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91,800 | This equality between a sum and a product, discovered by Euler, is called an Euler product. The Euler product can be derived from the fundamental theorem of arithmetic, and shows the close connection between the zeta function and the prime numbers. It leads to another proof that there are infinitely many primes: if the... | Odd prime | 0.780419 |
91,801 | They also postulate the existence of a Poincaré-invariant state called the vacuum and demand it to be unique. Moreover, the axioms assume that the vacuum is "cyclic", i.e., that the set of all vectors obtainable by evaluating at the vacuum-state elements of the polynomial algebra generated by the smeared field operator... | Wightman function | 0.780419 |
91,802 | W—Watt WACOG—weighted average cost of gas WAMS—Wide area measurement system, also Wide area monitoring system - see description in phasor measurement unit article. (electricity) WCMC—World Conservation Monitoring Centre WCRE—World Commission on Renewable Energy WEA—World Energy Assessment WEC—World Energy Council WECC—... | List of energy abbreviations | 0.780418 |
91,803 | BA—Balancing Authority BA—Biological Assessment BACT—Best Available Control Technology BBL/D—Barrel per day BBL/SD—Barrel per day, on stream days BBL—barrel (42 gallons) —Balgzand Bacton Line (BBL Pipeline) BCD—Barrel per day, on calendar days BCF—billion cubic feet BCP—Blackstart Capability Plan BES—Bulk electric syst... | List of energy abbreviations | 0.780418 |
91,804 | Balancing Market (electricity) RTEP—Regional transmission expansion plan RTG—Regional Transmission Group (US) RTO—Regional transmission organization (US) RTP—Real time Pricing RTU—Remote Terminal Unit RUS—Rural Utilities Service RVP—Reid vapor pressure | List of energy abbreviations | 0.780418 |
91,805 | R/P—Reserve on Production —Reserves to Production RAB—Regional Advisory Body (US) RAC—Refiners' acquisition cost RAP—Regulatory Assistance Project RAR—Reasonable assured resources RAS—Remedial Action Scheme RATC—Recallable Available Transmission Capability RBMK—Russian: Реактор Большой Мощности Канальный = "High Power ... | List of energy abbreviations | 0.780418 |
91,806 | JRC—Joint Research Centre JREC—Johannesburg Renewable Energy Coalition | List of energy abbreviations | 0.780418 |
91,807 | Mammalian alcohol dehydrogenases also have a structural zinc site. This Zn ion plays a structural role and is crucial for protein stability. The structures of the catalytic and structural zinc sites in horse liver alcohol dehydrogenase (HLADH) as revealed in crystallographic structures, which has been studied computati... | Alcohol dehydrogenase | 0.780416 |
91,808 | The isoperimetric inequality: Among all closed curves with a given perimeter, the circle has the unique maximum area. The convex hull of every bounded rectifiable closed curve C has perimeter at most the length of C, with equality only when C is already a convex curve. Cauchy's surface area formula: Given any convex co... | Crofton formula | 0.780416 |
91,809 | Given compact convex subset S ⊂ R n {\displaystyle S\subset \mathbb {R} ^{n}} , let l {\displaystyle l} be a random line, and P {\displaystyle P} be a random hyperplane, then where E {\displaystyle E} is the average width of S {\displaystyle S} , that is, the expected length of the orthogonal projection of S {\display... | Crofton formula | 0.780416 |
91,810 | In mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line intersects it. | Crofton formula | 0.780416 |
91,811 | The problem with the above example is that the value measure of partner 2 is finitely-additive but not countably-additive. The compactness part of the DS theorem immediately implies that:: 7 If all value measures are countably-additive and nonatomic, then a utilitarian-optimal division exists.In this special case, non-... | Dubins–Spanier moving-knife procedure | 0.780415 |
91,812 | A cake partition X {\displaystyle X} to n pieces (one piece per partner) is called leximin-optimal with weights w 1 , w 2 , . . . , w n {\displaystyle w_{1},w_{2},...,w_{n}} if it maximizes the lexicographically-ordered vector of relative values. I.e, it maximizes the following vector: V 1 ( X 1 ) w 1 , V 2 ( X 2 ) w 2... | Dubins–Spanier moving-knife procedure | 0.780415 |
