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12,100 | In plane geometry, the square root of 7 can be constructed via a sequence of dynamic rectangles, that is, as the largest diagonal of those rectangles illustrated here.The minimal enclosing rectangle of an equilateral triangle of edge length 2 has a diagonal of the square root of 7.Due to the Pythagorean theorem and Leg... | Square root of 7 | 0.81735 |
12,101 | {\displaystyle 7^{\frac {1}{2}}.} It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are: 2.64575131106459059050161575363926042571025918308245018036833....which can be rounded up to 2.646 to within about 99.99% accuracy (about 1 part in 10000); that is, it differs from the... | Square root of 7 | 0.81735 |
12,102 | In robotics, nonholonomic has been particularly studied in the scope of motion planning and feedback linearization for mobile robots. | Nonholonomic constraints | 0.817343 |
12,103 | The design had been based on that of an operating microscope featuring a long working distance, it also had a tumbler rotating magnification system and a common objective. The design was a complete deviation from that of the previous Prior Greenough type microscope. Fire at the Bishop Stortford factory in 1988 meant th... | Prior Scientific | 0.817341 |
12,104 | The provision of a cine camera enabled continuous or time-lapse cine-photography to be carried out. The Cinemicroscope was adaptable for still photography or closed circuit television. This microscope was one of the fore-runners of the modern inverted microscope - now such an essential tool in cell biology and tissue c... | Prior Scientific | 0.817341 |
12,105 | The Flexible Image Transport System (FITS) standard is a widely used data format in astronomy that incorporates metadata and ASCII or binary data in the same file. However, the FITS standard has several limitations that make it difficult to use for complicated and hierarchical data. For example, the FITS 'cards' have k... | Advanced Scientific Data Format | 0.817339 |
12,106 | A molecular hydride may be able to bind to hydrogen molecules acting as a ligand. The complexes are termed non-classical covalent hydrides. These complexes contain more hydrogen than the classical covalent hydrides, but are only stable at very low temperatures. They may be isolated in inert gas matrix, or as a cryogeni... | Binary compounds of hydrogen | 0.817335 |
12,107 | One application of Boolean algebra is digital circuit design, with one goal to minimize the number of gates and another to minimize the settling time. There are sixteen possible functions of two variables, but in digital logic hardware, the simplest gate circuits implement only four of them: conjunction (AND), disjunct... | Canonical form (Boolean algebra) | 0.817331 |
12,108 | A hyperbola with equation y = a x − b + c , a ≠ 0 {\displaystyle y={\tfrac {a}{x-b}}+c,\ a\neq 0} is uniquely determined by three points ( x 1 , y 1 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) {\displaystyle (x_{1},y_{1}),\;(x_{2},y_{2}),\;(x_{3},y_{3})} with different x- and y-coordinates. A simple way to determine the shape pa... | Rectangular hyperbola | 0.81733 |
12,109 | So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve y ( x ) = 1 / x {\displaystyle y(x)=1/x} the asymptotes are the two coordinate axes.Hyperbolas sh... | Rectangular hyperbola | 0.81733 |
12,110 | However, biological computers, even if both highly artificial and intelligent, are typically distinguished from synthetic, often silicon-based, computers – they could however be combined or used for the design of either. Moreover, many tasks may be carried out inadequately by artificial intelligence even if its algorit... | Applications of AI | 0.817327 |
12,111 | Artificial intelligence is used in astronomy to analyze increasing amounts of available data and applications, mainly for "classification, regression, clustering, forecasting, generation, discovery, and the development of new scientific insights" for example for discovering exoplanets, forecasting solar activity, and d... | Applications of AI | 0.817327 |
12,112 | Artificial intelligence has been combined with digital spectrometry by IdeaCuria Inc., enable applications such as at-home water quality monitoring. | Applications of AI | 0.817327 |
12,113 | Artificial intelligence (AI) has been used in applications to alleviate certain problems throughout industry and academia. AI, like electricity or computers, is a general purpose technology that has a multitude of applications. It has been used in fields of language translation, image recognition, credit scoring, e-com... | Applications of AI | 0.817327 |
