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90,000 | In Feynman's path integral, the classical notion of a unique trajectory for a particle is replaced by an infinite sum of classical paths, each weighted differently according to its classical properties. Functional integration is central to quantization techniques in theoretical physics. The algebraic properties of func... | Functional integral | 0.781059 |
90,001 | Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of ... | Functional integral | 0.781059 |
90,002 | The probability for the class of paths can be found by multiplying the probabilities of starting in one region and then being at the next. The Wiener measure can be developed by considering the limit of many small regions. Itō and Stratonovich calculus | Functional integral | 0.781059 |
90,003 | Waldhausen introduced the idea of a trace map from the algebraic K-theory of a ring to its Hochschild homology; by way of this map, information can be obtained about the K-theory from the Hochschild homology. Bökstedt factorized this trace map, leading to the idea of a functor known as the topological Hochschild homolo... | K-theory of a category | 0.781059 |
90,004 | For instance, the K-theory is a 'universal additive invariant' of dg-categories and small stable ∞-categories.The motivation for this notion comes from algebraic K-theory of rings. For a ring R Daniel Quillen in Quillen (1973) introduced two equivalent ways to find the higher K-theory. The plus construction expresses K... | K-theory of a category | 0.781059 |
90,005 | In algebraic K-theory, the K-theory of a category C (usually equipped with some kind of additional data) is a sequence of abelian groups Ki(C) associated to it. If C is an abelian category, there is no need for extra data, but in general it only makes sense to speak of K-theory after specifying on C a structure of an e... | K-theory of a category | 0.781059 |
90,006 | In algebra, the S-construction is a construction in algebraic K-theory that produces a model that can be used to define higher K-groups. It is due to Friedhelm Waldhausen and concerns a category with cofibrations and weak equivalences; such a category is called a Waldhausen category and generalizes Quillen's exact cate... | K-theory of a category | 0.781059 |
90,007 | Consider the category of pointed finite sets. This category has an object k + = { 0 , 1 , … , k } {\textstyle k_{+}=\{0,1,\ldots ,k\}} for every natural number k, and the morphisms in this category are the functions f: m + → n + {\textstyle f:m_{+}\to n_{+}} which preserve the zero element. A theorem of Barratt, Priddy... | K-theory of a category | 0.781059 |
90,008 | This category has a natural Waldhausen structure, and the forgetful functor ↦ ( A , A ′ ) {\displaystyle \mapsto (A,A')} from E ( C ) {\displaystyle {\mathcal {E}}(C)} to C × C respects it. The additivity theorem says that the induced map on K-theory spaces K ( E ( C ) ) → K ( C ) × K ( C ) {\displaystyle K({\mathcal ... | K-theory of a category | 0.781059 |
90,009 | Most basic properties of algebraic K-theory of categories are consequences of the following important theorem. There are versions of it in all available settings. Here's a statement for Waldhausen categories. | K-theory of a category | 0.781059 |
90,010 | Pedometric mapping, or statistical soil mapping, is data-driven generation of soil property and class maps that is based on use of statistical methods. Its main objectives are to predict values of some soil variable at unobserved locations, and to access the uncertainty of that estimate using statistical inference i.e.... | Pedometric mapping | 0.781057 |
90,011 | Pedometric analyses rely strictly on geostatistics, whereas digital soil mapping uses more traditional soil-mapping concepts not strictly pedometric in nature. Also referred to as predictive soil mapping, digital soil mapping relies on computer-assisted inference of soil properties to produce digital maps of discrete s... | Pedometric mapping | 0.781057 |