91,813 | In cryptography, padding is any of a number of distinct practices which all include adding data to the beginning, middle, or end of a message prior to encryption. In classical cryptography, padding may include adding nonsense phrases to a message to obscure the fact that many messages end in predictable ways, e.g. sinc... | Cryptographic padding | 0.780414 |
91,814 | In public key cryptography, padding is the process of preparing a message for encryption or signing using a specification or scheme such as PKCS#1 v2.2, OAEP, PSS, PSSR, IEEE P1363 EMSA2 and EMSA5. A modern form of padding for asymmetric primitives is OAEP applied to the RSA algorithm, when it is used to encrypt a limi... | Cryptographic padding | 0.780414 |
91,815 | In 2017 the RingwooditE Co Ltd was formed in order to explore Thermonuclear Trap Technology (TTT) for the purpose of cleaning all sources of water from pollution and toxic contents. This patented nanotechnology uses a high pressure and temperature chamber to separate isotopes that should by nature not be in drinking wa... | Green nanotechnology | 0.780412 |
91,816 | On one hand it describes the environment friendly technologies utilized to synthesize particles in nano scale; on the other hand it refers to the nanoparticles synthesis mediated by extracts of chlorophyllus plants. Green nanotechnology has been described as the development of clean technologies, "to minimize potential... | Green nanotechnology | 0.780412 |
91,817 | Green nanotechnology refers to the use of nanotechnology to enhance the environmental sustainability of processes producing negative externalities. It also refers to the use of the products of nanotechnology to enhance sustainability. It includes making green nano-products and using nano-products in support of sustaina... | Green nanotechnology | 0.780412 |
91,818 | Materials with small nanosized pores may be suitable for hydrogen storage. Nanotechnology may also find applications in batteries, where the use of nanomaterials may enable batteries with higher energy content or supercapacitors with a higher rate of recharging.Nanotechnology is already used to provide improved perform... | Green nanotechnology | 0.780412 |
91,819 | Research is underway to use nanomaterials for purposes including more efficient solar cells, practical fuel cells, and environmentally friendly batteries. The most advanced nanotechnology projects related to energy are: storage, conversion, manufacturing improvements by reducing materials and process rates, energy savi... | Green nanotechnology | 0.780412 |
91,820 | Nanotechnology offers the potential of novel nanomaterials for the treatment of surface water, groundwater, wastewater, and other environmental materials contaminated by toxic metal ions, organic and inorganic solutes, and microorganisms. Due to their unique activity toward recalcitrant contaminants, many nanomaterials... | Green nanotechnology | 0.780412 |
91,821 | In formulating the project, the automotive and industrial partners recognised the need for a wide range of skills and cooperated with over forty research establishments to create a programme consisting of seven sub-projects. Under a steering committee were three projects on industrial research and four on basic researc... | Eureka Prometheus Project | 0.780411 |
91,822 | The second sense of the term is the metric geometry over a non-Archimedean valued field, or ultrametric space. In such a space, even more contradictions to Euclidean geometry result. For example, all triangles are isosceles, and overlapping balls nest. | Non-Archimedean geometry | 0.780411 |
91,823 | The first sense of the term is the geometry over a non-Archimedean ordered field, or a subset thereof. The aforementioned Dehn plane takes the self-product of the finite portion of a certain non-Archimedean ordered field based on the field of rational functions. In this geometry, there are significant differences from ... | Non-Archimedean geometry | 0.780411 |
