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In projective geometry every line has a point at infinity or "figurative point" where it crosses all the lines that are parallel to it. The ellipse, parabola, and hyperbola of Euclidean geometry are called conics in projective geometry and may be constructed as Steiner conics from a projectivity that is not a perspecti...
Center (geometry)
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Substitution can also be applied to other kinds of formal objects built from symbols, for instance elements of free groups. In order for substitution to be defined, one needs an algebraic structure with an appropriate universal property, that asserts the existence of unique homomorphisms that send indeterminates to spe...
Substitution instance
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Substitution is a basic operation in algebra, in particular in computer algebra.A common case of substitution involves polynomials, where substitution of a numerical value (or another expression) for the indeterminate of a univariate polynomial amounts to evaluating the polynomial at that value. Indeed, this operation ...
Substitution instance
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In genetics and bioinformatics, a single-nucleotide polymorphism (SNP ; plural SNPs ) is a germline substitution of a single nucleotide at a specific position in the genome that is present in a sufficiently large fraction of considered population (generally regarded as 1% or more).For example, a G nucleotide present at...
Single-nucleotide polymorphisms
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Pharmacogenetics focuses on identifying genetic variations including SNPs associated with differential responses to treatment. Many drug metabolizing enzymes, drug targets, or target pathways can be influenced by SNPs. The SNPs involved in drug metabolizing enzyme activities can change drug pharmacokinetics, while the ...
Single-nucleotide polymorphisms
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V. Buzek and M. Hillery, Quantum cloning, Physics World 14 (11) (2001), pp. 25–29.
No-cloning theorem
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Quantum states cannot be discriminated perfectly. The no cloning theorem prevents an interpretation of the holographic principle for black holes as meaning that there are two copies of information, one lying at the event horizon and the other in the black hole interior. This leads to more radical interpretations, such ...
No-cloning theorem
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Similarly, cloning would violate the no-teleportation theorem, which says that it is impossible to convert a quantum state into a sequence of classical bits (even an infinite sequence of bits), copy those bits to some new location, and recreate a copy of the original quantum state in the new location. This should not b...
No-cloning theorem
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The no-cloning theorem prevents the use of certain classical error correction techniques on quantum states. For example, backup copies of a state in the middle of a quantum computation cannot be created and used for correcting subsequent errors. Error correction is vital for practical quantum computing, and for some ti...
No-cloning theorem
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In such a case the qubit can be represented by just two real numbers (one polar angle and one radius equal to 1), while the value of the third can be arbitrary in such a representation. Yet a realisation of a qubit (polarisation-encoded photon, for example) is capable of storing the whole qubit information support with...
No-cloning theorem
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Therefore, a single universal U cannot clone a general quantum state. This proves the no-cloning theorem.
No-cloning theorem
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The extra phase factor expresses the fact that a quantum-mechanical state defines a normalised vector in Hilbert space only up to a phase factor i.e. as an element of projectivised Hilbert space. To prove the theorem, we select an arbitrary pair of states | ϕ ⟩ A {\displaystyle |\phi \rangle _{A}} and | ψ ⟩ A {\display...
No-cloning theorem
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Evolving up to some fixed time t 0 {\displaystyle t_{0}} yields a unitary operator U on H ⊗ H {\displaystyle H\otimes H} , the Hilbert space of the combined system. However, no such unitary operator U can clone all states.The no-cloning theorem answers the following question in the negative: Is it possible to construct...
No-cloning theorem
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27,213
Radiation chemistry is a subdivision of nuclear chemistry which studies the chemical effects of ionizing radiation on matter. This is quite different from radiochemistry, as no radioactivity needs to be present in the material which is being chemically changed by the radiation. An example is the conversion of water int...
Radiation chemistry
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Finally, the solvated electron can react with solutes such as solvated protons or oxygen molecules to form hydrogen atoms and dioxygen radical anions, respectively. The fact that oxygen changes the radiation chemistry might be one reason why oxygenated tissues are more sensitive to irradiation than the deoxygenated tis...