90,012 | In an injective space, the radius of the minimum ball that contains any set S {\displaystyle S} is equal to half the diameter of S {\displaystyle S} . This follows since the balls of radius half the diameter, centered at the points of S {\displaystyle S} , intersect pairwise and therefore by hyperconvexity have a commo... | Injective metric space | 0.781057 |
90,013 | In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher-dimensional vector spaces. These properties can be defined in two seemingly different ways: hyperconvexity involves the i... | Injective metric space | 0.781057 |
90,014 | A collection of isometries typically form a group, the isometry group. When the group is a continuous group, the infinitesimal generators of the group are the Killing vector fields. The Myers–Steenrod theorem states that every isometry between two connected Riemannian manifolds is smooth (differentiable). A second form... | Orthonormal transformation | 0.781054 |
90,015 | {\displaystyle AA^{\dagger }=\operatorname {I} _{V}\ .} By the Mazur–Ulam theorem, any isometry of normed vector spaces over R {\displaystyle \mathbb {R} } is affine. A linear isometry also necessarily preserves angles, therefore a linear isometry transformation is a conformal linear transformation. ExamplesA linear ma... | Orthonormal transformation | 0.781054 |
90,016 | This brings one to idea of using approximate factorization LU of A as the iteration matrix M. A version of incomplete lower-upper decomposition method was proposed by Stone in 1968. This method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a penta... | Stone method | 0.781051 |
90,017 | Relativistic fluid dynamics studies the macroscopic and microscopic fluid motion at large velocities comparable to the velocity of light. This branch of fluid dynamics accounts for the relativistic effects both from the special theory of relativity and the general theory of relativity. The governing equations are deriv... | Flow characteristic | 0.781051 |
90,018 | In 2010, a new unifying model of aging and the development of complex diseases was proposed, incorporating classical aging theories and epigenetics. Horvath and Raj extended this theory, proposing an epigenetic clock theory of aging with the following tenets: Biological aging results as an unintended consequence of bot... | Epigenetics of aging | 0.781051 |
90,019 | 6) de Lima Camillo et al. (2022) used an optimized deep neural network to create a highly accurate, robust pan-tissue epigenetic clock. The predictor, dubbed AltumAge, was trained on 142 datasets and uses 20,318 CpG sites to achieve one of the lowest reported median absolute errors for human epigenetic age prediction o... | Epigenetics of aging | 0.781051 |
90,020 | They propose the evaluation of DNA methylation at ELOVL2, FHL2, and PENK genes in DNA recovered from both cementum and pulp of the same modern teeth. They wish to apply this method also to historical and relatively ancient human teeth. 4) Galkin et al. used deep neural networks to train an epigenetic aging clock of unp... | Epigenetics of aging | 0.781051 |
90,021 | The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising. The model assumes that the rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market, the loss due to forgetting or... | Sethi model | 0.78105 |
90,022 | The Waterloo Institute for Nanotechnology (WIN) is located at the University of Waterloo and is co-located with the Institute for Quantum Computing in the Mike and Ophelia Lazaridis Quantum-Nano Centre (QNC). WIN is currently headed by Dr. Sushanta Mitra. The Waterloo Institute for Nanotechnology comprises 96 faculty f... | Waterloo Institute for Nanotechnology | 0.781048 |
90,023 | WATlab is a nano-materials metrology research facility, equipped with surface and nano-materials research tools for exploring areas of nanotechnology and nano-scale sciences. | Waterloo Institute for Nanotechnology | 0.781048 |
90,024 | The Institute of Chemistry PNG is the professional organisation supporting chemical sciences in Papua New Guinea and a learned society promoting the science and practice of chemistry. | The Institute of Chemists PNG | 0.781047 |
90,025 | The Institute of Chemistry PNG is a member of the Federation of Asian Chemical Societies (FACS). | The Institute of Chemists PNG | 0.781047 |