91,824 | In mathematics, non-Archimedean geometry is any of a number of forms of geometry in which the axiom of Archimedes is negated. An example of such a geometry is the Dehn plane. Non-Archimedean geometries may, as the example indicates, have properties significantly different from Euclidean geometry. There are two senses i... | Non-Archimedean geometry | 0.780411 |
91,825 | In 1993, it created the Feynman Prize in Nanotechnology, named after physicist Richard Feynman. In May 2005, the Foresight Institute changed its name to "Foresight Nanotech Institute", though it reverted to its original name in June 2009. In 2020, following the COVID-19 pandemic, the institute moved its programs online... | Foresight Institute | 0.78041 |
91,826 | The Foresight Institute was founded in 1986 by Christine Peterson, K. Eric Drexler, and James C. Bennett to support the development of nanotechnology. Many of the institute's initial members came to it from the L5 Society, who were hoping to form a smaller group more focused on nanotechnology. In 1991, the Foresight In... | Foresight Institute | 0.78041 |
91,827 | Others are trying to steer us towards a world where we are robustly well-prepared to face whatever obstacles come – they are seeking to increase existential hope. Foresight's stated strategy is to focus on creating a community that promotes beneficial uses of new technologies and reduce misuse and accidents potentially... | Foresight Institute | 0.78041 |
91,828 | The Foresight Institute (Foresight) is a San Francisco-based research non-profit that promotes the development of nanotechnology and other emerging technologies, such as safe AGI, biotech and longevity.Foresight runs four cross-disciplinary program tracks to research, advance, and govern maturing technologies for the l... | Foresight Institute | 0.78041 |
91,829 | The prize is named in honor of physicist Richard Feynman, whose 1959 talk "There's Plenty of Room at the Bottom" is considered to have inspired and informed the start of the field of nanotechnology. Author Colin Milburn refers to the prize as an example of "fetishizing" its namesake Feynman, due to his "prestige as a s... | Foresight Institute | 0.78041 |
91,830 | The Feynman Prize in Nanotechnology is an award given by the Foresight Institute for significant advances in nanotechnology. Between 1993 and 1997, one prize was given biennially. Since 1997, two prizes have been given each year, divided into the categories of theory and experimentation. | Foresight Institute | 0.78041 |
91,831 | The Wadge hierarchy plays an important role in models of the axiom of determinacy. Further interest in Wadge degrees comes from computer science, where some papers have suggested Wadge degrees are relevant to algorithmic complexity. Wadge's lemma states that under the axiom of determinacy (AD), for any two subsets A , ... | Wadge hierarchy | 0.78041 |
91,832 | School of Electrical Engineering and Computer Science School of Mechanical Engineering School of Materials Science and Engineering School of Earth Sciences and Environmental Engineering School of Life Sciences School of Physics and Chemistry Department of Physics and Photon Science Archived 28 February 2014 at the Wayb... | Gwangju Institute of Science and Technology | 0.78041 |
91,833 | Nuclear medicine is a technology embedded medical specialty depending upon physics (Medical physics) to understand radioisotopes and radiation, engineering to design instruments that can image and measure gamma rays and X-rays, radiation biology and health physics to understand therapy and radiation protection, chemist... | American Board of Nuclear Medicine | 0.78041 |
91,834 | Division of Liberal Arts and Sciences (freshmen) Majors (sophomores, juniors and seniors) Physics Concentration Chemistry Concentration Life Science Concentration Engineering and Applied Science Concentrations Electrical Engineering and Computer Science Concentration Mechanical Engineering Concentration Materials Scien... | Gwangju Institute of Science and Technology | 0.78041 |
91,835 | In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output. Blind deconvoluti... | Blind deconvolution | 0.780409 |
91,836 | Blind deconvolution algorithms often make use of high-order statistics, with moments higher than two. This can be implicit or explicit. | Blind deconvolution | 0.780409 |
