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95,700 | Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by French physicist Loui... | De Broglie Hypothesis | 0.778582 |
95,701 | Rifts are linear zones of localized crustal extension. They range in width from somewhat less than 100 km up to several hundred km, consisting of one or more normal faults and related fault blocks. In individual rift segments, one polarity (i.e. dip direction) normally dominates, giving a half-graben geometry. Other co... | Extensional tectonics | 0.778582 |
95,702 | The VVD method is based on a theorem, that circulation in viscous fluid is conserved on contours travelling with speed u = V + V d ; V d = − ν ∇ Ω | Ω | ; Ω = {\displaystyle \mathbf {u} =\mathbf {V} +\mathbf {V} _{d};~~~\mathbf {V} _{d}=-\nu {\dfrac {\nabla \mathbf {\Omega } }{|\mathbf {\Omega } |}};~~~\mathbf {\Omega... | Viscous vortex domains method | 0.77858 |
95,703 | Non-imaging modalities vary, and are often undertaken in addition to imaging modalities. They commonly include: Academia – Education role. Clinical Management – Clinical managerial role which can be varied; may include managing audits, rotas, department budgets, etc. Clinical Research – Research role. Medical Physics –... | Radiographer | 0.77858 |
95,704 | Revered for his technological ingenuity, he conceptualized flying machines, a type of armored fighting vehicle, concentrated solar power, a ratio machine that could be used in an adding machine, and the double hull. Relatively few of his designs were constructed or were even feasible during his lifetime, as the modern ... | Leonardo da Vinci | 0.778579 |
95,705 | Leonardo di ser Piero da Vinci (15 April 1452 – 2 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested on his achievements as a painter, he also became known for his notebooks, in which... | Leonardo da Vinci | 0.778579 |
95,706 | Other famous painters apprenticed in the workshop or associated with it include Ghirlandaio, Perugino, Botticelli, and Lorenzo di Credi. Leonardo was exposed to both theoretical training and a wide range of technical skills, including drafting, chemistry, metallurgy, metal working, plaster casting, leather working, mec... | Leonardo da Vinci | 0.778579 |
95,707 | Despite the recent awareness and admiration of Leonardo as a scientist and inventor, for the better part of four hundred years his fame rested on his achievements as a painter. A handful of works that are either authenticated or attributed to him have been regarded as among the great masterpieces. These paintings are f... | Leonardo da Vinci | 0.778579 |
95,708 | Blockchain technology depends on cryptographic operations. Safeguarding private keys is essential to maintain the security of blockchain processes that utilize asymmetric cryptography. The synergy between HSMs and blockchain is mentioned in several papers, emphasizing their role in securing private keys and verifying i... | Hardware Security Module | 0.778577 |
95,709 | For some applications, such as certificate authorities and digital signing, the cryptographic material is asymmetric key pairs (and certificates) used in public-key cryptography. With other applications, such as data encryption or financial payment systems, the cryptographic material consists mainly of symmetric keys.S... | Hardware Security Module | 0.778577 |
95,710 | A hardware security module can be employed in any application that uses digital keys. Typically, the keys would be of high value - meaning there would be a significant, negative impact to the owner of the key if it were compromised. The functions of an HSM are: onboard secure cryptographic key generation onboard secure... | Hardware Security Module | 0.778577 |
95,711 | However, with performance ranges from 1 to 10,000 1024-bit RSA signs per second, HSMs can provide significant CPU offload for asymmetric key operations. Since the National Institute of Standards and Technology (NIST) is recommending the use of 2,048 bit RSA keys from year 2010, performance at longer key sizes has becom... | Hardware Security Module | 0.778577 |
95,712 | In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. | Proper map | 0.778575 |
95,713 | The Gel'fand–Raikov (Гельфанд–Райков) theorem is a theorem in the theory of locally compact topological groups. It states that a locally compact group is completely determined by its (possibly infinite dimensional) unitary representations. The theorem was first published in 1943.A unitary representation ρ: G → U ( H ) ... | Gelfand–Raikov theorem | 0.778574 |
