id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
33,100 | Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry, medi... | Neuroscience | 0.803588 |
33,101 | Modern neuroscience education and research activities can be very roughly categorized into the following major branches, based on the subject and scale of the system in examination as well as distinct experimental or curricular approaches. Individual neuroscientists, however, often work on questions that span several d... | Neuroscience | 0.803588 |
33,102 | Rather, the total complexity of m {\displaystyle m} cells is at most Θ ( m 2 / 3 n 2 / 3 + n ) {\displaystyle \Theta (m^{2/3}n^{2/3}+n)} , almost the same bound as occurs in the Szemerédi–Trotter theorem on point-line incidences in the plane. A simple proof of this follows from the crossing number inequality: if m {\di... | Arrangements of lines | 0.803586 |
33,103 | Finding matching upper and lower bounds for the complexity of a k {\displaystyle k} -level remains a major open problem in discrete geometry. The best upper bound is O ( n k 1 / 3 ) {\displaystyle O(nk^{1/3})} , while the best lower bound is n 2 Ω ( log k ) {\displaystyle n2^{\Omega ({\sqrt {\log k}})}} . In contrast... | Arrangements of lines | 0.803586 |
33,104 | The zone theorem states that the total number of edges in the cells of a single zone is linear. More precisely, the total number of edges of the cells belonging to a single side of line ℓ {\displaystyle \ell } is at most 5 n − 1 {\displaystyle 5n-1} , and the total number of edges of the cells belonging to both sides o... | Arrangements of lines | 0.803586 |
33,105 | In geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines. Problems of counting the features of arrangements have been studied in discrete geometry, and computational geometers have found algorithms for the efficient construction of arrangements. | Arrangements of lines | 0.803586 |
33,106 | A line arrangement in the projective plane differs from its Euclidean counterpart in that the two Euclidean rays at either end of a line are replaced by a single edge in the projective plane that connects the leftmost and rightmost vertices on that line, and in that pairs of unbounded Euclidean cells are replaced in th... | Arrangements of lines | 0.803586 |
33,107 | It is often convenient to study line arrangements not in the Euclidean plane but in the projective plane, due to the fact that in projective geometry every pair of lines has a crossing point. In the projective plane, it is not possible to define arrangements using sides of lines, because a line in the projective plane ... | Arrangements of lines | 0.803586 |
33,108 | This includes further education about microbial, molecular and cell biology. Classes can include cell biology, virology, microbial and plant biology | Environmental engineering science | 0.803584 |
33,109 | The upper division classes in Environmental Engineering Science prepares the student for work in the fields of engineering and science with coursework in subjects including the following: Fluid mechanics Mechanics of materials Thermodynamics Environmental engineering Advanced math and statistics Geology Physical, organ... | Environmental engineering science | 0.803584 |
33,110 | The multidisciplinary approach in Environmental Engineering Science gives the student expertise in technical fields related to their own personal interest. While some graduates choose to use this major to go to graduate school, students who choose to work often go into the fields of civil and environmental engineering,... | Environmental engineering science | 0.803584 |
33,111 | For this track, students take classes introducing them to ways to conserve natural resources. This can include classes in water chemistry, sanitation, combustion, air pollution and radioactive waste management. | Environmental engineering science | 0.803584 |
33,112 | Environmental engineering science (EES) is a multidisciplinary field of engineering science that combines the biological, chemical and physical sciences with the field of engineering. This major traditionally requires the student to take basic engineering classes in fields such as thermodynamics, advanced math, compute... | Environmental engineering science | 0.803584 |
33,113 | At MIT, the major is described in their curriculum, including the following: The Bachelor of Science in Environmental Engineering Science emphasizes the fundamental physical, chemical, and biological processes necessary for understanding the interactions between man and the environment. Issues considered include the pr... | Environmental engineering science | 0.803584 |
33,114 | This is meant to direct the environmental engineer into a field where they will more than likely assist in building treatment facilities, preparing environmental impact assessments or helping to mitigate air pollution from specific point sources. Meanwhile, the environmental engineering science student will choose a di... | Environmental engineering science | 0.803584 |
