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26,100 | If two reduced words represent the same element of a Coxeter group, then Matsumoto's theorem states that the first word can be transformed into the second by repeatedly transforming xyxy... to yxyx... (or vice versa)where xyxy... = yxyx...is one of the defining relations of the Coxeter group. | Matsumoto's theorem (group theory) | 0.807306 |
26,101 | In group theory, Matsumoto's theorem, proved by Hideya Matsumoto (1964), gives conditions for two reduced words of a Coxeter group to represent the same element. | Matsumoto's theorem (group theory) | 0.807306 |
26,102 | Matsumoto's theorem implies that there is a natural map (not a group homomorphism) from a Coxeter group to the corresponding braid group, taking any element of the Coxeter group represented by some reduced word in the generators to the same word in the generators of the braid group. | Matsumoto's theorem (group theory) | 0.807306 |
26,103 | Hirschhorn et al. (1999) show that a pizza sliced in the same way as the pizza theorem, into a number n of sectors with equal angles where n is divisible by four, can also be shared equally among n/4 people. For instance, a pizza divided into 12 sectors can be shared equally by three people as well as by two; however, ... | Pizza theorem | 0.807305 |
26,104 | Brailov (2021), Brailov (2022), Ehrenborg, Morel & Readdy (2022) extends this result to higher dimensions, i.e. for certain arrangements of hyperplanes, the alternating sum of volumes cut out by the hyperplanes is zero. Compare with the ham sandwich theorem, a result about slicing n-dimensional objects. The two-dimensi... | Pizza theorem | 0.807305 |
26,105 | Let p be an interior point of the disk, and let n be a multiple of 4 that is greater than or equal to 8. Form n sectors of the disk with equal angles by choosing an arbitrary line through p, rotating the line n/2 − 1 times by an angle of 2π/n radians, and slicing the disk on each of the resulting n/2 lines. Number the ... | Pizza theorem | 0.807305 |
26,106 | The requirement that the number of sectors be a multiple of four is necessary: as Don Coppersmith showed, dividing a disk into four sectors, or a number of sectors that is not divisible by four, does not in general produce equal areas. Mabry & Deiermann (2009) answered a problem of Carter & Wagon (1994b) by providing a... | Pizza theorem | 0.807305 |
26,107 | The pizza theorem was originally proposed as a challenge problem by Upton (1967). The published solution to this problem, by Michael Goldberg, involved direct manipulation of the algebraic expressions for the areas of the sectors. Carter & Wagon (1994a) provide an alternative proof by dissection. They show how to parti... | Pizza theorem | 0.807305 |
26,108 | In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because it mimics a traditional pizza slicing technique. It shows that if two people share a pizza sliced into 8 pieces (or any multiple of 4 greater than 8), and t... | Pizza theorem | 0.807305 |
26,109 | Even within a single person this competition produces a highly complex behavior which does not fit any simple model.Nevertheless, the individual strategies can be understood. In finance this is equivalent to understanding different financial products as information derivatives i.e. as products which are derived from al... | Equity premium puzzle | 0.807304 |
26,110 | The simplest scientific interpretation of the puzzle suggests that consumption optimization is not responsible for the equity premium. More precisely, the timeseries of aggregate consumption is not a leading explanatory factor of the equity premium.The human brain is (simultaneously) engaged in many strategies. Each of... | Equity premium puzzle | 0.807304 |
26,111 | The standard model represents consumers as continuously-optimizing dynamically-consistent expected-utility maximizers. These assumptions provide a tight link between attitudes to risk and attitudes to variations in intertemporal consumption which is crucial in deriving the equity premium puzzle. Solutions of this kind ... | Equity premium puzzle | 0.807304 |
26,112 | Some explanations rely on assumptions about individual behavior and preferences different from those made by Mehra and Prescott. Examples include the prospect theory model of Benartzi and Thaler (1995) based on loss aversion. A problem for this model is the lack of a general model of portfolio choice and asset valuatio... | Equity premium puzzle | 0.807304 |
26,113 | In 2021, the 30th year of the International Aerial Robotics Competition, the 9th mission will commence. The Official Rules for the 9th mission are available at the Competition web site along with a video summarizing the objectives of the 9th mission. Mission 9 focuses on fully autonomous flight using ONLY onboard compu... | International Aerial Robotics Competition | 0.807304 |
