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9,500 | Although genetics has its roots back in the 19th century with the work of the Bohemian monk Gregor Mendel and other pioneering scientists, human genetics emerged later. It started to develop, albeit slowly, during the first half of the 20th century. Mendelian (single-gene) inheritance was studied in a number of importa... | Clinical genetics | 0.820095 |
9,501 | The clinical setting in which patients are evaluated determines the scope of practice, diagnostic, and therapeutic interventions. For the purposes of general discussion, the typical encounters between patients and genetic practitioners may involve: Referral to an out-patient genetics clinic (pediatric, adult, or combin... | Clinical genetics | 0.820095 |
9,502 | Medical genetics is the branch of medicine that involves the diagnosis and management of hereditary disorders. Medical genetics differs from human genetics in that human genetics is a field of scientific research that may or may not apply to medicine, while medical genetics refers to the application of genetics to medi... | Clinical genetics | 0.820095 |
9,503 | In some ways, many of the individual fields within medical genetics are hybrids between clinical care and research. This is due in part to recent advances in science and technology (for example, see the Human Genome Project) that have enabled an unprecedented understanding of genetic disorders. | Clinical genetics | 0.820095 |
9,504 | Mitochondrial genetics concerns the diagnosis and management of mitochondrial disorders, which have a molecular basis but often result in biochemical abnormalities due to deficient energy production. There exists some overlap between medical genetic diagnostic laboratories and molecular pathology. | Clinical genetics | 0.820095 |
9,505 | In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/NA) between the number of elementary entities (N) and the Avogadro constant (NA). The entities are usually molecules, atoms, or ions of a specified kind. The particular substance sampled may be specified using a su... | Amount of substance | 0.820089 |
9,506 | Historically, the mole was defined as the amount of substance in 12 grams of the carbon-12 isotope. As a consequence, the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the mass of one molecule of the compound, in daltons, and the molar mass of an isotope in gram... | Amount of substance | 0.820089 |
9,507 | Thus, for example, one liter of standard vodka contains about 0.40 L of ethanol (315 g, 6.85 mol) and 0.60 L of water. The amount concentration of ethanol is therefore (6.85 mol of ethanol)/(1 L of vodka) = 6.85 mol/L, not (6.85 mol of ethanol)/(0.60 L of water), which would be 11.4 mol/L. In chemistry, it is customary... | Amount of substance | 0.820088 |
9,508 | Another important derived quantity is the amount of substance concentration (also called amount concentration, or substance concentration in clinical chemistry; which is defined as the amount of a specific substance in a sample of a solution (or some other mixture), divided by the volume of the sample. The SI unit of t... | Amount of substance | 0.820088 |
9,509 | 1921: Soddy receives the Nobel Prize in Chemistry "for his work on the chemistry of radioactive substances and investigations into isotopes". 1922: Aston receives the Nobel Prize in Chemistry "for his discovery of isotopes in a large number of non-radioactive elements, and for his whole-number rule". 1926: Perrin recei... | Amount of substance | 0.820088 |
9,510 | 1913: Discovery of isotopes of non-radioactive elements by Soddy and Thomson. 1914: Richards receives the Nobel Prize in Chemistry for "his determinations of the atomic weight of a large number of elements". 1920: Aston proposes the whole number rule, an updated version of Prout's hypothesis. | Amount of substance | 0.820088 |
9,511 | 1789: Lavoisier publishes Treatise of Elementary Chemistry, introducing the concept of a chemical element and clarifying the Law of conservation of mass for chemical reactions. 1792: Richter publishes the first volume of Stoichiometry or the Art of Measuring the Chemical Elements (publication of subsequent volumes cont... | Amount of substance | 0.820088 |
9,512 | The alchemists, and especially the early metallurgists, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758, Mikhail Lomonosov questioned the idea that mass was the only measure of the quantity of matter, but he did so on... | Amount of substance | 0.820088 |
9,513 | A molecular probe is a group of atoms or molecules used in molecular biology or chemistry to study the properties of other molecules or structures. If some measurable property of the molecular probe used changes when it interacts with the analyte (such as a change in absorbance), the interactions between the probe and ... | Molecular probe | 0.820088 |