95,714 | Following this, in the early universe, the evolution of the universe proceeded according to known high energy physics. This is when the first protons, electrons and neutrons formed, then nuclei and finally atoms. With the formation of neutral hydrogen, the cosmic microwave background was emitted. Finally, the epoch of ... | Cosmological model | 0.778574 |
95,715 | If it were, there would be X-rays and gamma rays produced as a result of annihilation, but this is not observed. Therefore, some process in the early universe must have created a small excess of matter over antimatter, and this (currently not understood) process is called baryogenesis. Three required conditions for bar... | Cosmological model | 0.778574 |
95,716 | The physical model behind cosmic inflation is extremely simple, but it has not yet been confirmed by particle physics, and there are difficult problems reconciling inflation and quantum field theory. Some cosmologists think that string theory and brane cosmology will provide an alternative to inflation.Another major pr... | Cosmological model | 0.778574 |
95,717 | The early, hot universe appears to be well explained by the Big Bang from roughly 10−33 seconds onwards, but there are several problems. One is that there is no compelling reason, using current particle physics, for the universe to be flat, homogeneous, and isotropic (see the cosmological principle). Moreover, grand un... | Cosmological model | 0.778574 |
95,718 | Gravitational waves are ripples in the curvature of spacetime that propagate as waves at the speed of light, generated in certain gravitational interactions that propagate outward from their source. Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves to co... | Cosmological model | 0.778574 |
95,719 | The quality of peer review at the journal has been heavily criticized. It was identified as a predatory journal by Jeffrey Beall. The journal promotes fringe viewpoints and speculative viewpoints on astrobiology, astrophysics, and quantum physics. Skeptical blogger and biologist PZ Myers said of the journal "it isn't a... | Journal of Cosmology | 0.778573 |
95,720 | In early March 2011, the journal drew widespread controversy for the publication of a paper by Richard B. Hoover, a retired NASA scientist, with claims of evidence in meteorites that life on Earth could have come from space via debris carrying life from a comet. The journal dismissed the criticism as "a barrage of slan... | Journal of Cosmology | 0.778573 |
95,721 | The Journal of Cosmology is an online publication that contains material on a wide range of subjects in cosmology, astronomy, astrobiology, and Earth and planetary sciences. Writing on biology, geology, physics, chemistry, extinction, the origin and evolution of life, panspermia and Martian colonization and exploration... | Journal of Cosmology | 0.778573 |
95,722 | A coupled pair consists of a male nipple or plug and a female coupler or socket. One side is connected to a flexible supply hose; the other may be attached to a manifold, valve, tool, or another hose. A female coupler is used on the supply side, and a male nipple is used on the receiving side. Fitting profiles have ide... | Air-Line Fittings | 0.778572 |
95,723 | Thus, the diameter of the radio source is slightly less than the distance from Mercury to the Sun. Scientists at the Max Planck Institute for Extraterrestrial Physics in Germany using Chilean telescopes have confirmed the existence of a supermassive black hole at the Galactic Center, on the order of 4.3 million solar m... | Galactic Centre | 0.778572 |
95,724 | A group G acts naturally on itself by left and right multiplication, each giving rise to a homomorphism from G into the symmetric group on the underlying set of G. One homomorphism is defined as λ: G → Sym(G), λ g {\displaystyle \lambda _{g}} (h) = g·h. That is, g is mapped to the permutation obtained by left-multiplyi... | Holomorph (mathematics) | 0.778572 |
95,725 | In mathematics, especially in the area of algebra known as group theory, the holomorph of a group is a group that simultaneously contains (copies of) the group and its automorphism group. The holomorph provides interesting examples of groups, and allows one to treat group elements and group automorphisms in a uniform c... | Holomorph (mathematics) | 0.778572 |