26,114 | In 2018, the 27th year of the International Aerial Robotics Competition, the 8th mission was announced. The Official Rules for the 8th mission are available at the Competition web site along with a video summarizing the 8th mission. Mission 8 focuses on non-electronic human-machine interaction for the first time, with ... | International Aerial Robotics Competition | 0.807304 |
26,115 | The International Aerial Robotics Competition was first held on the campus of the Georgia Institute of Technology (first mission, 1991–1995). Walt Disney World's EPCOT Center asked that the competition move to its location for the second mission, where it was held at the entrance to the park during 1996 and 1997. The U... | International Aerial Robotics Competition | 0.807304 |
26,116 | The primary goal of the competition has been to provide a reason for the state of the art in aerial robotics to move forward. Challenges set before the international collegiate community have been geared towards producing advances in the state of the art at an increasingly aggressive pace. From 1991 through 2009, a tot... | International Aerial Robotics Competition | 0.807304 |
26,117 | The International Aerial Robotics Competition (IARC) began in 1991 on the campus of the Georgia Institute of Technology and is the longest running university-based robotics competition in the world. Since 1991, collegiate teams with the backing of industry and government have fielded autonomous flying robots in an atte... | International Aerial Robotics Competition | 0.807304 |
26,118 | Michelson, R.C., “Autonomous Aerial Robots,” Unmanned Systems, Volume 29 - No. 10, October 2011, Association for Unmanned Vehicle Systems International, Washington, D.C., pp 38–42 Howe, J., Vogl, M., Banik, J., et al., "Design and Development of South Dakota School of Mines and Technology’s Aerial Robotic Reconnaissanc... | International Aerial Robotics Competition | 0.807304 |
26,119 | There are three main types of computer environments for studying school geometry: supposers, dynamic geometry environments (DGEs) and Logo-based programs. Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Ge... | Interactive geometry software | 0.807301 |
26,120 | GeoKone.NET is an interactive recursive natural geometry (or "sacred geometry") generator that runs in a web browser. GeoKone allows the user to create geometric figures using naturalistic rules of recursive copying, such as the Golden ratio. | Interactive geometry software | 0.807301 |
26,121 | GeoGebra is software that combines geometry, algebra and calculus for mathematics education in schools and universities. It is available free of charge for non-commercial users. License: open source under GPL license (free of charge) Languages: 55 Geometry: points, lines, all conic sections, vectors, parametric curves,... | Interactive geometry software | 0.807301 |
26,122 | Cinderella, written in Java, is very different from The Geometer's Sketchpad. The later version Cinderella.2 also includes a physics simulation engine and a scripting language. Also, it now supports macros, line segments, calculations, arbitrary functions, plots, etc. Full documentation is available online. | Interactive geometry software | 0.807301 |
26,123 | Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines, circles o... | Interactive geometry software | 0.807301 |
26,124 | Type theories are defined by their rules of inference. There are rules for a "§ functional core", described above, and rules that create types and terms. Below is a non-exhaustive list of common types and their associated terms. The list ends with "§ inductive types", which is a powerful technique that is able to const... | Typed logic | 0.807295 |
26,125 | Type Theory at nLab, which has articles on many topics. Intuitionistic Type Theory article at the Stanford Encyclopedia of Philosophy Lambda Calculus with Types book by Henk Barendregt Calculus of Constructions / Typed Lambda Calculus textbook style paper by Helmut Brandl Intuitionistic Type Theory notes by Per Martin-... | Typed logic | 0.807295 |
26,126 | This led to proposals such as Lawvere's Elementary Theory of the Category of Sets (ETCS). Homotopy type theory continues in this line using type theory. Researchers are exploring connections between dependent types (especially the identity type) and algebraic topology (specifically homotopy). | Typed logic | 0.807295 |
26,127 | Many programs that work with type theory (e.g., interactive theorem provers) also do type inferencing. It lets them select the rules that the user intends, with fewer actions by the user. | Typed logic | 0.807295 |
26,128 | Some combinations of types are equivalent to other combinations of types. When functions are considered "exponentiation", the combinations of types can be written similar to algebraic identities. Thus, 0 + A ≅ A {\displaystyle {\mathbb {0} }+A\cong A} , 1 × A ≅ A {\displaystyle {\mathbb {1} }\times A\cong A} , 1 + 1 ≅ ... | Typed logic | 0.807295 |
