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25,500 | They must be capable of using these strategies at will.However, these last two conditions introduce the construct that accuracy goals include a conscious process of utilizing cognitive strategies in motivated reasoning. This construct is called into question by neuroscience research that concludes that motivated reason... | Motivated reasoning | 0.80758 |
25,501 | This can create pathways within the neural network that further ingrains the reasoned beliefs of that individual along similar neural networks where logical reasoning occurs. This causes the strong emotion to reoccur when confronted with contradictory information, time and time again. This is referred to by Lodge and T... | Motivated reasoning | 0.80758 |
25,502 | A neuroimaging study by Drew Westen and colleagues does not support the use of cognitive processes in motivated reasoning, lending greater support to affective processing as a key mechanism in supporting bias. This study, designed to test the neural circuitry of individuals engaged in motivated reasoning, found that mo... | Motivated reasoning | 0.80758 |
25,503 | In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis mS = −1, 0, or +1, giving the name "triplet". Spin, in the context of quantum mechanics, ... | Spin triplet | 0.80758 |
25,504 | In terms of representation theory, what has happened is that the two conjugate 2-dimensional spin representations of the spin group SU(2) = Spin(3) (as it sits inside the 3-dimensional Clifford algebra) have tensored to produce a 4 dimensional representation. The 4 dimensional representation descends to the usual ortho... | Spin triplet | 0.80758 |
25,505 | In particular, the vanishing of the mean curvature vector is seen as being equivalent to submanifold being a critical point of the volume functional. This shows how a minimal submanifold can be characterized either by the critical point theory of the volume functional or by an explicit partial differential equation for... | First variation of area formula | 0.80758 |
25,506 | In that case it is immediate from Stokes' theorem that d d t vol ( f t ) = − ∫ S ⟨ W t , H ( f t ) ⟩ g ω t + ∫ ∂ S ι W t ∥ ω t . {\displaystyle {\frac {d}{dt}}\operatorname {vol} (f_{t})=-\int _{S}\left\langle W_{t},H(f_{t})\right\rangle _{g}\omega _{t}+\int _{\partial S}\iota _{W_{t}^{\parallel }}\omega _{t}.} | First variation of area formula | 0.80758 |
25,507 | In the mathematical field of Riemannian geometry, every submanifold of a Riemannian manifold has a surface area. The first variation of area formula is a fundamental computation for how this quantity is affected by the deformation of the submanifold. The fundamental quantity is to do with the mean curvature. Let (M, g)... | First variation of area formula | 0.80758 |
25,508 | Moment-resisting frame is a rectilinear assemblage of beams and columns, with the beams rigidly connected to the columns. Resistance to lateral forces is provided primarily by rigid frame action – that is, by the development of bending moment and shear force in the frame members and joints. By virtue of the rigid beam–... | Steel Moment Resisting Frame | 0.807578 |
25,509 | In software engineering, a plain old Java object (POJO) is an ordinary Java object, not bound by any special restriction. The term was coined by Martin Fowler, Rebecca Parsons and Josh MacKenzie in September 2000: "We wondered why people were so against using regular objects in their systems and concluded that it was b... | Plain old Java object | 0.807578 |
25,510 | There are two contrasting points of view on what Leibniz meant by calculus ratiocinator. The first is associated with computer software, the second is associated with computer hardware. | Calculus ratiocinator | 0.807569 |
25,511 | Frege intended his "concept script" to be a calculus ratiocinator as well as a universal characteristics. That part of formal logic relevant to the calculus comes under the heading of proof theory. From this perspective the calculus ratiocinator is only a part (or a subset) of the universal characteristics, and a compl... | Calculus ratiocinator | 0.807569 |
25,512 | The received point of view in analytic philosophy and formal logic, is that the calculus ratiocinator anticipates mathematical logic—an "algebra of logic". The analytic point of view understands that the calculus ratiocinator is a formal inference engine or computer program, which can be designed so as to grant primacy... | Calculus ratiocinator | 0.807569 |
25,513 | Leibniz constructed just such a machine for mathematical calculations, which was also called a "stepped reckoner". As a computing machine, the ideal calculus ratiocinator would perform Leibniz's integral and differential calculus. In this way the meaning of the word, "ratiocinator" is clarified and can be understood as... | Calculus ratiocinator | 0.807569 |