95,726 | Modern 3D CAD applications allow for the insertion of engineering information such as dimensions, GD&T, notes and other product details within the 3D digital data set for components and assemblies. MBD uses such capabilities to establish the 3D digital data set as the source of these specifications and design authority... | Model based definition | 0.778571 |
95,727 | Limited Dimension Drawing (LDD), sometimes Reduced Dimension Drawing, are 2D drawings that only contain critical information, noting that all missing information is to be taken from an associated 3D model. For companies in transition to MBD from traditional 2D documentation a Limited Dimension Drawing allows for refere... | Model based definition | 0.778571 |
95,728 | Some general effects of tool wear include: increased cutting forces increased cutting temperatures poor surface finish decreased accuracy of finished part May lead to tool breakage Causes change in tool geometryReduction in tool wear can be accomplished by using lubricants and coolants while machining. These reduce fri... | Tool wear | 0.778571 |
95,729 | Originates from Machine Translation Research Group of Computer Science Department, Harbin Institute of Technology, which was started Li in 1985. It is one of the earliest institutions engaged in MT research in China, featured by its investigations into Chinese-English machine translation. It is now running under the Re... | Li Sheng (computer scientist) | 0.77857 |
95,730 | Li Sheng (Chinese: 李生; born 1943), is a professor at the School of Computer Science and Engineering, Harbin Institute of Technology (HIT), China. He began his research on Chinese-English machine translation in 1985, making himself one of the earliest Chinese scholars in this field. After that, he pursued in vast topics... | Li Sheng (computer scientist) | 0.77857 |
95,731 | Apart from intrinsic properties of neurons, biological neural network properties are also an important source of oscillatory activity. Neurons communicate with one another via synapses and affect the timing of spike trains in the post-synaptic neurons. Depending on the properties of the connection, such as the coupling... | Neural oscillations | 0.778569 |
95,732 | The mathematics of the Hodgkin–Huxley model are quite complicated and several simplifications have been proposed, such as the FitzHugh–Nagumo model, the Hindmarsh–Rose model or the capacitor-switch model as an extension of the integrate-and-fire model. Such models only capture the basic neuronal dynamics, such as rhyth... | Neural oscillations | 0.778569 |
95,733 | A model of a biological neuron is a mathematical description of the properties of nerve cells, or neurons, that is designed to accurately describe and predict its biological processes. The most successful and widely used model of neurons, the Hodgkin–Huxley model, is based on data from the squid giant axon. It is a set... | Neural oscillations | 0.778569 |
95,734 | The study of the QGP, which has both a high temperature and density, is part of this effort to consolidate the grand theory of particle physics. The study of the QGP is also a testing ground for finite temperature field theory, a branch of theoretical physics which seeks to understand particle physics under conditions ... | Quark gluon plasma | 0.778568 |
95,735 | QCD is one part of the modern theory of particle physics called the Standard Model. Other parts of this theory deal with electroweak interactions and neutrinos. The theory of electrodynamics has been tested and found correct to a few parts in a billion. The theory of weak interactions has been tested and found correct ... | Quark gluon plasma | 0.778568 |
95,736 | The dot product includes a factor of cos θ {\displaystyle \cos \theta } , where θ {\displaystyle \theta } is the angle between the polarization of the light and the transition dipole moment. When they are parallel the interaction is strongest, when they are perpendicular there is no interaction at all. If we rewrite ... | Rabi frequency | 0.778567 |
95,737 | In most implementations, a cell, or group of cells in a column or row, can be "named" enabling the user to refer to those cells by a name rather than by a grid reference. Names must be unique within the spreadsheet, but when using multiple sheets in a spreadsheet file, an identically named cell range on each sheet can ... | Spreadsheet software | 0.778566 |