Radiation chemistry
0.806764
27,215
Both the harmful effects of radiation upon biological systems (induction of cancer and acute radiation injuries) and the useful effects of radiotherapy involve the radiation chemistry of water. The vast majority of biological molecules are present in an aqueous medium; when water is exposed to radiation, the water abso...
Radiation chemistry
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27,216
Another key area uses radiation chemistry to modify polymers. Using radiation, it is possible to convert monomers to polymers, to crosslink polymers, and to break polymer chains. Both man-made and natural polymers (such as carbohydrates) can be processed in this way.
Radiation chemistry
0.806764
27,217
When agriculture is considered with ecology, the sustainablility of an operation is considered. However, modern agrochemical industry has gained a reputation for its maximising profits while violating sustainable and ecologically viable agricultural principles. Eutrophication, the prevalence of genetically modified cro...
Agricultural chemistry
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The goals of agricultural chemistry are to expand understanding of the causes and effects of biochemical reactions related to plant and animal growth, to reveal opportunities for controlling those reactions, and to develop chemical products that will provide the desired assistance or control. Agricultural chemistry is ...
Agricultural chemistry
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Agricultural chemistry often aims at preserving or increasing the fertility of soil, maintaining or improving the agricultural yield, and improving the quality of the crop. The discovery of the Haber-Bosch process led to increase in production of crops in the 20th century. This process involves converting nitrogen and ...
Agricultural chemistry
0.806763
27,220
Agricultural chemistry is the study of chemistry, especially organic chemistry and biochemistry, as they relate to agriculture. This includes agricultural production, the use of ammonia in fertilizer, pesticides, and how plant biochemistry can be used to genetically alter crops. Agricultural chemistry is not a distinct...
Agricultural chemistry
0.806763
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Plant biochemistry is the study of chemical reactions that occur within plants. Scientists use plant biochemistry to understand the genetic makeup of a plant in order to discover which DNA creates which plant characteristics. Innovations in plant biochemistry seek to increase plant resilience and discover new, more eff...
Agricultural chemistry
0.806763
27,222
The DUNE far detector design is based on state-of-the-art Liquid Argon Time Projection Chamber (LArTPC) technology. The far detector will consist of a total volume of 70-kilotons of liquid argon located deep underground, 1.5 kilometers (4,850 ft) under the surface. The current design divides the liquid argon between fo...
NP04 experiment
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Determination of the ordering of the neutrino masses. Studies of supernovae and the formation of a neutron star or black hole, even though the detector is 1,490 meters (0.93 mi) deep underground with no direct view of the sky. Search for proton decay, which has never been observed but is predicted by theories that unif...
NP04 experiment
0.806762
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Systems and Synthetic Biology is a peer-reviewed scientific journal covering systems and synthetic biology. It was established in 2007 and was published by Springer Science+Business Media. The editors-in-chief were Pawan K. Dhar (University of Kerala) and Ron Weiss (Massachusetts Institute of Technology). The journal's...
Systems and Synthetic Biology
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A number of statistics can be shown to have t-distributions for samples of moderate size under null hypotheses that are of interest, so that the t-distribution forms the basis for significance tests. For example, the distribution of Spearman's rank correlation coefficient ρ, in the null case (zero correlation) is well ...
Student distribution
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In statistics, the t-distribution was first derived as a posterior distribution in 1876 by Helmert and Lüroth. The t-distribution also appeared in a more general form as Pearson Type IV distribution in Karl Pearson's 1895 paper.In the English-language literature, the distribution takes its name from William Sealy Gosse...
Student distribution
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It is methodologically individualistic, in that it aggregates preferences and behaviors of individual members of society. Using elements of formal logic for generality, analysis proceeds from a set of seemingly reasonable axioms of social choice to form a social welfare function (or constitution). Results uncovered the...
Social Choice
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Kenneth Arrow's Social Choice and Individual Values (1951) and Arrow's impossibility theorem are often acknowledged as the basis of the modern social choice theory and public choice theory. In addition to Arrow's theorem and the voting paradox, the Gibbard–Satterthwaite theorem, the Condorcet jury theorem, the median v...