25,514 | Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's calculus ratiocinator." "...like his predecessor Pascal, was interested in the construction of computing machines in the Metal. ... just as the calculus of arithmetic lends itself to a mechanization progressing through the abac... | Calculus ratiocinator | 0.807569 |
25,515 | A contrasting point of view stems from synthetic philosophy and fields such as cybernetics, electronic engineering, and general systems theory. It is little appreciated in analytic philosophy. The synthetic view understands the calculus ratiocinator as referring to a "calculating machine". The cybernetician Norbert Wie... | Calculus ratiocinator | 0.807569 |
25,516 | The calculus ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned characteristica universalis, a universal conceptual language. | Calculus ratiocinator | 0.807569 |
25,517 | Let θ ∈ Θ {\displaystyle \theta \in \Theta } . To see that C ∗ ( θ ) {\displaystyle C^{*}(\theta )} is nonempty, observe that the function f θ: C ( θ ) → R {\displaystyle f_{\theta }:C(\theta )\to \mathbb {R} } by f θ ( x ) = f ( x , θ ) {\displaystyle f_{\theta }(x)=f(x,\theta )} is continuous on the compact set C ( θ... | Maximum theorem | 0.807567 |
25,518 | Lemma.If A , B: Θ ⇉ X {\displaystyle A,B:\Theta \rightrightarrows X} are correspondences, A {\displaystyle A} is upper hemicontinuous and compact-valued, and B {\displaystyle B} is closed, then A ∩ B: Θ ⇉ X {\displaystyle A\cap B:\Theta \rightrightarrows X} defined by ( A ∩ B ) ( θ ) = A ( θ ) ∩ B ( θ ) {\displaystyle ... | Maximum theorem | 0.807567 |
25,519 | Consider a utility maximization problem where a consumer makes a choice from their budget set. Translating from the notation above to the standard consumer theory notation, X = R + l {\displaystyle X=\mathbb {R} _{+}^{l}} is the space of all bundles of l {\displaystyle l} commodities, Θ = R + + l × R + + {\displaystyle... | Maximum theorem | 0.807567 |
25,520 | Theorem 2.If f {\displaystyle f} is lower semicontinuous and C {\displaystyle C} is lower hemicontinuous, then f ∗ {\displaystyle f^{*}} is lower semicontinuous. Under the hypotheses of the Maximum theorem, f ∗ {\displaystyle f^{*}} is continuous. It remains to verify that C ∗ {\displaystyle C^{*}} is an upper hemicont... | Maximum theorem | 0.807567 |
25,521 | Throughout this proof we will use the term neighborhood to refer to an open set containing a particular point. We preface with a preliminary lemma, which is a general fact in the calculus of correspondences. Recall that a correspondence is closed if its graph is closed. | Maximum theorem | 0.807567 |
25,522 | The theorem is typically interpreted as providing conditions for a parametric optimization problem to have continuous solutions with regard to the parameter. In this case, Θ {\displaystyle \Theta } is the parameter space, f ( x , θ ) {\displaystyle f(x,\theta )} is the function to be maximized, and C ( θ ) {\displaysty... | Maximum theorem | 0.807567 |
25,523 | The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. The theorem is primarily used in mathematical economics and optimal control. | Maximum theorem | 0.807567 |
25,524 | A natural generalization from the above results gives sufficient local conditions for f ∗ {\displaystyle f^{*}} to be continuous and C ∗ {\displaystyle C^{*}} to be nonempty, compact-valued, and upper semi-continuous. If in addition to the conditions above, f {\displaystyle f} is quasiconcave in x {\displaystyle x} for... | Maximum theorem | 0.807567 |
25,525 | Union of the observational and theoretical subfields of astrophysics has been a major focus of the CfA since its founding.In 2018, the CfA rebranded, changing its official name to the "Center for Astrophysics | Harvard & Smithsonian" in an effort to reflect its unique status as a joint collaboration between Harvard Uni... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,526 | SAO is one of the 13 stakeholder institutes for the Event Horizon Telescope Board, and the CfA hosts its Array Operations Center. In 2019, the project revealed the first direct image of a black hole. The result is widely regarded as a triumph not only of observational astronomy, but of its intersection with theoretical... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,527 | The CfA, via the Smithsonian Astrophysical Observatory, recently played a major role in the Lynx X-ray Observatory, a NASA-funded large mission concept study commissioned as part of the 2020 Astronomy and Astrophysics Decadal Survey ("Astro2020"). If launched, Lynx would be the most powerful X-ray observatory construct... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,528 | The CfA estimates that roughly 10% of the professional astrophysics community in the United States spent at least a portion of their career or education there.The CfA is either a lead or major partner in the operations of the Fred Lawrence Whipple Observatory, the Submillimeter Array, MMT Observatory, the South Pole Te... