id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
83,400 | Every call in CPS is a tail call, and the continuation is explicitly passed. Using CPS without tail call optimization (TCO) will cause not only the constructed continuation to potentially grow during recursion, but also the call stack. This is usually undesirable, but has been used in interesting ways—see the Chicken S... | Direct style | 0.783773 |
83,401 | N'Ko is a literary language devised by Solomana Kante in 1949 as a writing system for the Mande languages of West Africa. It blends the principal elements of the partially mutually intelligible Manding languages. The movement promoting N'Ko literacy was instrumental in shaping the Maninka cultural identity in Guinea, a... | Formal writing | 0.783772 |
83,402 | Outside of computer science, CPS is of more general interest as an alternative to the conventional method of composing simple expressions into complex expressions. For example, within linguistic semantics, Chris Barker and his collaborators have suggested that specifying the denotations of sentences using CPS might exp... | Direct style | 0.783772 |
83,403 | Both of the following theorems are referred to as the Krein-Smulian Theorem. | Krein–Smulian theorem | 0.783772 |
83,404 | In mathematics, particularly in functional analysis, the Krein-Smulian theorem can refer to two theorems relating the closed convex hull and compactness in the weak topology. They are named after Mark Krein and Vitold Shmulyan, who published them in 1940. | Krein–Smulian theorem | 0.783772 |
83,405 | Most bayesians are rather unconcerned about unbiasedness (at least in the formal sampling-theory sense above) of their estimates. For example, Gelman and coauthors (1995) write: "From a Bayesian perspective, the principle of unbiasedness is reasonable in the limit of large samples, but otherwise it is potentially misle... | Bias of an estimator | 0.783772 |
83,406 | "Chapter 9 - The Somatosensory System: Touch and Proprioception". Neuroscience (6th ed.). Sinauer Associates. | Golgi tendon organ | 0.783772 |
83,407 | The higher-order logic programming languages λProlog and Twelf have switched from full higher-order unification to implementing only the pattern fragment; surprisingly pattern unification is sufficient for almost all programs, if each non-pattern unification problem is suspended until a subsequent substitution puts the... | Syntactic unification | 0.783772 |
83,408 | The first demonstration of an "inverse opal" structure with a complete photonic bandgap came in 2000, from researchers at the University of Toronto, Canada, and Institute of Materials Science of Madrid (ICMM-CSIC), Spain. The ever-expanding field of natural photonics, bioinspiration and biomimetics—the study of natural... | Photonic crystal | 0.783771 |
83,409 | Photonic crystals have been studied in one form or another since 1887, but no one used the term photonic crystal until over 100 years later—after Eli Yablonovitch and Sajeev John published two milestone papers on photonic crystals in 1987. The early history is well-documented in the form of a story when it was identifi... | Photonic crystal | 0.783771 |
83,410 | GeoQuest Systems was a company offering geology software, systems integration, and information-management services and software to the oil and gas industry from 1984& to 2001). | GeoQuest Systems | 0.783769 |
83,411 | In July 1999, GeoQuest acquired Merak Projects, a reserves, economics and field-optimization software company. In 2001, the company was integrated into Schlumberger Information Solutions (SIS). == References == | GeoQuest Systems | 0.783769 |
83,412 | The operation was based in a converted mansion in a suburb of Abu Dhabi in Khalifa City nicknamed "the Villa. "From around 2014 to 2016, CyberPoint supplied U.S.-trained contractors to Project Raven. In 2016, news reports emerged that CyberPoint had contracted with the Italian spyware company Hacking Team, which damage... | DarkMatter Group | 0.783769 |
83,413 | Let us denote M n ( R ) {\displaystyle {\mathcal {M}}_{n}(R)} the set of n×n square matrices with entries in a ring R, which, in practice, is often a field. In M n ( R ) {\displaystyle {\mathcal {M}}_{n}(R)} , the product is defined for every pair of matrices. This makes M n ( R ) {\displaystyle {\mathcal {M}}_{n}(R)} ... | Matrix product | 0.783767 |