Social Choice
0.806758
27,229
Synapto-pHluorin is a genetically encoded optical indicator of vesicle release and recycling. It is used in neuroscience to study transmitter release. It consists of a pH-sensitive form of green fluorescent protein (GFP) fused to the luminal side of a vesicle-associated membrane protein (VAMP).
Synapto-pHluorin
0.806756
27,230
Moving to modern renewable energy has very large health benefits due to reducing air pollution from fossil fuels.Renewable sources other than biomass such as wind power, photovoltaics, and hydroelectricity have the advantage of being able to conserve water, lower pollution and reduce CO2 emissions. Solar panels change ...
Renewable energy technologies
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27,231
Typed lambda calculus Typed and untyped languages Type signature Type inference Datatype Algebraic data type (generalized) Type variable First-class value Polymorphism Calculus of constructions
List of functional programming topics
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Fixed point combinator SKI combinator calculus B, C, K, W system SECD machine Graph reduction machine
List of functional programming topics
0.806754
27,233
Domain theory Directed complete partial order Knaster–Tarski theorem
List of functional programming topics
0.806754
27,234
Currying Lambda abstraction Church–Rosser theorem Extensionality Church numeral
List of functional programming topics
0.806754
27,235
Sequent, sequent calculus Natural deduction Intuitionistic type theory BHK interpretation Curry–Howard correspondence Linear logic Game semantics
List of functional programming topics
0.806754
27,236
Biomechanics: (biology, physics) The branch of biophysics that deals with the mechanics of the human or animal body; especially concerned with muscles and the skeleton. The study of biomechanical influences upon nervous system function and load bearing joints. Research: Research on established ideal mechanical models f...
Neuro biomechanics
0.806753
27,237
The Nifty Assignments session is one of the most popular sessions at the conference. Started by Nick Parlante in 1999, the session serves as a place for educators to share ideas and materials for successful computer science assignments. Nifty assignments are shared publicly for general reference and usage.Presenters ha...
SIGCSE Technical Symposium on Computer Science Education
0.80675
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The Association for Computing Machinery's Special Interest Group on Computer Science Education (SIGCSE) Technical Symposium is the main ACM conference for computer science educators. It has been held annually in February or March in the United States since 1970, with the exception of 2020 when it was cancelled due to C...
SIGCSE Technical Symposium on Computer Science Education
0.80675
27,239
MeshLab is available for most platforms, including Linux, Mac OS X, Windows and, with reduced functionality, on Android and iOS and even as a pure client-side JavaScript application called MeshLabJS. The system supports input/output in the following formats: PLY, STL, OFF, OBJ, 3DS, VRML 2.0, X3D and COLLADA. MeshLab c...
MeshLab
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The Tensor Contraction Engine (TCE) is a compiler for a domain-specific language that allows chemists to specify the computation in a high-level Mathematica-style language. It transforms tensor summation expressions to low-level code (C/Fortran) for specific hardware being mindful of memory availability, communication ...
Tensor Contraction Engine
0.806749
27,241
Public databases which may be searched using the National Center for Biotechnology Information Basic Local Alignment Search Tool (NCBI BLAST), lack peer-reviewed sequences of type strains and sequences of non-type strains. On the other hand, while commercial databases potentially contain high-quality filtered sequence ...
GenBank
0.806748
27,242
C3 photosynthesis has been found in a wide variety of genera. The family has also evolved a unique chemistry. Many legumes contain toxic and indigestible substances, antinutrients, which may be removed through various processing methods. Pterocarpans are a class of molecules (derivatives of isoflavonoids) found only in...
Fabaceae
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All the different approaches yielded similar results regarding the relationships between the family's main clades. Following extensive discussion in the legume phylogenetics community, the Legume Phylogeny Working Group reclassified Fabaceae into six subfamilies, which necessitated the segregation of four new subfamili...
Fabaceae
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27,244
Defining constants: c, mp, ħ, ε0.Here, mp is the proton rest mass. Strong units, also called quantum chromodynamics (QCD) units, are "convenient for work in QCD and nuclear physics, where quantum mechanics and relativity are omnipresent and the proton is an object of central interest".