90,026 | The Nagell–Lutz theorem generalizes to arbitrary number fields and more general cubic equations. For curves over the rationals, the generalization says that, for a nonsingular cubic curve whose Weierstrass form y 2 + a 1 x y + a 3 y = x 3 + a 2 x 2 + a 4 x + a 6 {\displaystyle y^{2}+a_{1}xy+a_{3}y=x^{3}+a_{2}x^{2}+a_{4... | Nagell–Lutz theorem | 0.781046 |
90,027 | In mathematics, the Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers. It is named for Trygve Nagell and Élisabeth Lutz. | Nagell–Lutz theorem | 0.781046 |
90,028 | In number theory, a bi-twin chain of length k + 1 is a sequence of natural numbers n − 1 , n + 1 , 2 n − 1 , 2 n + 1 , … , 2 k n − 1 , 2 k n + 1 {\displaystyle n-1,n+1,2n-1,2n+1,\dots ,2^{k}n-1,2^{k}n+1\,} in which every number is prime.The numbers n − 1 , 2 n − 1 , … , 2 k n − 1 {\displaystyle n-1,2n-1,\dots ,2^{k}n-1... | Bi-twin chain | 0.781045 |
90,029 | In order to demonstrate the usefulness of the partition function, let us calculate the thermodynamic value of the total energy. This is simply the expected value, or ensemble average for the energy, which is the sum of the microstate energies weighted by their probabilities: or, equivalently, Incidentally, one should n... | Canonical partition function | 0.781044 |
90,030 | In the astronomy of the Solar System, Chrysalis is a hypothetical moon of Saturn, named in 2022 by scientists of the Massachusetts Institute of Technology using data from the Cassini–Huygens mission. The moon would have been torn apart by Saturn's tidal forces, somewhere between 200 and 100 million years ago. Up to 99%... | Chrysalis (hypothetical moon) | 0.781044 |
90,031 | The only exceptions in Fibonacci case for n up to 12 are: F(1) = 1 and F(2) = 1, which have no prime divisors F(6) = 8, whose only prime divisor is 2 (which is F(3)) F(12) = 144, whose only prime divisors are 2 (which is F(3)) and 3 (which is F(4))The smallest primitive prime divisor of F(n) are 1, 1, 2, 3, 5, 1, 13, 7... | Carmichael's theorem | 0.781044 |
90,032 | Given two relatively prime integers P and Q, such that D = P 2 − 4 Q > 0 {\displaystyle D=P^{2}-4Q>0} and PQ ≠ 0, let Un(P, Q) be the Lucas sequence of the first kind defined by U 0 ( P , Q ) = 0 , U 1 ( P , Q ) = 1 , U n ( P , Q ) = P ⋅ U n − 1 ( P , Q ) − Q ⋅ U n − 2 ( P , Q ) for n > 1. {\displaystyle {\begin{aligne... | Carmichael's theorem | 0.781044 |
90,033 | In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind Un(P, Q) with relatively prime parameters P, Q and positive discriminant, an element Un with n ≠ 1, 2, 6 has at least one prime divisor that does not divid... | Carmichael's theorem | 0.781044 |
90,034 | "Advanced" means the character has evolved within a later subgroup of the clade. Phylogenetics is utilized to determine evolutionary relationships and relatedness, to ultimately depict accurate evolutionary lineages. Evolutionary relatedness between living species can be connected by descent from common ancestry. | Primitive (phylogenetics) | 0.781043 |
90,035 | These terms in biology contain no judgement about the sophistication, superiority, value or adaptiveness of the named trait. "Primitive" in biology means only that the character appeared first in the common ancestor of a clade group and has been passed on largely intact to more recent members of the clade. | Primitive (phylogenetics) | 0.781043 |
90,036 | In phylogenetics, a primitive (or ancestral) character, trait, or feature of a lineage or taxon is one that is inherited from the common ancestor of a clade (or clade group) and has undergone little change since. Conversely, a trait that appears within the clade group (that is, is present in any subgroup within the cla... | Primitive (phylogenetics) | 0.781043 |
90,037 | Do-calculus, and specifically the do operator, is used to describe causal relationships in the language of probability. A notation used in do-calculus is, for instance: P ( Y | d o ( X ) ) = P ( Y ) {\displaystyle P(Y|do(X))=P(Y)~} ,which can be read as: “the probability of Y {\displaystyle Y} given that you do X {\dis... | Causal notation | 0.781042 |