26,129 | Metastability in the brain is a phenomenon studied in computational neuroscience to elucidate how the human brain recognizes patterns. Here, the term metastability is used rather loosely. There is no lower-energy state, but there are semi-transient signals in the brain that persist for a while and are different than th... | Metastable state | 0.807295 |
26,130 | Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. It is related to, but distinct from, quasi-Newton methods. Starting at some estimate of the optimal solution, the method is based on solving a sequenc... | Successive linear programming | 0.807294 |
26,131 | Electron nuclear double resonance (ENDOR) is a magnetic resonance technique for elucidating the molecular and electronic structure of paramagnetic species. The technique was first introduced to resolve interactions in electron paramagnetic resonance (EPR) spectra. It is currently practiced in a variety of modalities, m... | Electron nuclear double resonance | 0.807293 |
26,132 | Additional applications have been to magnetic resonance imaging contrast agents. HF ENDOR has been used as a characterization tool for porous materials, for the electronic properties of donors/acceptors in semiconductors, and for electronic properties of endohedral fullerenes. Framework Substitution with W-band ENDOR h... | Electron nuclear double resonance | 0.807293 |
26,133 | Such advantages are the generation of distortion-less line shapes, manipulation of spins through a variety of pulse sequences, and the lack of dependence on a sensitive balance between electron and nuclear spin relaxation rates and applied power (given long enough relaxation rates).HF pulsed ENDOR is generally applied ... | Electron nuclear double resonance | 0.807293 |
26,134 | The structure of a hairpin stator differs from conventional stators only in the type of winding system - other components of the stator are little changed. The stack of sheets consists of many layers of individual sheets, each insulated by a thin coating. The housing is another subcomponent that does not generally requ... | Hairpin technology | 0.807292 |
26,135 | Hairpin technology is a winding technology for stators in electric motors and generators and is also used for traction applications in electric vehicles. In contrast to conventional winding technologies, the hairpin technology is based on solid, flat copper bars which are inserted into the stator stack. These copper ba... | Hairpin technology | 0.807292 |
26,136 | Particularly in traction drives, a major implementation challenge is process reliability, particularly bending and welding processes. The bending process must not damage the insulation and exactly match the required geometry. Incorrectly welded hairpin ends can cause electrical losses – and possibly a non-functioning s... | Hairpin technology | 0.807292 |
26,137 | Next the pins are inserted into the stator stack. The insertion process is limited by overlaps in the winding head geometry. The hairpins are usually pre-assembled in an assembly nest. | Hairpin technology | 0.807292 |
26,138 | In the first process, a flat copper wire, which is usually already enameled, is continuously unwound and straightened in several stages to reduce residual curvature and stresses. In preparation for welding of the copper ends in a later process step, this insulation is partially removed. Laser-based and mechanical proce... | Hairpin technology | 0.807292 |
26,139 | The hairpin stator process chain is based on an indirect winding approach. Due to the solid cross section, hairpins can be shaped into their final geometry ahead of the actual assembly process. In contrast to conventional stator production, in which winding-based assembly processes predominate, a forming process is app... | Hairpin technology | 0.807292 |
26,140 | Government and industry are funding hairpin technology research projects. These include:: Pro-E-Traktion (Production, BMW AG) HaPiPro2 (Production, PEM of RWTH Aachen University) AnStaHa (Production, Karlsruhe Institute of Technology) IPANEMA (Machine Learning, API Hard- and Software GmbH) KIPrEMo (Artificial Intellige... | Hairpin technology | 0.807292 |
26,141 | The Journal of Universal Computer Science (J.UCS) is a monthly peer-reviewed open-access scientific journal covering all aspects of computer science. | Journal of Universal Computer Science | 0.807292 |
26,142 | 256 bits is a common key size for symmetric ciphers in cryptography, such as Advanced Encryption Standard (AES). Increasing the word size can accelerate multiple precision mathematical libraries. Applications include cryptography. Researchers at the University of Cambridge use a 256-bit capability pointer, which includ... | 256-bit computing | 0.807291 |
26,143 | In physics, a quantum instrument is a mathematical abstraction of a quantum measurement, capturing both the classical and quantum outputs. It combines the concepts of measurement and quantum operation. It can be equivalently understood as a quantum channel that takes as input a quantum system and has as its output two ... | Quantum instrument | 0.807283 |