Natural units
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The Stoney unit system uses the following defining constants: c, G, ke, e,where c is the speed of light, G is the gravitational constant, ke is the Coulomb constant, and e is the elementary charge. George Johnstone Stoney's unit system preceded that of Planck. He presented the idea in a lecture entitled "On the Physica...
Natural units
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27,246
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain...
Collocation point
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27,247
The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (...
Stokes parameters
0.806743
27,248
To any quadratic module (M, h, q) defined by a J-sesquilinear form f on M over a form ring (R, Λ) one can associate the unitary group U ( M ) := { σ ∈ G L ( M ): ∀ x , y ∈ M , h ( σ x , σ y ) = h ( x , y ) and q ( σ x ) = q ( x ) } . {\displaystyle U(M):=\{\sigma \in GL(M)\ :\ \forall x,y\in M,h(\sigma x,\sigma y)=h(x,...
Indefinite unitary group
0.806743
27,249
The unitary group of a quadratic module is a generalisation of the linear algebraic group U just defined, which incorporates as special cases many different classical algebraic groups. The definition goes back to Anthony Bak's thesis.To define it, one has to define quadratic modules first: Let R be a ring with anti-aut...
Indefinite unitary group
0.806743
27,250
The equations defining a unitary group are polynomial equations over k (but not over K): for the standard form Φ = I, the equations are given in matrices as A∗A = I, where A ∗ = A ¯ T {\displaystyle A^{*}={\bar {A}}^{\mathsf {T}}} is the conjugate transpose. Given a different form, they are A∗ΦA = Φ. The unitary group ...
Indefinite unitary group
0.806743
27,251
From the point of view of Lie theory, the classical unitary group is a real form of the Steinberg group 2 A n {\displaystyle {}^{2}\!A_{n}} , which is an algebraic group that arises from the combination of the diagram automorphism of the general linear group (reversing the Dynkin diagram An, which corresponds to transp...
Indefinite unitary group
0.806743
27,252
More generally, given a field k and a degree-2 separable k-algebra K (which may be a field extension but need not be), one can define unitary groups with respect to this extension. First, there is a unique k-automorphism of K a ↦ a ¯ {\displaystyle a\mapsto {\bar {a}}} which is an involution and fixes exactly k ( a = a...
Indefinite unitary group
0.806743
27,253
In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable states. QSL are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and Igor Tamm derived a time-energy uncertainty relation that bounds the speed...
Quantum speed limit
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27,254
While his sculptures may not be as famous as those of Phidias, they are much admired. In his Canon, a treatise he wrote designed to document the "perfect" body proportions of the male nude, Polykleitos gives us a mathematical approach towards sculpturing the human body.The Canon itself has been lost but it is conjectur...
Mathematics-inspired sculptures
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27,255
The historian Vasari in his Lives of the Painters calls Piero the "greatest geometer of his time, or perhaps of any time." Piero's interest in perspective can be seen in his paintings including the Polyptych of Perugia, the San Agostino altarpiece and The Flagellation of Christ. His work on geometry influenced later ma...
Mathematics-inspired sculptures
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27,256
1435–1460): broken lances lie conveniently along perspective lines.The painter Piero della Francesca (c. 1415–1492) exemplified this new shift in Italian Renaissance thinking. He was an expert mathematician and geometer, writing books on solid geometry and perspective, including De prospectiva pingendi (On Perspective ...
Mathematics-inspired sculptures
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27,257
Two major motives drove artists in the late Middle Ages and the Renaissance towards mathematics. First, painters needed to figure out how to depict three-dimensional scenes on a two-dimensional canvas. Second, philosophers and artists alike were convinced that mathematics was the true essence of the physical world and ...
Mathematics-inspired sculptures
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27,258
A strand of art from Ancient Greece onwards sees God as the geometer of the world, and the world's geometry therefore as sacred. The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Con...
Mathematics-inspired sculptures
0.806743
27,259
The Mars Environmental Dynamics Analyzer (MEDA) is an instrument on board the Mars 2020 Perseverance rover that will characterize the dust size and morphology, as well as surface weather. Specifically, the information obtained will help address future human exploration objectives, as dust sizes and shapes, daily weathe...