9,514 | Some say that the small wavelengths are enslaved by the large (e.g. synergetics). Inertial manifolds may also appear as slow manifolds common in meteorology, or as the center manifold in any bifurcation. Computationally, numerical schemes for partial differential equations seek to capture the long term dynamics and so ... | Inertial manifold | 0.820087 |
9,515 | Elbakyan has released download request logs from Sci-Hub servers covering periods from 2011-2013, 2015-2016, and 2017. Studies of the 2017 Sci-Hub download logs indicated that: less than 1% of all journals contribute to over 50% of all downloads while 50% of the least popular journals contribute to ca. 1% of all downlo... | Sci-Hub | 0.820086 |
9,516 | The Sci-Hub website provides access to articles from almost all academic publishers, including Elsevier, Springer, Institute of Electrical and Electronics Engineers, American Chemical Society, Wiley Blackwell, and the Royal Society of Chemistry, as well as open-access works, and distributes them without regard to publi... | Sci-Hub | 0.820086 |
9,517 | The cybersecurity threat posed by Sci-Hub has been questioned and the suggestion made that the threat has been exaggerated by large publishers keen to protect their business model by discrediting Sci-Hub or pushing universities to block students access to Sci-Hub.Moreover, even prominent Western institutions such as Ha... | Sci-Hub | 0.820086 |
9,518 | The site has cycled through different domain names since then.Sci-Hub has been lauded by some in the scientific, academic, and publishing communities for providing access to knowledge generated by the scientific community, which is usually funded by taxpayers (government grants) and with zero royalties paid to the auth... | Sci-Hub | 0.820086 |
9,519 | The complete Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager sets (Balcar & Jech 2006). It is isomorphic to the completion of the countable Cantor algebra. (The complete Cantor algebra is sometimes called the Cohen algebra, though "Cohen algebra" usually refers to a different ... | Cantor algebra | 0.820085 |
9,520 | In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators. Up to isomorphism... | Cantor algebra | 0.820085 |
9,521 | The limbic system is a group of unique brain areas that work together in many interrelated processes involved in emotion, motivation, learning and memory. Current thinking indicates that the limbic system shares anatomy with a component of the neostriatum already credited with the major task of controlling procedural m... | Procedural memory | 0.820081 |
9,522 | Disorders have been important for the understanding of memory systems. The memory abilities and inhibitions of patients with various diseases played a major role in establishing the distinction that long-term memory consists of different types of memory, more specifically declarative memory and procedural memory. Furth... | Procedural memory | 0.820081 |
9,523 | Therefore, some of the differences people show after extended practice increasingly reflects their genetics. The study also confirmed the idea that practice improves skill learning by showing that, in both the identical and fraternal groups, more practice aided in shedding ineffective tendencies in order to improve exe... | Procedural memory | 0.82008 |
9,524 | These receptors are important for the consolidation of procedural memory. These increased dopamine levels in the brain resultant of cocaine use is similar to the increased dopamine levels in the brain found in schizophrenics. Studies have compared the common memory deficits caused by both cases to further understand th... | Procedural memory | 0.82008 |
9,525 | All preceding applications, and many others, show that the resultant is a fundamental tool in computer algebra. In fact most computer algebra systems include an efficient implementation of the computation of resultants. | Multivariate resultant | 0.820077 |
9,526 | The U-resultant factorizes over an algebraically closed extension of k into a product of linear forms. If α 1 u 1 + … + α n u n {\displaystyle \alpha _{1}u_{1}+\ldots +\alpha _{n}u_{n}} is such a linear factor, then α 1 , … , α n {\displaystyle \alpha _{1},\ldots ,\alpha _{n}} are the homogeneous coordinates of a commo... | Multivariate resultant | 0.820077 |
9,527 | The U-resultant is a homogeneous polynomial in k . {\displaystyle k.} It is zero if and only if the common zeros of P 1 , … , P n − 1 {\displaystyle P_{1},\ldots ,P_{n-1}} form a projective algebraic set of positive dimension (that is, there are infinitely many projective zeros over an algebraically closed extension o... | Multivariate resultant | 0.820077 |