90,038 | In nature and human societies, many phenomena have causal relationships where one phenomenon A (a cause) impacts another phenomenon B (an effect). Establishing causal relationships is the aim of many scientific studies across fields ranging from biology and physics to social sciences and economics. It is also a subject... | Causal notation | 0.781042 |
90,039 | In chemistry, many chemical reactions are reversible and described using equations which tend towards a dynamic chemical equilibrium. In these reactions, adding a reactant or a product causes the reaction to occur producing more product, or more reactant, respectively. It is standard to draw “harpoon-type” arrows in pl... | Causal notation | 0.781042 |
90,040 | In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving... | Strange attractors | 0.78104 |
90,041 | There exists a neighborhood of A {\displaystyle A} , called the basin of attraction for A {\displaystyle A} and denoted B ( A ) {\displaystyle B(A)} , which consists of all points b {\displaystyle b} that "enter" A {\displaystyle A} in the limit t → ∞ {\displaystyle t\to \infty } . More formally, B ( A ) {\displaystyle... | Strange attractors | 0.78104 |
90,042 | In the 1940s, researchers, originally at Dow's Chemical Physics Lab, led by Ray McIntire, found a way to make foamed polystyrene. They rediscovered a method first used by Swedish inventor Carl Georg Munters, and obtained an exclusive license to Munters's patent in the United States. Dow found ways to adapt Munters's me... | Styrofoam | 0.781039 |
90,043 | The Split Bregman method solves problems of the form min u | Φ ( u ) | 1 + H ( u ) {\displaystyle \min _{u}|\Phi (u)|_{1}+H(u)} , where Φ {\displaystyle \Phi } and H {\displaystyle H} are both convex, particularly problems of the form min u | Φ u | 1 + | K u − f | 2 {\displaystyle \min _{u}|\Phi u|_{1}+|Ku-f|^{2}} . We... | Bregman method | 0.781037 |
90,044 | The Bregman method is an iterative algorithm to solve certain convex optimization problems involving regularization. The original version is due to Lev M. Bregman, who published it in 1967.The algorithm is a row-action method accessing constraint functions one by one and the method is particularly suited for large opti... | Bregman method | 0.781037 |
90,045 | Learning it turns one into an unwilling traitor as it alters perception and thought. Ted Chiang's 1998 short story "Story of Your Life" developed the concept of the Sapir–Whorf hypothesis as applied to an alien species which visits Earth. The aliens' biology contributes to their spoken and written languages, which are ... | Sapir-Whorf Hypothesis | 0.781037 |
90,046 | It requires an understanding of the dynamics of physical geography, as well as the ways in which human societies conceptualize the environment (human geography). Thus, to a certain degree, it may be seen as a successor of Physische Anthropogeographie (English: "physical anthropogeography")—a term coined by University o... | Integrated geography | 0.781037 |
90,047 | In the mathematical field of integral geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating a function on great circles of the sphere. It was introduced by Paul Funk in 1911, based on the work of Minkowski... | Funk Radon Transform | 0.781035 |
90,048 | As a result, the API remained largely the same with a few existing extensions being promoted to core functionality. Among some developer groups this decision caused something of an uproar, with many developers professing that they would switch to DirectX in protest. Most complaints revolved around the lack of communica... | OpenGL | 0.781034 |
90,049 | Release date: July 31, 2017 more efficient, GPU-sided, geometry processing more efficient shader execution (AZDO) more information through statistics, overflow query and counters higher performance through no error handling contexts clamping of polygon offset function, solves a shadow rendering problem SPIR-V shaders I... | OpenGL | 0.781034 |