95,738 | The International Code of Nomenclature of Prokaryotes inherits the concept of a valid publication from the ICBN. To be considered valid, a name must be found in the Approved Lists of Bacterial Names, or is published in the International Journal of Systematic and Evolutionary Microbiology (formerly the International Jou... | Validly published name | 0.778565 |
95,739 | The Reading Intermediate General Circulation Model (IGCM), is a simplified or "intermediate" Global climate model, which is developed by members of the Department of Meteorology at the University of Reading, and by members of the Stratospheric Dynamics and Chemistry Group of the Department of Atmospheric and Oceanic Sc... | Intermediate General Circulation Model | 0.778563 |
95,740 | The variable space-weather conditions of geospace are affected by the behavior of the Sun and the solar wind; the subject of geospace is interlinked with heliophysics—the study of the Sun and its impact on the planets of the Solar System.The day-side magnetopause is compressed by solar-wind pressure—the subsolar distan... | Outer space | 0.778562 |
95,741 | c 2 d τ 2 = c 2 d t 2 − d x 2 − d y 2 − d z 2 {\displaystyle c^{2}\,d\tau ^{2}=c^{2}\,dt^{2}-dx^{2}-dy^{2}-dz^{2}\,\!} which may be written in spherical coordinates as c 2 d τ 2 = c 2 d t 2 − d r 2 − r 2 d θ 2 − r 2 sin 2 θ d φ 2 {\displaystyle c^{2}\,d\tau ^{2}=c^{2}\,dt^{2}-dr^{2}-r^{2}\,d\theta ^{2}-r^{2}\sin ^{2}... | Two-body problem in general relativity | 0.778562 |
95,742 | where the nine functions gxx, gxy, …, gzz constitute the metric tensor, which defines the geometry of the space in Riemannian geometry. In the spherical-coordinates example above, there are no cross-terms; the only nonzero metric tensor components are grr = 1, gθθ = r2 and gφφ = r2 sin2 θ. In his special theory of rela... | Two-body problem in general relativity | 0.778562 |
95,743 | In the normal Euclidean geometry, triangles obey the Pythagorean theorem, which states that the square distance ds2 between two points in space is the sum of the squares of its perpendicular components d s 2 = d x 2 + d y 2 + d z 2 {\displaystyle ds^{2}=dx^{2}+dy^{2}+dz^{2}\,\!} where dx, dy and dz represent the infini... | Two-body problem in general relativity | 0.778562 |
95,744 | The environmental benefits of renewable energy technologies are widely recognised, but the contribution that they can make to energy security is less well known. Renewable technologies can enhance energy security in electricity generation, heat supply, and transportation. | Energy security and renewable technology | 0.778561 |
95,745 | Variability will rarely be a barrier to increased renewable energy deployment. But at high levels of market penetration it requires careful analysis and management, and additional costs may be required for back-up or system modification.Renewable electricity supply in the 20-50+% penetration range has already been impl... | Energy security and renewable technology | 0.778561 |
95,746 | These threats to our old energy systems provide a rationale for investing in renewable energy. Shifting to renewable energy "can help us to meet the dual goals of reducing greenhouse gas emissions, thereby limiting future extreme weather and climate impacts, and ensuring reliable, timely, and cost-efficient delivery of... | Energy security and renewable technology | 0.778561 |
95,747 | The Combined Power Plant, a project linking 36 wind, solar, biomass, and hydroelectric installations throughout Germany, has demonstrated that a combination of renewable sources and more-effective control can balance out short-term power fluctuations and provide reliable electricity with 100 percent renewable energy. | Energy security and renewable technology | 0.778561 |
95,748 | It has been argued that investor-state dispute settlement rights may grant investors in carbon-intensive industries a mechanism to inhibit government policies promoting renewable energy technologies. The impact of dispute settlement through international arbitration or negotiation, however, is also deemed to be a usefu... | Energy security and renewable technology | 0.778561 |
95,749 | In those countries where growing dependence on imported gas is a pressing energy security issue, renewable energy technologies can provide alternative sources of electric power production as well as displacing electricity demand through production of direct heat. The IEA suggests that the direct contribution that renew... | Energy security and renewable technology | 0.778561 |