9,528 | In symbolic integration, for computing the antiderivative of a rational fraction, one uses partial fraction decomposition for decomposing the integral into a "rational part", which is a sum of rational fractions whose antiprimitives are rational fractions, and a "logarithmic part" which is a sum of rational fractions o... | Multivariate resultant | 0.820077 |
9,529 | It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation. The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usu... | Multivariate resultant | 0.820077 |
9,530 | In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also call... | Multivariate resultant | 0.820077 |
9,531 | (The capitalization of "Res" is used here for distinguishing the two resultants, although there is no standard rule for the capitalization of the abbreviation). The homogeneous resultant has essentially the same properties as the usual resultant, with essentially two differences: instead of polynomial roots, one consid... | Multivariate resultant | 0.820077 |
9,532 | He introduced genus theory, which gives a powerful way to understand the quotient of the class group by the subgroup of squares. (Gauss and many subsequent authors wrote 2b in place of b; the modern convention allowing the coefficient of xy to be odd is due to Eisenstein). These investigations of Gauss strongly influen... | Binary quadratic form | 0.820077 |
9,533 | The third edition of this work includes two supplements by Dedekind. Supplement XI introduces ring theory, and from then on, especially after the 1897 publication of Hilbert's Zahlbericht, the theory of binary quadratic forms lost its preeminent position in algebraic number theory and became overshadowed by the more ge... | Binary quadratic form | 0.820077 |
9,534 | Several centuries later, his ideas were extended to a complete solution of Pell's equation known as the chakravala method, attributed to either of the Indian mathematicians Jayadeva or Bhāskara II. The problem of representing integers by sums of two squares was considered in the 3rd century by Diophantus. In the 17th c... | Binary quadratic form | 0.820077 |
9,535 | There is circumstantial evidence of protohistoric knowledge of algebraic identities involving binary quadratic forms. The first problem concerning binary quadratic forms asks for the existence or construction of representations of integers by particular binary quadratic forms. The prime examples are the solution of Pel... | Binary quadratic form | 0.820077 |
9,536 | x 2 + y 2 , x 2 + 2 y 2 , x 2 − 3 y 2 {\displaystyle x^{2}+y^{2},x^{2}+2y^{2},x^{2}-3y^{2}} and so on are quadratic forms, and the theory of quadratic forms gives a unified way of looking at and proving these theorems. Another instance of quadratic forms is Pell's equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1}... | Binary quadratic form | 0.820077 |
9,537 | This choice is motivated by their status as the driving force behind the development of algebraic number theory. Since the late nineteenth century, binary quadratic forms have given up their preeminence in algebraic number theory to quadratic and more general number fields, but advances specific to binary quadratic for... | Binary quadratic form | 0.820077 |
9,538 | Composition most commonly refers to a binary operation on primitive equivalence classes of forms of the same discriminant, one of the deepest discoveries of Gauss, which makes this set into a finite abelian group called the form class group (or simply class group) of discriminant Δ {\displaystyle \Delta } . Class group... | Binary quadratic form | 0.820077 |
9,539 | They both use cluster centers to model the data; however, k-means clustering tends to find clusters of comparable spatial extent, while the Gaussian mixture model allows clusters to have different shapes. The unsupervised k-means algorithm has a loose relationship to the k-nearest neighbor classifier, a popular supervi... | K-means algorithm | 0.820074 |
9,540 | The EM result is thus able to accommodate clusters of variable size much better than k-means as well as correlated clusters (not in this example). In counterpart, EM requires the optimization of a larger number of free parameters and poses some methodological issues due to vanishing clusters or badly-conditioned covari... | K-means algorithm | 0.820074 |
9,541 | The most common algorithm uses an iterative refinement technique. Due to its ubiquity, it is often called "the k-means algorithm"; it is also referred to as Lloyd's algorithm, particularly in the computer science community. It is sometimes also referred to as "naïve k-means", because there exist much faster alternative... | K-means algorithm | 0.820074 |