12,114 | AI tutors allow students to get one-on-one help. They can reduce anxiety and stress for students stemming from tutor labs or human tutors.AI can create a dysfunctional environment with revenge effects such as technology that hinders students' ability to stay on task. In another scenario, AI can provide early prediction... | Applications of AI | 0.817327 |
12,115 | Another study reported on an AI that was as good as doctors in identifying skin cancers. Another project monitors multiple high-risk patients by asking each patient questions based on data acquired from doctor/patient interactions. In one study done with transfer learning, an AI diagnosed eye conditions similar to an o... | Applications of AI | 0.817327 |
12,116 | Current research has indicated that non-cardiac vascular illnesses are also being treated with artificial intelligence (AI). For certain disorders, AI algorithms can assist with diagnosis, recommended treatments, outcome prediction, and patient progress tracking. | Applications of AI | 0.817327 |
12,117 | AI could be used for materials optimization and discovery such as the discovery of stable materials and the prediction of their crystal structure. | Applications of AI | 0.817327 |
12,118 | GitHub Copilot is an artificial intelligence model developed by GitHub and OpenAI that is able to autocomplete code in multiple programming languages. Price for individuals: $10/mo or $100/yr, with one free month trial. Tabnine was created by Jacob Jackson and was originally owned by Tabnine company. | Applications of AI | 0.817327 |
12,119 | For example, AI-based buying and selling platforms estimate individualized demand and supply curves and thus enable individualized pricing. AI machines reduce information asymmetry in the market and thus make markets more efficient. The application of artificial intelligence in the financial industry can alleviate the ... | Applications of AI | 0.817327 |
12,120 | Financial institutions have long used artificial neural network systems to detect charges or claims outside of the norm, flagging these for human investigation. The use of AI in banking began in 1987 when Security Pacific National Bank launched a fraud prevention taskforce to counter the unauthorized use of debit cards... | Applications of AI | 0.817327 |
12,121 | Cyber security companies are adopting neural networks, machine learning, and natural language processing to improve their systems.Applications of AI in cyber security include: Network protection: Machine learning improves intrusion detection systems by broadening the search beyond previously identified threats. Endpoin... | Applications of AI | 0.817327 |
12,122 | In 1993 FinCEN Artificial Intelligence System (FAIS) launched. It was able to review over 200,000 transactions per week and over two years it helped identify 400 potential cases of money laundering equal to $1 billion. These expert systems were later replaced by machine learning systems.AI can enhance entrepreneurial a... | Applications of AI | 0.817327 |
12,123 | The noisy-storage model refers to a cryptographic model employed in quantum cryptography. It assumes that the quantum memory device of an attacker (adversary) trying to break the protocol is imperfect (noisy). The main goal of this model is to enable the secure implementation of two-party cryptographic primitives, such... | Noisy-storage model | 0.817326 |
12,124 | In information theoretic cryptography physical assumptions appear, which do not rely on any hardness assumptions, but merely assume a limit on some other resource. In classical cryptography, the bounded-storage model introduced by Ueli Maurer assumes that the adversary can only store a certain number of classical bits.... | Noisy-storage model | 0.817326 |
12,125 | Security then holds as long as these assumptions are satisfied. In classical cryptography, i.e., without the use of quantum tools, most of these are computational assumptions. Such assumptions consists of two parts. | Noisy-storage model | 0.817326 |
12,126 | In molecular biology, the ATP-cone is an evolutionarily mobile, ATP-binding regulatory domain which is found in a variety of proteins including ribonucleotide reductases, phosphoglycerate kinases and transcriptional regulators.In ribonucleotide reductase protein R1 from Escherichia coli this domain is located at the N ... | ATP cone | 0.817322 |
12,127 | The next step in the proof is to obtain a statement which, indirectly, asserts its own unprovability. Although Gödel constructed this statement directly, the existence of at least one such statement follows from the diagonal lemma, which says that for any sufficiently strong formal system and any statement form F there... | Incompleteness Theorem | 0.81732 |
12,128 | The incompleteness theorems are among a relatively small number of nontrivial theorems that have been transformed into formalized theorems that can be completely verified by proof assistant software. Gödel's original proofs of the incompleteness theorems, like most mathematical proofs, were written in natural language ... | Incompleteness Theorem | 0.81732 |