91,837 | Whitening usually leaves some phase distortion in the results. Most blind deconvolution techniques use higher-order statistics of the signals, and permit the correction of such phase distortions. We can optimize the equalizer to obtain a signal with a PSF approximating what we know about the original PSF. | Blind deconvolution | 0.780409 |
91,838 | The Hurewicz theorem for topological spaces can also be stated for n-connected simplicial sets satisfying the Kan condition. | Hurewicz theorem | 0.780407 |
91,839 | Together with OSRF, these two organizations came to be officially known as Open Robotics in May 2017. In 2018, Open Robotics opened its first overseas office in Singapore, and announced its collaboration with the Singapore Government to work on robotics applications for the healthcare sector.In December 2022, OSRC and ... | Open Robotics | 0.780401 |
91,840 | The beginnings of Open Robotics can be traced to Willow Garage, a robotics research lab and incubator created by Scott Hassan, an early Google engineer and billionaire technology entrepreneur. It was here that the first official Robot Operating System (ROS) distribution was released in May 2010, and quickly gained wide... | Open Robotics | 0.780401 |
91,841 | Open Robotics is a nonprofit corporation headquartered in Mountain View, California. It is the primary maintainer of the Robot Operating System, the Gazebo simulator, and the Ignition libraries that are set to supersede Gazebo by 2025. Its stated mission is to support "the development, distribution and adoption of open... | Open Robotics | 0.780401 |
91,842 | Oxamic acid is an organic compound with the formula NH2C(O)COOH. It is a white, water-soluble solid. It is the monoamide of oxalic acid. Oxamic acid inhibits lactate dehydrogenase A. The active site of lactate dehydrogenase (LDH) is closed off once oxamic acid attaches to the LDH-NADH complex, effectively inhibiting it... | C2H3NO3 | 0.7804 |
91,843 | As another example from physics, consider a parallel-plate capacitor, in which the plates can move relative to one another. Such a capacitor would allow transfer of the electric energy which is stored in the capacitor into external mechanical work, done by the force acting on the plates. One may think of the electric c... | Legendre transformation | 0.7804 |
91,844 | In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (s... | Legendre transformation | 0.7804 |
91,845 | Male stoats (Mustela erminea) will sometimes mate with infant females of their species. This is a natural part of their reproductive biology – they have a delayed gestation period, so these females give birth the following year when they are fully grown. In one reported observation, a male spotted hyena attempted to ma... | Animal co-opted sexual behavior | 0.7804 |
91,846 | The book is divided into eight chapters, each of which advances Ginzburg and Colyvan's argument for an inertial model of population dynamics. It begins with an explanation of planetary orbits and population growth, and argues that an analogy between the two might be fruitful for theoretical ecology. Chapter 2 engages i... | Ecological Orbits | 0.780398 |
91,847 | He also thought that this would allow some of the philosophical arguments, which he thought some readers may find "unsatisfying", to be developed in more depth. For example, he argues that the book's argument that laws of nature in physics and ecology are equally open to question could lead us to conclude that neither ... | Ecological Orbits | 0.780398 |
91,848 | He described Ginzburg "an eager and capable revolutionary" for his work in ecology and says that the philosophy in the book "should not scare away the prospective reader as it is presented in a very lighthearted way. "John Matthewson reviewed the book in the Australasian Journal of Philosophy, describing it as brief bu... | Ecological Orbits | 0.780398 |
91,849 | He thought that it was "a pleasure to read" and had a tone that was "disarming and engaging", making it accessible for undergraduates and interested non-scientists. However, he felt that the philosophical portion of the book focusing on whether ecology has laws was engaging in a "misguided" dispute and was "a bit tires... | Ecological Orbits | 0.780398 |