33,115 | As a recently created program, environmental engineering science has not yet been incorporated into the terminology found among environmentally focused professionals. In the few engineering colleges that offer this major, the curriculum shares more classes in common with environmental engineering than it does with envi... | Environmental engineering science | 0.803584 |
33,116 | The College of Engineering at UF defines Environmental Engineering Science as follows: The broad undergraduate environmental engineering curriculum of EES has earned the department a ranking as a leading undergraduate program. The ABET accredited engineering bachelor's degree is comprehensively based on physical, chemi... | Environmental engineering science | 0.803584 |
33,117 | The College of Engineering at UC Berkeley defines Environmental Engineering Science, including the following: This is a multidisciplinary field requiring an integration of physical, chemical and biological principles with engineering analysis for environmental protection and restoration. The program incorporates course... | Environmental engineering science | 0.803584 |
33,118 | The Civil and Environmental Engineering department at Stanford University provides the following description for their program in Environmental Engineering and Science: The Environmental Engineering and Science (EES) program focuses on the chemical and biological processes involved in water quality engineering, water a... | Environmental engineering science | 0.803584 |
33,119 | On this track, students are introduced to the fundamental reaction mechanisms in the field of chemical and biochemical engineering. | Environmental engineering science | 0.803584 |
33,120 | Lower division coursework in this field requires the student to take several laboratory-based classes in calculus-based physics, chemistry, biology, programming and analysis. This is intended to give the student background information in order to introduce them to the engineering fields and to prepare them for more tec... | Environmental engineering science | 0.803584 |
33,121 | In the lambda calculus, a term is in beta normal form if no beta reduction is possible. A term is in beta-eta normal form if neither a beta reduction nor an eta reduction is possible. A term is in head normal form if there is no beta-redex in head position. The normal form of a term, if one exists, is unique (as a coro... | Beta normal form | 0.803584 |
33,122 | A head normal form is a term that does not contain a beta redex in head position, i.e. that cannot be further reduced by a head reduction. When considering the simple lambda calculus (viz. without the addition of constant or function symbols, meant to be reduced by additional delta rule), head normal forms are the term... | Beta normal form | 0.803584 |
33,123 | In the lambda calculus, a beta redex is a term of the form: ( λ x . A ) M {\displaystyle (\mathbf {\lambda } x.A)M} .A redex r {\displaystyle r} is in head position in a term t {\displaystyle t} , if t {\displaystyle t} has the following shape (note that application has higher priority than abstraction, and that the fo... | Beta normal form | 0.803584 |
33,124 | Since 2002 the journal has been hosted by the David R. Cheriton School of Computer Science at the University of Waterloo, with Waterloo professor Jeffrey Shallit as its editor-in-chief. There are no page charges for authors, and all papers are free to all readers. The journal publishes approximately 50–75 papers annual... | Journal of Integer Sequences | 0.80358 |
33,125 | (527.702, 527.712) Synergetics does not aim to replace or invalidate pre-existing geometry or mathematics, as evidenced by the opening dedication to H.S.M. Coxeter, whom Fuller considered the greatest geometer of his era. Fuller acknowledges his vocabulary is "remote" even while defending his word choices. (250.30) | Synergetics coordinates | 0.803578 |
33,126 | Synergetics is the empirical study of systems in transformation, with an emphasis on whole system behaviors unpredicted by the behavior of any components in isolation. R. Buckminster Fuller (1895–1983) named and pioneered the field. His two-volume work Synergetics: Explorations in the Geometry of Thinking, in collabora... | Synergetics coordinates | 0.803578 |
33,127 | Many have tried to create automatic control and monitoring systems and some of these demonstrated a level of success. For instance, researchers were able to introduce automation in a small scale aquaponic system to achieve a cost-effective and sustainable farming system. Commercial development of automation technologie... | Aquaponics | 0.803577 |