26,144 | In probability theory, Kramkov's optional decomposition theorem (or just optional decomposition theorem) is a mathematical theorem on the decomposition of a positive supermartingale V {\displaystyle V} with respect to a family of equivalent martingale measures into the form V t = V 0 + ( H ⋅ X ) t − C t , t ≥ 0 , {\dis... | Kramkov's optional decomposition theorem | 0.807281 |
26,145 | The abstract list type L with elements of some type E (a monomorphic list) is defined by the following functions: nil: () → L cons: E × L → L first: L → E rest: L → Lwith the axioms first (cons (e, l)) = e rest (cons (e, l)) = lfor any element e and any list l. It is implicit that cons (e, l) ≠ l cons (e, l) ≠ e cons (... | List (abstract data type) | 0.807278 |
26,146 | The study of such algebraic solutions involves examining the topology of the deformation parameter space (and in particular, its mapping class group); for the case of simple poles, this amounts to the study of the action of braid groups. For the particularly important case of the sixth Painlevé equation, there has been... | Schlesinger equations | 0.807276 |
26,147 | In general, solutions of the isomonodromy equations cannot be expressed in terms of simpler functions such as solutions of linear differential equations. However, for particular (more precisely, reducible) choices of extended monodromy data, solutions can be expressed in terms of such functions (or at least, in terms o... | Schlesinger equations | 0.807276 |
26,148 | In mathematics, the equations governing the isomonodromic deformation of meromorphic linear systems of ordinary differential equations are, in a fairly precise sense, the most fundamental exact nonlinear differential equations. As a result, their solutions and properties lie at the heart of the field of exact nonlinear... | Schlesinger equations | 0.807276 |
26,149 | Some examples include web services,computer graphics,embedded systems,simulation and modeling,machine learning,decision support,bioinformatics,components,numerical analysis, and compilers. The first major survey of the field of MT was conducted in 2016. It was followed by another major survey in 2018, which highlights ... | Metamorphic testing | 0.807275 |
26,150 | Then J {\displaystyle J} is sequentially weakly lower semi-continuous in W 1 , p ( Ω , R m ) {\displaystyle W^{1,p}(\Omega ,\mathbb {R} ^{m})} .A converse like theorem in this case is the following: Assume that F {\displaystyle F} is continuous and satisfies | F ( x , y , A ) | ≤ a ( x , | y | , | A | ) {\displaystyle ... | Direct method in calculus of variations | 0.807275 |
26,151 | The following theorem proves sequential lower semi-continuity using a weaker notion of convexity: Assume that F: Ω × R m × R m n → [ 0 , ∞ ) {\displaystyle F:\Omega \times \mathbb {R} ^{m}\times \mathbb {R} ^{mn}\to [0,\infty )} is a function that has the following properties: The function F {\displaystyle F} is a Cara... | Direct method in calculus of variations | 0.807275 |
26,152 | If the function A ↦ F ( x , y , A ) {\displaystyle A\mapsto F(x,y,A)} is convex for almost every x ∈ Ω {\displaystyle x\in \Omega } and every y ∈ R m {\displaystyle y\in \mathbb {R} ^{m}} , then J {\displaystyle J} is sequentially weakly lower semi-continuous.When n = 1 {\displaystyle n=1} or m = 1 {\displaystyle m=1} ... | Direct method in calculus of variations | 0.807275 |
26,153 | Show that ( u n ) {\displaystyle (u_{n})} admits some subsequence ( u n k ) {\displaystyle (u_{n_{k}})} , that converges to a u 0 ∈ V {\displaystyle u_{0}\in V} with respect to a topology τ {\displaystyle \tau } on V {\displaystyle V} . Show that J {\displaystyle J} is sequentially lower semi-continuous with respect to... | Direct method in calculus of variations | 0.807275 |
26,154 | The calculus of variations deals with functionals J: V → R ¯ {\displaystyle J:V\to {\bar {\mathbb {R} }}} , where V {\displaystyle V} is some function space and R ¯ = R ∪ { ∞ } {\displaystyle {\bar {\mathbb {R} }}=\mathbb {R} \cup \{\infty \}} . The main interest of the subject is to find minimizers for such functional... | Direct method in calculus of variations | 0.807275 |
26,155 | An example is J ( x ) ≥ α ‖ x ‖ q − β {\displaystyle J(x)\geq \alpha \lVert x\rVert ^{q}-\beta } for some α > 0 {\displaystyle \alpha >0} , q ≥ 1 {\displaystyle q\geq 1} and β ≥ 0 {\displaystyle \beta \geq 0} .A functional with this property is sometimes called coercive. Showing sequential lower semi-continuity is usua... | Direct method in calculus of variations | 0.807275 |
26,156 | The direct method may often be applied with success when the space V {\displaystyle V} is a subset of a separable reflexive Banach space W {\displaystyle W} . In this case the sequential Banach–Alaoglu theorem implies that any bounded sequence ( u n ) {\displaystyle (u_{n})} in V {\displaystyle V} has a subsequence tha... | Direct method in calculus of variations | 0.807275 |