Mars Environmental Dynamics Analyzer
0.80674
27,260
Many modern processors now contain multiple processing cores, and multi-threaded programming is usually the most efficient way to use more computational power in a single program. Some modern processors are highly optimized with techniques including out-of-order execution, but with complex logic to detect when this can...
Von Neumann programming languages
0.806739
27,261
John Backus asserted that assignment statements in von Neumann languages split programming into two worlds. The first world consists of expressions, an orderly mathematical space with potentially useful algebraic properties: most computation takes place here. The second world consists of statements, a disorderly mathem...
Von Neumann programming languages
0.806739
27,262
In 1997, Material ConneXion was launched by George Beylerian, former vice president of marketing and creative director of Steelcase Furniture. At Steelcase, Beylerian created a small exhibition of new materials, and recognized the need for a materials library service.Material ConneXion was acquired by SANDOW in 2011.In...
Material ConneXion
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27,263
Material ConneXion clients have included design and architecture firms, government agencies, and large corporations such as Adidas, Target Corporation, PUMA, and BMW.In 2001, designer Sandy Chilewich discovered a woven vinyl material in Material ConneXion's library that led to her Chilewich brand of household products ...
Material ConneXion
0.806738
27,264
One example is the pentaphosphide ]− where all Rh---Rh edges are bridged by PPh2. A carbide-containing butterfly cluster is 2− where the carbide is bonded to all four Fe centers.Bonding in such clusters is often discussed in the context of polyhedral skeletal electron pair theory. This theory predicts that tetrametalli...
Butterfly cluster compound
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27,265
In the area of metal cluster chemistry, a butterfly cluster compound usually describes tetrametallic clusters containing five M-M bonds. A prototype of this motif is 2−. Most butterfly clusters have additional bridging ligands.
Butterfly cluster compound
0.806733
27,266
In physics and optics, the Fraunhofer lines are a set of spectral absorption lines named after the German physicist Joseph von Fraunhofer (1787–1826). The lines were originally observed as dark features (absorption lines) in the optical spectrum of the Sun (white light) .
Calcium K-line
0.806733
27,267
In physics, the study of rigid body motion allows for several ways to define the acceleration of a body. The usual definition of acceleration entails following a single particle/point of a rigid body and observing its changes in velocity. Spatial acceleration entails looking at a fixed (unmoving) point in space and obs...
Spatial acceleration
0.806732
27,268
In mathematics, an algebra bundle is a fiber bundle whose fibers are algebras and local trivializations respect the algebra structure. It follows that the transition functions are algebra isomorphisms. Since algebras are also vector spaces, every algebra bundle is a vector bundle. Examples include the tensor-algebra bu...
Algebra bundle
0.806732
27,269
This property is called Wren's theorem. The more common generation of a one-sheet hyperboloid of revolution is rotating a hyperbola around its semi-minor axis (see picture; rotating the hyperbola around its other axis gives a two-sheet hyperbola of revolution). A hyperboloid of one sheet is projectively equivalent to a...
Hyperboloid of one sheet
0.806727
27,270
ISCB organizes the Intelligent Systems for Molecular Biology (ISMB) conference every year, a growing number of smaller, more regionally or topically focused annual and bi-annual conferences, and has three official journals: ISCB Community Journal, PLOS Computational Biology and Bioinformatics. The society awards three ...
International Society for Computational Biology
0.806726
27,271
ISCB began expanding its conference offerings with the introduction of the annual Rocky Mountain Bioinformatics Conference series in 2003, the Conference on Semantics in Healthcare and Life Sciences (CSHALS) in 2008, the bi-annual ISCB Africa ASBCB Bioinformatics Conference in 2009, and the bi-annual ISCB Latin America...
International Society for Computational Biology
0.806726
27,272
ISCB grew out of the need for a stable organizational structure to support the planning and manage the finances of the Intelligent Systems for Molecular Biology (ISMB) conference series, which had its start in 1993. ISMB is ISCB's most prominent annual activity, toward which a significant portion of resources are dedic...
