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32,700 | Certain bilevel programs, notably those having a convex lower level and satisfying a regularity condition (e.g. Slater's condition), can be reformulated to single level by replacing the lower-level problem by its Karush-Kuhn-Tucker conditions. This yields a single-level mathematical program with complementarity constra... | Bilevel program | 0.80377 |
32,701 | Bilevel optimization has a number of applications in defense, like strategic offensive and defensive force structure design, strategic bomber force structure, and allocation of tactical aircraft to missions. The offensive entity in this case may be considered a leader and the defensive entity in this case may be consid... | Bilevel program | 0.80377 |
32,702 | Bilevel optimization can serve as a decision support tool for firms in real-life settings to improve workforce and human resources decisions. The first level reflects the company’s goal to maximize profitability. The second level reflects employees goal to minimize the gap between desired salary and a preferred work pl... | Bilevel program | 0.80377 |
32,703 | A general formulation of the bilevel optimization problem can be written as follows: min x ∈ X , y ∈ Y F ( x , y ) {\displaystyle \min \limits _{x\in X,y\in Y}\;\;F(x,y)} subject to: G i ( x , y ) ≤ 0 {\displaystyle G_{i}(x,y)\leq 0} , for i ∈ { 1 , 2 , … , I } {\displaystyle i\in \{1,2,\ldots ,I\}} y ∈ arg min z ∈ Y... | Bilevel program | 0.80377 |
32,704 | Phrase chunking is a phase of natural language processing that separates and segments a sentence into its subconstituents, such as noun, verb, and prepositional phrases, abbreviated as NP, VP, and PP, respectively. Typically, each subconstituent or chunk is denoted by brackets. | Phrase chunking | 0.803769 |
32,705 | A 2008 study of zircons found that Australian Hadean rock contains minerals pointing to the existence of plate tectonics as early as 4 billion years ago (approximately 600 million years after Earth's formation). However, some geologists suggest that the zircons could have been formed by meteorite impacts. The direct ev... | Prebiotic world | 0.803767 |
32,706 | Wedderburn's little theorem asserts that any finite division ring is necessarily commutative: If every nonzero element r of a finite ring R has a multiplicative inverse, then R is commutative (and therefore a finite field).Nathan Jacobson later discovered yet another condition which guarantees commutativity of a ring: ... | Finite ring | 0.803763 |
32,707 | There is an interesting display of the discriminatory tools (nilpotents, zero-divisors, idempotents, and left- and right-identities) in Gregory Dresden's lecture notes.The occurrence of non-commutativity in finite rings was described in (Eldridge 1968) in two theorems: If the order m of a finite ring with 1 has a cube-... | Finite ring | 0.803763 |
32,708 | The theory of finite fields is perhaps the most important aspect of finite ring theory due to its intimate connections with algebraic geometry, Galois theory and number theory. An important, but fairly old aspect of the theory is the classification of finite fields: The order or number of elements of a finite field equ... | Finite ring | 0.803763 |
32,709 | For instance, the classification of finite simple groups was one of the major breakthroughs of 20th century mathematics, its proof spanning thousands of journal pages. On the other hand, it has been known since 1907 that any finite simple ring is isomorphic to the ring M n ( F q ) {\displaystyle \mathrm {M} _{n}(\mathb... | Finite ring | 0.803763 |
32,710 | In mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent h... | Finite ring | 0.803763 |
32,711 | However, perhaps due to the obscurity of the journals in which the papers of Lemaître and Synge were published their conclusions went unnoticed, with many of the major players in the field including Einstein believing that the singularity at the Schwarzschild radius was physical. Synge's later derivation of the Szekere... | Schwarzschild solution | 0.803763 |
32,712 | Thomas Alva Edison (1847–1931) – inventor, entrepreneur Chaim Elata (born 1929) – Israeli professor of mechanical engineering, President of Ben-Gurion University of the Negev, and Chairman of the Israel Public Utility Authority for Electricity John Ericsson (1803–1889) – steam engine design, propeller design, iron clad... | List of mechanical engineers | 0.803761 |
32,713 | This is a list of mechanical engineers, noted for their contribution to the field of mechanical engineering. See also List of engineers for links to other engineering professions. | List of mechanical engineers | 0.803761 |
32,714 | Ralph Sarich (born 1938) – invented orbital engine Thomas Savery (c. 1650–1715) – early steam engine patent holder, author of A Miner's Friend; or An Engine to Raise Water by Fire Per Georg Scheutz (1785–1873) – pioneer in computer technology (Scheutzian calculation engine) Dan Shechtman (born 1941) – discovered Icosah... | List of mechanical engineers | 0.803761 |
