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7,500 | Among other things, Jordan defined a notion of isomorphism, although limited to the context of permutation groups. It was also Jordan who put the term group in wide use. An abstract notion of a (finite) group appeared for the first time in Arthur Cayley's 1854 paper On the theory of groups, as depending on the symbolic... | History of group theory | 0.822674 |
7,501 | He did not use primitive group but called equation primitive an equation whose Galois group is primitive. He discovered the notion of normal subgroups and found that a solvable primitive group may be identified to a subgroup of the affine group of an affine space over a finite field of prime order.Groups similar to Gal... | History of group theory | 0.822674 |
7,502 | To study the properties of these functions, he invented a Calcul des Combinaisons. The contemporary work of Alexandre-Théophile Vandermonde (1770) developed the theory of symmetric functions and solution of cyclotomic polynomials. Leopold Kronecker has been quoted as saying that a new boom in algebra began with Vanderm... | History of group theory | 0.822674 |
7,503 | Waring proved the fundamental theorem of symmetric polynomials, and specially considered the relation between the roots of a quartic equation and its resolvent cubic.Lagrange's goal (1770, 1771) was to understand why equations of third and fourth degree admit formulas for solutions, and a key object was the group of pe... | History of group theory | 0.822674 |
7,504 | In his investigations of composition of binary quadratic forms, Gauss explicitly stated the associative law for the composition of forms. In 1870, Leopold Kronecker gave a definition of an abelian group in the context of ideal class groups of a number field, generalizing Gauss's work. Ernst Kummer's attempts to prove F... | History of group theory | 0.822674 |
7,505 | The third root of group theory was number theory. Leonhard Euler considered algebraic operations on numbers modulo an integer—modular arithmetic—in his generalization of Fermat's little theorem. These investigations were taken much further by Carl Friedrich Gauss, who considered the structure of multiplicative groups o... | History of group theory | 0.822674 |
7,506 | Questions such as William Thurston's 1982 geometrization conjecture, inspired entirely new techniques in geometric group theory and low-dimensional topology, and was involved in the solution of one of the Millennium Prize Problems, the Poincaré conjecture. Continuous groups saw the solution of the problem of hearing th... | History of group theory | 0.822674 |
7,507 | The last twenty years of the 20th century enjoyed the successes of over one hundred years of study in group theory. In finite groups, post classification results included the O'Nan–Scott theorem, the Aschbacher classification, the classification of multiply transitive finite groups, the determination of the maximal sub... | History of group theory | 0.822674 |
7,508 | The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early res... | History of group theory | 0.822674 |
7,509 | The study was continued by Frank Nelson Cole (up to 660) and Burnside (up to 1092), and finally in an early "millennium project", up to 2001 by Miller and Ling in 1900. Continuous groups in the 1870-1900 period developed rapidly. Killing and Lie's foundational papers were published, Hilbert's theorem in invariant theor... | History of group theory | 0.822674 |
7,510 | The work on the Burnside problem increased interest in Lie algebras in exponent p, and the methods of Michel Lazard began to see a wider impact, especially in the study of p-groups. Continuous groups broadened considerably, with p-adic analytic questions becoming important. Many conjectures were made during this time, ... | History of group theory | 0.822674 |
7,511 | One had the influential idea of the Carter subgroup, and the subsequent creation of formation theory and the theory of classes of groups. One had the remarkable extensions of Clifford theory by Green to the indecomposable modules of group algebras. During this era, the field of computational group theory became a recog... | History of group theory | 0.822674 |
7,512 | Secondly, the systematic use of groups in geometry, mainly in the guise of symmetry groups, was initiated by Felix Klein's 1872 Erlangen program. The study of what are now called Lie groups started systematically in 1884 with Sophus Lie, followed by work of Wilhelm Killing, Eduard Study, Issai Schur, Ludwig Maurer, and... | History of group theory | 0.822674 |
7,513 | This period witnessed the birth of character theory by Frobenius, Burnside, and Schur which helped answer many of the 19th century questions in permutation groups, and opened the way to entirely new techniques in abstract finite groups. This period saw the work of Philip Hall: on a generalization of Sylow's theorem to ... | History of group theory | 0.822674 |