9,542 | Jenks natural breaks optimization: k-means applied to univariate data k-medians clustering uses the median in each dimension instead of the mean, and this way minimizes L 1 {\displaystyle L_{1}} norm (Taxicab geometry). k-medoids (also: Partitioning Around Medoids, PAM) uses the medoid instead of the mean, and this way... | K-means algorithm | 0.820074 |
9,543 | The particles were used as templates for the fabrication of a range of metallized nanotube structures using mineralization techniques. TMV particles have also been utilized to generate various structures (nanotubes and nanowires) for use in batteries and data storage devices.Viral capsids have attracted great interest ... | Virus nanotechnology | 0.820074 |
9,544 | Later in the 1970s, viruses are used as a vector for the benefit of humans. Since that, often viruses are used as vectors for gene therapy, cancer control and control of harmful or damaging organisms, in both agriculture and medicine.Recently, a new approach to exploiting viruses and their capsids for biotechnology beg... | Virus nanotechnology | 0.820074 |
9,545 | Viruses have long been studied as deadly pathogens to cause disease in all living forms. By the 1950s, researchers had begun thinking of viruses as tools in addition of pathogens. Bacteriophage genomes and components of the protein expression machinery have been widely utilized as tools for understanding the fundamenta... | Virus nanotechnology | 0.820074 |
9,546 | Viruses cause several destructive plant diseases and are accountable for massive losses in crop production and quality in all parts of the world. Infected plants may show a range of symptoms depending on the disease but often there is severe leaf curling, stunting (abnormalities in the whole plant) and leaf yellowing (... | Virus nanotechnology | 0.820074 |
9,547 | Because of their nanometer size dimensions, viruses have been considered as naturally occurring nanoparticles. Virus nanoparticles have been subject to the nanoscience and nanoengineering disciplines. Viruses can be regarded as prefabricated nanoparticles. Many different viruses have been studied for various applicatio... | Virus nanotechnology | 0.820074 |
9,548 | Virus nanotechnology is the use of viruses as a source of nanoparticles for biomedical purposes. Viruses are made up of a genome and a capsid; and some viruses are enveloped. Most virus capsids measure between 20-500 nm in diameter. | Virus nanotechnology | 0.820074 |
9,549 | Virus nanotechnology is one of the very promising and emerging disciplines in nanotechnology. A highly interdisciplinary field, viral nanotechnology occupies the interface between virology, biotechnology, chemistry, and materials science. The fields employs viral nanoparticles (VNPs) and its counterparts of virus-like ... | Virus nanotechnology | 0.820074 |
9,550 | Virus-like particles (VLPs) can be produced that lack the viral genome; these VLPs are non-infectious also toward plants and thus considered safe also from an agricultural point of view. Viruses and their non-infectious counterparts can be produced through molecular farming in plants or fermentation in cell culture. Th... | Virus nanotechnology | 0.820074 |
9,551 | In view of their relative simplicity and ease of production, plant virus particles or virus-like particles (VLPs) have attracted much interest over the past 20 years for applications in both bio- and nanotechnology . As result, plant virus particles have been subjected to both genetic and chemical modification, have be... | Virus nanotechnology | 0.820074 |
9,552 | This bottom-up approach requires less material and causes less pollution. Nanotechnology has had several commercial applications in advanced laser technology, hard coatings, photography, pharmaceuticals, printing, chemical-mechanical polishing, and cosmetics. Soon, there will be lighter cars using nanoparticle reinforc... | Virus nanotechnology | 0.820074 |
9,553 | Nanotechnology has an almost limitless string of applications in biology, biotechnology, and biomedicine. Nanotechnology has engendered a growing sense of excitement due to the ability to produce and utilize materials, devices, and systems through the control of matter on the nanometer scale (1 to 50 nm). | Virus nanotechnology | 0.820074 |
9,554 | So that a virus can also call as a nanoparticle. The word nanotechnology is generally used when referring to materials with the size of 0.1 to 100 nanometres, however, it is also inherent that these materials should display different properties from bulk (or micrometric and larger) materials as a result of their size. ... | Virus nanotechnology | 0.820074 |