95,750 | In organic chemistry, the sulfonamide functional group (also spelled sulphonamide) is an organosulfur group with the structure R−S(=O)2−NR2. It consists of a sulfonyl group (O=S=O) connected to an amine group (−NH2). Relatively speaking this group is unreactive. Because of the rigidity of the functional group, sulfonam... | Sulfonamide | 0.77856 |
95,751 | A helium-3 refrigerator is a simple device used in experimental physics for obtaining temperatures down to about 0.2 kelvins. By evaporative cooling of helium-4 (the more common isotope of helium), a 1-K pot liquefies a small amount of helium-3 in a small vessel called a helium-3 pot. Evaporative cooling at low pressur... | Helium-3 refrigerator | 0.778557 |
95,752 | Theorem: If f {\displaystyle f} is entire, nonconstant, and has finite, non-integer order ρ {\displaystyle \rho } , then it assumes the whole complex plane infinitely many times. Proof: For any w ∈ C {\displaystyle w\in \mathbb {C} } , it suffices to prove f ( z ) − w {\displaystyle f(z)-w} has infinitely many roots. E... | Hadamard factorization theorem | 0.778557 |
95,753 | With Hadamard factorization we can prove some special cases of Picard's little theorem. Theorem: If f {\displaystyle f} is entire, nonconstant, and has finite order, then it assumes either the whole complex plane or the plane minus a single point. Proof: If f {\displaystyle f} does not assume value z 0 {\displaystyle z... | Hadamard factorization theorem | 0.778557 |
95,754 | Since f ( z ) / z m {\displaystyle f(z)/z^{m}} is also an entire function with the same order ρ {\displaystyle \rho } and genus, we can wlog assume m = 1 {\displaystyle m=1} . If f {\displaystyle f} has only finitely many roots, then f ( z ) = e Q ( z ) ∏ k = 1 n E 0 ( z / a k ) {\displaystyle f(z)=e^{Q(z)}\prod _{k=1}... | Hadamard factorization theorem | 0.778557 |
95,755 | In mathematics, and particularly in the field of complex analysis, the Hadamard factorization theorem asserts that every entire function with finite order can be represented as a product involving its zeroes and an exponential of a polynomial. It is named for Jacques Hadamard. The theorem may be viewed as an extension ... | Hadamard factorization theorem | 0.778557 |
95,756 | In calculus, often the growth rate of the coefficients of a power series can be used to deduce a radius of convergence for the power series. The reverse can also hold; often the radius of convergence for a generating function can be used to deduce the asymptotic growth of the underlying sequence. For instance, if an or... | Exponential generating function | 0.778556 |
95,757 | In this example, we reformulate a generating function example given in Section 7.3 of Concrete Mathematics (see also Section 7.1 of the same reference for pretty pictures of generating function series). In particular, suppose that we seek the total number of ways (denoted Un) to tile a 3-by-n rectangle with unmarked 2-... | Exponential generating function | 0.778556 |
95,758 | 2,5-Furandicarboxylic acid (FDCA) is an organic chemical compound consisting of two carboxylic acid groups attached to a central furan ring. It was first reported as dehydromucic acid by Rudolph Fittig and Heinzelmann in 1876, who produced it via the action of concentrated hydrobromic acid upon mucic acid. It can be pr... | 2,5-Furandicarboxylic acid | 0.778555 |
95,759 | Parallelization of this approach beyond a few hundred processors is challenging, due to the complex dependencies among various subcomputations, which lead to complex communication optimization and load balancing problems. Using Charm++ and its concept of processor virtualization, the phases are discretized into multipl... | OpenAtom | 0.778555 |
95,760 | OpenAtom is a massively parallel quantum chemistry application written in Charm++ for simulations on supercomputers. Its developmental version was called LeanCP. Many important problems in material science, chemistry, solid-state physics, and biophysics require a modeling approach based on fundamental quantum mechanica... | OpenAtom | 0.778555 |
95,761 | Similarly, cryptography provides a means to exchange information privately across a non-secure channel, but no guarantees about the confidentiality of the data are given once it is decrypted. In low level information flow analysis, each variable is usually assigned a security level. The basic model comprises two distin... | Information flow (information theory) | 0.778554 |