7,514 | Topological groups began to be studied as such. There were many great achievements in continuous groups: Cartan's classification of semisimple Lie algebras, Hermann Weyl's theory of representations of compact groups, Alfréd Haar's work in the locally compact case. Finite groups in the 1900-1940 grew immensely. | History of group theory | 0.822674 |
7,515 | In the period 1900–1940, infinite "discontinuous" (now called discrete groups) groups gained life of their own. Burnside's famous problem ushered in the study of arbitrary subgroups of finite-dimensional linear groups over arbitrary fields, and indeed arbitrary groups. Fundamental groups and reflection groups encourage... | History of group theory | 0.822674 |
7,516 | Sir Humphry Davy's work with electrolysis led to the conclusion that the production of electricity in simple electrolytic cells resulted from chemical action and that chemical combination occurred between substances of opposite charge. This work led directly to the isolation of metallic sodium and potassium by electrol... | Electrochemical reactions | 0.822672 |
7,517 | A concentration cell is an electrochemical cell where the two electrodes are the same material, the electrolytes on the two half-cells involve the same ions, but the electrolyte concentration differs between the two half-cells. An example is an electrochemical cell, where two copper electrodes are submerged in two copp... | Electrochemical reactions | 0.822672 |
7,518 | Many types of battery have been commercialized and represent an important practical application of electrochemistry. Early wet cells powered the first telegraph and telephone systems, and were the source of current for electroplating. The zinc-manganese dioxide dry cell was the first portable, non-spillable battery typ... | Electrochemical reactions | 0.822672 |
7,519 | Monte Carlo methods are used in various fields of computational biology, for example for Bayesian inference in phylogeny, or for studying biological systems such as genomes, proteins, or membranes. The systems can be studied in the coarse-grained or ab initio frameworks depending on the desired accuracy. Computer simul... | Monte Carlo Method | 0.82267 |
7,520 | The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from a ( v ) = b ( v ) = d ( v ) = 1 , and e... | Test theories of special relativity | 0.822666 |
7,521 | In molecular biology, quantitation of nucleic acids is commonly performed to determine the average concentrations of DNA or RNA present in a mixture, as well as their purity. Reactions that use nucleic acids often require particular amounts and purity for optimum performance. To date, there are two main approaches used... | Quantification of nucleic acids | 0.822649 |
7,522 | Funding from the Canada Foundation for Innovation (CFI) enabled TCAG to form by consolidating existing core facilities including the Medical Research Council of Canada Genome Resource Facility, the Canadian Genetic Diseases Network (CGDN) large insert clone core, the CGDN DNA Sequencing Core and the SickKids Biotechnol... | Centre for Applied Genomics | 0.822648 |
7,523 | High-level scientific oversight of TCAG's scientific mandate and operations is provided through an external scientific advisory board (SAB). The SAB members are: Edward M. Rubin (Chair), Metabiota Mark Blaxter, Tree of Life Programme, Wellcome Sanger Institute Elaine Mardis, Institute for Genomic Medicine, Nationwide C... | Centre for Applied Genomics | 0.822648 |
7,524 | As a Science and Technology Innovation Centre of Genome Canada, TCAG currently supports numerous large-scale projects, including research on autism spectrum disorders, structural variation of the human genome, integrative biology, conditional mouse mutagenesis, interactions of signaling molecules, type I diabetes, canc... | Centre for Applied Genomics | 0.822648 |
7,525 | The Genetic Analysis area includes capillary-based genotyping (Applied Biosystems TaqMan and SNaPshot, microsatellites), custom genotyping (e.g. heteroduplex analysis), mouse genotyping (for cross progeny and genetic linkage analysis), and methylation analysis (for epigenetics research). | Centre for Applied Genomics | 0.822648 |
7,526 | The Centre for Applied Genomics is a genome centre in the Research Institute of The Hospital for Sick Children, and is affiliated with the University of Toronto. TCAG also operates as a Science and Technology Innovation Centre of Genome Canada, with an emphasis on next-generation sequencing (NGS) and bioinformatics sup... | Centre for Applied Genomics | 0.822648 |
7,527 | The Bioinformatics team assists with data handling and analysis, and develops new algorithms and analytical methods, with a focus on the analysis of high-throughput ("next-generation") sequencing data. The Statistical Analysis group provides project consultation and power analysis, statistical analysis (genetic, microa... | Centre for Applied Genomics | 0.822648 |