12,129 | Gödel had independently obtained the second incompleteness theorem and included it in his submitted manuscript, which was received by Monatshefte für Mathematik on November 17, 1930. Gödel's paper was published in the Monatshefte in 1931 under the title "Über formal unentscheidbare Sätze der Principia Mathematica und v... | Incompleteness Theorem | 0.81732 |
12,130 | The announcement drew little attention apart from that of von Neumann, who pulled Gödel aside for conversation. Later that year, working independently with knowledge of the first incompleteness theorem, von Neumann obtained a proof of the second incompleteness theorem, which he announced to Gödel in a letter dated Nove... | Incompleteness Theorem | 0.81732 |
12,131 | Although Gödel was likely in attendance for Hilbert's address, the two never met face to face (Dawson 1996, p. 72). Gödel announced his first incompleteness theorem at a roundtable discussion session on the third day of the conference. | Incompleteness Theorem | 0.81732 |
12,132 | a topological group with a discrete topology whose elements form a finite or a countable set. One of the most prominent discrete symmetries in physics is parity symmetry. It manifests itself in various elementary physical quantum systems, such as quantum harmonic oscillator, electron orbitals of Hydrogen-like atoms by ... | Discrete symmetry | 0.817316 |
12,133 | In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type o... | Discrete symmetry | 0.817316 |
12,134 | UniProt is an online repository of protein sequence and annotation data, distributed in UniProt Knowledgebase (UniProt KB), UniProt Reference Clusters (UniRef) and UniProt Archive (UniParc) databases. Originally conceived as the individual ventures of EMBL-EBI, Swiss Institute of Bioinformatics (SIB) (together maintain... | Macromolecular Structure Database | 0.817316 |
12,135 | National Center for Biotechnology Information (NCBI), United States National Library of Medicine National Institute of Genetics (DNA Data Bank of Japan) Swiss Institute of Bioinformatics (SIB: Expasy) Australia Bioinformatics Resource BIG Data Center (National Genomics Data Center), Beijing Institute of Genomics, Chine... | Macromolecular Structure Database | 0.817316 |
12,136 | A nanofountain probe (NFP) is a device for 'drawing' micropatterns of liquid chemicals at extremely small resolution. An NFP contains a cantilevered micro-fluidic device terminated in a nanofountain. The embedded microfluidics facilitates rapid and continuous delivery of molecules from the on-chip reservoirs to the fou... | Nanofountain probe | 0.817315 |
12,137 | Taking advantage of the unique tip geometry of the NFP nanomaterials are directly injected into live cells with minimal invasiveness. This enables unique studies of nanoparticle-mediated delivery, as well as cellular pathways and toxicity. Whereas typical in vitro studies are limited to cell populations, these broadly-... | Nanofountain probe | 0.817315 |
12,138 | The rotation group is a group under function composition (or equivalently the product of linear transformations). It is a subgroup of the general linear group consisting of all invertible linear transformations of the real 3-space R 3 {\displaystyle \mathbb {R} ^{3}} .Furthermore, the rotation group is nonabelian. That... | Space of 3D rotations | 0.817308 |
12,139 | As announced above, one can identify any matrix in this Lie algebra with an Euler vector ω = ( x , y , z ) ∈ R 3 , {\displaystyle {\boldsymbol {\omega }}=(x,y,z)\in \mathbb {R} ^{3},} ω ^ = ω ⋅ L = x L x + y L y + z L z = ∈ s o ( 3 ) . {\displaystyle {\widehat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}\cdot {\bo... | Space of 3D rotations | 0.817308 |
12,140 | This can be used to show that the Lie algebra s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} (with commutator) is isomorphic to the Lie algebra R 3 {\displaystyle \mathbb {R} ^{3}} (with cross product). Under this isomorphism, an Euler vector ω ∈ R 3 {\displaystyle {\boldsymbol {\omega }}\in \mathbb {R} ^{3}} correspond... | Space of 3D rotations | 0.817308 |
12,141 | The Lie algebra bracket captures the essence of the Lie group product in a sense made precise by the Baker–Campbell–Hausdorff formula. The elements of s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} are the "infinitesimal generators" of rotations, i.e., they are the elements of the tangent space of the manifold SO(3) at ... | Space of 3D rotations | 0.817308 |
12,142 | Associated with every Lie group is its Lie algebra, a linear space of the same dimension as the Lie group, closed under a bilinear alternating product called the Lie bracket. The Lie algebra of SO(3) is denoted by s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} and consists of all skew-symmetric 3 × 3 matrices. This may ... | Space of 3D rotations | 0.817308 |