9,555 | Nanotechnology is the manipulation or self-assembly of individual atoms, molecules, or, molecular clusters into structures to create materials and devices with new or vastly different properties. Nanotechnology can work from the top down (which means reducing the size of the smallest structures to the nanoscale) or bot... | Virus nanotechnology | 0.820074 |
9,556 | As expected, due to the NP-hardness of the subjacent optimization problem, the computational time of optimal algorithms for K-means quickly increases beyond this size. Optimal solutions for small- and medium-scale still remain valuable as a benchmark tool, to evaluate the quality of other heuristics. To find high-quali... | K-means algorithm | 0.820074 |
9,557 | The classical k-means algorithm and its variations are known to only converge to local minima of the minimum-sum-of-squares clustering problem defined as Many studies have attempted to improve the convergence behavior of the algorithm and maximize the chances of attaining the global optimum (or at least, local minima o... | K-means algorithm | 0.820074 |
9,558 | Pharmacogenomics is also known as companion diagnostics, meaning tests being bundled with drugs. Examples include KRAS test with cetuximab and EGFR test with gefitinib. Beside efficacy, germline pharmacogenetics can help to identify patients likely to undergo severe toxicities when given cytotoxics showing impaired det... | Extensive metabolizer | 0.820073 |
9,559 | Computational advances have enabled cheaper and faster sequencing. Research has focused on combinatorial chemistry, genomic mining, omic technologies, and high throughput screening. As the cost per genetic test decreases, the development of personalized drug therapies will increase. | Extensive metabolizer | 0.820073 |
9,560 | Sequence2Script is a "free online tool to help healthcare providers and clinical laboratories translate pharmacogenetic test results into clinically useful recommendations." This tool "creates a report that outlines medication and dosing recommendations based on a patient’s known genotypes. The recommendations made by ... | Extensive metabolizer | 0.820073 |
9,561 | Pharmacogenetics has become a controversial issue in the area of bioethics. Privacy and confidentiality are major concerns. The evidence of benefit or risk from a genetic test may only be suggestive, which could cause dilemmas for providers. | Extensive metabolizer | 0.820073 |
9,562 | The companies use the same genotyping chips that are used in GWAS studies and provide customers with a write-up of individual risk for various traits and diseases and testing for 500,000 known SNPs. Costs range from $995 to $2500 and include updates with new data from studies as they become available. The more expensiv... | Extensive metabolizer | 0.820073 |
9,563 | Technology now allows for genetic analysis of hundreds of target genes involved in medication metabolism and response in less than 24 hours for under $1,000. This a huge step towards bringing pharmacogenetic technology into everyday medical decisions. Likewise, companies like deCODE genetics, MD Labs Pharmacogenetics, ... | Extensive metabolizer | 0.820073 |
9,564 | Such studies constitute the realm of human molecular genetics. With the advent of the Human Genome and International HapMap Project, it has become feasible to explore subtle genetic influences on many common disease conditions such as diabetes, asthma, migraine, schizophrenia, etc. Although some causal links have been ... | Protein-coding gene | 0.820071 |
9,565 | Molecularly characterized genetic disorders are those for which the underlying causal gene has been identified. Currently there are approximately 2,200 such disorders annotated in the OMIM database.Studies of genetic disorders are often performed by means of family-based studies. In some instances, population based app... | Protein-coding gene | 0.820071 |
9,566 | Most aspects of human biology involve both genetic (inherited) and non-genetic (environmental) factors. Some inherited variation influences aspects of our biology that are not medical in nature (height, eye color, ability to taste or smell certain compounds, etc.). Moreover, some genetic disorders only cause disease in... | Protein-coding gene | 0.820071 |
9,567 | Founded in 1979, the BPhO has been used as a qualifier for selection into the UK Physics Team for the International Physics Olympiad. The organisation aims to encourage the study of Physics and through ten annual Physics and Astronomy & Astrophysics competitions. Competitions include: Round 1, Round 2, Physics Challeng... | British Physics Olympiad | 0.820071 |
9,568 | Following Round 2, the best students eligible to represent the UK at the International Physics Olympiad (IPhO) will be invited to attend the Training Camp. Problem solving skills will be developed, practical skills enhanced, as well as some coverage of new material (Thermodynamics, Relativity, etc.). At the Training Ca... | British Physics Olympiad | 0.820071 |