7,528 | The facility uses conventional capillary Sanger sequencing on Applied Biosystems 3730xl instruments, governed by a Laboratory Information Management System (LIMS). Additionally, next-generation sequencing (NGS) using Illumina HiSeq 2500 and HiScan SQ instruments, Life Technologies Ion Proton and Applied Biosystems SOLi... | Centre for Applied Genomics | 0.822648 |
7,529 | Current research at TCAG centres around large-scale projects performed by facility personnel, including support of Genome Canada projects, and a significant focus on the genetics of autism spectrum disorders and structural variation of the human genome. Service work is also performed for over 600 other academic, privat... | Centre for Applied Genomics | 0.822648 |
7,530 | In mechanical engineering, limits and fits are a set of rules regarding the dimensions and tolerances of mating machined parts if they are to achieve the desired ease of assembly, and security after assembly - sliding fit, interference fit, rotating fit, non-sliding fit, loose fit, etc. Tolerances are typically specifi... | Limits and fits | 0.822642 |
7,531 | It is zero if these distances do not change, as happens when all particles in some region are moving with the same velocity (same speed and direction) and/or rotating with the same angular velocity, as if that part of the medium were a rigid body. The strain rate is a concept of materials science and continuum mechanic... | Strain rate | 0.822637 |
7,532 | In mechanics and materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1 (or its multiples). The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material... | Strain rate | 0.822637 |
7,533 | The definition of strain rate was first introduced in 1867 by American metallurgist Jade LeCocq, who defined it as "the rate at which strain occurs. It is the time rate of change of strain." In physics the strain rate is generally defined as the derivative of the strain with respect to time. | Strain rate | 0.822637 |
7,534 | In 1905, Austrian physicist Ludwig Boltzmann pointed out that with reduction of a body into infinitesimally smaller volume elements, the inner reactions have to meet all static conditions for mechanical equilibrium. Cauchy's stress theorem handles the equilibrium in terms of force. For the analogous statement in terms ... | Balance of angular momentum | 0.822626 |
7,535 | The balance of angular momentum or Euler's second law in classical mechanics is a law of physics, stating that to alter the angular momentum of a body a torque must be applied to it. An example of use is the playground merry-go-round in the picture. To put it in rotation it must be pushed. Technically one summons a tor... | Balance of angular momentum | 0.822626 |
7,536 | With a rigid body this is expressed by the moment of inertia. With a rotation around a fixed axis, the torque is proportional to the angular acceleration with the moment of inertia as proportionality factor. Here it is to be noted that the moment of inertia is not only dependent on the position of the axis of rotation ... | Balance of angular momentum | 0.822626 |
7,537 | Pattern blocks consist of various wooden shapes (green triangles, red trapezoids, yellow hexagons, orange squares, tan (long) rhombi, and blue (wide) rhombi) that are sized in such a way that students will be able to see relationships among shapes. For example, three green triangles make a red trapezoid; two red trapez... | Mathematical manipulative | 0.822623 |
7,538 | Soil mapping is the identification, description, ad delineation on a map of different types of soil based on direct field observations or on indirect inferences from souch sources such as aerial photographs. Soil maps can depict soil properties and functions in the context of specific soil functions such as agricultura... | Soil functions | 0.822623 |
7,539 | In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.Correspondence theories claim that true beliefs and true statements corr... | Correspondence theory of truth | 0.82262 |
7,540 | In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries ... | Constant-energy surface | 0.822602 |
7,541 | The European Bioinformatics Institute (EMBL-EBI) is an intergovernmental organization (IGO) which, as part of the European Molecular Biology Laboratory (EMBL) family, focuses on research and services in bioinformatics. It is located on the Wellcome Genome Campus in Hinxton near Cambridge, and employs over 600 full-time... | European Bioinformatics Institute | 0.822602 |
7,542 | A division ring is a generalization of field. Division rings are not assumed to be commutative. There are no non-commutative finite division rings: Wedderburn's little theorem states that all finite division rings are commutative, and hence are finite fields. This result holds even if we relax the associativity axiom t... | Finite fields | 0.822589 |