12,143 | The kernel of a Lie algebra homomorphism is an ideal, but 𝖘𝖔(3), being simple, has no nontrivial ideals and all nontrivial representations are hence faithful. It holds in particular in the doublet or spinor representation. The same explicit formula thus follows in a simpler way through Pauli matrices, cf. the 2×2 der... | Space of 3D rotations | 0.817308 |
12,144 | The infinite expansion in the BCH formula for SO(3) reduces to a compact form, Z = α X + β Y + γ , {\displaystyle Z=\alpha X+\beta Y+\gamma ,} for suitable trigonometric function coefficients (α, β, γ). It is worthwhile to write this composite rotation generator as α X + β Y + γ = s o ( 3 ) X + Y + 1 2 + 1 12 ] − 1... | Space of 3D rotations | 0.817308 |
12,145 | Suppose X and Y in the Lie algebra are given. Their exponentials, exp(X) and exp(Y), are rotation matrices, which can be multiplied. Since the exponential map is a surjection, for some Z in the Lie algebra, exp(Z) = exp(X) exp(Y), and one may tentatively write Z = C ( X , Y ) , {\displaystyle Z=C(X,Y),} for C some expr... | Space of 3D rotations | 0.817308 |
12,146 | The book has been translated into several languages and has sold over a million copies, and has been continuously in print since its first publication. Marvin Minsky said in his paper Steps Toward Artificial Intelligence that "everyone should know the work of George Pólya on how to solve problems." Pólya's book has had... | How to Solve It | 0.817307 |
12,147 | The field of medicine includes nutrition, genetics, biophysics, and pharmacology; industry includes beverage and food technology, toxicology, and vaccine production; while the governmental and environmental fields includes forensic science, wildlife management, marine biology, and viticulture. The average income of a b... | Biochemist | 0.817305 |
12,148 | Because of a biochemists' background in both biology and chemistry, they may also be employed in the medical, industrial, governmental, and environmental fields. Slightly more than half of the biological scientists are employed by the Federal State and local governments. | Biochemist | 0.817305 |
12,149 | Biochemists are typically employed in the life sciences, where they work in the pharmaceutical or biotechnology industry in a research role. They are also employed in academic institutes, where in addition to pursuing their research they may also be involved with teaching undergraduates, training graduate students, and... | Biochemist | 0.817305 |
12,150 | Biochemists also prepare pharmaceutical compounds for commercial distribution. Modern biochemistry is considered a sub-discipline of the biological sciences, due to its increased reliance on, and training, in accord with modern molecular biology. Historically, even before the term biochemist was formally recognized, in... | Biochemist | 0.817305 |
12,151 | In biochemistry, researchers often break down complicated biological systems into their component parts. They study the effects of foods, drugs, allergens and other substances on living tissues; they research molecular biology, the study of life at the molecular level and the study of genes and gene expression; and the... | Biochemist | 0.817305 |
12,152 | Biochemists are scientists who are trained in biochemistry. They study chemical processes and chemical transformations in living organisms. Biochemists study DNA, proteins and cell parts. The word "biochemist" is a portmanteau of "biological chemist." | Biochemist | 0.817305 |
12,153 | In the private industries for businesses, it is imperative to possess strong business management skills as well as communication skills. Biochemists must also be familiar with regulatory rules and management techniques.Biochemistry Blog publishes high quality research articles, papers, posts and jobs related to biochem... | Biochemist | 0.817305 |
12,154 | All types of chemistry are required, with emphasis on biochemistry, organic chemistry and physical chemistry. Basic classes in biology, including microbiology, molecular biology, molecular genetics, cell biology, and genomics, are focused on. Some instruction in experimental techniques and quantification is also part o... | Biochemist | 0.817305 |
12,155 | Biochemists must pass a qualifying exam or a preliminary exam to continue their studies when receiving a Ph.D. in biochemistry. Biochemistry requires an understanding of organic and inorganic chemistry. | Biochemist | 0.817305 |
12,156 | A degree in biochemistry or a related science such as chemistry is the minimum requirement for any work in this field. This is sufficient for a position as a technical assistant in industry or in academic settings. A Ph.D. | Biochemist | 0.817305 |