32,715 | Ma Jun (fl. 220-265) – 3rd-century China, invented the south-pointing chariot, mechanical puppet theaters, chain pumps, improved silk looms Felice Matteucci (1808–1887) – early developer of internal combustion engine Henry Maudslay (1771–1831) – considered a founding father of machine tool technology, helped perfect th... | List of mechanical engineers | 0.803761 |
32,716 | Leonardo da Vinci (1452–1519) – polymath Rudolf Diesel (1858–1913) – inventor of the diesel engine Bryan Donkin (1768–1855) – associated with paper making and printing machinery, tinned food, beam engines, gas valves and the Babbage difference engine; employed on civil engineering projects such as the Thames Tunnel, Ch... | List of mechanical engineers | 0.803761 |
32,717 | He was instrumental in proposing a matrix concept independent of equation systems. In 1858 Cayley published his A memoir on the theory of matrices in which he proposed and demonstrated the Cayley–Hamilton theorem.The English mathematician Cuthbert Edmund Cullis was the first to use modern bracket notation for matrices ... | Matrix operation | 0.803759 |
32,718 | Matrices can be generalized in different ways. Abstract algebra uses matrices with entries in more general fields or even rings, while linear algebra codifies properties of matrices in the notion of linear maps. It is possible to consider matrices with infinitely many columns and rows. Another extension is tensors, whi... | Matrix operation | 0.803759 |
32,719 | A general application of matrices in physics is the description of linearly coupled harmonic systems. The equations of motion of such systems can be described in matrix form, with a mass matrix multiplying a generalized velocity to give the kinetic term, and a force matrix multiplying a displacement vector to character... | Matrix operation | 0.803759 |
32,720 | In systems theory, closed-loop poles are the positions of the poles (or eigenvalues) of a closed-loop transfer function in the s-plane. The open-loop transfer function is equal to the product of all transfer function blocks in the forward path in the block diagram. The closed-loop transfer function is obtained by divid... | Closed-loop pole | 0.803758 |
32,721 | In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaos pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is... | Double Pendulum | 0.803757 |
32,722 | A chemical transport model (CTM) is a type of computer numerical model which typically simulates atmospheric chemistry and may give air pollution forecasting. | Chemistry transport model | 0.803756 |
32,723 | In organic and organometallic chemistry, an organyl group is an organic substituent with one (sometimes more) free valence(-s) at a carbon atom. The term is often used in chemical patent literature to protect claims over a broad scope. | Organyl group | 0.803755 |
32,724 | The reaction allows for alkylation of electron deficient heterocyclic species which is not possible with Friedel-Crafts chemistry. A method for alkylating electron deficient arenes, nucleophilic aromatic substitution, is also unavailable to electron deficient heterocycles as the ionic nucleophilic species used will dep... | Minisci reaction | 0.803751 |
32,725 | A typical reaction is that between pyridine and pivalic acid with silver nitrate, sulfuric acid and ammonium persulfate to form 2-tert-butylpyridine. The reaction resembles Friedel-Crafts alkylation but with opposite reactivity and selectivity.The Minisci reaction often produces a mixture of regioisomers that can compl... | Minisci reaction | 0.803751 |
32,726 | The Minisci reaction (Italian: ) is a named reaction in organic chemistry. It is a nucleophilic radical substitution to an electron deficient aromatic compound, most commonly the introduction of an alkyl group to a nitrogen containing heterocycle. The reaction was published in 1971 by F. Minisci. In the case of N-Heter... | Minisci reaction | 0.803751 |
32,727 | In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the ... | Collision of bodies | 0.803751 |
32,728 | It is convenient to suppose that two molecules exert a negligible effect on each other unless their center of gravity approach within a critical distance b. A collision therefore begins when the respective centers of gravity arrive at this critical distance, and is completed when they again reach this critical distance... | Collision of bodies | 0.803751 |
32,729 | In 2017, the concept of nanoallotropy was proposed by Prof. Rafal Klajn of the Organic Chemistry Department of the Weizmann Institute of Science. Nanoallotropes, or allotropes of nanomaterials, are nanoporous materials that have the same chemical composition (e.g., Au), but differ in their architecture at the nanoscale... | Allotropes of nonmetals | 0.803751 |