33,128 | It is known as the universal property of free groups, and the generating set S is called a basis for FS. The basis for a free group is not uniquely determined. Being characterized by a universal property is the standard feature of free objects in universal algebra. In the language of category theory, the construction o... | Free group | 0.803577 |
33,129 | In mathematics, the free group FS over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t−1 for s,t,u ∈ S). The members of S are called generators of FS, and the number of generat... | Free group | 0.803577 |
33,130 | This method employs incremental layer by layer training based on regression analysis, where useless units in hidden layers are pruned with the help of a validation set. The history of recurrent neural networks (RNNs) goes back even further to the 1920s. Wilhelm Lenz (1920) and Ernst Ising (1925) created and analyzed th... | Parallel distributed processing | 0.803575 |
33,131 | The second wave begun in late 1980s, following the 1987 book about the Parallel Distributed Processing by James L. McClelland, David E. Rumelhart et al., which has introduced a couple of improvements to the simple perceptron idea, such as intermediate processors (known as "hidden layers" now) alongside input and output... | Parallel distributed processing | 0.803575 |
33,132 | In 1972, Shun'ichi Amari made this architecture adaptive. The first deep learning MLP trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari. In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classi... | Parallel distributed processing | 0.803574 |
33,133 | The first wave begun in 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach, and Frank Rosenblatt who published the 1958 book “The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain” in Psycho... | Parallel distributed processing | 0.803574 |
33,134 | Their work has, in turn, built upon that of John Hopfield, who was a key figure investigating the mathematical characteristics of sigmoid activation functions. From the late 1980s to the mid-1990s, connectionism took on an almost revolutionary tone when Schneider, Terence Horgan and Tienson posed the question of whethe... | Parallel distributed processing | 0.803574 |
33,135 | Connectionism (coined by Edward Thorndike in the 1930s) is a name of an approach to the study of human mental processes and cognition that utilizes mathematical models known as connectionist networks or artificial neural networks. Connectionism has had many 'waves' along the time since its beginnings. The first wave ap... | Parallel distributed processing | 0.803574 |
33,136 | Some researchers suggest that the analysis gap is the consequence of connectionist mechanisms giving rise to emergent phenomena that may be describable in computational terms.In the 2000s, the popularity of dynamical systems in philosophy of mind have added a new perspective on the debate; some authors now argue that a... | Parallel distributed processing | 0.803574 |
33,137 | Neural networks follow two basic principles: Any mental state can be described as an (N)-dimensional vector of numeric activation values over neural units in a network. Memory and learning are created by modifying the 'weights' of the connections between neural units, generally represented as an N×M matrix. The weights... | Parallel distributed processing | 0.803574 |
33,138 | However, some engineers in other fields obtain licenses for the ability to serve as professional witnesses in courts, before government committees or just for prestige—even though they may never actually sign and seal design documents. Areas that include much of mechanical, aerospace and chemical engineering may be spe... | Professional engineering | 0.803574 |
33,139 | For instance, the state of Florida requires businesses offering engineering services to be registered with the state and have a Florida licensed professional engineer qualify the business.Civil engineers account for a large portion of licensed professional engineers. In Texas, for example, about 37 percent of licenses ... | Professional engineering | 0.803574 |
33,140 | Others, known as "discipline states", issue licenses for specific disciplines of engineering, such as civil engineering, mechanical engineering, nuclear engineering, electrical engineering and chemical engineering. However, in all cases engineers are ethically required to limit their practice to their area of competenc... | Professional engineering | 0.803574 |
33,141 | Some states also have state-specific examinations. California requires two additional exams in land surveying and earthquake engineering for civil engineering candidates and many states have exams based on their individual laws and ethics requirements. Some states issue generic professional engineering licenses. | Professional engineering | 0.803574 |