12,157 | In mathematics, a gradually varied surface is a special type of digital surfaces. It is a function from a 2D digital space (see digital geometry) to an ordered set or a chain. A gradually varied function is a function from a digital space Σ {\displaystyle \Sigma } to { A 1 , … , A m } {\displaystyle \{A_{1},\dots ,A_{m... | Gradually varied surface | 0.817299 |
12,158 | Founded in 2002, the MBE course is delivered by faculty of the Institute of Biotechnology and Judge Business School. | Master of Bioscience Enterprise | 0.817295 |
12,159 | The Postgraduate Diploma year has five core papers required for the Postgraduate Diploma in Bioscience Enterprise. Students are also required to take three electives, which are generally science-based papers. SCIENT 701 (15 points) Accounting and Finance for Scientists SCIENT 702 (15 points) Marketing for Scientific an... | Master of Bioscience Enterprise | 0.817295 |
12,160 | The prerequisite for the first year (the Postgraduate Diploma) is a Bachelor of Science with a major or specialisation in Biological Sciences, Bioinformatics, Biomedical Science, Food Science, Medicinal Chemistry, Pharmacology or Physiology; a Bachelor of Engineering in Biomedical Engineering; a Bachelor of Pharmacy; o... | Master of Bioscience Enterprise | 0.817295 |
12,161 | A Master of Bioscience Enterprise (abbreviated MBE or MBioEnt) is a specialised degree taught at The University of Auckland, New Zealand, Karolinska Institute, Sweden and The University of Cambridge, United Kingdom. The MBE is an interdisciplinary programme incorporating multiple faculties and includes significant indu... | Master of Bioscience Enterprise | 0.817295 |
12,162 | In the Masters year (year two), students undertake an internship within the biotechnology industry either in New Zealand or internationally for six months. During the internships, students complete a project for the company which generally relates to and influences the thesis topic, which is written during the internsh... | Master of Bioscience Enterprise | 0.817295 |
12,163 | Deductive methods solve this problem by building a set of half-spaces that describe the interior of the geometry. These half-spaces are used to describe primitives that can be combined to get the final model.Another approach decouples the detection of primitive shapes and the computation of the CSG tree that defines th... | Boolean operations in computer-aided design | 0.817292 |
12,164 | This can be important for some manufacturing or engineering computation applications. By comparison, when creating geometry based upon boundary representations, additional topological data is required, or consistency checks must be performed to assure that the given boundary description specifies a valid solid object.A... | Boolean operations in computer-aided design | 0.817292 |
12,165 | CSG is popular because a modeler can use a set of relatively simple objects to create very complicated geometry. When CSG is procedural or parametric, the user can revise their complex geometry by changing the position of objects or by changing the Boolean operation used to combine those objects. One of the advantages ... | Boolean operations in computer-aided design | 0.817292 |
12,166 | Constructive solid geometry has a number of practical uses. It is used in cases where simple geometric objects are desired, or where mathematical accuracy is important. Nearly all engineering CAD packages use CSG (where it may be useful for representing tool cuts, and features where parts must fit together). The Quake ... | Boolean operations in computer-aided design | 0.817292 |
12,167 | Rendering of constructive solid geometry is particularly simple when ray tracing. Ray tracers intersect a ray with both primitives that are being operated on, apply the operator to the intersection intervals along the 1D ray, and then take the point closest to the camera along the ray as being the result. | Boolean operations in computer-aided design | 0.817292 |
12,168 | The Society's wholly owned publishing subsidiary, Portland Press, publishes books, a magazine, The Biochemist, and several print and online academic journals: Biochemical Journal Biochemical Society Symposium (online only) Biochemical Society Transactions Cell Signalling Biology Clinical Science Essays in Biochemistry ... | Biochemical Society | 0.81729 |
12,169 | The Biochemical Society is a learned society in the United Kingdom in the field of biochemistry, including all the cellular and molecular biosciences. | Biochemical Society | 0.81729 |
12,170 | The type system uses data type information to check correctness of computer programs that access or manipulate the data. A compiler may use the static type of a value to optimize the storage it needs and the choice of algorithms for operations on the value. In many C compilers the float data type, for example, is repre... | Data types | 0.817289 |