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,529 | The following decade saw the start of the landmark CfA Redshift Survey (the first attempt to map the large scale structure of the Universe), as well as the release of the "Field Report", a highly influential Astronomy and Astrophysics Decadal Survey chaired by the outgoing CfA Director George Field. He would be replace... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,530 | The founding of the CfA also coincided with the birth of X-ray astronomy as a new, major field that was largely dominated by CfA scientists in its early years. Riccardo Giacconi, regarded as the "father of X-ray astronomy", founded the High Energy Astrophysics Division within the new CfA by moving most of his research ... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,531 | This joint relationship was formalized as the new Harvard–Smithsonian Center for Astrophysics on July 1, 1973. George B. Field, then affiliated with Berkeley, was appointed as its first director. That same year, a new astronomical journal, the CfA Preprint Series was created, and a CfA/SAO instrument flying aboard Skyl... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,532 | The collaborative foundation for what would ultimately give rise to the Center for Astrophysics began with SAO's move to Cambridge in 1955. Fred Whipple, who was already chair of the Harvard Astronomy Department (housed within HCO since 1931), was named SAO's new director at the start of this new era; an early test of ... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,533 | Fred Lawrence Whipple, then the chairman of the Harvard Astronomy Department, was named the new director of SAO. The collaborative relationship between SAO and HCO therefore predates the official creation of the CfA by 18 years. SAO's move to Harvard's campus also resulted in a rapid expansion of its research program. ... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,534 | Charles Alcock, known for a number of major works related to massive compact halo objects, was named the third director of the CfA in 2004. Today Alcock oversees one of the largest and most productive astronomical institutes in the world, with more than 850 staff and an annual budget in excess of $100 million. The Harv... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,535 | Chandra X-ray Center (CXC), the science operations center for NASA's Chandra X-ray Observatory Institute for Theory and Computation (ITC) Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP) Center for Parallel Astrophysical Computing (CPAC) Minor Planet Center (MPC) Telescope Data Center (TDC) Radi... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,536 | Atomic and Molecular Physics (AMP) High Energy Astrophysics (HEA) Optical and Infrared Astronomy (OIR) Radio and Geoastronomy (RG) Solar, Stellar, and Planetary Sciences (SSP) Theoretical Astrophysics (TA) | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,537 | Chandra, the second of NASA's Great Observatories and still the most powerful X-ray telescope in history, continues operations today as part of the CfA's Chandra X-ray Center. Giacconi would later win the 2002 Nobel Prize in Physics for his foundational work in X-ray astronomy. Shortly after the launch of the Einstein ... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,538 | The Center for Astrophysics | Harvard & Smithsonian is not formally an independent legal organization, but rather an institutional entity operated under a memorandum of understanding between Harvard University and the Smithsonian Institution. This collaboration was formalized on July 1, 1973, with the goal of coordinat... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,539 | Its projects have included Nobel Prize-winning advances in cosmology and high energy astrophysics, the discovery of many exoplanets, and the first image of a black hole. The CfA also serves a major role in the global astrophysics research community: the CfA's Astrophysics Data System (ADS), for example, has been univer... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,540 | The Center for Astrophysics | Harvard & Smithsonian (CfA), previously known as the Harvard–Smithsonian Center for Astrophysics, is an astrophysics research institute jointly operated by the Harvard College Observatory and Smithsonian Astrophysical Observatory. Founded in 1973 and headquartered in Cambridge, Massachuset... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,541 | This era of the observatory was made famous by the work of Cecelia Payne-Gaposchkin, who became the first woman to earn a PhD in astronomy from Radcliffe College (a short walk from the observatory). Payne-Gapochkin's 1925 thesis proposed that stars were composed primarily of hydrogen and helium, an idea thought ridicul... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,542 | Henrietta Swan Leavitt, for example, discovered the so-called period-luminosity relation for Classical Cepheid variable stars, establishing the first major "standard candle" with which to measure the distance to galaxies. Now called "Leavitt's law", the discovery is regarded as one of the most foundational and importan... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,543 | Partly in response to renewed public interest in astronomy following the 1835 return of Halley's Comet, the Harvard College Observatory was founded in 1839, when the Harvard Corporation appointed William Cranch Bond as an "Astronomical Observer to the University". For its first four years of operation, the observatory ... | Harvard–Smithsonian Center for Astrophysics | 0.80756 |