33,142 | Regulation and titling of engineers in Europe are handled differently by various countries. In Germany and some other European and Latin American countries, the term diploma engineer implies that the person has completed typically one year of academic work beyond the basic Bachelor of Engineering degree and completed a... | Professional engineering | 0.803574 |
33,143 | The efficient coding hypothesis was proposed by Horace Barlow in 1961 as a theoretical model of sensory coding in the brain. Within the brain, neurons communicate with one another by sending electrical impulses referred to as action potentials or spikes. One goal of sensory neuroscience is to decipher the meaning of th... | Efficient coding hypothesis | 0.803574 |
33,144 | Central to Barlow's hypothesis is information theory, which when applied to neuroscience, argues that an efficiently coding neural system "should match the statistics of the signals they represent". Therefore, it is important to be able to determine the statistics of the natural images that are producing these signals.... | Efficient coding hypothesis | 0.803574 |
33,145 | 1. Predicted model approach In one study by Doi et al. in 2012, the researchers created a predicted response model of the retinal ganglion cells that would be based on the statistics of the natural images used, while considering noise and biological constraints. They then compared the actual information transmission as... | Efficient coding hypothesis | 0.803574 |
33,146 | Simoncelli and Olshausen outline the three major concepts that are assumed to be involved in the development of systems neuroscience: an organism has specific tasks to perform neurons have capabilities and limitations an organism is in a particular environment.One assumption used in testing the Efficient Coding Hypothe... | Efficient coding hypothesis | 0.803574 |
33,147 | Researchers should consider how the visual information is used: The hypothesis does not explain how the information from a visual scene is used—which is the main purpose of the visual system. It seems necessary to understand why we are processing image statistics from the environment because this may be relevant to how... | Efficient coding hypothesis | 0.803574 |
33,148 | One of the implications of the efficient coding hypothesis is that the neural coding depends upon the statistics of the sensory signals. These statistics are a function of not only the environment (e.g., the statistics of the natural environment), but also the organism's behavior (e.g., how it moves within that environ... | Efficient coding hypothesis | 0.803574 |
33,149 | One approach is to design a model for early sensory processing based on the statistics of a natural image and then compare this predicted model to how real neurons actually respond to the natural image. The second approach is to measure a neural system responding to a natural environment, and analyze the results to see... | Efficient coding hypothesis | 0.803574 |
33,150 | Diseases (Hepatitis A: 甲型肝炎 jiǎxíng gānyán; Hepatitis B: 乙型肝炎 yǐxíng gānyán) Sports leagues (Serie A: 意甲 yìjiǎ) Vitamins (although currently, in this case, the ABC system is more popular) Characters conversing in a short text (甲 speaks first, 乙 answers) Students' grades in Taiwan: with an additional Yōu (優 "Excellence"... | Celestial Stems | 0.803571 |
33,151 | The catalytic residues of the cytoplasmic PNGase is known to reside in a domain called transglutaminase domain. NGLY1, when compared with the yeast orthologues, possesses extended N-terminal and C-terminal sequences in addition to the transglutaminase domain. Among the additional domains found in NGLY1, the PUB (PNGase... | N-glycanase 1 | 0.803567 |
33,152 | Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point. A change of value of t... | Cerebellar Model Arithmetic Computer | 0.803567 |
33,153 | The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory.The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 ... | Cerebellar Model Arithmetic Computer | 0.803567 |
33,154 | Adding zero to any number, does not change the number; this means that zero is the identity element for addition, and is also known as the additive identity. In symbols, for every a, one has a + 0 = 0 + a = a.This law was first identified in Brahmagupta's Brahmasphutasiddhanta in 628 AD, although he wrote it as three s... | Addition table | 0.803567 |
33,155 | This identity allows multiplication to be carried out by consulting a table of logarithms and computing addition by hand; it also enables multiplication on a slide rule. The formula is still a good first-order approximation in the broad context of Lie groups, where it relates multiplication of infinitesimal group eleme... | Addition table | 0.803567 |
33,156 | To find the minimums a variational method is used, resulting in a set of nonlinear differential equations, called Brown's equations after William Fuller Brown Jr. Although in principle these equations can be solved for the stable domain configurations M(x), in practice only the simplest examples can be solved. Analytic... | Multidomain (magnetic) | 0.803565 |