7,543 | Using optogenetics, a team of RIKEN-MIT scientists caused the mice to incorrectly associate a benign environment with a prior unpleasant experience from different surroundings. Some scientists believe that the study may have implications in studying false memory formation in humans, and in treating PTSD and schizophren... | Human memory | 0.822587 |
7,544 | Study of the genetics of human memory is in its infancy though many genes have been investigated for their association to memory in humans and non-human animals. A notable initial success was the association of APOE with memory dysfunction in Alzheimer's disease. The search for genes associated with normally varying me... | Human memory | 0.822587 |
7,545 | Younger infants (6-month-olds) can only recall one step of a two-step sequence. Researchers have suggested that these age differences are probably due to the fact that the dentate gyrus of the hippocampus and the frontal components of the neural network are not fully developed at the age of 6-months.In fact, the term '... | Human memory | 0.822587 |
7,546 | One question that is crucial in cognitive neuroscience is how information and mental experiences are coded and represented in the brain. Scientists have gained much knowledge about the neuronal codes from the studies of plasticity, but most of such research has been focused on simple learning in simple neuronal circuit... | Human memory | 0.822587 |
7,547 | These alterations in methylation pattern occurred at many genes that were down-regulated, often due to the formation of new 5-methylcytosine sites in CpG rich regions of the genome. Furthermore, many other genes were upregulated, likely often due to hypomethylation. Hypomethylation often results from the removal of met... | Human memory | 0.822587 |
7,548 | Programmers can then arrange the access patterns of their code so that no two pages with the same virtual color are in use at the same time. There is a wide literature on such optimizations (e.g. loop nest optimization), largely coming from the High Performance Computing (HPC) community. The snag is that while all the ... | CPU Cache | 0.822578 |
7,549 | Microarrays can be fabricated using a variety of technologies, including printing with fine-pointed pins onto glass slides, photolithography using pre-made masks, photolithography using dynamic micromirror devices, ink-jet printing, or electrochemistry on microelectrode arrays. In spotted microarrays, the probes are ol... | DNA microarrays | 0.822577 |
7,550 | Microarray data is difficult to exchange due to the lack of standardization in platform fabrication, assay protocols, and analysis methods. This presents an interoperability problem in bioinformatics. Various grass-roots open-source projects are trying to ease the exchange and analysis of data produced with non-proprie... | DNA microarrays | 0.822577 |
7,551 | A statistical ensemble in quantum mechanics (also known as a mixed state) is most often represented by a density matrix, denoted by ρ ^ {\displaystyle {\hat {\rho }}} . The density matrix provides a fully general tool that can incorporate both quantum uncertainties (present even if the state of the system were complete... | Statistical ensemble | 0.822574 |
7,552 | Each one of these values is a 0 (or no) or a 1 (yes). Assume the following time average exists: σ ( E ) = lim N → ∞ 1 N ∑ k = 1 N Meas ( E , X k ) {\displaystyle \sigma (E)=\lim _{N\rightarrow \infty }{\frac {1}{N}}\sum _{k=1}^{N}\operatorname {Meas} (E,X_{k})} For quantum mechanical systems, an important assumption ... | Statistical ensemble | 0.822574 |
7,553 | Suppose we have a preparation procedure for a system in a physics lab: For example, the procedure might involve a physical apparatus and some protocols for manipulating the apparatus. As a result of this preparation procedure, some system is produced and maintained in isolation for some small period of time. By repeati... | Statistical ensemble | 0.822574 |
7,554 | The word "ensemble" is also used for a smaller set of possibilities sampled from the full set of possible states. For example, a collection of walkers in a Markov chain Monte Carlo iteration is called an ensemble in some of the literature. The term "ensemble" is often used in physics and the physics-influenced literatu... | Statistical ensemble | 0.822574 |
7,555 | There is a class of Azumaya algebras called cyclic algebras which generate all similarity classes of Azumaya algebras over a field K {\displaystyle K} , hence all elements in the Brauer group Br ( K ) {\displaystyle {\text{Br}}(K)} (defined below). Given a finite cyclic Galois field extension L / K {\displaystyle L/K} ... | Azumaya algebra | 0.822567 |
7,556 | There have been significant applications of Azumaya algebras in diophantine geometry, following work of Yuri Manin. The Manin obstruction to the Hasse principle is defined using the Brauer group of schemes. | Azumaya algebra | 0.822567 |