25,544 | In mathematics, in the field of geometry, a polar space of rank n (n ≥ 3), or projective index n − 1, consists of a set P, conventionally called the set of points, together with certain subsets of P, called subspaces, that satisfy these axioms: Every subspace is isomorphic to a projective space Pd(K) with −1 ≤ d ≤ (n −... | Polar space | 0.807559 |
25,545 | nQuery is used for adaptive clinical trial design. Trials with an adaptive design have been reported to be more efficient, informative, and ethical than trials with a traditional fixed design because they conserve resources such as time and money and often require fewer participants.nQuery allows researchers to apply b... | NQuery Sample Size Software | 0.807558 |
25,546 | Janet Dixon Elashoff, creator of nQuery, is a retired American statistician and daughter of the mathematician and statistician Wilfrid Joseph Dixon, creator of BMDP. Elashoff is also the retired Director of the Division of Biostatistics, Cedars-Sinai Medical Center. While at UCLA and Cedars-Sinai during the 1990s, she ... | NQuery Sample Size Software | 0.807558 |
25,547 | In this scenario, the equation of state p = w ρ {\displaystyle p=w\rho } of the dark energy, relating its pressure and energy density, can cross the boundary w = − 1 {\displaystyle w=-1} associated with the cosmological constant. The boundary separates the phantom-energy-like behavior with w < − 1 {\displaystyle w<-1} ... | Quintom scenario | 0.807555 |
25,548 | In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself. The classification theorem states that the list of finite simple groups consists of 18 ... | Sporadic groups | 0.807554 |
25,549 | Ignoring the propagating degrees of freedom, the interaction between nonrelativistic electrons is the coulomb repulsion. In 2+1 dimensions, this is: V ( x , y ) = j 2 | y − x | . {\displaystyle V(x,y)={j^{2} \over |y-x|}.} When coupled to an external potential to model classical positions of nuclei, a Schrödinger field... | Schrödinger field | 0.807553 |
25,550 | These nonlinear equations describe the classical wave limit of a system of interacting identical particles. The path integral of a Schrödinger field is also known as a coherent state path integral, because the field itself is an annihilation operator whose eigenstates can be thought of as coherent states of the harmoni... | Schrödinger field | 0.807553 |
25,551 | In quantum mechanics and quantum field theory, a Schrödinger field, named after Erwin Schrödinger, is a quantum field which obeys the Schrödinger equation. While any situation described by a Schrödinger field can also be described by a many-body Schrödinger equation for identical particles, the field theory is more sui... | Schrödinger field | 0.807553 |
25,552 | The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables.The existence of multiple theories seems unnecessarily complex since ratios are, to a large extent, identified with quotients and their prospective values. However, this is a comp... | Ratio analysis | 0.807553 |
25,553 | The Pythagoreans developed a theory of ratio and proportion as applied to numbers. The Pythagoreans' conception of number included only what would today be called rational numbers, casting doubt on the validity of the theory in geometry where, as the Pythagoreans also discovered, incommensurable ratios (corresponding t... | Ratio analysis | 0.807553 |
25,554 | This approach is motivated by variational principles and the physics of surfaces, which dictate that a constrained surface will assume the shape which minimizes the total energy of deformation (analogous to a soap bubble). Expressing the energy of a surface in terms of its local deformation (the energy is due to a comb... | Soft body dynamics | 0.80755 |
25,555 | This is a more physically accurate approach, which uses the widely used finite element method to solve the partial differential equations which govern the dynamics of an elastic material. The body is modeled as a three-dimensional elastic continuum by breaking it into a large number of solid elements which fit together... | Soft body dynamics | 0.807549 |
25,556 | In this approach, the body is modeled as a set of point masses (nodes) connected by ideal weightless elastic springs obeying some variant of Hooke's law. The nodes may either derive from the edges of a two-dimensional polygonal mesh representation of the surface of the object, or from a three-dimensional network of nod... | Soft body dynamics | 0.807549 |