9,569 | The British Physics Olympiad (BPhO) is a series of ten competitions in the study of physics for students in years 11–13 in the United Kingdom.On a day-to-day basis, the BPhO is run by five committee members as well as a large team of volunteer physics teachers and academics from across the UK. The BPhO's administrative... | British Physics Olympiad | 0.820071 |
9,570 | The BPhO Round 1 is a two-sectioned paper consisting of Section A and Section B, both lasting for 1 hour and 20 minutes (+5 mins reading for section B). Section A has only one question, with many independent parts that test the candidate on a variety of topics in physics. Section A can be awarded a maximum of 50 marks,... | British Physics Olympiad | 0.820071 |
9,571 | Position of these stationary layer regarding cell walls depends on the cell geometry. It is possible to focus microscope on this stationary layers and observe particles motion not affected with electro-osmosis. | Microelectrophoresis | 0.82007 |
9,572 | Static layouts allow for more control over the aesthetics, and thorough optimization of space around and overlapping irregular-shaped content than dynamic layouts. In web design, this is sometimes referred to as a fixed width layout; but the entire layout may be scalable in size while still maintaining the original pro... | Page layout | 0.820068 |
9,573 | If the substrate that is under nucleophilic attack is chiral, the reaction will therefore lead to an inversion of its stereochemistry, called a Walden inversion. SN2 attack may occur if the backside route of attack is not sterically hindered by substituents on the substrate. Therefore, this mechanism usually occurs at ... | Substitution reaction | 0.82006 |
9,574 | If the substrate has a chiral carbon, this mechanism can result in either inversion of the stereochemistry or retention of configuration. Usually, both occur without preference. The result is racemization. | Substitution reaction | 0.82006 |
9,575 | American Society for Precision Engineering euspen - European Society for Precision Engineering and Nanotechnology JSPE- The Japan Society for Precision Engineering DSPE - Dutch Society for Precision Engineering SPETA - Singapore Precision Engineering and Technology Association | Precision engineering | 0.820044 |
9,576 | Precision engineering is a subdiscipline of electrical engineering, software engineering, electronics engineering, mechanical engineering, and optical engineering concerned with designing machines, fixtures, and other structures that have exceptionally low tolerances, are repeatable, and are stable over time. These app... | Precision engineering | 0.820044 |
9,577 | The Borel functional calculus for self-adjoint operators is constructed using integrals with respect to PVMs. In quantum mechanics, PVMs are the mathematical description of projective measurements. They are generalized by positive operator valued measures (POVMs) in the same sense that a mixed state or density matrix g... | Projective measurement | 0.820035 |
9,578 | In mathematics, particularly in functional analysis, a projection-valued measure (PVM) is a function defined on certain subsets of a fixed set and whose values are self-adjoint projections on a fixed Hilbert space. Projection-valued measures are formally similar to real-valued measures, except that their values are sel... | Projective measurement | 0.820035 |
9,579 | {\displaystyle \operatorname {T} _{\pi }(f)=\int _{X}f(x)\,d\pi (x)=\int _{X}f\,d\pi .} The theorem is also correct for unbounded measurable functions f, but then T π ( f ) {\displaystyle \operatorname {T} _{\pi }(f)} will be an unbounded linear operator on the Hilbert space H. The spectral theorem says that every se... | Projective measurement | 0.820034 |
9,580 | If π is a projection-valued measure on a measurable space (X, M), then the map χ E ↦ π ( E ) {\displaystyle \chi _{E}\mapsto \pi (E)} extends to a linear map on the vector space of step functions on X. In fact, it is easy to check that this map is a ring homomorphism. This map extends in a canonical way to all bounded ... | Projective measurement | 0.820034 |
9,581 | For any commutative ring R, the (non-commutative) ring of n-by-n matrices M n ( R ) {\displaystyle M_{n}(R)} is a separable R-algebra. For any 1 ≤ j ≤ n {\displaystyle 1\leq j\leq n} , a separability idempotent is given by ∑ i = 1 n e i j ⊗ e j i {\displaystyle \sum _{i=1}^{n}e_{ij}\otimes e_{ji}} , where e i j {\displ... | Separability idempotent | 0.820033 |
