontogenetic trajectories which ultimately influence the direction and outcome of evolutionary change by affecting the rates, magnitudes, directions and limits of trait evolution. Historically, the term was synonymous with de... | Developmental constraint | 0.804413 |
31,490 | Describing and understanding the drivers of the distribution of phenotypic variation in nature is one of the main goals in evolutionary biology. One way to study the distribution of phenotypic variation is through depicting the volume of the morphospace occupied by a set of organisms or species. Theoretically, there ca... | Developmental constraint | 0.804413 |
31,491 | To solve a shape optimization problem, one needs to find a way to represent a shape in the computer memory, and follow its evolution. Several approaches are usually used. One approach is to follow the boundary of the shape. | Structural optimization | 0.804412 |
31,492 | Topology optimization is, in addition, concerned with the number of connected components/boundaries belonging to the domain. Such methods are needed since typically shape optimization methods work in a subset of allowable shapes which have fixed topological properties, such as having a fixed number of holes in them. To... | Structural optimization | 0.804412 |
31,493 | Shape optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the solution of a given partial differential equation defi... | Structural optimization | 0.804412 |
31,494 | In this method the constrained shape design problem is adapted to an unconstrained problem with utilizing the constraints in the objective function as a penalty factor. Most of the time penalty factor is dependent to the amount of constraint variation rather than constraint number. The GA real-coded technique is applie... | Structural optimization | 0.804412 |
31,495 | The multi-objective Pareto optimization (NSGA II) could be utilized as a powerful approach for shape optimization. In this regard, the Pareto optimization approach displays useful advantages in design method such as the effect of area constraint that other multi-objective optimization cannot declare it. The approach of... | Structural optimization | 0.804412 |
31,496 | Shape optimization can be faced using standard optimization methods if a parametrization of the geometry is defined. Such parametrization is very important in CAE field where goal functions are usually complex functions evaluated using numerical models (CFD, FEA,...). A convenient approach, suitable for a wide class of... | Structural optimization | 0.804412 |
31,497 | Sometimes additional constraints need to be imposed to that end to ensure well-posedness of the problem and uniqueness of the solution. Shape optimization is an infinite-dimensional optimization problem. Furthermore, the space of allowable shapes over which the optimization is performed does not admit a vector space st... | Structural optimization | 0.804412 |
31,498 | Mathematically, shape optimization can be posed as the problem of finding a bounded set Ω {\displaystyle \Omega } , minimizing a functional F ( Ω ) {\displaystyle {\mathcal {F}}(\Omega )} ,possibly subject to a constraint of the form G ( Ω ) = 0. {\displaystyle {\mathcal {G}}(\Omega )=0.} Usually we are interested in s... | Structural optimization | 0.804412 |
31,499 | Differential forms provide an approach to multivariable calculus that is independent of coordinates. | Differential form | 0.80441 |
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