95,762 | Securing the data manipulated by computing systems has been a challenge in the past years. Several methods to limit the information disclosure exist today, such as access control lists, firewalls, and cryptography. However, although these methods do impose limits on the information that is released by a system, they pr... | Information flow (information theory) | 0.778554 |
95,763 | In mathematics, the Stieltjes polynomials En are polynomials associated to a family of orthogonal polynomials Pn. They are unrelated to the Stieltjes polynomial solutions of differential equations. Stieltjes originally considered the case where the orthogonal polynomials Pn are the Legendre polynomials. The Gauss–Kronr... | Stieltjes polynomials | 0.778552 |
95,764 | The length of the longest increasing subsequence of σ1, ..., σn is equal to the length of the first row of P (and of Q). The length of the longest decreasing subsequence of σ1, ..., σn is equal to the length of the first column of P (and of Q), as follows from the previous two properties. The descent set {i: σi > σi+1}... | Robinson–Schensted correspondence | 0.778552 |
95,765 | Ambient intelligence requires several vital technologies to exist. These include hidden, user-friendly hardware such as miniaturization, nanotechnology, and smart devices, as well as human-centric computer interfaces (intelligent agents, multimodal interaction, context awareness, etc.). These systems and devices operat... | Ambient intelligence | 0.778551 |
95,766 | Ambient intelligence is primarily interesting because of its relationship and advancement in sensor technology and sensor networks. The interest in user experience grew its importance in the late 1990s as a result of the increasing volume and importance of digital products and services that were difficult to understand... | Ambient intelligence | 0.778551 |
95,767 | A variety of technologies can be used to enable ambient intelligence environments, such as: Bluetooth Low Energy RFID Microchip implant Sensors: Ambient light sensor (photodetector), thermometers, proximity sensors, and motion detectors Software agents Affective computing Nanotechnology Biometrics | Ambient intelligence | 0.778551 |
95,768 | Minority Report (2002 film): One scene illustrates adaptive advertising in the future-consumers are identified via retinal scans and receive targeted ads. The Hitchhiker's Guide to the Galaxy by Douglas Adams: The doors have emotion and express this when people use them. The Diamond Age by Neal Stephenson: It depicts a... | Ambient intelligence | 0.778551 |
95,769 | The ATLAS system was developed within the Applied Physics Group at the School of Physics, Trinity College, Dublin. The experimental procedure is relatively straightforward, when compared to lithography or other approaches, meaning that only standard equipment is needed. The set-up consists of an ultrahigh vacuum chambe... | Atomic-terrace low-angle shadowing | 0.77855 |
95,770 | Research suggests that the implied methane destruction lifetime is as long as ≈ 4 Earth years and as short as ≈ 0.6 Earth years. This unexplained fast destruction rate also suggests a very active replenishing source. A team from the Italian National Institute for Astrophysics suspects that the methane detected by the C... | Natural methane on Mars | 0.778546 |
95,771 | Methanogens do not require oxygen or organic nutrients, are non-photosynthetic, use hydrogen as their energy source, and carbon dioxide (CO2) as their carbon source, so they could exist in subsurface environments on Mars. If microscopic Martian life is producing the methane, it probably resides far below the surface, w... | Natural methane on Mars | 0.778546 |
95,772 | Similar arguments about the Hilbert inner product (which can be demonstrated to be a Hermitian form, therefore justifying the name "inner product") lead to the conclusion that its neutral space is precisely K 00 = ( K 0 ∩ K + ) ⊕ ( K 0 ∩ K − ) {\displaystyle K_{00}=(K_{0}\cap K_{+})\oplus (K_{0}\cap K_{-})} , that elem... | Indefinite inner product space | 0.778546 |
95,773 | If this decomposition is such that K + ⊂ K + 0 {\displaystyle K_{+}\subset K_{+0}} and K − ⊂ K − 0 {\displaystyle K_{-}\subset K_{-0}} , then K {\displaystyle K} is called an indefinite inner product space; if K ± ⊂ K ± ± ∪ { 0 } {\displaystyle K_{\pm }\subset K_{\pm \pm }\cup \{0\}} , then K {\displaystyle K} is calle... | Indefinite inner product space | 0.778546 |