9,582 | A separable algebra is said to be strongly separable if there exists a separability idempotent that is symmetric, meaning e = ∑ i = 1 n x i ⊗ y i = ∑ i = 1 n y i ⊗ x i {\displaystyle e=\sum _{i=1}^{n}x_{i}\otimes y_{i}=\sum _{i=1}^{n}y_{i}\otimes x_{i}} An algebra is strongly separable if and only if its trace form is ... | Separability idempotent | 0.820033 |
9,583 | In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension. | Separability idempotent | 0.820033 |
9,584 | Random number tables have been used in statistics for tasks such as selected random samples. This was much more effective than manually selecting the random samples (with dice, cards, etc.). Nowadays, tables of random numbers have been replaced by computational random number generators. | Random number table | 0.820032 |
9,585 | An even nontotient may be one more than a prime number, but never one less, since all numbers below a prime number are, by definition, coprime to it. To put it algebraically, for p prime: φ(p) = p − 1. Also, a pronic number n(n − 1) is certainly not a nontotient if n is prime since φ(p2) = p(p − 1). If a natural number... | Nontotient | 0.820021 |
9,586 | Ronald Fagin's 1974 proof that the complexity class NP was characterised exactly by those classes of structures axiomatizable in existential second-order logic was the starting point of descriptive complexity theory.Since the complement of an existential formula is a universal formula, it follows immediately that co-NP... | SO (complexity) | 0.820017 |
9,587 | A loop in a Feynman diagram requires an integral over a continuum of possible energies and momenta. In general, the integrals of products of Feynman propagators diverge at propagator poles, and the divergences must be removed by renormalization. The process of renormalization might be thought of as a theory of cancella... | Pole mass | 0.82001 |
9,588 | In quantum field theory, quantities like coupling constant and mass "run" with the energy scale of high energy physics. The running mass of a fermion or massive boson depends on the energy scale at which the observation occurs, in a way described by a renormalization group equation (RGE) and calculated by a renormaliza... | Pole mass | 0.82001 |
9,589 | An association scheme is a collection of binary relations satisfying certain compatibility conditions. Association schemes provide a unified approach to many topics, for example combinatorial designs and coding theory. In algebra, association schemes generalize groups, and the theory of association schemes generalizes ... | Algebraic combinatorics | 0.820007 |
9,590 | Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. | Algebraic combinatorics | 0.820007 |
9,591 | Algebraic combinatorics has come to be seen more expansively as an area of mathematics where the interaction of combinatorial and algebraic methods is particularly strong and significant. Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometr... | Algebraic combinatorics | 0.820007 |
9,592 | A matroid is a structure that captures and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions. Matroid theory borrows ext... | Algebraic combinatorics | 0.820007 |
9,593 | Other significant types of finite geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs such as higher finite inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector sp... | Algebraic combinatorics | 0.820007 |
9,594 | A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite... | Algebraic combinatorics | 0.820007 |
9,595 | A Young tableau (pl. : tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. | Algebraic combinatorics | 0.820007 |
9,596 | The term "algebraic combinatorics" was introduced in the late 1970s. Through the early or mid-1990s, typical combinatorial objects of interest in algebraic combinatorics either admitted a lot of symmetries (association schemes, strongly regular graphs, posets with a group action) or possessed a rich algebraic structure... | Algebraic combinatorics | 0.820007 |
9,597 | The combinatorial extension method of structural alignment generates a pairwise structural alignment by using local geometry to align short fragments of the two proteins being analyzed and then assembles these fragments into a larger alignment. Based on measures such as rigid-body root mean square distance, residue dis... | Protein sequence alignment | 0.820007 |
9,598 | In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Intuitively, IVs are used when an... | Two-stage least squares | 0.820003 |
9,599 | If G {\displaystyle G} is a Lie group with Lie algebra g {\displaystyle {\mathfrak {g}}} , the choice of a nondegenerate invariant bilinear form on g {\displaystyle {\mathfrak {g}}} corresponds to a choice of bi-invariant Riemannian metric on G {\displaystyle G} . Then under the identification of the universal envelopi... | Casimir element | 0.819995 |
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