91,850 | Nonetheless, he thought the writing style "was generally quite good" and that the book "should be of obvious interest to theoretical ecologists" whilst also being accessible to graduate students and advanced undergraduates.In Ecology, Robert P. Freckleton criticised the book for presenting a completely deterministic mo... | Ecological Orbits | 0.780398 |
91,851 | He described Ginzburg and Colyvan's argument as "persuasive" and says his "only complaint" is that the term "maternal effects" was "used too loosely to mean all delayed effects by which one generation affects the biology of the following generations, rather than being restricted to the biological mechanisms".In a revie... | Ecological Orbits | 0.780398 |
91,852 | Günter Wagner reviewed the book in Science, describing it as "an exciting read on many levels" due to Ginzburg and Colyvan's explanations throughout the book. He said that the book placing individual energy consumption at the centre of its theory was "novel" and that if Ginzburg and Colyvan were right about the practic... | Ecological Orbits | 0.780398 |
91,853 | Ecological Orbits: How Planets Move and Populations Grow is a book on population ecology by ecologist Lev R. Ginzburg and philosopher of science Mark Colyvan that argues for an inertial model of population dynamics. | Ecological Orbits | 0.780398 |
91,854 | A fastidious organism is any organism that has complex or particular nutritional requirements. In other words, a fastidious organism will only grow when specific nutrients are included in its medium. The more restrictive term fastidious microorganism is used in microbiology to describe microorganisms that will grow onl... | Fastidious organism | 0.780397 |
91,855 | When there is a need to determine which bacteria or fungi are present (in agriculture, medicine, or biotechnology), scientists can also turn to other tools besides cultures, such as nucleic acid tests (which instead detect that organism's DNA or RNA, even if only in fragments or spores as opposed to entire cells) or im... | Fastidious organism | 0.780397 |
91,856 | : p.352-353, 355–358 This was remedied by the quenched-spark and rotary gap transmitters (below). In recognition of their achievements in radio, Marconi and Braun shared the 1909 Nobel Prize in physics. : p.352-353, 355–358 | Rotary gap | 0.780393 |
91,857 | In 1924 Edward V. Appleton demonstrated the existence of this layer, now called the "Kennelly–Heaviside layer" or "E-layer", for which he received the 1947 Nobel Prize in Physics. Knowledgeable sources today doubt whether Marconi actually received this transmission. : p.387-392 Ionospheric conditions should not have al... | Rotary gap | 0.780393 |
91,858 | A special case of the Tate conjecture can be phrased in terms of Tate modules. Suppose K is finitely generated over its prime field (e.g. a finite field, an algebraic number field, a global function field), of characteristic different from p, and A and B are two abelian varieties over K. The Tate conjecture then predic... | Tate module of a number field | 0.780393 |
91,859 | Then Tp(K) is a pro-p-group and so a Zp-module. Using class field theory one can describe Tp(K) as isomorphic to the inverse limit of the class groups Cm of the Km under norm.Iwasawa exhibited Tp(K) as a module over the completion Zp] and this implies a formula for the exponent of p in the order of the class groups Cm ... | Tate module of a number field | 0.780393 |
91,860 | The description of the Tate module for the function field of a curve over a finite field suggests a definition for a Tate module of an algebraic number field, the other class of global field, introduced by Kenkichi Iwasawa. For a number field K we let Km denote the extension by pm-power roots of unity, K ^ {\displaysty... | Tate module of a number field | 0.780393 |
91,861 | In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency). The FSC is t... | Fourier shell correlation | 0.780392 |
91,862 | Low molecular weight polyols are widely used in polymer chemistry where they function as crosslinking agents and chain extenders. Alkyd resins for example, use polyols in their synthesis and are used in paints and in molds for casting. They are the dominant resin or "binder" in most commercial "oil-based" coatings. App... | Polyol | 0.780387 |