95,774 | Krein spaces arise naturally in situations where the indefinite inner product has an analytically useful property (such as Lorentz invariance) which the Hilbert inner product lacks. It is also common for one of the two inner products, usually the indefinite one, to be globally defined on a manifold and the other to be ... | Indefinite inner product space | 0.778546 |
95,775 | In mathematics, in the field of functional analysis, an indefinite inner product space ( K , ⟨ ⋅ , ⋅ ⟩ , J ) {\displaystyle (K,\langle \cdot ,\,\cdot \rangle ,J)} is an infinite-dimensional complex vector space K {\displaystyle K} equipped with both an indefinite inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\,... | Indefinite inner product space | 0.778546 |
95,776 | This problem employs the KKT conditions as a constraint. Also, the equality constraint ∇ f ( x ) + ∑ j = 1 m u j ∇ g j ( x ) {\displaystyle \nabla f(x)+\sum _{j=1}^{m}u_{j}\nabla g_{j}(x)} is nonlinear in general, so the Wolfe dual problem may be a nonconvex optimization problem. In any case, weak duality holds. | Wolfe duality | 0.778545 |
95,777 | In mathematical optimization, Wolfe duality, named after Philip Wolfe, is type of dual problem in which the objective function and constraints are all differentiable functions. Using this concept a lower bound for a minimization problem can be found because of the weak duality principle. | Wolfe duality | 0.778545 |
95,778 | Koopman, Howard Raiffa, Robert Schlaifer and Alan Turing. In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods, which removed many of the computational problems, and an increasing interest in nonstandard, compl... | History of statistics | 0.778544 |
95,779 | Other well-known proponents of Bayesian probability theory include I.J. Good, B.O. | History of statistics | 0.778544 |
95,780 | In 1957, Edwin Jaynes promoted the concept of maximum entropy for constructing priors, which is an important principle in the formulation of objective methods, mainly for discrete problems. In 1965, Dennis Lindley's 2-volume work "Introduction to Probability and Statistics from a Bayesian Viewpoint" brought Bayesian me... | History of statistics | 0.778544 |
95,781 | Neyman started out as a "quasi-Bayesian", but subsequently developed confidence intervals (a key method in frequentist statistics) because "the whole theory would look nicer if it were built from the start without reference to Bayesianism and priors". The word Bayesian appeared around 1950, and by the 1960s it became t... | History of statistics | 0.778544 |
95,782 | Their methods came to be called frequentist statistics. Fisher rejected the Bayesian view, writing that "the theory of inverse probability is founded upon an error, and must be wholly rejected". At the end of his life, however, Fisher expressed greater respect for the essay of Bayes, which Fisher believed to have antic... | History of statistics | 0.778544 |
95,783 | Laplace also introduced primitive versions of conjugate priors and the theorem of von Mises and Bernstein, according to which the posteriors corresponding to initially differing priors ultimately agree, as the number of observations increases. This early Bayesian inference, which used uniform priors following Laplace's... | History of statistics | 0.778544 |
95,784 | The term Bayesian refers to Thomas Bayes (1702–1761), who proved that probabilistic limits could be placed on an unknown event. However it was Pierre-Simon Laplace (1749–1827) who introduced (as principle VI) what is now called Bayes' theorem and applied it to celestial mechanics, medical statistics, reliability, and j... | History of statistics | 0.778544 |
95,785 | Lind is today often described as a one-factor-at-a-time experimenter. Similar one-factor-at-a-time (OFAT) experimentation was performed at the Rothamsted Research Station in the 1840s by Sir John Lawes to determine the optimal inorganic fertilizer for use on wheat.A theory of statistical inference was developed by Char... | History of statistics | 0.778544 |
95,786 | Applications arose early in demography and economics; large areas of micro- and macro-economics today are "statistics" with an emphasis on time-series analyses. With its emphasis on learning from data and making best predictions, statistics also has been shaped by areas of academic research including psychological test... | History of statistics | 0.778544 |
95,787 | By the 1970s, Johnson and Kotz produced a four-volume Compendium on Statistical Distributions (1st ed., 1969–1972), which is still an invaluable resource. Applied statistics can be regarded as not a field of mathematics but an autonomous mathematical science, like computer science and operations research. Unlike mathem... | History of statistics | 0.778544 |