7,557 | Given a local commutative ring ( R , m ) {\displaystyle (R,{\mathfrak {m}})} , an R {\displaystyle R} -algebra A {\displaystyle A} is Azumaya if and only if A is free of positive finite rank as an R-module, and the algebra A ⊗ R ( R / m ) {\displaystyle A\otimes _{R}(R/{\mathfrak {m}})} is a central simple algebra over... | Azumaya algebra | 0.822567 |
7,558 | Recall there is the Kummer sequence 1 → μ n → G m → ⋅ n G m → 1 {\displaystyle 1\to \mu _{n}\to \mathbb {G} _{m}\xrightarrow {\cdot n} \mathbb {G} _{m}\to 1} giving a long exact sequence in cohomology for a field F {\displaystyle F} . Since Hilbert's Theorem 90 implies H 1 ( F , G m ) = 0 {\displaystyle H^{1}(F,\mathbb... | Azumaya algebra | 0.822567 |
7,559 | Over fields, there is a cohomological classification of Azumaya algebras using Étale cohomology. In fact, this group, called the Brauer group, can be also defined as the similarity classes: 3 of Azumaya algebras over a ring R {\displaystyle R} , where rings A , A ′ {\displaystyle A,A'} are similar if there is an isomor... | Azumaya algebra | 0.822567 |
7,560 | Over a field k {\displaystyle k} , Azumaya algebras are completely classified by the Artin-Wedderburn theorem since they are the same as central simple algebras. These are algebras isomorphic to the matrix ring M n ( D ) {\displaystyle M_{n}(D)} for some division algebra D {\displaystyle D} over k {\displaystyle k} who... | Azumaya algebra | 0.822567 |
7,561 | This is important because it directly relates to the cohomological classification of similarity classes of Azumaya algebras over a scheme. In particular, it implies an Azumaya algebra has structure group PGL n {\displaystyle {\text{PGL}}_{n}} for some n {\displaystyle n} , and the Čech cohomology group H ˇ 1 ( ( X ) e ... | Azumaya algebra | 0.822567 |
7,562 | One of the important structure results about Azumaya algebras is the Skolem-Noether theorem: given a local commutative ring R {\displaystyle R} and an Azumaya algebra R → A {\displaystyle R\to A} , the only automorphisms of A {\displaystyle A} are inner. Meaning, the following map is surjective: { A ∗ → Aut ( A ) a ↦ (... | Azumaya algebra | 0.822567 |
7,563 | An Azumaya algebraover a commutative ring R {\displaystyle R} is an R {\displaystyle R} -algebra A {\displaystyle A} obeying any of the following equivalent conditions: There exists an R {\displaystyle R} -algebra B {\displaystyle B} such that the tensor product of R {\displaystyle R} -algebras B ⊗ R A {\displaystyle B... | Azumaya algebra | 0.822567 |
7,564 | The Brauer group B ( X ) {\displaystyle B(X)} of X (an analogue of the Brauer group of a field) is the set of equivalence classes of Azumaya algebras. The group operation is given by tensor product, and the inverse is given by the opposite algebra. Note that this is distinct from the cohomological Brauer group which is... | Azumaya algebra | 0.822567 |
7,565 | The construction of a quaternion algebra over a field can be globalized to Spec ( Z ) {\displaystyle {\text{Spec}}(\mathbb {Z} )} by considering the noncommutative Z {\displaystyle \mathbb {Z} } -algebra A a , b = Z ⟨ i , j , k ⟩ i 2 − a , j 2 − b , i j − k , j i + k {\displaystyle A_{a,b}={\frac {\mathbb {Z} \langl... | Azumaya algebra | 0.822567 |
7,566 | Over P k n {\displaystyle \mathbb {P} _{k}^{n}} Azumaya algebras can be constructed as E n d k ( E ) ⊗ k A {\displaystyle {\mathcal {End}}_{k}({\mathcal {E}})\otimes _{k}A} for an Azumaya algebra A {\displaystyle A} over a field k {\displaystyle k} . For example, the endomorphism sheaf of O ( a ) ⊕ O ( b ) {\displaysty... | Azumaya algebra | 0.822567 |
7,567 | Milne, John. Etale cohomology. Ch IV Knus, Max-Albert; Ojanguren, Manuel (1974), Théorie de la descente et algèbres d'Azumaya, Lecture Notes in Mathematics, vol. 389, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0057799, MR 0417149, Zbl 0284.13002 Mathoverflow Thread on "Explicit examples of Azumaya algebras" | Azumaya algebra | 0.822567 |
7,568 | Knus, Max-Albert (1991), Quadratic and Hermitian forms over rings, Grundlehren der Mathematischen Wissenschaften, vol. 294, Berlin etc.: Springer-Verlag, ISBN 3-540-52117-8, Zbl 0756.11008 Saltman, David J. (1999). Lectures on division algebras. | Azumaya algebra | 0.822567 |
7,569 | In mathematics, an Azumaya algebra is a generalization of central simple algebras to R-algebras where R need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where R is a commutative local ring. The notion was developed further in ring theory, and in algebraic geometry, where A... | Azumaya algebra | 0.822567 |
7,570 | Dynamic programming is both a mathematical optimization method and a computer programming method. It refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do... | Constraint solver | 0.822566 |
7,571 | Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. C... | Constraint solver | 0.822566 |