25,557 | In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a specified probability distribution) and connecting two nodes by a link if and only if their distance is in a given range... | Random geometric graph | 0.807549 |
25,558 | As a result full connectivity can be expressed as a sum of the contributions from the bulk and the geometries boundaries. A more general analysis of the connection functions in wireless networks has shown that the probability of full connectivity can be well approximated expressed by a few moments of the connection fun... | Random geometric graph | 0.807549 |
25,559 | An example of a theoretical formal analysis framework for the verification and profiling of the control-flow aspects of scientific workflows and their data flow aspects for the Discovery Net system is described in the paper, "The design and implementation of a workflow analysis tool" by Curcin et al.The authors note th... | Scientific workflow system | 0.807549 |
25,560 | Each directed edge in the graph of a workflow typically represents a connection from the output of one application to the input of the next. A sequence of such edges may be called a pipeline. A bioinformatics workflow management system is a specialized scientific workflow system focused on bioinformatics. | Scientific workflow system | 0.807549 |
25,561 | Notable scientific workflow systems include: Anduril, bioinformatics and image analysis Apache Airavata, a general purpose workflow management system Apache Airflow, a general purpose workflow management system Apache Taverna, widely used in bioinformatics, astronomy, biodiversity BioBIKE, a cloud-based bioinformatics ... | Scientific workflow system | 0.807549 |
25,562 | The first EMACs with three metal atoms were synthesized in the early 1990s independently by the groups of Shie-Ming Peng (NTU) and F. Albert Cotton (Texas A&M), who coined the term extended metal atom chains. The cobalt-containing molecule Co3(dpa)4Cl2 (dpa = 2,2'-dipyridylamide) was synthesized by both research groups... | Extended metal atom chains | 0.807548 |
25,563 | In organometallic chemistry, extended metal atom chains (EMACs) are molecules that consist of a linear chain of directly bonded metal atoms, surrounded by organic ligands. These compounds represent the smallest molecular wires. Such species are researched for the bottom-up approach to nanoelectronics, although no appli... | Extended metal atom chains | 0.807548 |
25,564 | In statistics, the Behrens–Fisher problem, named after Walter-Ulrich Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on... | Behrens–Fisher problem | 0.807545 |
25,565 | Hunter was born in Mamaroneck, New York, and was educated at Williams College, the University of Chicago, and New York University, where he obtained his doctorate. He later became chairman of the biology department at his alma mater, De Witt Clinton High School, a public secondary school for boys in Manhattan. During h... | Civic Biology | 0.807544 |
25,566 | These efforts tried to incorporate progressive educational ideologies and apply the biological sciences to human society.Civic Biology was an example of the new approaches to scientific instruction emerging in the education sector. This modern education focused on applying scientific principles to human society by deve... | Civic Biology | 0.807544 |
25,567 | Charles Darwin had published his evolutionary theories 60 years before the public controversy over Civic Biology with the Scopes Trial. Prior to the Scopes Trial and controversy over Civic Biology, most science textbooks included Darwinian concepts in order to keep abreast with prevalent scientific ideas. In the early ... | Civic Biology | 0.807544 |
25,568 | The book did mention natural selection (page 383), homology (page 237), classification of plants and animals (Chapter XXI, pages 234–252) (including mention of "man" as a vertebrate, a mammal, and a primate, page 250), and had a short biography of Charles Darwin among the "Great Names in Biology" (pages 411–412).This n... | Civic Biology | 0.807544 |
25,569 | A Civic Biology: Presented in Problems (usually referred to as just Civic Biology) was a biology textbook written by George William Hunter, published in 1914. It is the book which the state of Tennessee required high school teachers to use in 1925 and is best known for its section about evolution that was ruled by a lo... | Civic Biology | 0.807544 |
25,570 | The content of Civic Biology was not specifically discussed in the trial; rather the trial focused on the merits and problems with Darwin's theory of evolution. The Scopes Trial used Civic Biology as a tool to have a publicized and public debate on whether evolution should continue to be taught. The prosecution argued ... | Civic Biology | 0.807544 |
25,571 | In the first edition of Civic Biology, Hunter briefly discusses eugenics on one page of the 432 page textbook. Along with many other evolutionary biologists, Hunter embraced the idea of eugenics as a social doctrine. It was a popular idea in the early 20th century, and several states had enacted laws to compel the sexu... | Civic Biology | 0.807544 |