83,414 | To study the formation of singularities it is useful, as in the study of other non-linear differential equations, to consider blow-ups limits. Intuitively speaking, one zooms into the singular region of the Ricci flow by rescaling time and space. Under certain assumptions, the zoomed in flow tends to a limiting Ricci f... | Ricci flow | 0.783767 |
83,415 | Geometry is being used here in a precise manner akin to Klein's notion of geometry (see Geometrization conjecture for further details). In particular, the result of geometrization may be a geometry that is not isotropic. In most cases including the cases of constant curvature, the geometry is unique. An important theme... | Ricci flow | 0.783767 |
83,416 | Indeed, a triumph of nineteenth-century geometry was the proof of the uniformization theorem, the analogous topological classification of smooth two-manifolds, where Hamilton showed that the Ricci flow does indeed evolve a negatively curved two-manifold into a two-dimensional multi-holed torus which is locally isometri... | Ricci flow | 0.783767 |
83,417 | Hamilton succeeded in proving that any smooth closed three-manifold which admits a metric of positive Ricci curvature also admits a unique Thurston geometry, namely a spherical metric, which does indeed act like an attracting fixed point under the Ricci flow, renormalized to preserve volume. (Under the unrenormalized R... | Ricci flow | 0.783767 |
83,418 | Hamilton's first work on Ricci flow was published at the same time as William Thurston's geometrization conjecture, which concerns the topological classification of three-dimensional smooth manifolds. Hamilton's idea was to define a kind of nonlinear diffusion equation which would tend to smooth out irregularities in t... | Ricci flow | 0.783767 |
83,419 | A fundamental problem in Ricci flow is to understand all the possible geometries of singularities. When successful, this can lead to insights into the topology of manifolds. For instance, analyzing the geometry of singular regions that may develop in 3d Ricci flow, is the crucial ingredient in Perelman's proof the Poin... | Ricci flow | 0.783767 |
83,420 | Given any n larger than two, there exist many closed n-dimensional smooth manifolds which do not have any smooth Riemannian metrics of constant curvature. So one cannot hope to be able to simply drop the curvature conditions from the above convergence theorems. It could be possible to replace the curvature conditions b... | Ricci flow | 0.783767 |
83,421 | Twenty years later, Christoph Böhm and Burkhard Wilking found a new algebraic method of constructing "pinching sets", thereby removing the assumption of four-dimensionality from Hamilton's result (Böhm & Wilking 2008). Simon Brendle and Richard Schoen showed that positivity of the isotropic curvature is preserved by th... | Ricci flow | 0.783767 |
83,422 | (2003). Collected Papers on Ricci Flow. Series in Geometry and Topology. | Ricci flow | 0.783767 |
83,423 | ISBN 978-3-642-16285-5. Brendle, Simon (2010). Ricci Flow and the Sphere Theorem. | Ricci flow | 0.783767 |
83,424 | Andrews, Ben; Hopper, Christopher (2011). The Ricci Flow in Riemannian Geometry: A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem. Lecture Notes in Mathematics. Vol. | Ricci flow | 0.783767 |
83,425 | The converse also holds, by reversing the above calculations. The primary reason for considering the normalized Ricci flow is that it allows a convenient statement of the major convergence theorems for Ricci flow. However, it is not essential to do so, and for virtually all purposes it suffices to consider Ricci flow i... | Ricci flow | 0.783767 |
83,426 | Note that if M is not simply-connected, then one may consider the universal cover π: M ′ → M , {\displaystyle \pi :M'\to M,} and then the above theorem applies to ( M ′ , π ∗ g , f ∘ π ) . {\displaystyle (M',\pi ^{\ast }g,f\circ \pi ).} There is not yet a good understanding of gradient shrinking Ricci solitons in any h... | Ricci flow | 0.783767 |
83,427 | An example of a 3-dimensional steady Ricci soliton is the Bryant soliton, which is rotationally symmetric, has positive curvature, and is obtained by solving a system of ordinary differential equations. A similar construction works in arbitrary dimension. | Ricci flow | 0.783767 |