32,730 | The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848). The term is derived from Greek άλλοτροπἱα (allotropia) 'variability, changeableness'. After the acceptance of Avogadro's hypothesis in 1860, it was understood that elements could exist as polyatomic... | Allotropes of nonmetals | 0.803751 |
32,731 | In molecular biology, the CFC domain (Cripto_Frl-1_Cryptic domain) is a protein domain found at the C-terminus of a number of proteins including Cripto (or teratocarcinoma-derived growth factor). It is structurally similar to the C-terminal extracellular portions of Jagged 1 and Jagged 2. CFC is approx 40-residues long... | CFC domain | 0.80375 |
32,732 | The program includes extensive classroom and clinical training in geometric, physical, physiological and ophthalmic optics, specialty contact lens evaluation, general anatomy, ocular anatomy, ocular disease, pharmacology, ocular pharmacology, neuroanatomy and neurophysiology of the visual system, pediatric visual devel... | Eye care | 0.803749 |
32,733 | Optometric history is tied to the development of vision science (related areas of medicine, microbiology, neurology, physiology, psychology, etc.) optics, optical aids optical instruments, imaging techniques other eye care professionsThe history of optometry can be traced back to the early studies on optics and image f... | Eye care | 0.803749 |
32,734 | In Italy Optometry is an unregulated profession. It is taught at seven universities: Padua, Turin, Milan, Salento, Florence, Naples and Rome, as three years course (like a BSc) of "Scienze e tecnologie fisiche" as a sector of the Physics Department. Additionally, courses are available at some private institutions (as a... | Eye care | 0.803749 |
32,735 | Newton described any variable that changed its value as a fluent – for example, the velocity of a ball thrown in the air. The derivative of a fluent is known as a fluxion, the main focus of Newton's calculus. A fluent can be found from its corresponding fluxion through integration. | Fluent (mathematics) | 0.803748 |
32,736 | A fluent is a time-varying quantity or variable. The term was used by Isaac Newton in his early calculus to describe his form of a function. The concept was introduced by Newton in 1665 and detailed in his mathematical treatise, Method of Fluxions. | Fluent (mathematics) | 0.803748 |
32,737 | There is a unique connected 0-dimensional manifold, namely the point, and disconnected 0-dimensional manifolds are just discrete sets, classified by cardinality. They have no geometry, and their study is combinatorics. A connected 1-dimensional manifold without boundary is either the circle (if compact) or the real lin... | Classification of manifolds | 0.803747 |
32,738 | In dimension 5 and above (and 4 dimensions topologically), manifolds are classified by surgery theory. The reason for dimension 5 is that the Whitney trick works in the middle dimension in dimension 5 and more: two Whitney disks generically don't intersect in dimension 5 and above, by general position ( 2 + 2 < 5 {\dis... | Classification of manifolds | 0.803747 |
32,739 | Every connected closed 2-dimensional manifold (surface) admits a constant curvature metric, by the uniformization theorem. There are 3 such curvatures (positive, zero, and negative). This is a classical result, and as stated, easy (the full uniformization theorem is subtler). The study of surfaces is deeply connected w... | Classification of manifolds | 0.803747 |
32,740 | In codimension 1, a codimension 1 embedding separates a manifold, and these are tractable. In codimension 0, a codimension 0 (proper) immersion is a covering space, which are classified algebraically, and these are more naturally thought of as submersions. In relative dimension, a submersion with compact domain is a fi... | Classification of manifolds | 0.803747 |
32,741 | The Euler characteristic is a homological invariant, and thus can be effectively computed given a CW structure, so 2-manifolds are classified homologically. Characteristic classes and characteristic numbers are the corresponding generalized homological invariants, but they do not classify manifolds in higher dimension ... | Classification of manifolds | 0.803747 |
32,742 | Particularly topologically interesting classes of maps include embeddings, immersions, and submersions. Geometrically interesting are isometries and isometric immersions. Fundamental results in embeddings and immersions include: Whitney embedding theorem Whitney immersion theorem Nash embedding theorem Smale-Hirsch the... | Classification of manifolds | 0.803747 |
32,743 | Many classical theorems in Riemannian geometry show that manifolds with positive curvature are constrained, most dramatically the 1/4-pinched sphere theorem. Conversely, negative curvature is generic: for instance, any manifold of dimension n ≥ 3 {\displaystyle n\geq 3} admits a metric with negative Ricci curvature. Th... | Classification of manifolds | 0.803747 |