12,171 | In microbiology and virology, the term variant or genetic variant is used to describe a subtype of a microorganism that is genetically distinct from a main strain, but not sufficiently different to be termed a distinct strain. A similar distinction is made in botany between different cultivated varieties of a species o... | Variant (biology) | 0.817284 |
12,172 | (2014). "9: Linear Momentum and Collisions". Physics for scientists and engineers with modern physics (9th ed.). | Elastic collision | 0.817269 |
12,173 | A Radically Modern Approach to Introductory Physics. Vol. 1: Fundamental Principles. | Elastic collision | 0.817269 |
12,174 | In the field of compiler optimizations, available expressions is an analysis algorithm that determines for each point in the program the set of expressions that need not be recomputed. Those expressions are said to be available at such a point. To be available on a program point, the operands of the expression should n... | Available expression | 0.817268 |
12,175 | The highest possible value for the shape factor of a flywheel rotor, is K = 1 {\displaystyle K=1} , which can be achieved only by the theoretical constant-stress disc geometry. A constant-thickness disc geometry has a shape factor of K = 0.606 {\displaystyle K=0.606} , while for a rod of constant thickness the value is... | Flywheel energy storage | 0.81726 |
12,176 | Tokamak fusion experiments need very high currents for brief intervals (mainly to power large electromagnets for a few seconds). JET (the Joint European Torus) has two 775 t (854 short tons; 763 long tons) flywheels (installed in 1981) that spin up to 225 rpm. Each flywheel stores 3.75 GJ and can deliver at up to 400 M... | Flywheel energy storage | 0.81726 |
12,177 | The maximal specific energy of a flywheel rotor is mainly dependent on two factors: the first being the rotor's geometry, and the second being the properties of the material being used. For single-material, isotropic rotors this relationship can be expressed as E m = K ( σ ρ ) , {\displaystyle {\frac {E}{m}}=K\left({\f... | Flywheel energy storage | 0.81726 |
12,178 | Several modern flywheel rotors are made from composite materials. Examples include the carbon-fiber composite flywheel from Beacon Power Corporation and the PowerThru flywheel from Phillips Service Industries. Alternatively, Calnetix utilizes aerospace-grade high-performance steel in their flywheel construction.For the... | Flywheel energy storage | 0.81726 |
12,179 | For most applications, a special kind of topological manifold, namely, a differentiable manifold, is used. If the local charts on a manifold are compatible in a certain sense, one can define directions, tangent spaces, and differentiable functions on that manifold. In particular it is possible to use calculus on a diff... | Two-dimensional manifold | 0.817255 |
12,180 | In the case of a differentiable manifold, a set of charts called an atlas, whose transition functions (see below) are all differentiable, allows us to do calculus on it. Polar coordinates, for example, form a chart for the plane R 2 {\displaystyle \mathbb {R} ^{2}} minus the positive x-axis and the origin. Another exam... | Two-dimensional manifold | 0.817255 |
12,181 | A complex manifold is a manifold whose charts take values in C n {\displaystyle \mathbb {C} ^{n}} and whose transition functions are holomorphic on the overlaps. These manifolds are the basic objects of study in complex geometry. A one-complex-dimensional manifold is called a Riemann surface. An n {\displaystyle n} -di... | Two-dimensional manifold | 0.817255 |
12,182 | The Cartesian product of manifolds is also a manifold. The dimension of the product manifold is the sum of the dimensions of its factors. Its topology is the product topology, and a Cartesian product of charts is a chart for the product manifold. Thus, an atlas for the product manifold can be constructed using atlases ... | Two-dimensional manifold | 0.817255 |
12,183 | Geometrical and topological aspects of classical mechanics were emphasized by Henri Poincaré, one of the founders of topology. Riemann was the first one to do extensive work generalizing the idea of a surface to higher dimensions. | Two-dimensional manifold | 0.817255 |
12,184 | The frequentist procedures of significance testing and confidence intervals can be constructed without regard to utility functions. However, some elements of frequentist statistics, such as statistical decision theory, do incorporate utility functions. In particular, frequentist developments of optimal inference (such ... | Predictive inference | 0.817254 |