83,428 | Ricci solitons are Ricci flows that may change their size but not their shape up to diffeomorphisms. Cylinders Sk × Rl (for k ≥ 2) shrink self similarly under the Ricci flow up to diffeomorphisms A significant 2-dimensional example is the cigar soliton, which is given by the metric (dx2 + dy2)/(e4t + x2 + y2) on the Eu... | Ricci flow | 0.783767 |
83,429 | The parameter t is usually called time, although this is only as part of standard informal terminology in the mathematical field of partial differential equations. It is not physically meaningful terminology. In fact, in the standard quantum field theoretic interpretation of the Ricci flow in terms of the renormalizati... | Ricci flow | 0.783767 |
83,430 | So, with this very trivial change of parameters, the number −2 appearing in the definition of the Ricci flow could be replaced by any other nonzero number. For this reason, the use of −2 can be regarded as an arbitrary convention, albeit one which essentially every paper and exposition on Ricci flow follows. The only s... | Ricci flow | 0.783767 |
83,431 | On a smooth manifold M, a smooth Riemannian metric g automatically determines the Ricci tensor Ricg. For each element p of M, by definition gp is a positive-definite inner product on the tangent space TpM at p. If given a one-parameter family of Riemannian metrics gt, one may then consider the derivative ∂/∂t gt, which... | Ricci flow | 0.783767 |
83,432 | Dennis DeTurck subsequently gave a proof of the above results which uses the Banach implicit function theorem instead. His work is essentially a simpler Riemannian version of Yvonne Choquet-Bruhat's well-known proof and interpretation of well-posedness for the Einstein equations in Lorentzian geometry. As a consequence... | Ricci flow | 0.783767 |
83,433 | Let M {\displaystyle M} be a smooth closed manifold, and let g 0 {\displaystyle g_{0}} be any smooth Riemannian metric on M {\displaystyle M} . Making use of the Nash–Moser implicit function theorem, Hamilton (1982) showed the following existence theorem: There exists a positive number T {\displaystyle T} and a Ricci f... | Ricci flow | 0.783767 |
83,434 | Let ( M , g ) {\displaystyle (M,g)} be a Riemannian manifold which is Einstein, meaning that there is a number λ {\displaystyle \lambda } such that Ric g = λ g {\displaystyle {\text{Ric}}^{g}=\lambda g} . Then g t = ( 1 − 2 λ t ) g {\displaystyle g_{t}=(1-2\lambda t)g} is a Ricci flow with g 0 = g {\displaystyle g_{0}=... | Ricci flow | 0.783767 |
83,435 | But notice that the flat Euclidean plane is given by taking p ( x , y ) = 0 {\displaystyle p(x,y)=0} . So if p {\displaystyle p} is small in magnitude, we can consider it to define small deviations from the geometry of a flat plane, and if we retain only first order terms in computing the exponential, the Ricci flow on... | Ricci flow | 0.783767 |
83,436 | Since any Ricci flow on a two-dimensional manifold is confined to a single conformal class, it can be recast as a partial differential equation for a scalar function on the fixed Riemannian manifold (M, g0). As such, the Ricci flow in this setting can also be studied by purely analytic methods; correspondingly, there a... | Ricci flow | 0.783767 |
83,437 | Hamilton's proof, inspired by and loosely modeled upon James Eells and Joseph Sampson's epochal 1964 paper on convergence of the harmonic map heat flow, included many novel features, such as an extension of the maximum principle to the setting of symmetric 2-tensors. His paper (together with that of Eells−Sampson) is a... | Ricci flow | 0.783767 |
83,438 | Complete expositions of the following convergence theorems are given in Andrews & Hopper (2011) and Brendle (2010). Let (M, g0) be a smooth closed Riemannian manifold. Under any of the following three conditions: M is two-dimensional M is three-dimensional and g0 has positive Ricci curvature M has dimension greater tha... | Ricci flow | 0.783767 |
83,439 | The terms on the right hand side of Perelman's Li–Yau inequality motivates the definition of his "reduced length" functional, the analysis of which leads to his "noncollapsing theorem". The noncollapsing theorem allows application of Hamilton's compactness theorem (Hamilton 1995) to construct "singularity models", whic... | Ricci flow | 0.783767 |