32,744 | Low-dimensional manifolds are classified by geometric structure; high-dimensional manifolds are classified algebraically, by surgery theory. "Low dimensions" means dimensions up to 4; "high dimensions" means 5 or more dimensions. The case of dimension 4 is somehow a boundary case, as it manifests "low dimensional" beha... | Classification of manifolds | 0.803747 |
32,745 | In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. | Classification of manifolds | 0.803747 |
32,746 | There are two usual ways to give a classification: explicitly, by an enumeration, or implicitly, in terms of invariants. For instance, for orientable surfaces, the classification of surfaces enumerates them as the connect sum of n ≥ 0 {\displaystyle n\geq 0} tori, and an invariant that classifies them is the genus or E... | Classification of manifolds | 0.803747 |
32,747 | Dimensions 0 and 1 are trivial. Low dimension manifolds (dimensions 2 and 3) admit geometry. Middle dimension manifolds (dimension 4 differentiably) exhibit exotic phenomena. High dimension manifolds (dimension 5 and more differentiably, dimension 4 and more topologically) are classified by surgery theory.Thus dimensio... | Classification of manifolds | 0.803747 |
32,748 | The ISR (standing for "Intersecting Storage Rings") was a particle accelerator at CERN. It was the world's first hadron collider, and ran from 1971 to 1984, with a maximum center of mass energy of 62 GeV. From its initial startup, the collider itself had the capability to produce particles like the J/ψ and the upsilon,... | Intersecting Storage Rings | 0.803747 |
32,749 | Thus, probabilistic design is a tool that is mostly used in areas that are concerned with quality and reliability. For example, product design, quality control, systems engineering, machine design, civil engineering (particularly useful in limit state design) and manufacturing. It differs from the classical approach to... | Probabilistic design | 0.803746 |
32,750 | As mentioned, motivations for settling problems that belong today to intensional logic have a long past. As for attempts of formalizations, the development of calculi often preceded the finding of their corresponding formal semantics. Intensional logic is not alone in that: also Gottlob Frege accompanied his (extension... | Extensional logic | 0.803745 |
32,751 | For this model of collective intelligence, the formal definition of IQS (IQ Social) was proposed and was defined as "the probability function over the time and domain of N-element inferences which are reflecting inference activity of the social structure". While IQS seems to be computationally hard, modeling of social ... | Collective Intelligence | 0.803744 |
32,752 | Skeptics, especially those critical of artificial intelligence and more inclined to believe that risk of bodily harm and bodily action are the basis of all unity between people, are more likely to emphasize the capacity of a group to take action and withstand harm as one fluid mass mobilization, shrugging off harms the... | Collective Intelligence | 0.803744 |
32,753 | In organic chemistry, a methylidene group is any part of a molecule that consists of two hydrogen atoms bound to a carbon atom, which is connected to the remainder of the molecule by a double bond. The group may be represented as =CH2, where the '=' denotes the double bond. This stands in contrast to methylene, the −CH... | Methylidene group | 0.803742 |
32,754 | The geometry in the sub-systems is then used to define more detail in the levels below. Depending on the complexity of the product, a number of levels of this assembly are created until the basic definition of components can be identified, such as position and principal dimensions. This information is then associativel... | Product cycle | 0.80374 |
32,755 | A part-centric top–down design may eliminate some of the risks of top–down design. This starts with a layout model, often a simple 2D sketch defining basic sizes and some major defining parameters, which may include some Industrial design elements. Geometry from this is associatively copied down to the next level, whic... | Product cycle | 0.80374 |
32,756 | Individual components cannot be constructed in isolation. CAD and CAID models of components are created within the context of some or all of the other components within the product being developed. This is achieved using assembly modelling techniques. The geometry of other components can be seen and referenced within t... | Product cycle | 0.80374 |
32,757 | Within PLM there are five primary areas; Systems engineering (SE) is focused on meeting all requirements, primarily meeting customer needs, and coordinating the systems design process by involving all relevant disciplines. An important aspect of lifecycle management is a subset within Systems Engineering called Reliabi... | Product cycle | 0.80374 |