12,185 | Incorrect assumptions of Normality in the population also invalidates some forms of regression-based inference. The use of any parametric model is viewed skeptically by most experts in sampling human populations: "most sampling statisticians, when they deal with confidence intervals at all, limit themselves to statemen... | Predictive inference | 0.817254 |
12,186 | For example, limiting results are often invoked to justify the generalized method of moments and the use of generalized estimating equations, which are popular in econometrics and biostatistics. The magnitude of the difference between the limiting distribution and the true distribution (formally, the 'error' of the app... | Predictive inference | 0.817254 |
12,187 | In this approach, the metric geometry of probability distributions is studied; this approach quantifies approximation error with, for example, the Kullback–Leibler divergence, Bregman divergence, and the Hellinger distance.With indefinitely large samples, limiting results like the central limit theorem describe the sam... | Predictive inference | 0.817254 |
12,188 | Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these. With finite samples, approximation results measure how close a limiting distribution approaches the statistic's sample distribution: For example, with 10,000 independent samples the nor... | Predictive inference | 0.817254 |
12,189 | Time emerges from a deeper external-parameter "clock-time" and the graphs lead to a natural metrical structure.Simplicial quantum gravity by Lehto, Nielsen and Ninomiya Spacetime is described as having a deeper pregeometric structure based on three dynamical variables, vertices of an abstract simplicial complex, and a ... | Pregeometry (physics) | 0.817253 |
12,190 | A definition of distance between any two monads is defined and from this and probabilistic mathematical tools emerges a three-dimensional space.Axiomatic pregeometry by Perez, Bergliaffa, Romero and Vucetich An assortment of ontological presuppositions describes spacetime a result of relations between objectively exist... | Pregeometry (physics) | 0.817253 |
12,191 | This discrete-space structure assumes the metric of spacetime and assumes composite geometric objects so it is not a pregeometric scheme in line with Wheeler's original conception of pregeometry.Pregeometric graph by Wilson Spacetime is described by a generalized graph consisting of a very large or infinite set of vert... | Pregeometry (physics) | 0.817253 |
12,192 | A 2006 paper provided a survey and critique of pregeometry or near-pregeometry proposals up to that time. A summary of these is given below: Discrete spacetime by Hill A proposal anticipating Wheeler's pregeometry, though assuming some geometric notions embedded in quantum mechanics and special relativity. | Pregeometry (physics) | 0.817253 |
12,193 | Where geometry could describe the properties of a known surface, the physics of a hypothetical region with predefined properties, "pregeometry" might allow one to work with deeper underlying rules of physics that were not so strongly dependent on simplified classical assumptions about the properties of space. No single... | Pregeometry (physics) | 0.817253 |
12,194 | In physics, a pregeometry is a hypothetical structure from which the geometry of the universe develops. Some cosmological models feature a pregeometric universe before the Big Bang. The term was championed by John Archibald Wheeler in the 1960s and 1970s as a possible route to a theory of quantum gravity. Since quantum... | Pregeometry (physics) | 0.817253 |
12,195 | In 2000, Eliezer Yudkowsky founded the Singularity Institute for Artificial Intelligence with funding from Brian and Sabine Atkins, with the purpose of accelerating the development of artificial intelligence (AI). However, Yudkowsky began to be concerned that AI systems developed in the future could become superintelli... | Machine Intelligence Research Institute | 0.817253 |
12,196 | "Quantilizers: A Safer Alternative to Maximizers for Limited Optimization". Workshops at the Thirtieth AAAI Conference on Artificial Intelligence. Yudkowsky, Eliezer (2011). | Machine Intelligence Research Institute | 0.817253 |
12,197 | "Artificial Intelligence as a Positive and Negative Factor in Global Risk" (PDF). In Bostrom, Nick; Ćirković, Milan (eds.). Global Catastrophic Risks. | Machine Intelligence Research Institute | 0.817253 |
12,198 | AAAI Workshops: Workshops at the Twenty-Ninth AAAI Conference on Artificial Intelligence, Austin, TX, January 25–26, 2015. AAAI Publications. Soares, Nate; Fallenstein, Benja (2015). | Machine Intelligence Research Institute | 0.817253 |
12,199 | Retrieved 28 July 2018. LaVictoire, Patrick; Fallenstein, Benja; Yudkowsky, Eliezer; Bárász, Mihály; Christiano, Paul; Herreshoff, Marcello (2014). "Program Equilibrium in the Prisoner's Dilemma via Löb's Theorem". | Machine Intelligence Research Institute | 0.817253 |
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