83,440 | Making use of a technique pioneered by Peter Li and Shing-Tung Yau for parabolic differential equations on Riemannian manifolds, Hamilton (1993a) proved the following "Li–Yau inequality". Let M {\displaystyle M} be a smooth manifold, and let g t {\displaystyle g_{t}} be a solution of the Ricci flow with t ∈ ( 0 , T ) {... | Ricci flow | 0.783767 |
83,441 | In 2002 and 2003, Grigori Perelman presented a number of fundamental new results about the Ricci flow, including a novel variant of some technical aspects of Hamilton's program. Perelman's work is now widely regarded as forming the proof of the Thurston conjecture and the Poincaré conjecture, regarded as a special case... | Ricci flow | 0.783767 |
83,442 | Later extensions of Hamilton's methods by various authors resulted in new applications to geometry, including the resolution of the differentiable sphere conjecture by Simon Brendle and Richard Schoen. Following Shing-Tung Yau's suggestion that the singularities of solutions of the Ricci flow could identify the topolog... | Ricci flow | 0.783767 |
83,443 | In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( REE-chee, Italian: ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due... | Ricci flow | 0.783767 |
83,444 | Let's suppose the suspected message contains the word "replica". Most people who are used to receiving e-mail know that this message is likely to be spam, more precisely a proposal to sell counterfeit copies of well-known brands of watches. The spam detection software, however, does not "know" such facts; all it can do... | Naive Bayes spam filtering | 0.783766 |
83,445 | It was sponsored by Canonical Ltd., for a period. The project was started in April 2002 in response to an article on linux.com by astrophysics student Henrik Nilsen Omma.In September 2007, project lead Chris Gray left the project to pursue his own open-source disc, called OpenDisc, citing numerous difficulties which he... | OpenCD | 0.783766 |
83,446 | Naive Bayes classifiers are a popular statistical technique of e-mail filtering. They typically use bag-of-words features to identify email spam, an approach commonly used in text classification. Naive Bayes classifiers work by correlating the use of tokens (typically words, or sometimes other things), with spam and no... | Naive Bayes spam filtering | 0.783766 |
83,447 | Many data structures and databases implement immutable objects, effectively making their data structures append-only. Implementing an append-only data structure has many benefits, such as ensuring data consistency, improving performance, and permitting rollbacks.The prototypical append-only data structure is the log fi... | Append-only | 0.783765 |
83,448 | This structure theory assigns to a stable isometric action of a finitely generated group G a certain "normal form" approximation of that action by a stable action of G on a simplicial tree and hence a splitting of G in the sense of Bass–Serre theory. Group actions on real trees arise naturally in several contexts in ge... | Bass–Serre theory | 0.783765 |
83,449 | The theory of isometric group actions on real trees (or R-trees) which are metric spaces generalizing the graph-theoretic notion of a tree (graph theory). The theory was developed largely in the 1990s, where the Rips machine of Eliyahu Rips on the structure theory of stable group actions on R-trees played a key role (s... | Bass–Serre theory | 0.783765 |
83,450 | There have been several generalizations of Bass–Serre theory: The theory of complexes of groups (see Haefliger, Corson Bridson-Haefliger) provides a higher-dimensional generalization of Bass–Serre theory. The notion of a graph of groups is replaced by that of a complex of groups, where groups are assigned to each cell ... | Bass–Serre theory | 0.783765 |
83,451 | There are two equivalent definitions of the notion of the fundamental group of a graph of groups: the first is a direct algebraic definition via an explicit group presentation (as a certain iterated application of amalgamated free products and HNN extensions), and the second using the language of groupoids. The algebra... | Bass–Serre theory | 0.783765 |