33,157 | The National Center for Education Statistics (NCES) conducted a distance education study based on the 2001-2002 academic year at United States 2-year and 4-year degree-granting institutions that were eligible for U.S. federal student aid. The study reported that 56 percent of institutions surveyed offered distance educ... | Online degree | 0.803565 |
33,158 | This reduces the chance of inadvertently introducing bugs. Both coarse-grained and fine-grained parallelism are possible. In irregular multi-physics applications which do not adhere solely to the SPMD mode of computation, as encountered in tightly coupled fluid-particulate systems, the flexibility of OpenMP can have a ... | OpenMP | 0.803563 |
33,159 | copyprivate: used with single to support the copying of data values from private objects on one thread (the single thread) to the corresponding objects on other threads in the team.Reduction reduction (operator | intrinsic: list): the variable has a local copy in each thread, but the values of the local copies will be ... | OpenMP | 0.803563 |
33,160 | In July 1987, Lower Saxony’s minister of Science and Art approved the establishment of the ICBM as a cooperation of the university departments of mathematics, biology, physics and chemistry. In 1991, the ICBM was approved as a central organisation of the University of Oldenburg. The registered association „Centre for R... | Institute for Chemistry and Biology of the Marine Environment | 0.803562 |
33,161 | The courses of study are closely related to the research activities to provide interdisciplinary and research-oriented training. The institute offers a broad bachelor programme with contents of marine, environmental and landscape-ecological sciences as well as four Master Programmes which are: Marine Environmental Scie... | Institute for Chemistry and Biology of the Marine Environment | 0.803562 |
33,162 | The Institute for Chemistry and Biology of the Marine Environment of the Carl von Ossietzky University of Oldenburg (German: Institut für Chemie und Biologie des Meeres der Carl von Ossietzky Universität Oldenburg, abbreviated ICBM) is one of the marine science institutes at the German coast and the only university-bas... | Institute for Chemistry and Biology of the Marine Environment | 0.803562 |
33,163 | The ICBM cooperates closely with the Max Planck Institute for Marine Microbiology und MARUM, both located in Bremen; with the Alfred Wegener Institute in Bremerhaven, as well as with the Senckenberg Institute by the Sea and the Jade University of Applied Sciences, both located in Wilhelmshaven. The ICBM is a member of ... | Institute for Chemistry and Biology of the Marine Environment | 0.803562 |
33,164 | The ICBM carries out fundamental and applied research in marine and environmental sciences. Interdisciplinary research will provide understanding of the various interactions of marine environmental systems. The research focuses on marine biogeochemical cycles and energy fluxes, as well as on the functional role of mari... | Institute for Chemistry and Biology of the Marine Environment | 0.803562 |
33,165 | A plasma actuator induces a local flow speed perturbation, which will be developed downstream to a vortex sheet. As a result, plasma actuators can behave as vortex generators. The difference between this and traditional vortex generation is that there are no mechanical moving parts or any drilling holes on aerodynamic ... | Plasma actuator | 0.80356 |
33,166 | Asset valuation is another question that needs to be addressed. Thus, best educated opinions and available statistics are the primary sources of information. Nevertheless, risk assessment should produce such information for senior executives of the organization that the primary risks are easy to understand and that the... | Risk Management | 0.80356 |
33,167 | Several other genus-specific research communities (e.g., Drosophila fruit flies, Mus mice) have adopted nomenclature standards, as well, and have published them on the relevant model organism websites and in scientific journals, including the Trends in Genetics Genetic Nomenclature Guide. Scientists familiar with a par... | Gene nomenclature | 0.803559 |
33,168 | Some basic conventions, such as (1) that animal/human homolog (ortholog) pairs differ in letter case (title case and all caps, respectively) and (2) that the symbol is italicized when referring to the gene but nonitalic when referring to the protein, are often not followed by contributors to medical journals. Many jour... | Gene nomenclature | 0.803559 |
33,169 | The HUGO Gene Nomenclature Committee is responsible for providing human gene naming guidelines and approving new, unique human gene names and symbols (short identifiers typically created by abbreviating). For some nonhuman species, model organism databases serve as central repositories of guidelines and help resources,... | Gene nomenclature | 0.803559 |