26,157 | In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to p... | Direct method in calculus of variations | 0.807275 |
26,158 | The initial impetus for developing a classification of mental disorders in the United States was the need to collect statistical information. The first official attempt was the 1840 census, which used a single category: "idiocy/insanity". Three years later, the American Statistical Association made an official protest ... | Multiaxial diagnosis | 0.807273 |
26,159 | Some have argued that instead of replacing metaphysical terms like "desire" or "purpose" the DSM chose to legitimize them by giving them operational definitions. However, this may have served only to provide a "reassurance fetish" for mainstream methodological practice, rather than representing a substantial and meanin... | Multiaxial diagnosis | 0.807273 |
26,160 | Hospitals, clinics, and insurance companies in the United States may require a DSM diagnosis for all patients with mental disorders. Health-care researchers use the DSM to categorize patients for research purposes. The DSM evolved from systems for collecting census and psychiatric hospital statistics, as well as from a... | Multiaxial diagnosis | 0.807273 |
26,161 | The APA Committee on Nomenclature and Statistics was empowered to develop a version of Medical 203 specifically for use in the United States, to standardize the diverse and confused usage of different documents. In 1950, the APA committee undertook a review and consultation. It circulated an adaptation of Medical 203, ... | Multiaxial diagnosis | 0.807273 |
26,162 | Computational neuroscience is the study of brain function in terms of the information processing properties of the nervous system. A subset of neuroscience, it looks to model the brain to examine specific aspects of the neurological system. Models of the brain include: Realistic Brain Models: These models look to repre... | Computational evolutionary biology | 0.80727 |
26,163 | The missing Y chromosome was added in January 2022. Since the late 1990s, computational biology has become an important part of biology, leading to numerous subfields. Today, the International Society for Computational Biology recognizes 21 different 'Communities of Special Interest', each representing a slice of the l... | Computational evolutionary biology | 0.80727 |
26,164 | Supervised learning is a type of algorithm that learns from labeled data and learns how to assign labels to future data that is unlabeled. In biology supervised learning can be helpful when we have data that we know how to categorize and we would like to categorize more data into those categories. A common supervised l... | Computational evolutionary biology | 0.80727 |
26,165 | There are several large conferences that are concerned with computational biology. Some notable examples are Intelligent Systems for Molecular Biology, European Conference on Computational Biology and Research in Computational Molecular Biology. There are also numerous journals dedicated to computational biology. Some ... | Computational evolutionary biology | 0.80727 |
26,166 | This is a direct result of major pharmaceutical companies needing more qualified analysts of the large data sets required for producing new drugs.Similarly, computational oncology aims to determine the future mutations in cancer through algorithmic approaches. Research in this field has led to the use of high-throughpu... | Computational evolutionary biology | 0.80727 |
26,167 | Scientists and researchers develop computational methods to analyze these massive data sets. This allows for an efficient comparison between the notable data points and allows for more accurate drugs to be developed.Analysts project that if major medications fail due to patents, that computational biology will be neces... | Computational evolutionary biology | 0.80727 |
26,168 | Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has foundations in applied mathematics, chemistry, and genetics. It differs from bi... | Computational evolutionary biology | 0.80727 |
26,169 | Computational biology has assisted evolutionary biology by: Using DNA data to reconstruct the tree of life with computational phylogenetics Fitting population genetics models (either forward time or backward time) to DNA data to make inferences about demographic or selective history Building population genetics models ... | Computational evolutionary biology | 0.80727 |
26,170 | Bioinformatics, the analysis of informatics processes in biological systems, began in the early 1970s. At this time, research in artificial intelligence was using network models of the human brain in order to generate new algorithms. This use of biological data pushed biological researchers to use computers to evaluate... | Computational evolutionary biology | 0.80727 |