83,452 | The group G = π1(A, T) defined above admits an algebraic description in terms of iterated amalgamated free products and HNN extensions. First, form a group B as a quotient of the free product ( ∗ v ∈ V A v ) ∗ F ( E + T ) {\displaystyle (\ast _{v\in V}A_{v})*F(E^{+}T)} subject to the relations e−1αe(g)e = ωe(g) for eve... | Bass–Serre theory | 0.783765 |
83,453 | The group G is called an X-lattice if vol(A)< ∞. The theory of tree lattices turns out to be useful in the study of discrete subgroups of algebraic groups over non-archimedean local fields and in the study of Kac–Moody groups.Development of foldings and Nielsen methods for approximating group actions on trees and analy... | Bass–Serre theory | 0.783765 |
83,454 | Important developments in Bass–Serre theory in the last 30 years include: Various accessibility results for finitely presented groups that bound the complexity (that is, the number of edges) in a graph of groups decomposition of a finitely presented group, where some algebraic or geometric restrictions on the types of ... | Bass–Serre theory | 0.783765 |
83,455 | Mathematically, Bass–Serre theory builds on exploiting and generalizing the properties of two older group-theoretic constructions: free product with amalgamation and HNN extension. However, unlike the traditional algebraic study of these two constructions, Bass–Serre theory uses the geometric language of covering theor... | Bass–Serre theory | 0.783765 |
83,456 | Bass–Serre theory was developed by Jean-Pierre Serre in the 1970s and formalized in Trees, Serre's 1977 monograph (developed in collaboration with Hyman Bass) on the subject. Serre's original motivation was to understand the structure of certain algebraic groups whose Bruhat–Tits buildings are trees. However, the theor... | Bass–Serre theory | 0.783765 |
83,457 | Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation ... | Bass–Serre theory | 0.783765 |
83,458 | An isomorphism between a group G and the fundamental group of a graph of groups is called a splitting of G. If the edge groups in the splitting come from a particular class of groups (e.g. finite, cyclic, abelian, etc.), the splitting is said to be a splitting over that class. Thus a splitting where all edge groups are... | Bass–Serre theory | 0.783765 |
83,459 | Typically, only nontrivial actions on trees are studied in Bass–Serre theory since trivial graphs of groups do not carry any interesting algebraic information, although trivial actions in the above sense (e. g. actions of groups by automorphisms on rooted trees) may also be interesting for other mathematical reasons. O... | Bass–Serre theory | 0.783765 |
83,460 | Serre's formalism of graphs is slightly different from the standard formalism from graph theory. Here a graph A consists of a vertex set V, an edge set E, an edge reversal map E → E , e ↦ e ¯ {\displaystyle E\to E,\ e\mapsto {\overline {e}}} such that e ≠ e and e ¯ ¯ = e {\displaystyle {\overline {\overline {e}}}=e} fo... | Bass–Serre theory | 0.783765 |
83,461 | Let G be a group acting on a tree X without inversions. Let A be the quotient graph of groups and let v be a base-vertex in A. Then G is isomorphic to the group π1(A, v) and there is an equivariant isomorphism between the tree X and the Bass–Serre covering tree A ~ {\displaystyle {\tilde {\mathbf {A} }}} . More precise... | Bass–Serre theory | 0.783765 |
83,462 | Let A be a graph of groups with underlying graph A such that all the vertex and edge groups in A are trivial. Let v be a base-vertex in A. Then π1(A,v) is equal to the fundamental group π1(A,v) of the underlying graph A in the standard sense of algebraic topology and the Bass–Serre covering tree A ~ {\displaystyle {\ti... | Bass–Serre theory | 0.783765 |
83,463 | Let g be an element of G = π1(A, T) represented as a product of the form g = a 0 e 1 a 1 … e n a n , {\displaystyle g=a_{0}e_{1}a_{1}\dots e_{n}a_{n},} where e1, ..., en is a closed edge-path in A with the vertex sequence v0, v1, ..., vn = v0 (that is v0=o(e1), vn = t(en) and vi = t(ei) = o(ei+1) for 0 < i < n) and whe... | Bass–Serre theory | 0.783765 |
83,464 | Some software packages and specialized applications either developed for or hosted on Ridge and Bull-SEMS SPS 9 computers are listed below: The CDA 5000 design automation system from Cericor Inc. was offered for the Ridge 32C and Ridge 32S in February 1985. Silicon Graphics' Geometry Engine was integrated with the Ridg... | Ridge Computers | 0.783765 |