91,863 | In organic chemistry, a polyol is an organic compound containing multiple hydroxyl groups (−OH). The term "polyol" can have slightly different meanings depending on whether it is used in food science or polymer chemistry. Polyols containing two, three and four hydroxyl groups are diols, triols, and tetrols, respectivel... | Polyol | 0.780387 |
91,864 | Originally, in the actual data transfer each set of resource records for a single domain name and type was transferred in a separate response message from the server to the client. However, this is inefficient, and some DNS server software implemented optimizations, geared at allowing the response compression mechanism... | Zone transfer | 0.780387 |
91,865 | In mathematics, more specifically in geometric topology, the Kirby–Siebenmann class is an obstruction for topological manifolds to allow a PL-structure. | Kirby–Siebenmann class | 0.780386 |
91,866 | The reduction in heterozygosity can be measured using F-statistics. | Wahlund effect | 0.780383 |
91,867 | In population genetics, the Wahlund effect is a reduction of heterozygosity (that is when an organism has two different alleles at a locus) in a population caused by subpopulation structure. Namely, if two or more subpopulations are in a Hardy–Weinberg equilibrium but have different allele frequencies, the overall hete... | Wahlund effect | 0.780383 |
91,868 | In the 1990s, Dassault Systèmes' software was used to develop seven out of every ten new airplanes and four out of every ten new cars worldwide. Major players in the aviation and automotive industries, including Honda, Mercedes-Benz, BMW and Boeing, were able to design and mock-up their products in CATIA rather than us... | Dassault Systèmes | 0.780381 |
91,869 | Sparrow is a deep neural network based on the transformer machine learning model architecture. It is fine-tuned from DeepMind’s Chinchilla AI pre-trained large language model (LLM), which has 70 Billion parameters.Sparrow is trained using reinforcement learning from human feedback (RLHF), although some supervised fine-... | Sparrow (bot) | 0.780379 |
91,870 | Sparrow is a chatbot developed by the artificial intelligence research lab DeepMind, a subsidiary of Alphabet Inc. It is designed to answer users' questions correctly, while reducing the risk of unsafe and inappropriate answers. One motivation behind Sparrow is to address the problem of language models producing incorr... | Sparrow (bot) | 0.780379 |
91,871 | (Cyclopentadienyl)titanium trichloride is an organotitanium compound with the formula (C5H5)TiCl3. It is a moisture sensitive orange solid. The compound adopts a piano stool geometry. | (Cyclopentadienyl)titanium trichloride | 0.780378 |
91,872 | The current solar income of the Earth, or any ecoregion of the earth, is the amount of solar energy that falls on it as sunlight. This is thought important in some branches of green economics, as the ultimate measure of renewable energy. Buckminster Fuller first described the concept in his 1970 paper Cosmic Costing, c... | Current solar income | 0.780377 |
91,873 | In molecular biology the SPR domain is a protein domain found in the Sprouty (Spry) and Spred (Sprouty related EVH1 domain) proteins. These have been identified as inhibitors of the Ras/mitogen-activated protein kinase (MAPK) cascade, a pathway crucial for developmental processes initiated by activation of various rece... | SPR domain | 0.780376 |
91,874 | The Fifth Generation Computer Systems (FGCS; Japanese: 第五世代コンピュータ, romanized: daigosedai konpyūta) was a 10-year initiative begun in 1982 by Japan's Ministry of International Trade and Industry (MITI) to create computers using massively parallel computing and logic programming. It aimed to create an "epoch-making compu... | Fifth generation computer | 0.780376 |
91,875 | Subsecunda plants vary in color from green to yellow and orange (but never red), and are found in hollows, lawns, or are aquatic. Species always with unisexual gametophytes. Examples: Sphagnum lescurii and Sphagnum pylaesii.The reciprocal monophyly of these sections and two other minor ones (Rigida and Squarrosa) has b... | Sphagnum moss | 0.780376 |