32,758 | In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and reductive logic. They form the most general definition of goal-directed proof-search—in which someone chooses a formula and performs hereditary red... | Focused proof | 0.803739 |
32,759 | In either case one can safely apply rules in any order to hereditary sub-formulas of the same polarity. In the case of a right rule applied to a positive formula, or a left rule applied to a negative formula, one may result in invalid sequents e.g., in LK and LJ there is no proof of the sequent B ∨ A ⟹ A ∨ B {\displays... | Focused proof | 0.803739 |
32,760 | According to the rules in the sequent calculus, formulas are canonically put into one of two classes called positive and negative e.g., in LK and LJ the formula ϕ ∨ ψ {\displaystyle \phi \lor \psi } is positive. The only freedom is over atoms are assigned a polarity freely. For negative formulas provability is invarian... | Focused proof | 0.803739 |
32,761 | A sequent calculus is often shown to have the focusing property by working in a related calculus where polarity explicitly controls which rules apply. Proofs in such systems are in focused, unfocused, or neutral phases, where the first two are characterised by hereditary decomposition; and the latter by forcing a choic... | Focused proof | 0.803739 |
32,762 | In the sequent calculus for an intuitionistic logic, the uniform proofs can be characterised as those in which the upward reading performs all right rules before the left rules. Typically, uniform proofs are not complete for the logic i.e., not all sequents or formulas admit a uniform proof, so one considers fragments ... | Focused proof | 0.803739 |
32,763 | However, there are some concerns with the use of nanoparticles for drug delivery. Some studies have shown that nanoparticles may contribute to the development of tumors in other parts of the body. There is also growing concern that nanoparticles may have harmful effects on the environment. Despite these potential drawb... | Controlled Drug Delivery | 0.803738 |
32,764 | This is a process by which nanoparticles are used to carry and deliver drugs to a specific area in the body. There are several advantages of using nanotechnology for drug delivery, including precise targeting of specific cells, increased drug potency, and lowered toxicity to the cells that are targeted. Nanoparticles c... | Controlled Drug Delivery | 0.803738 |
32,765 | Nanotechnology is a broad field of research and development that deals with the manipulation of matter at the atomic or subatomic level. It is used in fields such as medicine, energy, aerospace engineering, and more. One of the applications of nanotechnology in drug delivery. | Controlled Drug Delivery | 0.803738 |
32,766 | One may define a partial order on the idempotents of a ring as follows: if a and b are idempotents, we write a ≤ b if and only if ab = ba = a. With respect to this order, 0 is the smallest and 1 the largest idempotent. For orthogonal idempotents a and b, a + b is also idempotent, and we have a ≤ a + b and b ≤ a + b. Th... | Idempotent (ring theory) | 0.803737 |
32,767 | One may consider the ring of integers modulo n where n is squarefree. By the Chinese remainder theorem, this ring factors into the product of rings of integers modulo p where p is prime. Now each of these factors is a field, so it is clear that the factors' only idempotents will be 0 and 1. That is, each factor has two... | Idempotent (ring theory) | 0.803737 |
32,768 | In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that a = a2 = a3 = a4 = ... = an for any positive integer n. For example, an idempot... | Idempotent (ring theory) | 0.803737 |
32,769 | A 2012 report from the U.S. National Research Council calls for a new focus on glycoscience, a field that explores the structures and functions of glycans and promises great advances in areas as diverse as medicine, energy generation, and materials science. Until now, glycans have received little attention from the res... | N-linked glycan | 0.803737 |
32,770 | National Center for Functional Glycomics (NCFG) The focus of the NCFG is the development in the glycosciences, with an emphasis on exploring the molecular mechanisms of glycan recognition by proteins important in human biology and disease. They have a number of resources for glycan analysis as well as training in glyco... | N-linked glycan | 0.803737 |
32,771 | In mathematics, especially linear algebra, the exchange matrices (also called the reversal matrix, backward identity, or standard involutory permutation) are special cases of permutation matrices, where the 1 elements reside on the antidiagonal and all other elements are zero. In other words, they are 'row-reversed' or... | Exchange matrix | 0.803737 |