90,050 | Innovation may occur due to effort from a range of different agents, by chance, or as a result of a major system failure. According to Peter F. Drucker, the general sources of innovations are changes in industry structure, in market structure, in local and global demographics, in human perception, in the amount of avai... | Incremental innovation | 0.781029 |
90,051 | ALMA was initially a 50-50 collaboration between the National Radio Astronomy Observatory and European Southern Observatory (ESO) and later extended with the help of the other Japanese, Taiwanese, and Chilean partners. ALMA is the largest and most expensive ground-based astronomical project, costing between US$1.4 and ... | Atacama Large Millimetre Array | 0.781028 |
90,052 | The complex was built primarily by European, U.S., Japanese, and Canadian companies and universities. Three prototype antennae have undergone evaluation at the Very Large Array since 2002. General Dynamics C4 Systems and its SATCOM Technologies division was contracted by Associated Universities, Inc. to provide twenty-... | Atacama Large Millimetre Array | 0.781028 |
90,053 | The Bianchi identity says that d ∇ F ∇ = 0 {\displaystyle d_{\nabla }F_{\nabla }=0} .This succinctly captures the complicated tensor formulae of the Bianchi identity in the case of Riemannian manifolds, and one may translate from this equation to the standard Bianchi identities by expanding the connection and curvature... | Connection (vector bundle) | 0.781028 |
90,054 | A version of the second (differential) Bianchi identity from Riemannian geometry holds for a connection on any vector bundle. Recall that a connection ∇ {\displaystyle \nabla } on a vector bundle E → M {\displaystyle E\to M} induces an endomorphism connection on End ( E ) {\displaystyle \operatorname {End} (E)} . Thi... | Connection (vector bundle) | 0.781028 |
90,055 | Since the symmetric power and exterior power of a vector bundle may be viewed naturally as subspaces of the tensor power, S k E , Λ k E ⊂ E ⊗ k {\displaystyle S^{k}E,\Lambda ^{k}E\subset E^{\otimes k}} , the definition of the tensor product connection applies in a straightforward manner to this setting. Indeed, since t... | Connection (vector bundle) | 0.781028 |
90,056 | Evolutionarily, egocentric navigation likely comes from our ancestors who would forage for their food and need to be able to return to the same places daily to find edible plants. This foraging usually occurred in relatively nearby areas and was most commonly done by the females in hunter-gatherer societies. Females, t... | Navigation research | 0.781028 |
90,057 | Thereby, spatial cognition studies also have helped to link cognitive psychology and neuroscience. Scientists in both fields work together to figure out what role spatial cognition plays in the brain as well as to determine the surrounding neurobiological infrastructure. In humans, spatial cognition is closely related ... | Navigation research | 0.781028 |
90,058 | Spatial cognition is the acquisition, organization, utilization, and revision of knowledge about spatial environments. It is most about how animals including humans behave within space and the knowledge they built around it, rather than space itself. These capabilities enable individuals to manage basic and high-level ... | Navigation research | 0.781028 |
90,059 | In mathematics, a smooth compact manifold M is called almost flat if for any ε > 0 {\displaystyle \varepsilon >0} there is a Riemannian metric g ε {\displaystyle g_{\varepsilon }} on M such that diam ( M , g ε ) ≤ 1 {\displaystyle {\mbox{diam}}(M,g_{\varepsilon })\leq 1} and g ε {\displaystyle g_{\varepsilon }} is ε {\... | Gromov-Ruh theorem | 0.781027 |
90,060 | The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables. The operation here is a special case... | Convolution of probability distributions | 0.781025 |
90,061 | In organic chemistry, a diethynylbenzene dianion is an anion consisting of two ethynyl anions as substituents on a benzene ring. With the chemical formula C6H4C2−4, three positional isomers are possible, differing in the relative positions of the two substituents around the ring: ortho-diethynylbenzene dianion meta-die... | Diethynylbenzene dianion | 0.781025 |