International Society for Computational Biology
0.806726
27,273
ISCB Communities of Special Interest (COSIs) are member communities of shared interest that have self-organized and have multiple activities or interactions throughout the year, rather than solely meeting during the SIG program of the ISMB conference. An important goal of any COSI is to foster a topically-focused colla...
International Society for Computational Biology
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27,274
The International Society for Computational Biology (ISCB) is a scholarly society for researchers in computational biology and bioinformatics. The society was founded in 1997 to provide a stable financial home for the Intelligent Systems for Molecular Biology (ISMB) conference and has grown to become a larger society w...
International Society for Computational Biology
0.806726
27,275
The Intelligent Systems for Molecular Biology (ISMB) conference series began in 1993. As a response to the expansion of the conference, the ISCB was founded in 1997 with a significant part of its remit being to provide a stable financial home for ISMB. The ISCB was legally incorporated in early 1997, with Lawrence Hunt...
International Society for Computational Biology
0.806726
27,276
The ISCB has several affiliated organizations (mainly regional), including the European Molecular Biology Network (EMBnet), the Netherlands Bioinformatics Centre (NBIC), the African Society for Bioinformatics and Computational Biology and the Japanese Society for Bioinformatics.The ISCB is also a founding member of Glo...
International Society for Computational Biology
0.806726
27,277
The ISCB has elected Fellows since 2009. These distinctions are awarded in honour of outstanding contributions to the fields of computational biology and bioinformatics. The inaugural Class was given to previous recipients of the ISCB Accomplishment by a Senior Scientist Award; in following years, the ISCB has sought n...
International Society for Computational Biology
0.806726
27,278
The first issue of the new journal coincided with the opening day of ISMB 2005, held in Detroit, Michigan. Burkhard Rost, then professor in the department of biochemistry and molecular biophysics at Columbia University and now the Alexander von Humboldt Professor and chair of bioinformatics and computational biology, c...
International Society for Computational Biology
0.806726
27,279
In 2005, as part of the society's discussions about the role of publications and the society's official journal, accompanied by the advent of open access publishing, the ISCB announced a partnership with the Public Library of Science and launched a new open access journal, PLoS Computational Biology. The journal is int...
International Society for Computational Biology
0.806726
27,280
In part to reduce ISCB's dependence on ISMB proceeds to fund the society's activities and annual overhead costs, a pilot regional conference was hosted in the US to gauge interest in smaller, localized meetings. In December 2003, the Rocky Mountain Regional Bioinformatics conference, Rocky 1, was launched in Aspen, Col...
International Society for Computational Biology
0.806726
27,281
In 2004, the ISCB Student Council was founded by Manuel Corpas to promote the development of a worldwide community for computational biology students. One of the main roles of the student council is to promote soft skills in order to develop potential in bioinformatics and computational biology trainees. As of 2017, th...
International Society for Computational Biology
0.806726
27,282
In 2004, as many ISCB members had institutional subscriptions to Bioinformatics, ISCB decided not to renew its contract with the journal. In January 2009 Bioinformatics again became an official journal of the ISCB, alongside PLOS Computational Biology. PLOS Computational Biology is an open-access, peer-reviewed journal...
International Society for Computational Biology
0.806726
27,283
In 1998 Bioinformatics became the official journal of the ISCB. Dues-paying members of the society benefited from an online subscription to the journal. ISMB conference proceedings have been published in Bioinformatics since 2001.
International Society for Computational Biology
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27,284
A president, an executive committee, and a board of directors comprise ISCB's scientific leadership, drawing on distinguished, internationally renowned researchers who are elected for their term by the general society membership. The executive director leads the ISCB staff and supports a diverse set of committees dedic...
International Society for Computational Biology
0.806726
27,285
The simplest model for elliptic geometry is a sphere, where lines are "great circles" (such as the equator or the meridians on a globe), and points opposite each other (called antipodal points) are identified (considered the same). This is also one of the standard models of the real projective plane. The difference is ...