25,572 | The defense crafted arguments that largely fit within a modernist ideology. They argued that evolution should be taught to high school students under the protection of freedom of speech. The defendants proposed a more liberal and innovative science curriculum be provided to students, one that keeps up with popular scie... | Civic Biology | 0.807544 |
25,573 | As a result, modern scholars now believe that overall, biology textbooks were not heavily influenced by anti-evolution rhetoric after the Scopes Trial.While biology textbooks did not yield heavy influence from the Scopes Trial, some laws emerged that affected high school teachers. After the Scopes Trial, many teachers,... | Civic Biology | 0.807544 |
25,574 | The Scopes Trial, with its controversy over Civic Biology, was a major setback for anti-evolution groups because of the 15 states with anti-evolution legislation pending in 1925, only 2 enacted laws restricting the teaching of Darwin's evolutionary theories. While this public controversy had some political implications... | Civic Biology | 0.807544 |
25,575 | Several socio-cultural events shaped the publication and reaction to Civic Biology. Following World War I, a cultural movement emerged that poised two ideological groups against each other: the traditionalists and the modernists. The modernists embraced intellectual experimentation by exploring new philosophies such as... | Civic Biology | 0.807544 |
25,576 | The coordination number 6 is typical for Sc(III). In the larger Y3+ and La3+ ions, coordination numbers of 8 and 9 are common. Scandium triflate is sometimes used as a Lewis acid catalyst in organic chemistry. | Scandium compounds | 0.807544 |
25,577 | Scandium compounds are compounds containing the element scandium. The chemistry of scandium is almost completely dominated by the trivalent ion, Sc3+, due to its electron configuration, 3d14s2. The radii of M3+ ions in the table below indicate that the chemical properties of scandium ions have more in common with yttr... | Scandium compounds | 0.807544 |
25,578 | The original "GCTA" software package is the most widely used; its primary functionality covers the GREML estimation of SNP heritability, but includes other functionality: Estimate the genetic relationship from genome-wide SNPs; Estimate the inbreeding coefficient from genome-wide SNPs; Estimate the variance explained b... | Genome-wide complex trait analysis | 0.807543 |
25,579 | Genome-wide complex trait analysis (GCTA) Genome-based restricted maximum likelihood (GREML) is a statistical method for heritability estimation in genetics, which quantifies the total additive contribution of a set of genetic variants to a trait. GCTA is typically applied to common single nucleotide polymorphisms (SNP... | Genome-wide complex trait analysis | 0.807543 |
25,580 | In this case, the GCTA estimate will additionally capture the contribution of any genetic variation correlated with the genetic relationship: either direct genetic effects or correlated environment. The presence of "indirect" genetic effects. When genetic variants present in the relatedness matrix are correlated with v... | Genome-wide complex trait analysis | 0.807543 |
25,581 | In humans, unlike the original animal/plant applications, relatedness is usually known with high confidence in the 'wild population', and the benefit of GCTA is connected more to avoiding assumptions of classic behavioral genetics designs and verifying their results, and partitioning heritability by SNP class and chrom... | Genome-wide complex trait analysis | 0.807543 |
25,582 | Estimation in biology/animal breeding using standard ANOVA/REML methods of variance components such as heritability, shared-environment, maternal effects etc. typically requires individuals of known relatedness such as parent/child; this is often unavailable or the pedigree data unreliable, leading to inability to appl... | Genome-wide complex trait analysis | 0.807543 |
25,583 | Need for raw data: GCTA requires genetic similarity of all subjects and thus their raw genetic information; due to privacy concerns, individual patient data is rarely shared. GCTA cannot be run on the summary statistics reported publicly by many GWAS projects, and if pooling multiple GCTA estimates, a meta-analysis mus... | Genome-wide complex trait analysis | 0.807543 |
25,584 | In quantum mechanics the expression ⟨φ|ψ⟩ is typically interpreted as the probability amplitude for the state ψ to collapse into the state φ. Mathematically, this means the coefficient for the projection of ψ onto φ. It is also described as the projection of state ψ onto state φ. | Ket vector | 0.807541 |
25,585 | Dynamics are also described by linear operators on the Hilbert space. For example, in the Schrödinger picture, there is a linear time evolution operator U with the property that if an electron is in state |ψ⟩ right now, at a later time it will be in the state U|ψ⟩, the same U for every possible |ψ⟩. Wave function norma... | Ket vector | 0.807541 |