90,062 | The addition of lime to soils which are poor in calcium can reduce the uptake of strontium by plants. Likewise in areas where the soil is low in potassium, the addition of a potassium fertilizer can discourage the uptake of cesium into plants. However such treatments with either lime or potash should not be undertaken ... | Fission product | 0.781024 |
90,063 | The shell has several layers, and is typically made of calcium carbonate precipitated out into an organic matrix. It is secreted by a part of the molluscan body known as the mantle. The shells of bivalves are equal sides connected by a hinge. Bivalve shells are collected by professional and amateur conchologists and ar... | Bivalve shell | 0.781021 |
90,064 | When X is the sum of n independent random variables X1, ..., Xn, the moment generating function of X is the product of the individual moment generating functions, giving that: and: Pr ( X ≤ a ) ≤ inf t < 0 e − t a ∏ i E {\displaystyle \Pr(X\leq a)\leq \inf _{t<0}e^{-ta}\prod _{i}\operatorname {E} \left} Specific Che... | Chernoff bound | 0.781021 |
90,065 | If p ≥ 1/2, then D ( p + ε ∥ p ) ≥ ε 2 2 p ( 1 − p ) {\displaystyle D(p+\varepsilon \parallel p)\geq {\tfrac {\varepsilon ^{2}}{2p(1-p)}}} which means Pr ( 1 n ∑ X i > p + x ) ≤ exp ( − x 2 n 2 p ( 1 − p ) ) . {\displaystyle \Pr \left({\frac {1}{n}}\sum X_{i}>p+x\right)\leq \exp \left(-{\frac {x^{2}n}{2p(1-p)}}\right... | Chernoff bound | 0.781021 |
90,066 | The following theorem is due to Wassily Hoeffding and hence is called the Chernoff–Hoeffding theorem. Chernoff–Hoeffding theorem. Suppose X1, ..., Xn are i.i.d. | Chernoff bound | 0.781021 |
90,067 | Therefore, we can easily compute the infimum, using calculus: d d t ( p e ( 1 − q ) t + ( 1 − p ) e − q t ) = ( 1 − q ) p e ( 1 − q ) t − q ( 1 − p ) e − q t {\displaystyle {\frac {d}{dt}}\left(pe^{(1-q)t}+(1-p)e^{-qt}\right)=(1-q)pe^{(1-q)t}-q(1-p)e^{-qt}} Setting the equation to zero and solving, we have ( 1 − q ) p ... | Chernoff bound | 0.781021 |
90,068 | In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian). It is especial... | Chernoff bound | 0.781021 |
90,069 | {\displaystyle \Pr \left(\left\|{\frac {1}{t}}\sum _{i=1}^{t}M_{i}\right\|>\varepsilon \right)\leq (d_{1}+d_{2})\exp \left(-{\frac {3\varepsilon ^{2}t}{8\gamma ^{2}}}\right).} Notice that in order to conclude that the deviation from 0 is bounded by ε with high probability, we need to choose a number of samples t {\disp... | Chernoff bound | 0.781021 |
90,070 | Will Wright was introduced to James Lovelock by Stewart Brand, a former editor of CoEvolution Quarterly who lived near Wright, upon hearing about SimEarth. Lovelock advised the development team behind SimEarth, and particularly assisted with geophysical models. Lovelock stated in regards to the Gaia model that "Attempt... | SimEarth | 0.781017 |
90,071 | Once this stage is achieved, energy requirements are high and global warming starts to threaten your planet's habitability. Atomic Age, This stage is characterized by the use of nuclear energy. Information Age, This stage is associated with the mass use of telecommunication technologies and computers. Nanotech Age, Thi... | SimEarth | 0.781017 |
90,072 | Van Andel Institute Graduate School (VAIGS) offers an accredited program in cell and molecular genetics that is designed to foster problem-based thinking and research leadership. VAIGS also offers an M.D./Ph.D. program in partnership with Michigan State University College of Human Medicine and Western Michigan Universi... | Van Andel Institute | 0.781017 |
90,073 | Van Andel Institute (VAI) is a 501(c)(3) nonprofit biomedical research and science education organization in Grand Rapids, Michigan. VAI was founded by Jay and Betty Van Andel in 1996.The institute's research focuses on cancer epigenetics and Parkinson's disease. Its educational efforts support teacher development and ... | Van Andel Institute | 0.781017 |
90,074 | The institute's laboratories are supported by a Core Technologies and Services group that comprises eight shared scientific services: Bioinformatics and biostatistics Confocal microscopy and quantitative imaging Cryo-electron microscopy Flow cytometry Genomics Optical Imaging Pathology and biorepository Transgenics and... | Van Andel Institute | 0.781017 |