83,465 | The Arithmeum is a mathematics museum owned by the Forschungsinstitut für Diskrete Mathematik (Research Institute for Discrete Mathematics) at the University of Bonn. It was founded in 2008 by the director of the institute, Bernhard Korte, who contributed his private collection of calculating machines. The building's s... | Arithmeum | 0.783764 |
83,466 | The tangled nature model provides different methods for demonstrating and predicting trends in evolutionary ecology. The model analyzes an individual prone to mutation within a population as well as other factors such as extinction rate. The model was developed by Simon Laird, Daniel Lawson, and Henrik Jeldtoft Jensen ... | Evolutionary ecology | 0.783764 |
83,467 | The effects of evolutionary ecology and its consequences can be seen in the case of color variation among African cichlid fish. With over 2,000 species, cichlid fishes are very species-rich and capable of complex social interactions. Polychromatism, the variation of color patterns within a population, occurs within cic... | Evolutionary ecology | 0.783764 |
83,468 | George Evelyn Hutchinson’s (1903–1991) contributions to the field of ecology spanned over 60 years, in which he had significant influence in systems ecology, radiation ecology, limnology, and entomology. Described as the “father of modern ecology” by Stephen Jay Gould, Hutchinson was one of the first scientists to link... | Evolutionary ecology | 0.783764 |
83,469 | Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can be seen as an approach to the study of evolution that incorporates an under... | Evolutionary ecology | 0.783764 |
83,470 | Ecological genetics tie into evolutionary ecology through the study of how traits evolve in natural populations. Ecologists are concerned with how the environment and timeframe leads to genes becoming dominant. Organisms must continually adapt in order to survive in natural habitats. Genes define which organisms surviv... | Evolutionary ecology | 0.783764 |
83,471 | According to the University of Texas, Eric Pianka’s (1939–present) work in evolutionary ecology includes foraging strategies, reproductive tactics, competition and niche theory, community structure and organization, species diversity, and understanding rarity. Pianka is also known for his interest in lizards to study e... | Evolutionary ecology | 0.783764 |
83,472 | A large part of evolutionary ecology is about utilising models and finding empirical data as proof. Examples include the Lack clutch size model devised by David Lack and his study of Darwin's finches on the Galapagos Islands. Lack's study of Darwin's finches was important in analyzing the role of different ecological f... | Evolutionary ecology | 0.783764 |
83,473 | The basis of the central principles of evolutionary ecology can be attributed to Charles Darwin (1809–1882), specifically in referencing his theory of natural selection and population dynamics, which discusses how populations of a species change over time. According to Ernst Mayr, professor of Zoology at Harvard Univer... | Evolutionary ecology | 0.783764 |
83,474 | Robert MacArthur (1930–1972) is best known in the field of Evolutionary Ecology for his work The Theory of Island Biogeography, in which he and his co-author propose “that the number of species on any island reflects a balance between the rate at which new species colonize it and the rate at which populations of establ... | Evolutionary ecology | 0.783764 |
83,475 | R. A. Fisher (1890–1962), whose 1930 fundamental theorem of natural selection recognised the power of rigorous application of the theory of natural selection to population biology. David Lack (1910–1973), a follower of Charles Darwin, worked to merge the fields of evolutionary biology and ecology, focusing mainly on bi... | Evolutionary ecology | 0.783764 |
83,476 | Michael Rosenzweig's idea of reconciliation ecology was developed based on existing research, which was conducted on the principle first suggested by Alexander von Humboldt stating that larger areas of land will have increased species diversity as compared to smaller areas. This research focused on species-area relatio... | Evolutionary ecology | 0.783764 |