95,788 | Early probability theory and statistics was systematized in the 19th century and statistical reasoning and probability models were used by social scientists to advance the new sciences of experimental psychology and sociology, and by physical scientists in thermodynamics and statistical mechanics. The development of st... | History of statistics | 0.778544 |
95,789 | The relation between statistics and probability theory developed rather late, however. In the 19th century, statistics increasingly used probability theory, whose initial results were found in the 17th and 18th centuries, particularly in the analysis of games of chance (gambling). By 1800, astronomy used probability mo... | History of statistics | 0.778544 |
95,790 | Computers then produce simple, accurate summaries, and allow more tedious analyses, such as those that require inverting a large matrix or perform hundreds of steps of iteration, that would never be attempted by hand. Faster computing has allowed statisticians to develop "computer-intensive" methods which may look at a... | History of statistics | 0.778544 |
95,791 | By the 18th century, the term "statistics" designated the systematic collection of demographic and economic data by states. For at least two millennia, these data were mainly tabulations of human and material resources that might be taxed or put to military use. In the early 19th century, collection intensified, and th... | History of statistics | 0.778544 |
95,792 | In the 19th century authors on statistical theory included Laplace, S. Lacroix (1816), Littrow (1833), Dedekind (1860), Helmert (1872), Laurent (1873), Liagre, Didion, De Morgan and Boole. Gustav Theodor Fechner used the median (Centralwerth) in sociological and psychological phenomena. It had earlier been used only in... | History of statistics | 0.778544 |
95,793 | Antoine Augustin Cournot in 1843 was the first to use the term median (valeur médiane) for the value that divides a probability distribution into two equal halves. Other contributors to the theory of errors were Ellis (1844), De Morgan (1864), Glaisher (1872), and Giovanni Schiaparelli (1875). Peters's (1856) formula f... | History of statistics | 0.778544 |
95,794 | This method minimizing the sum of the absolute deviances. A method of estimating this slope was invented by Roger Joseph Boscovich in 1760 which he applied to astronomy. The term probable error (der wahrscheinliche Fehler) - the median deviation from the mean - was introduced in 1815 by the German astronomer Frederik W... | History of statistics | 0.778544 |
95,795 | In 1791 Sir John Sinclair introduced the term 'statistics' into English in his Statistical Accounts of Scotland. In 1802 Laplace estimated the population of France to be 28,328,612. He calculated this figure using the number of births in the previous year and census data for three communities. | History of statistics | 0.778544 |
95,796 | Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors. In 1786 William Playfair (1759-1823) introduced the idea of graphical representation into statistics. He invented the line chart, bar chart and histogram and incorporated them into his works on... | History of statistics | 0.778544 |
95,797 | Laplace in 1778 published his second law of errors wherein he noted that the frequency of an error was proportional to the exponential of the square of its magnitude. This was subsequently rediscovered by Gauss (possibly in 1795) and is now best known as the normal distribution which is of central importance in statist... | History of statistics | 0.778544 |
95,798 | Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's The Doctrine of Chances (1718) treated the subject as a branch of mathematics. In his book Bernoulli introduced the idea of representing complete certainty as one and probability as a number between zero and one. A key early application of sta... | History of statistics | 0.778544 |
95,799 | Although the original scope of statistics was limited to data useful for governance, the approach was extended to many fields of a scientific or commercial nature during the 19th century. The mathematical foundations for the subject heavily drew on the new probability theory, pioneered in the 16th century by Gerolamo C... | History of statistics | 0.778544 |
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