33,170 | Epidemiological diagnosis deals with determining and focusing on specific health issue(s) of the community, and the behavioral and environmental factors related to prioritized health needs of the community. Based on these priorities, achievable program goals and objectives for the program being developed are establishe... | PRECEDE-PROCEED model | 0.803558 |
33,171 | As health-related behaviors, such as smoking and excessive use of alcohol, increased or became more resistant to change, so did the recognition that these behaviors are influenced by factors such as the media, politics, and businesses, which are outside the direct control of the individuals. Hence more "ecological" met... | PRECEDE-PROCEED model | 0.803558 |
33,172 | E ∞ {\displaystyle E_{\infty }} -ring spectra While the LEFT is known to produce (homotopy) ring spectra out of M U ∗ {\displaystyle {\mathcal {}}MU_{*}} , it is a much more delicate question to understand when these spectra are actually E ∞ {\displaystyle E_{\infty }} -ring spectra. As of 2010, the best progress was m... | Landweber exact functor theorem | 0.803556 |
33,173 | The archetypical and first known (non-trivial) example is complex K-theory K. Complex K-theory is complex oriented and has as formal group law x + y + x y {\displaystyle x+y+xy} . The corresponding morphism M U ∗ → K ∗ {\displaystyle MU_{*}\to K_{*}} is also known as the Todd genus. We have then an isomorphism K ∗ ( X ... | Landweber exact functor theorem | 0.803556 |
33,174 | This allows to check flatness only against the B P ∗ / I n {\displaystyle BP_{*}/I_{n}} (see Landweber, 1976). The LEFT can be strengthened as follows: let E ∗ {\displaystyle {\mathcal {E}}_{*}} be the (homotopy) category of Landweber exact M U ∗ {\displaystyle MU_{*}} -modules and E {\displaystyle {\mathcal {E}}} the ... | Landweber exact functor theorem | 0.803556 |
33,175 | There is also a version for Brown–Peterson cohomology BP. The spectrum BP is a direct summand of M U ( p ) {\displaystyle MU_{(p)}} with coefficients Z ( p ) {\displaystyle \mathbb {Z} _{(p)}} . The statement of the LEFT stays true if one fixes a prime p and substitutes BP for MU. The classical proof of the LEFT uses ... | Landweber exact functor theorem | 0.803556 |
33,176 | Therefore, one can identify the stack quotient Spec L / / G {\displaystyle {\text{Spec }}L//G} with the stack of (1-dimensional) formal groups M f g {\displaystyle {\mathcal {M}}_{fg}} and M = M U ∗ ( X ) {\displaystyle M=MU_{*}(X)} defines a quasi-coherent sheaf over this stack. Now it is quite easy to see that it suf... | Landweber exact functor theorem | 0.803556 |
33,177 | A module M over M U ∗ {\displaystyle {\mathcal {}}MU_{*}} is the same as a quasi-coherent sheaf F {\displaystyle {\mathcal {F}}} over Spec L {\displaystyle {\text{Spec }}L} , where L is the Lazard ring. If M = M U ∗ ( X ) {\displaystyle M={\mathcal {}}MU_{*}(X)} , then M has the extra datum of a M U ∗ M U {\displaystyl... | Landweber exact functor theorem | 0.803556 |
33,178 | Define for a topological space X E ∗ ( X ) = M U ∗ ( X ) ⊗ M U ∗ R ∗ {\displaystyle E_{*}(X)=MU_{*}(X)\otimes _{MU_{*}}R_{*}} Here R ∗ {\displaystyle R_{*}} gets its M U ∗ {\displaystyle MU_{*}} -algebra structure via F. The question is: is E a homology theory? It is obviously a homotopy invariant functor, which fulfil... | Landweber exact functor theorem | 0.803556 |
33,179 | In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation of a homology theory leads to a formal group law. The Landweber exact functor theorem (or LEFT for short) can be seen as a method to reverse this process: it const... | Landweber exact functor theorem | 0.803556 |
33,180 | Precise positioning is increasingly used in the fields including robotics, autonomous navigation, agriculture, construction, and mining.The major weaknesses of PPP, compared with conventional consumer GNSS methods, are that it takes more processing power, it requires an outside ephemeris correction stream, and it takes... | Precise Point Positioning | 0.803554 |
33,181 | In other words, the varieties of distributive lattices and modular lattices are tolerance factorable, but not strongly tolerance factorable. : 40 Actually, every subvariety of the variety of lattices is tolerance factorable, and the only strongly tolerance factorable subvariety other than itself is the trivial subvarie... | Tolerance relation | 0.803553 |
33,182 | That is, given any lattice ( L , ∨ L , ∧ L ) {\displaystyle (L,\vee _{L},\wedge _{L})} and any tolerance relation ∼ {\displaystyle \sim } on L {\displaystyle L} , for each A , B ∈ L / ∼ {\displaystyle A,B\in L/{\sim }} there exist unique A ∨ L / ∼ B , A ∧ L / ∼ B ∈ L / ∼ {\displaystyle A\vee _{L/{\sim }}B,A\wedge _{L/{... | Tolerance relation | 0.803553 |