26,171 | Open source software provides a platform for computational biology where everyone can access and benefit from software developed in research. PLOS cites four main reasons for the use of open source software: Reproducibility: This allows for researchers to use the exact methods used to calculate the relations between bi... | Computational evolutionary biology | 0.80727 |
26,172 | For example, in medical science, correcting a falsehood may take decades and cost lives. Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything. Scientists have been known to f... | Data manipulation | 0.807269 |
26,173 | When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy. The false statistics trap can be quite damaging for the quest for knowledge. | Data manipulation | 0.807269 |
26,174 | Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the p... | Data manipulation | 0.807269 |
26,175 | Statistical significance is a measure of probability; practical significance is a measure of effect. A baldness cure is statistically significant if a sparse peach-fuzz usually covers the previously naked scalp. The cure is practically significant when a hat is no longer required in cold weather and the barber asks how... | Data manipulation | 0.807269 |
26,176 | Available data suggest that the odds would be in favour of double SIDS compared to double homicide by a factor of nine. The 1 in 73 million figure was also misleading as it was reached by finding the probability of a baby from an affluent, non-smoking family dying from SIDS and squaring it: this erroneously treats each... | Data manipulation | 0.807269 |
26,177 | Other misuses include comparing apples and oranges, using the wrong average, regression toward the mean, and the umbrella phrase garbage in, garbage out. Some statistics are simply irrelevant to an issue.Anscombe's quartet is a made-up dataset that exemplifies the shortcomings of simple descriptive statistics (and the ... | Data manipulation | 0.807269 |
26,178 | We learn that a clever propagandist, right or left, can almost always find a way to present the data on economic growth that seems to support her case. And we therefore also learn to take any statistical analysis from a strongly political source with handfuls of salt." The term statistics originates from numbers genera... | Data manipulation | 0.807269 |
26,179 | If the facts are not "newsworthy" (which may require exaggeration) they may not be published. The motives of advertisers are even more mixed. "Politicians use statistics in the same way that a drunk uses lamp posts—for support rather than illumination" – Andrew Lang (WikiQuote) "What do we learn from these two ways of ... | Data manipulation | 0.807269 |
26,180 | "The sole reliance on citation data provides at best an incomplete and often shallow understanding of research — an understanding that is valid only when reinforced by other judgments. Numbers are not inherently superior to sound judgments." A seemingly simple question about the number of words in the English language... | Data manipulation | 0.807269 |
26,181 | Many misuses of statistics occur because The source is a subject matter expert, not a statistics expert. The source may incorrectly use a method or interpret a result. The source is a statistician, not a subject matter expert. An expert should know when the numbers being compared describe different things. | Data manipulation | 0.807269 |
26,182 | There are potential risks associated with the use of algorithms in government. Those include algorithms becoming susceptible to bias, a lack of transparency in how an algorithm may make decisions, and the accountability for any such decisions. According to a 2016's book Weapons of Math Destruction, algorithms and big d... | Regulation by algorithms | 0.807265 |
26,183 | states and uses machine learning to generate various three-digit "risk scores" for precriptions of medications and an overall "Overdose Risk Score", collectively referred to as Narx Scores, in a process that potentially includes EMS and criminal justice data as well as court records.In Estonia, artificial intelligence ... | Regulation by algorithms | 0.807265 |
26,184 | From 2012, NOPD started a collaboration with Palantir Technologies in the field of predictive policing. Besides Palantir's Gotham software, other similar (numerical analysis software) used by police agencies (such as the NCRIC) include SAS.In the fight against money laundering, FinCEN employs the FinCEN Artificial Inte... | Regulation by algorithms | 0.807265 |
26,185 | According to a study of Stanford University, 45% of the studied US federal agencies have experimented with AI and related machine learning (ML) tools up to 2020. US federal agencies counted the number of artificial intelligence applications, which are listed below. 53% of these applications were produced by in-house ex... | Regulation by algorithms | 0.807265 |