90,075 | Jones's work helped established the field of epigenetics, particularly his seminal 1980 discovery that DNA methylation impacts gene expression and cellular differentiation. He is past president of the American Association for Cancer Research and is an elected fellow of the National Academy of Sciences, the American Aca... | Van Andel Institute | 0.781017 |
90,076 | Grand River Aseptic Manufacturing (GRAM) was founded in 2010 by Van Andel Institute and Grand Valley State University. Much of GRAM's initial funding was through angel investment that generated $5 million in 2010 and another $2 million in 2013.In September 2014, the institute partnered with The Cure Parkinson's Trust o... | Van Andel Institute | 0.781017 |
90,077 | She served in this role until 2011 when Jim Nicolette was appointed to the position of associate director.Steven J. Triezenberg served as director of VAEI between 2009 and 2015. Triezenberg previously served as a faculty member of the Department of Biochemistry and Molecular Biology at Michigan State University for mor... | Van Andel Institute | 0.781017 |
90,078 | Gordon Van Wylen was appointed director of VAEI in 1996. Before serving as director of VAEI, Van Wylen was elected dean of the Engineering Department at the University of Michigan in 1965 and later served as president of Hope College in Holland, Michigan, from 1972 to 1987.Gordon Van Harn was appointed director of VAEI... | Van Andel Institute | 0.781017 |
90,079 | The Center for Epigenetics was established in 2014 and is led by Peter Jones. Scientists in the Center focus on identifying epigenetic mechanisms in health and disease states, and translating their findings into new treatments for cancer and neurodegenerative diseases. | Van Andel Institute | 0.781017 |
90,080 | The Center for Cancer and Cell Biology is led by Bart Williams. It is the largest center at the institute. | Van Andel Institute | 0.781017 |
90,081 | Sufficient conditions comprise: F = F ∗ ∗ {\displaystyle F=F^{**}} where F {\displaystyle F} is the perturbation function relating the primal and dual problems and F ∗ ∗ {\displaystyle F^{**}} is the biconjugate of F {\displaystyle F} (follows by construction of the duality gap) F {\displaystyle F} is convex and lower ... | Strong duality | 0.781015 |
90,082 | Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. This is as opposed to weak duality (the primal problem has optimal value smaller than or equal to the dual problem, in other words the duality gap is greater than or equal to zero). | Strong duality | 0.781015 |
90,083 | There is a fundamental conflict, referred to as the problem of time, between the way the concept of time is used in quantum mechanics, and the role it plays in general relativity. In standard quantum theories time acts as an independent background through which states evolve, with the Hamiltonian operator acting as the... | Entanglement theory | 0.781013 |
90,084 | Later, however, the counterintuitive predictions of quantum mechanics were verified in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating Bell's inequality. In earlier tests, it could not be ruled out that the result at one point could have been subtly t... | Entanglement theory | 0.781013 |
90,085 | With entangled particles, such measurements affect the entangled system as a whole. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others c... | Entanglement theory | 0.781013 |
90,086 | Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance... | Entanglement theory | 0.781013 |
90,087 | The special case of two equal but opposite loops is called a zero-area Sagnac interferometer. The result is an interferometer that exhibits the stability of the Sagnac topology while being insensitive to rotation.The Laser Interferometer Gravitational-Wave Observatory (LIGO) consisted of two 4-km Michelson–Fabry–Pérot ... | Sagnac interferometer | 0.781013 |