91,876 | Of the four colored pictures at the top of the diagram, the first two represent the meso compound (the 2R,3S and 2S,3R isomers are equivalent), followed by the optically active pair of levotartaric acid (L-(R,R)-(+)-tartaric acid) and dextrotartaric acid (D-(S,S)-(-)-tartaric acid). The meso compound is bisected by an ... | Meso isomer | 0.780374 |
91,877 | Influence lines are based on Betti's theorem. From there, consider two external force systems, F i P {\displaystyle F_{i}^{P}} and F i Q {\displaystyle F_{i}^{Q}} , each one associated with a displacement field whose displacements measured in the force's point of application are represented by d i P {\displaystyle d_{i... | Influence line | 0.780374 |
91,878 | The maximum theorem implies that if: The utility function u ( x ) {\displaystyle u(x)} is continuous with respect to x {\displaystyle x} , The correspondence B ( p , I ) {\displaystyle B(p,I)} is non-empty, compact-valued, and continuous with respect to p , I {\displaystyle p,I} ,then x ∗ ( p , I ) {\displaystyle x^{*}... | Marshallian demand function | 0.780372 |
91,879 | The constrained optimization leads to the Marshallian demand function: x ∗ ( p 1 , p 2 , I ) = ( α I ( α + β ) p 1 , β I ( α + β ) p 2 ) . {\displaystyle x^{*}(p_{1},p_{2},I)=\left({\frac {\alpha I}{(\alpha +\beta )p_{1}}},{\frac {\beta I}{(\alpha +\beta )p_{2}}}\right).} 2. | Marshallian demand function | 0.780372 |
91,880 | For the general case, the dual problem is found by converting sums to integrals:and the strong duality still holds. This is the Kantorovich duality theorem. | Kantorovich metric | 0.78037 |
91,881 | The following is an intuitive proof which skips over technical points. A fully rigorous proof is found in.Discrete case: When M {\displaystyle M} is discrete, solving for the 1-Wasserstein distance is a problem in linear programming:where c: M × M → [ 0 , ∞ ) {\displaystyle c:M\times M\to [0,\infty )} is a general "cos... | Kantorovich metric | 0.78037 |
91,882 | If P {\displaystyle P} is an empirical measure with samples X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} and Q {\displaystyle Q} is an empirical measure with samples Y 1 , … , Y n {\displaystyle Y_{1},\ldots ,Y_{n}} , the distance is a simple function of the order statistics: W p ( P , Q ) = ( 1 n ∑ i = 1 n ‖ X ( ... | Kantorovich metric | 0.78037 |
91,883 | Benamou & Brenier found a dual representation of W 2 {\displaystyle W_{2}} by fluid mechanics, which allows efficient solution by convex optimization.Given two probability distributions on R n {\displaystyle \mathbb {R} ^{n}} with density p , q {\displaystyle p,q} , then where v ( x , t ) {\displaystyle v(x,t)} is a ve... | Kantorovich metric | 0.78037 |
91,884 | Because of this analogy, the metric is known in computer science as the earth mover's distance. The name "Wasserstein distance" was coined by R. L. Dobrushin in 1970, after learning of it in the work of Leonid Vaseršteĭn on Markov processes describing large systems of automata (Russian, 1969). However the metric was fi... | Kantorovich metric | 0.78037 |
91,885 | Recent advances in vehicle electronics have led to a move towards fewer, more capable computer processors on a vehicle. A typical vehicle in the early 2000s would have between 20 and 100 individual networked microcontroller/programmable logic controller modules with non-real-time operating systems. The current trend is... | Intelligent transport system | 0.780366 |
91,886 | The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function (SMHTAF), is a special S-shaped function based on the hyperbolic tangent, given by mtanh x = e a x − e − b x e c x + e − d x . {\displaystyle \operatorname {mtanh} x={\frac {e^{ax}-e^{-bx}}{e^... | Soboleva modified hyperbolic tangent | 0.780365 |
91,887 | The optimization of the volume of tissue within the capillaries in conjunction with the large respiratory surface area allow for an effective diffusion rate. Finally, in the avian respiratory system, the partial pressure of oxygen between the gas, lung, and the vascular capillaries depends upon the ventilation rate and... | Common raven physiology | 0.780365 |