83,477 | Michael L. Rosenzweig (1941–present) created and popularized Reconciliation ecology, which began with his theory that designated nature preserves would not be enough land to conserve the biodiversity of Earth, as humans have used so much land that they have negatively impacted biogeochemical cycles and had other ecolog... | Evolutionary ecology | 0.783764 |
83,478 | In quantum mechanics, spacetime transformations act on quantum states. The parity transformation, P ^ {\displaystyle {\hat {\mathcal {P}}}} , is a unitary operator, in general acting on a state ψ {\displaystyle \psi } as follows: P ^ ψ ( r ) = e i ϕ / 2 ψ ( − r ) {\displaystyle {\hat {\mathcal {P}}}\,\psi {\left(r\righ... | Parity transformation | 0.783764 |
83,479 | Undesired behavior may also arise from flaws in the system's perception (arising either from within the software or from sensor degradation), knowledge representation and reasoning, or from software bugs. : 14–18 They may arise from improper training, such as a user applying the same algorithm to two problems that do n... | Workplace impact of artificial intelligence | 0.783763 |
83,480 | There are several broad aspects of AI that may give rise to specific hazards. The risks depend on implementation rather than the mere presence of AI. : 2–3 Systems using sub-symbolic AI such as machine learning may behave unpredictably and are more prone to inscrutability in their decision-making. This is especially tr... | Workplace impact of artificial intelligence | 0.783763 |
83,481 | These include changes in the skills required of workers, increased monitoring leading to micromanagement, algorithms unintentionally or intentionally mimicking undesirable human biases, and assigning blame for machine errors to the human operator instead. AI may also lead to physical hazards in the form of human–robot ... | Workplace impact of artificial intelligence | 0.783763 |
83,482 | When used in the workplace, AI also presents the possibility of new hazards. These may arise from machine learning techniques leading to unpredictable behavior and inscrutability in their decision-making, or from cybersecurity and information privacy issues. Many hazards of AI are psychosocial due to its potential to c... | Workplace impact of artificial intelligence | 0.783763 |
83,483 | The impact of artificial intelligence on workers includes both applications to improve worker safety and health, and potential hazards that must be controlled. One potential application is using AI to eliminate hazards by removing humans from hazardous situations that involve risk of stress, overwork, or musculoskeleta... | Workplace impact of artificial intelligence | 0.783763 |
83,484 | AI, in common with other computational technologies, requires cybersecurity measures to stop software breaches and intrusions,: 17 as well as information privacy measures. Communication and transparency with workers about data usage is a control for psychosocial hazards arising from security and privacy issues. Propose... | Workplace impact of artificial intelligence | 0.783763 |
83,485 | AI can also be used to make the workplace safety and health workflow more efficient. One example is coding of workers' compensation claims, which are submitted in a prose narrative form and must manually be assigned standardized codes. AI is being investigated to perform this task faster, more cheaply, and with fewer e... | Workplace impact of artificial intelligence | 0.783763 |
83,486 | : 3–7 Decision support systems have a similar ability to be used to, for example, prevent industrial disasters or make disaster response more efficient.For manual material handling workers, predictive analytics and artificial intelligence may be used to reduce musculoskeletal injury. Traditional guidelines are based on... | Workplace impact of artificial intelligence | 0.783763 |
83,487 | Machine learning is used for people analytics to make predictions about worker behavior to assist management decision-making, such as hiring and performance assessment. These could also be used to improve worker health. The analytics may be based on inputs such as online activities, monitoring of communications, locati... | Workplace impact of artificial intelligence | 0.783763 |