26,186 | A smart city is an urban area where collected surveillance data is used to improve various operations. Increase in computational power allows more automated decision making and replacement of public agencies by algorithmic governance. In particular, the combined use of artificial intelligence and blockchains for IoT ma... | Regulation by algorithms | 0.807265 |
26,187 | A 2019 poll conducted by IE University's Center for the Governance of Change in Spain found that 25% of citizens from selected European countries were somewhat or totally in favor of letting an artificial intelligence make important decisions about how their country is run. The following table lists the results by coun... | Regulation by algorithms | 0.807265 |
26,188 | For a massive particle of rest mass (or invariant mass) m0, the four-momentum is given by: where the total energy of the moving particle is: and the total relativistic momentum is: Taking the inner product of the four-momentum with itself: and also: which leads to the energy–momentum relation: This last relation is use... | Four-vector | 0.807265 |
26,189 | A four-vector A can also be defined in using the Pauli matrices as a basis, again in various equivalent notations: or explicitly: and in this formulation, the four-vector is represented as a Hermitian matrix (the matrix transpose and complex conjugate of the matrix leaves it unchanged), rather than a real-valued column... | Four-vector | 0.807265 |
26,190 | : ch1 Four-vectors describe, for instance, position xμ in spacetime modeled as Minkowski space, a particle's four-momentum pμ, the amplitude of the electromagnetic four-potential Aμ(x) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra. The Lorentz group m... | Four-vector | 0.807265 |
26,191 | 5-Methylcytosine is a methylated form of the DNA base cytosine (C) that regulates gene transcription and takes several other biological roles. When cytosine is methylated, the DNA maintains the same sequence, but the expression of methylated genes can be altered (the study of this is part of the field of epigenetics). ... | 5 methyl cytosine | 0.807262 |
26,192 | Traditional Chinese astronomy has a system of dividing the celestial sphere into asterisms or constellations, known as "officials" (Chinese 星官 xīng guān).The Chinese asterisms are generally smaller than the constellations of Hellenistic tradition. The Song dynasty (13th-century) Suzhou planisphere shows a total of 283 ... | Three Enclosures | 0.807262 |
26,193 | It contains collections of earlier Chinese astronomers (Shi Shen, Gan De and Wu Xian) as well as of Indian astronomy (which had reached China in the early centuries AD). Gan De was a Warring States era (5th century BC) astronomer who according to the testimony of the Dunhuang Star Chart enumerated 810 stars in 138 aste... | Three Enclosures | 0.807262 |
26,194 | The Chinese system developed independently from the Greco-Roman system since at least the 5th century BC, although there may have been earlier mutual influence, suggested by parallels to ancient Babylonian astronomy.The system of twenty-eight lunar mansions is very similar (although not identical) to the Indian Nakshat... | Three Enclosures | 0.807262 |
26,195 | Phylogenetic profiling has led to numerous discoveries in biology, including previously unknown enzymes in metabolic pathways, transcription factors that bind to conserved regulatory sites, and explanations for roles of certain mutations in human disease. Improving the method itself is an active area of scientific rese... | Evolutionary profiles | 0.807261 |
26,196 | In quantum mechanics, the Redfield equation is a Markovian master equation that describes the time evolution of the reduced density matrix ρ of a strongly coupled quantum system that is weakly coupled to an environment. The equation is named in honor of Alfred G. Redfield, who first applied it, doing so for nuclear mag... | Redfield equation | 0.80726 |
26,197 | From Joule's law, it is equal to the total power P r a d {\displaystyle \ P_{\mathsf {rad}}\ } radiated as radio waves by the antenna, divided by the square of the RMS current I R M S {\displaystyle \ I_{\mathsf {RMS}}\ } into the antenna terminals: R r a d = P r a d / I R M S 2 . {\displaystyle \ R_{\mathsf {rad}}=P_{... | Radiation Resistance | 0.807258 |
26,198 | In molecular biology, the adaptor complexes medium subunit domain is a protein domain found at the C-terminus of the mu subunit from various clathrin adaptor protein complexes (AP1, AP2, AP3, AP4 and AP5) and muniscins. The C-terminal domain has an immunoglobulin-like beta-sandwich fold consisting of 9 strands in 2 she... | Adaptor complexes medium subunit domain | 0.807256 |
26,199 | It is not hard to see that ( A , A ∗ ) {\displaystyle (A,A^{*})} is an essential cut in Γ so that e ( G ) > 1 {\displaystyle e(G)>1} . A more precise version of this argument shows that for a finitely generated group G {\displaystyle G}: If G = H ∗ C K {\displaystyle G=H*_{C}K} is a free product with amalgamation where... | Stallings theorem about ends of groups | 0.807254 |
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