7,572 | A constraint optimization problem (COP) is a constraint satisfaction problem associated to an objective function. An optimal solution to a minimization (maximization) COP is a solution that minimizes (maximizes) the value of the objective function. During the search of the solutions of a COP, a user can wish for: findi... | Constraint solver | 0.822566 |
7,573 | Introduce unit vectors ı ^ , ȷ ^ , k ^ {\displaystyle {\hat {\boldsymbol {\imath }}},\ {\hat {\boldsymbol {\jmath }}},\ {\hat {\boldsymbol {k}}}} , now representing standard unit basis vectors in the general rotating frame. As they rotate they will remain normalized and perpendicular to each other. If they rotate at th... | Rotating reference frame | 0.82255 |
7,574 | Several software projects intentionally violate this portion of the C99 standard. For example, Python 2.x did so to implement reference counting, and required changes to the basic object structs in Python 3 to enable this optimization. The Linux kernel does this because strict aliasing causes problems with optimization... | Pointer aliasing | 0.82255 |
7,575 | To enable such optimizations in a predictable manner, the ISO standard for the C programming language (including its newer C99 edition, see section 6.5, paragraph 7) specifies that it is illegal (with some exceptions) to access the same memory location using pointers of different types. A compiler may therefore assume ... | Pointer aliasing | 0.82255 |
7,576 | Then, if the answer is no, x = 5 can be propagated safely. Another optimization impacted by aliasing is code reordering. If the compiler decides that x is not aliased by *y, then code that uses or changes the value of x can be moved before the assignment *y = 10, if this would improve scheduling or enable more loop opt... | Pointer aliasing | 0.82255 |
7,577 | Optimizers often have to make conservative assumptions about variables when aliasing is possible. For example, knowing the value of a variable (such as x is 5) normally allows certain optimizations (such as constant propagation). However, the compiler cannot use this information after an assignment to another variable ... | Pointer aliasing | 0.82255 |
7,578 | Or, a prediction that cybersecurity will become a major issue may cause organizations to implement more security cybersecurity measures, thus limiting the issue. In politics it is common to attempt to predict the outcome of elections via political forecasting techniques (or assess the popularity of politicians) through... | Scientific prediction | 0.822544 |
7,579 | Mathematical equations and models, and computer models, are frequently used to describe the past and future behaviour of a process within the boundaries of that model. In some cases the probability of an outcome, rather than a specific outcome, can be predicted, for example in much of quantum physics. In microprocessor... | Scientific prediction | 0.822544 |
7,580 | One of the earliest comprehensive physics textbooks to incorporate PER findings was written by Serway and Beichner. Apart from textbooks, instructional material for pre-college physics students now include PhET (Physics Education Technology) simulations. This is made possible through advances in personal computer hardw... | Physics education research | 0.822541 |
7,581 | Notable textbooks include Tutorials in Physics, Physics by Inquiry, Investigative Science Learning Environment, and Paradigms in Physics, as well as many new textbooks in introductory and junior level coursework. The Kansas State University Physics Education Research Group has developed a program, Visual Quantum Mechan... | Physics education research | 0.822541 |
7,582 | Technology: Student response systems (clickers) are based on Eric Mazur's work in Peer Instruction. Research in PER examines the influence, applications of, and possibilities for technology in the classroom. Instructional interventions: PER's curriculum design is based on more than two decades of research in physics ed... | Physics education research | 0.822541 |
7,583 | Student attitudes are often found to decline after traditional instruction, but recent work by Redish and Hammer show that this can be reversed and positive attitudinal gains can be seen if attention is paid to "explicate the epistemological elements of the implicit curriculum." Social aspects: Research has been conduc... | Physics education research | 0.822541 |
7,584 | Recently, a paper was published in PRL Special Section: PER that identified over 30 behaviors, attitudes, and skills that are used in the solving of a typical physics problem. Greater resolution and specific attention to the details are used in the field of problem solving. Attitudes: The University of Colorado develop... | Physics education research | 0.822541 |