32,772 | A congruence on the set of all trees over a ranked alphabet F is an equivalence relation such that u1 ≡ v1 and ... and un ≡ vn implies f(u1,...,un) ≡ f(v1,...,vn), for every f ∈ F. It is of finite index if its number of equivalence-classes is finite. For a given tree-language L, a congruence can be defined by u ≡L v if... | Tree automaton | 0.803736 |
32,773 | Nitrogen pentahydride, also known as ammonium hydride is a hypothetical compound with the chemical formula NH5. There are two theoretical structures of nitrogen pentahydride. One structure is trigonal bipyramidal molecular geometry type NH5 molecule. Its nitrogen atom and hydrogen atoms are covalently bounded, and its ... | Nitrogen pentahydride | 0.803734 |
32,774 | Isotopy of algebras was introduced by Albert (1942), who was inspired by work of Steenrod. Some authors use a slightly different definition that an isotopy is a triple of bijective linear maps a, b, c such that if xyz = 1 then a(x)b(y)c(z) = 1. For alternative division algebras such as the octonions the two definitions... | Isotopy of an algebra | 0.803734 |
32,775 | However associative algebras with identity elements can be isotopic to algebras without identity elements. The autotopy group of the octonions is the spin group Spin8, much larger than its automorphism group G2. If B is a mutation of the associative algebra A by an invertible element, then there is an isotopy from A to... | Isotopy of an algebra | 0.803734 |
32,776 | These form two commuting subgroups of the autotopy group, and the full autotopy group is generated by these two subgroups and the automorphism group. If an algebra (not assumed to be associative) with an identity element is isotopic to an associative algebra with an identity element, then the two algebras are isomorphi... | Isotopy of an algebra | 0.803734 |
32,777 | If a = b = c is an isomorphism then the triple (a, b, c) is an isotopy. Conversely, if the algebras have identity elements 1 that are preserved by the maps a and b of an isotopy, then a = b = c is an isomorphism. If A is an associative algebra with identity and a and c are left multiplication by some fixed invertible e... | Isotopy of an algebra | 0.803734 |
32,778 | In mathematics, an isotopy from a possibly non-associative algebra A to another is a triple of bijective linear maps (a, b, c) such that if xy = z then a(x)b(y) = c(z). This is similar to the definition of an isotopy of loops, except that it must also preserve the linear structure of the algebra. For a = b = c this is ... | Isotopy of an algebra | 0.803734 |
32,779 | More sophisticated versions of this idea can find curves from a cloud of noisy sample points that roughly follows the curve outline, by using the topology of the spanning tree to guide a moving least squares method.Another application of minimum spanning trees is a constant-factor approximation algorithm for the Euclid... | Euclidean minimum spanning tree | 0.803733 |
32,780 | More generally, similar methods can recognize curves drawn in a dotted or dashed style rather than as a single connected set. Applications of this curve-finding technique include particle physics, in automatically identifying the tracks left by particles in a bubble chamber. | Euclidean minimum spanning tree | 0.803733 |
32,781 | An asymptotic lower bound of Ω ( n log n ) {\displaystyle \Omega (n\log n)} of the Euclidean minimum spanning tree problem can be established in restricted models of computation. These include the algebraic decision tree and algebraic computation tree models, in which the algorithm has access to the input points only... | Euclidean minimum spanning tree | 0.803733 |
32,782 | The minimum moving spanning tree problem again concerns points moving linearly with constant speed, over an interval of time, and seeks a single tree that minimizes the maximum sum of weights occurring at any instant during this interval. It is NP-hard to compute exactly, but can be approximated to within a factor of t... | Euclidean minimum spanning tree | 0.803733 |
32,783 | For n {\displaystyle n} points moving linearly with constant speed, or with more general algebraic motions, the minimum spanning tree will change by a sequence of swaps, in which one edge is removed and another replaces it at a point in time where both have equal length. For linear motions, the number of changes is at ... | Euclidean minimum spanning tree | 0.803733 |
32,784 | For any edge u v {\displaystyle uv} of any Euclidean minimum spanning tree, the lens (or vesica piscis) formed by intersecting the two circles with u v {\displaystyle uv} as their radii cannot have any other given vertex w {\displaystyle w} in its interior. Put another way, if any tree has an edge u v {\displaystyle uv... | Euclidean minimum spanning tree | 0.803733 |
32,785 | These forms of investigation can arrive at conclusions about what forms of thought are rational and irrational without depending on empirical evidence.An important question in this field concerns the relation between descriptive and normative approaches to rationality. One difficulty in this regard is that there is in ... | Rational thinking | 0.803731 |