91,888 | The multiple zeta functions are defined by ζ ( s 1 , s 2 , … , s n ) = ∑ k 1 > k 2 > ⋯ > k n > 0 k 1 − s 1 k 2 − s 2 ⋯ k n − s n . {\displaystyle \zeta (s_{1},s_{2},\ldots ,s_{n})=\sum _{k_{1}>k_{2}>\cdots >k_{n}>0}{k_{1}}^{-s_{1}}{k_{2}}^{-s_{2}}\cdots {k_{n}}^{-s_{n}}.} One can analytically continue these functions t... | Riemann zeta-function | 0.780364 |
91,889 | The functional equation shows that the Riemann zeta function has zeros at −2, −4,.... These are called the trivial zeros. They are trivial in the sense that their existence is relatively easy to prove, for example, from sin πs/2 being 0 in the functional equation. The non-trivial zeros have captured far more attention ... | Riemann zeta-function | 0.780364 |
91,890 | Among those results are the mean value theorems for S(t) and its first integral S 1 ( t ) = ∫ 0 t S ( u ) d u {\displaystyle S_{1}(t)=\int _{0}^{t}S(u)\,\mathrm {d} u} on intervals of the real line, and also the theorem claiming that every interval (T, T + H] for H ≥ T 27 82 + ε {\displaystyle H\geq T^{{\frac {27}{82}}... | Riemann zeta-function | 0.780364 |
91,891 | The function S ( t ) = 1 π arg ζ ( 1 2 + i t ) {\displaystyle S(t)={\frac {1}{\pi }}\arg {\zeta \left({\tfrac {1}{2}}+it\right)}} is called the argument of the Riemann zeta function. Here arg ζ(1/2 + it) is the increment of an arbitrary continuous branch of arg ζ(s) along the broken line joining the points 2, 2 + it ... | Riemann zeta-function | 0.780364 |
91,892 | {\displaystyle J(x)=\sum {\frac {\pi \left(x^{\frac {1}{n}}\right)}{n}}.} Now ln ζ ( s ) = s ∫ 0 ∞ J ( x ) x − s − 1 d x . {\displaystyle \ln \zeta (s)=s\int _{0}^{\infty }J(x)x^{-s-1}\,\mathrm {d} x.} These expressions can be used to prove the prime number theorem by means of the inverse Mellin transform. Riemann's ... | Riemann zeta-function | 0.780364 |
91,893 | We can also find expressions which relate to prime numbers and the prime number theorem. If π(x) is the prime-counting function, then ln ζ ( s ) = s ∫ 0 ∞ π ( x ) x ( x s − 1 ) d x , {\displaystyle \ln \zeta (s)=s\int _{0}^{\infty }{\frac {\pi (x)}{x(x^{s}-1)}}\,\mathrm {d} x,} for values with Re(s) > 1. A similar Me... | Riemann zeta-function | 0.780364 |
91,894 | The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined as for Re ( s ) > 1 {\displaystyle \operatorname {Re} (s)>1} , and its analytic continuation elsewhere.The Riemann zeta function plays a pivotal role in analytic num... | Riemann zeta-function | 0.780364 |
91,895 | Paper's low costs and manifold applications make it an attractive substrate, however, its high roughness and high wettability have traditionally made it problematic for electronics. This is an active research area, however, and print-compatible metal deposition techniques have been demonstrated that adapt to the rough ... | Printed silicon electronics | 0.780362 |
91,896 | It remains active area of research to find efficient algorithm for performing this change of basis. Applications including efficient spherical harmonic expansion, analyzing certain Markov processes, robotics etc. Quantum FFTs Shor's fast algorithm for integer factorization on a quantum computer has a subroutine to comp... | Fast Fourier Transform | 0.780362 |
91,897 | Big FFTs With the explosion of big data in fields such as astronomy, the need for 512K FFTs has arisen for certain interferometry calculations. The data collected by projects such as WMAP and LIGO require FFTs of tens of billions of points. As this size does not fit into main memory, so called out-of-core FFTs are an a... | Fast Fourier Transform | 0.780362 |
91,898 | A fundamental question of longstanding theoretical interest is to prove lower bounds on the complexity and exact operation counts of fast Fourier transforms, and many open problems remain. It is not rigorously proved whether DFTs truly require Ω ( N log N ) {\textstyle \Omega (N\log N)} (i.e., order N log N {\displ... | Fast Fourier Transform | 0.780362 |
91,899 | Brain implants electrically stimulate, block or record (or both record and stimulate simultaneously) signals from single neurons or groups of neurons (biological neural networks) in the brain. This can only be done where the functional associations of these neurons are approximately known. Because of the complexity of ... | Neural implants | 0.780361 |
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