83,488 | In recent years, the adoption of modern robotics has led to net employment growth. However, many businesses anticipate that automation, or employing robots would result in job losses in the future. This is especially true for companies in Central and Eastern Europe. Other digital technologies, such as platforms or big ... | Workplace impact of artificial intelligence | 0.783763 |
83,489 | Understanding the Jacobson radical lies in a few different cases: namely its applications and the resulting geometric interpretations, and its algebraic interpretations. | Jacobson radical | 0.783763 |
83,490 | If f: R → S is a surjective ring homomorphism, then f(J(R)) ⊆ J(S). If R is a ring with unity and M is a finitely generated left R-module with J(R)M = M, then M = 0 (Nakayama's lemma). J(R) contains all central nilpotent elements, but contains no idempotent elements except for 0. J(R) contains every nil ideal of R. If ... | Jacobson radical | 0.783763 |
83,491 | If R is unital and is not the trivial ring {0}, the Jacobson radical is always distinct from R since rings with unity always have maximal right ideals. However, some important theorems and conjectures in ring theory consider the case when J(R) = R - "If R is a nil ring (that is, each of its elements is nilpotent), is t... | Jacobson radical | 0.783763 |
83,492 | In this case the nilradical and the Jacobson radical coincide. This means we could interpret the Jacobson radical as a measure for how far the ideal I {\displaystyle I} defining the ring R {\displaystyle R} is from defining the ring of functions on an algebraic variety because of the Hilbert Nullstellensatz theorem. Th... | Jacobson radical | 0.783763 |
83,493 | The Jacobson radical of a ring has various internal and external characterizations. The following equivalences appear in many noncommutative algebra texts such as (Anderson & Fuller 1992, §15), (Isaacs 1994, §13B), and (Lam 2001, Ch 2). The following are equivalent characterizations of the Jacobson radical in rings wit... | Jacobson radical | 0.783763 |
83,494 | Start with a finite, acyclic quiver Γ and a field K and consider the quiver algebra K Γ (as described in the Quiver article). The Jacobson radical of this ring is generated by all the paths in Γ of length ≥ 1. The Jacobson radical of a C*-algebra is {0}. This follows from the Gelfand–Naimark theorem and the fact that f... | Jacobson radical | 0.783763 |
83,495 | This is an important case because of its use in applying Nakayama's lemma. In particular, it implies if we have an algebraic vector bundle E → X {\displaystyle E\to X} over a scheme or algebraic variety X {\displaystyle X} , and we fix a basis of E | p {\displaystyle E|_{p}} for some point p ∈ X {\displaystyle p\in X} ... | Jacobson radical | 0.783763 |
83,496 | This was demonstrated in 2003 and in 2017 was used to image mouse brain at a voxel size of about one cubic micrometer (see below).With the applications continuing to grow, X-ray microscopy has become a routine, proven technique used in environmental and soil sciences, geo- and cosmo-chemistry, polymer sciences, biology... | X-ray microscope | 0.783762 |
83,497 | Microscopy methods including tomography, cryo-, and cryo-tomography were successfully demonstrated. With rapid development, X-ray microscopy found new applications in soil science, geochemistry, polymer sciences, and magnetism. The hardware was also miniaturized, so that researchers could perform experiments in their o... | X-ray microscope | 0.783762 |
83,498 | One early applications of X-ray microscopy in biology was contact imaging, pioneered by Goby in 1913. In this technique, soft x-rays irradiate a specimen and expose the x-ray sensitive emulsions beneath it. Then, magnified tomographic images of the emulsions, which correspond to the x-ray opacity maps of the specimen, ... | X-ray microscope | 0.783762 |
83,499 | Historic records indicate that preparations containing strychnine (presumably) had been used to kill dogs, cats, and birds in Europe as far back as 1640. It was also used during World War II by the Dirlewanger Brigade against civilian population.The structure of strychnine was first determined in 1946 by Sir Robert Rob... | Strychnine | 0.783762 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.