32,786 | These laws are highly relevant for the rationality of beliefs. A very influential conception of practical rationality is given in decision theory: it states that a decision is rational if the chosen option has the highest expected utility. Other relevant fields include game theory, Bayesianism, economics, and artificia... | Rational thinking | 0.803731 |
32,787 | However, this strong affirmation has been subjected to many criticisms, for example, that humans are not rational all the time and that non-human animals also show diverse forms of intelligence.The topic of rationality is relevant to a variety of disciplines. It plays a central role in philosophy, psychology, Bayesiani... | Rational thinking | 0.803731 |
32,788 | The field of artificial intelligence is concerned, among other things, with how problems of rationality can be implemented and solved by computers. Within artificial intelligence, a rational agent is typically one that maximizes its expected utility, given its current knowledge. Utility is the usefulness of the consequ... | Rational thinking | 0.80373 |
32,789 | In complex cases, inconsistencies may be difficult to detect, for example, when a person believes in the axioms of Euclidean geometry and is nonetheless convinced that it is possible to square the circle. Positive coherence refers to the support that different mental states provide for each other. For example, there is... | Rational thinking | 0.80373 |
32,790 | At many universities, a Bachelor of Science (BS) degree in Animal Science allows emphasis in certain areas. Typical areas are species-specific or career-specific. Species-specific areas of emphasis prepare students for a career in dairy management, beef management, swine management, sheep or small ruminant management, ... | Animal sciences | 0.80373 |
32,791 | Professional education in animal science prepares students for careers in areas such as animal breeding, food and fiber production, nutrition, animal agribusiness, animal behavior, and welfare. Courses in a typical Animal Science program may include genetics, microbiology, animal behavior, nutrition, physiology, and re... | Animal sciences | 0.80373 |
32,792 | Many schools that offer a degree option in Animal Science also offer a pre-veterinary emphasis such as Iowa State University, the University of Nebraska–Lincoln, and the University of Minnesota, for example. This option provides knowledge of the biological and physical sciences including nutrition, reproduction, physio... | Animal sciences | 0.80373 |
32,793 | The second chapter considers the symmetries of polyhedra, the Platonic solids and Archimedean solids, and the honeycombs formed by space-filling polyhedra. Chapter 3 covers the history of geometry in medieval Islam and early Europe, including connections to astronomy and the study of visual perspective, and Chapter 4 c... | Polyhedra (book) | 0.803729 |
32,794 | The book covers both the mathematics of polyhedra and its historical development, limiting itself only to three-dimensional geometry. The notion of what it means to be a polyhedron has varied over the history of the subject, as have other related definitions, an issue that the book handles largely by keeping definition... | Polyhedra (book) | 0.803729 |
32,795 | And Grabiner faults the book's history as naive or mistaken, citing as examples its claims that the discovery of irrational numbers ended Pythagorean mysticism, and that pre-Keplerian astronomy consisted only of observation and record-keeping. She accuses Cromwell of basing his narrative on secondary sources rather tha... | Polyhedra (book) | 0.803729 |
32,796 | Most of the book requires little in the way of mathematical background, and can be read by interested amateurs; however, some of the material on symmetry towards the end of the book requires some background in group theory. Reviewer Bill Casselman writes that it would probably not be appropriate to use as a textbook in... | Polyhedra (book) | 0.803729 |
32,797 | Modern orthographic projection is derived from Gaspard Monge's descriptive geometry. Monge defined a reference system of two viewing planes, horizontal H ("ground") and vertical V ("backdrop"). These two planes intersect to partition 3D space into 4 quadrants, which he labeled: I: above H, in front of V II: above H, be... | Third-angle projection | 0.803729 |
32,798 | In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, theoretical philosophy, or applied natural language pr... | Situation semantics | 0.803727 |
32,799 | The widespread use of confidence intervals in statistics is often justified using a statistical syllogism, in such words as "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time." The... | Statistical syllogism | 0.803723 |
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