33,183 | A set is an algebraic structure with no operations at all. In this case, tolerance relations are simply reflexive symmetric relations and it is trivial that the variety of sets is strongly tolerance factorable. | Tolerance relation | 0.803553 |
33,184 | Therefore, for a variety V {\displaystyle {\mathcal {V}}} of algebraic structures, we may consider the following two conditions. (Tolerance factorability) for any ( A , F ) ∈ V {\displaystyle (A,F)\in {\mathcal {V}}} and any tolerance relation ∼ {\displaystyle \sim } on ( A , F ) {\displaystyle (A,F)} , the uniqueness ... | Tolerance relation | 0.803553 |
33,185 | Let ( A , F ) {\displaystyle (A,F)} be an algebraic structure and let ∼ {\displaystyle \sim } be a tolerance relation on A {\displaystyle A} . Suppose that, for each n {\displaystyle n} -ary operation f ∈ F {\displaystyle f\in F} and C 1 , … , C n ∈ A / ∼ {\displaystyle C_{1},\dots ,C_{n}\in A/{\sim }} , there is a uni... | Tolerance relation | 0.803553 |
33,186 | In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. On a set, an algebraic structure with empty fam... | Tolerance relation | 0.803553 |
33,187 | A tolerance relation on an algebraic structure ( A , F ) {\displaystyle (A,F)} is usually defined to be a reflexive symmetric relation on A {\displaystyle A} that is compatible with every operation in F {\displaystyle F} . A tolerance relation can also be seen as a cover of A {\displaystyle A} that satisfies certain co... | Tolerance relation | 0.803553 |
33,188 | A tolerance relation on an algebraic structure ( A , F ) {\displaystyle (A,F)} is a cover C {\displaystyle {\mathcal {C}}} of A {\displaystyle A} that satisfies the following three conditions. : 307, Theorem 3 For every C ∈ C {\displaystyle C\in {\mathcal {C}}} and S ⊆ C {\displaystyle {\mathcal {S}}\subseteq {\mathcal... | Tolerance relation | 0.803553 |
33,189 | A tolerance relation on an algebraic structure ( A , F ) {\displaystyle (A,F)} is a binary relation ∼ {\displaystyle \sim } on A {\displaystyle A} that satisfies the following conditions. (Reflexivity) a ∼ a {\displaystyle a\sim a} for all a ∈ A {\displaystyle a\in A} (Symmetry) if a ∼ b {\displaystyle a\sim b} then b ... | Tolerance relation | 0.803553 |
33,190 | On a group, every tolerance relation is a congruence relation. In particular, this is true for all algebraic structures that are groups when some of their operations are forgot, e.g. rings, vector spaces, modules, Boolean algebras, etc.: 261–262 Therefore, the varieties of groups, rings, vector spaces, modules and Bool... | Tolerance relation | 0.803553 |
33,191 | Let ∼ {\displaystyle \sim } be a tolerance binary relation on an algebraic structure ( A , F ) {\displaystyle (A,F)} . Let A / ∼ {\displaystyle A/{\sim }} be the family of maximal subsets C ⊆ A {\displaystyle C\subseteq A} such that c ∼ d {\displaystyle c\sim d} for every c , d ∈ C {\displaystyle c,d\in C} . Using grap... | Tolerance relation | 0.803553 |
33,192 | In data analysis, the radius of gyration is used to calculate many different statistics including the spread of geographical locations. These locations have recently been collected from social media users to investigate the typical mentions of a user. This can be useful for understanding how a certain group of users on... | Radius of Gyration | 0.80355 |
33,193 | In polymer physics, the radius of gyration is used to describe the dimensions of a polymer chain. The radius of gyration of an individual homopolymer with degree of polymerization N at a given time is defined as: R g 2 = d e f 1 N ∑ k = 1 N | r k − r m e a n | 2 {\displaystyle R_{\mathrm {g} }^{2}\ {\stackrel {\mathrm ... | Radius of Gyration | 0.80355 |
33,194 | Anal. 17 (2008), no. 5, 1551–1620. (with Frédéric Haglund) A combination theorem for special cube complexes. | Oswald Veblen Prize in Geometry | 0.803549 |
33,195 | Topology 42 (2003), no. 5, 1003–1063. The symplectic topology of Ramanujam's surface. Comment. | Oswald Veblen Prize in Geometry | 0.803549 |
33,196 | (with Benedict Gross) Elliptic spectra, the Witten genus and the theorem of the cube. Invent. Math. | Oswald Veblen Prize in Geometry | 0.803549 |
33,197 | 30 (1994), no. 1, 76–86. (with Benedict Gross) Equivariant vector bundles on the Lubin-Tate moduli space. Topology and representation theory (Evanston, IL, 1992), 23–88, Contemp. | Oswald Veblen Prize in Geometry | 0.803549 |
33,198 | 46 (1997), no. 3, 406–480. (with Tobias Colding)2001 Yakov Eliashberg for:Combinatorial methods in symplectic geometry. Proceedings of the International Congress of Mathematicians, Vol. | Oswald Veblen Prize in Geometry | 0.803549 |
33,199 | 101 (1990), no. 1, 101–172. Compactness theorems for Kähler-Einstein manifolds of dimension 3 and up. J. Differential Geom. | Oswald Veblen Prize in Geometry | 0.803549 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.