90,088 | Likewise Michelson observed that the fringe pattern would remain stable even while holding a lighted match below the optical path; in most interferometers the fringes would shift wildly due to the refractive index fluctuations from the warm air above the match. Sagnac interferometers are almost completely insensitive t... | Sagnac interferometer | 0.781013 |
90,089 | The Sagnac topology was actually first described by Michelson in 1886, who employed an even-reflection variant of this interferometer in a repetition of the Fizeau experiment. Michelson noted the extreme stability of the fringes produced by this form of interferometer: White-light fringes were observed immediately upon... | Sagnac interferometer | 0.781013 |
90,090 | The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson–Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Ea... | Sagnac interferometer | 0.781013 |
90,091 | Protons are then accelerated to 2 GeV and injected into the Proton Synchrotron (PS), where they are accelerated to 26 GeV. Finally, the Super Proton Synchrotron (SPS) is used to increase their energy further to 450 GeV before they are at last injected (over a period of several minutes) into the main ring. Here, the pro... | Large Hadron Collider | 0.781009 |
90,092 | The beams intersect at four points around the ring, which is where the particle collisions take place. Some 1,232 dipole magnets keep the beams on their circular path (see image), while an additional 392 quadrupole magnets are used to keep the beams focused, with stronger quadrupole magnets close to the intersection po... | Large Hadron Collider | 0.781009 |
90,093 | The term hadron refers to subatomic composite particles composed of quarks held together by the strong force (analogous to the way that atoms and molecules are held together by the electromagnetic force). The best-known hadrons are the baryons such as protons and neutrons; hadrons also include mesons such as the pion a... | Large Hadron Collider | 0.781009 |
90,094 | The novel Angels & Demons, by Dan Brown, involves antimatter created at the LHC to be used in a weapon against the Vatican. In response, CERN published a "Fact or Fiction?" page discussing the accuracy of the book's portrayal of the LHC, CERN, and particle physics in general. The movie version of the book has footage f... | Large Hadron Collider | 0.781009 |
90,095 | The observed properties were consistent with the Higgs boson, but scientists were cautious as to whether it is formally identified as actually being the Higgs boson, pending further analysis. On 14 March 2013, CERN announced confirmation that the observed particle was indeed the predicted Higgs boson.On 8 November 2012... | Large Hadron Collider | 0.781009 |
90,096 | The first physics results from the LHC, involving 284 collisions which took place in the ALICE detector, were reported on 15 December 2009. The results of the first proton–proton collisions at energies higher than Fermilab's Tevatron proton–antiproton collisions were published by the CMS collaboration in early February... | Large Hadron Collider | 0.781009 |
90,097 | CERN has several preliminary designs for a Future Circular Collider (FCC)—which would be the most powerful particle accelerator ever built—with different types of collider ranging in cost from around €9 billion (US$10.2 billion) to €21 billion. It would use the LHC ring as preaccelerator, similar to how the LHC uses th... | Large Hadron Collider | 0.781009 |
90,098 | At the conference EPS-HEP 2015 in July, the collaborations presented first cross-section measurements of several particles at the higher collision energy. On 15 December 2015, the ATLAS and CMS experiments both reported a number of preliminary results for Higgs physics, supersymmetry (SUSY) searches and exotics searche... | Large Hadron Collider | 0.781009 |
90,099 | An initial focus of research was to investigate the possible existence of the Higgs boson, a key part of the Standard Model of physics which was predicted by theory, but had not yet been observed before due to its high mass and elusive nature. CERN scientists estimated that, if the Standard Model was correct, the LHC w... | Large Hadron Collider | 0.781009 |
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