25,586 | The mathematical structure of quantum mechanics is based in large part on linear algebra: Wave functions and other quantum states can be represented as vectors in a complex Hilbert space. (The exact structure of this Hilbert space depends on the situation.) In bra–ket notation, for example, an electron might be in the ... | Ket vector | 0.807541 |
25,587 | Bra–ket notation was designed to facilitate the formal manipulation of linear-algebraic expressions. Some of the properties that allow this manipulation are listed herein. In what follows, c1 and c2 denote arbitrary complex numbers, c* denotes the complex conjugate of c, A and B denote arbitrary linear operators, and t... | Ket vector | 0.807541 |
25,588 | A database clone is a complete and separate copy of a database system that includes the business data, the database management system software and any other application tiers that make up the environment. Cloning is a different kind of operation to replicate and backup, in that the cloned environment is both fully func... | Clone (computing) | 0.80754 |
25,589 | The first product in wide release by Inflection AI is a chatbot, Pi, named for “personal intelligence,” that is intended to function as an artificial intelligence-based personal assistant. Among the user experience goals that the company has stated for the Pi product are: providing an experience of emotional support fo... | Inflection AI | 0.807539 |
25,590 | Inflection AI, Inc. is a machine learning startup founded by entrepreneurs Reid Hoffman, Mustafa Suleyman and Karén Simonyan in 2022. The company is structured as a public benefit corporation and is headquartered in Palo Alto, California. | Inflection AI | 0.807539 |
25,591 | In contrast, the analytic approach is to define projective space based on linear algebra and utilizing homogeneous co-ordinates. The propositions of incidence are derived from the following basic result on vector spaces: given subspaces U and W of a (finite-dimensional) vector space V, the dimension of their intersecti... | Incidence (geometry) | 0.807536 |
25,592 | Historically, projective geometry was developed in order to make the propositions of incidence true without exceptions, such as those caused by the existence of parallels. From the point of view of synthetic geometry, projective geometry should be developed using such propositions as axioms. This is most significant fo... | Incidence (geometry) | 0.807536 |
25,593 | In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, P, and a line, l, sometimes denoted P I l. If P I l the pair (P, l)... | Incidence (geometry) | 0.807536 |
25,594 | Lines that meet at the same point are said to be concurrent. The set of all lines in a plane incident with the same point is called a pencil of lines centered at that point. The computation of the intersection of two lines shows that the entire pencil of lines centered at a point is determined by any two of the lines t... | Incidence (geometry) | 0.807536 |
25,595 | The European Society for Translational Medicine is a global non-profit and neutral healthcare organization whose principal objective is to enhance world-wide healthcare by using translational medicine approaches, resources and expertise.The society facilitates cooperation and interaction among clinicians, scientists, a... | Translational medicine | 0.807536 |
25,596 | For more general algebraic curves, lines could also be: i-secant lines, meeting the curve in i points counted without multiplicity, or asymptotes, which a curve approaches arbitrarily closely without touching it.With respect to triangles we have: the Euler line, the Simson lines, and central lines.For a convex quadrila... | Straight line | 0.807535 |
25,597 | In a sense, all lines in Euclidean geometry are equal, in that, without coordinates, one can not tell them apart from one another. However, lines may play special roles with respect to other objects in the geometry and be divided into types according to that relationship. For instance, with respect to a conic (a circle... | Straight line | 0.807535 |
25,598 | Descriptions of this type may be referred to, by some authors, as definitions in this informal style of presentation. These are not true definitions, and could not be used in formal proofs of statements. The "definition" of line in Euclid's Elements falls into this category. : 95 Even in the case where a specific geome... | Straight line | 0.807535 |
25,599 | The concept of line is often considered in geometry as a primitive notion in axiomatic systems,: 95 meaning it is not being defined by other concepts. In those situations where a line is a defined concept, as in coordinate geometry, some other fundamental ideas are taken as primitives. When the line concept is a primit... | Straight line | 0.807535 |
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