Non-Euclidian geometry
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27,286
{\displaystyle t^{\prime }+x^{\prime }\epsilon =(1+v\epsilon )(t+x\epsilon )=t+(x+vt)\epsilon .} Another view of special relativity as a non-Euclidean geometry was advanced by E. B. Wilson and Gilbert Lewis in Proceedings of the American Academy of Arts and Sciences in 1912. They revamped the analytic geometry implicit...
Non-Euclidian geometry
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27,287
The relevant structure is now called the hyperboloid model of hyperbolic geometry. The non-Euclidean planar algebras support kinematic geometries in the plane. For instance, the split-complex number z = eaj can represent a spacetime event one moment into the future of a frame of reference of rapidity a. Furthermore, mu...
Non-Euclidian geometry
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27,288
Hyperbolic geometry found an application in kinematics with the physical cosmology introduced by Hermann Minkowski in 1908. Minkowski introduced terms like worldline and proper time into mathematical physics. He realized that the submanifold, of events one moment of proper time into the future, could be considered a hy...
Non-Euclidian geometry
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27,289
Even after the work of Lobachevsky, Gauss, and Bolyai, the question remained: "Does such a model exist for hyperbolic geometry?". The model for hyperbolic geometry was answered by Eugenio Beltrami, in 1868, who first showed that a surface called the pseudosphere has the appropriate curvature to model a portion of hyper...
Non-Euclidian geometry
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27,290
In three dimensions, there are eight models of geometries. There are Euclidean, elliptic, and hyperbolic geometries, as in the two-dimensional case; mixed geometries that are partially Euclidean and partially hyperbolic or spherical; twisted versions of the mixed geometries; and one unusual geometry that is completely ...
Non-Euclidian geometry
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27,291
Structure and Interpretation of Classical Mechanics (SICM) is a classical mechanics textbook written by Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer. The first edition was published by MIT Press in 2001, and a second edition was released in 2015. The book is used at the Massachusetts Institute of Technolog...
Structure and Interpretation of Classical Mechanics
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27,292
In molecular biology, restriction fragment length polymorphism (RFLP) is a technique that exploits variations in homologous DNA sequences, known as polymorphisms, populations, or species or to pinpoint the locations of genes within a sequence. The term may refer to a polymorphism itself, as detected through the differi...
Restriction Fragment Length Polymorphism
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27,293
The application of technology in today's laboratories is required to achieve timely progress and remain competitive. Laboratories devoted to activities such as high-throughput screening, combinatorial chemistry, automated clinical and analytical testing, diagnostics, large-scale biorepositories, and many others, would ...
Laboratory automation
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27,294
Laboratory automation is a multi-disciplinary strategy to research, develop, optimize and capitalize on technologies in the laboratory that enable new and improved processes. Laboratory automation professionals are academic, commercial and government researchers, scientists and engineers who conduct research and develo...
Laboratory automation
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27,295
In fact all that is needed is one section running along the real time axis, as the route to the end point, t i − i β {\displaystyle t_{i}-i\beta } , is less important. The piecewise composition of the resulting complex time contour leads to a doubling of fields and more complicated Feynman rules, but obviates the need ...
Thermal field theory
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27,296
In theoretical physics, thermal quantum field theory (thermal field theory for short) or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature. In the Matsubara formalism, the basic idea (due to Felix Bloch) is that th...
Thermal field theory
0.80672
27,297
ESA was a novel (non-machine learning) based approach that represented words in the form of vectors with 100,000 dimensions (where each dimension represents an Article in Wikipedia). However practical applications of the approach are limited due to the large number of required dimensions in the vectors. More recently, ...
Semantic space
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27,298
Rule-based and machine learning based models are fixed on the keyword level and break down if the vocabulary differs from that defined in the rules or from the training material used for the statistical models. Research in semantic spaces dates back more than 20 years.
Semantic space
0.80672
27,299
Semantic spaces in the natural language domain aim to create representations of natural language that are capable of capturing meaning. The original motivation for semantic spaces stems from two core challenges of natural language: Vocabulary mismatch (the fact that the same meaning can be expressed in many ways) and a...
Semantic space
0.80672