7,585 | Problem solving: It plays an important role in the processes that advance physics research, featured in high numbers of exercises in conventional textbooks. Most research in this area rests on examining the difference between novice and expert problem solvers (freshmen and sophomores, and graduate-level and postdoctora... | Physics education research | 0.822541 |
7,586 | Theories on cognition in physics learning were put forward by Redish, Hammer, Elby and Scherr, who built off of diSessa's "Knowledge in Pieces". The Resources Framework, developed from this work, builds off of research in neuroscience, sociology, linguistics, education and psychology. Additional frameworks are forthcom... | Physics education research | 0.822541 |
7,587 | The broad goal of the PER community is to understand the processes involved in the teaching and learning of physics through rigorous scientific investigation. According to the University of Washington PER group, one of the pioneers in the field, work within PER tends to fall within one or more of several broad descript... | Physics education research | 0.822541 |
7,588 | Physics education research (PER) is a form of discipline-based education research specifically related to the study of the teaching and learning of physics, often with the aim of improving the effectiveness of student learning. PER draws from other disciplines, such as sociology, cognitive science, education and lingui... | Physics education research | 0.822541 |
7,589 | The audience for Physics Education Research Conference Proceedings (PERC) is designed for a mix of consumers and researchers. The latter provides a snapshot of the field and as such is open to preliminary results and research in progress, as well as papers that would simply be thought-provoking to the PER community. Ot... | Physics education research | 0.822541 |
7,590 | Physics education research papers in the United States are primarily issued among four publishing venues. Papers submitted to the American Journal of Physics: Physics Education Research Section (PERS) are mostly to consumers of physics education research. The Journal of the Learning Sciences (JLS) publishes papers that... | Physics education research | 0.822541 |
7,591 | Newton's laws of motion about interactions between forces and objects are central to the study of mechanics. Many students hold the Aristotelian misconception that a net force is required to keep a body moving; instead, motion is modeled in modern physics with Newton's first law of inertia, stating that a body will kee... | Physics education research | 0.822541 |
7,592 | One primary goal of PER is to develop pedagogical techniques and strategies that will help students learn physics more effectively and help instructors to implement these techniques. Because even basic ideas in physics can be confusing, together with the possibility of scientific misconceptions formed from teaching thr... | Physics education research | 0.822541 |
7,593 | In microbiology, serologic tests are used to determine if a person has antibodies against a specific pathogen, or to detect antigens associated with a pathogen in a person's sample. Serologic tests are especially useful for organisms that are difficult to culture by routine laboratory methods, like Treponema pallidum (... | Serology | 0.82254 |
7,594 | Two random variables X and Y are equal almost surely (denoted X = a.s. Y {\displaystyle X\;{\stackrel {\text{a.s. }}{=}}\;Y} ) if, and only if, the probability that they are different is zero: P ( X ≠ Y ) = 0. {\displaystyle \operatorname {P} (X\neq Y)=0.} For all practical purposes in probability theory, this notion... | Discrete Random Variable | 0.822536 |
7,595 | Thus one can consider random elements of other sets E {\displaystyle E} , such as random boolean values, categorical values, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, and functions. One may then specifically refer to a random variable of type E {\displaystyle E} , or an E {\displays... | Discrete Random Variable | 0.822536 |
7,596 | The term "random variable" in statistics is traditionally limited to the real-valued case ( E = R {\displaystyle E=\mathbb {R} } ). In this case, the structure of the real numbers makes it possible to define quantities such as the expected value and variance of a random variable, its cumulative distribution function, a... | Discrete Random Variable | 0.822536 |
7,597 | If there is no invertibility of g {\displaystyle g} but each y {\displaystyle y} admits at most a countable number of roots (i.e., a finite, or countably infinite, number of x i {\displaystyle x_{i}} such that y = g ( x i ) {\displaystyle y=g(x_{i})} ) then the previous relation between the probability density function... | Discrete Random Variable | 0.822536 |
7,598 | Another criticism was formulated by American physicist Herbert Ives in 1952 and the Israeli physicist Max Jammer in 1961, asserting that Einstein's derivation is based on begging the question. Other scholars, such as American and Chilean philosophers John Stachel and Roberto Torretti, have argued that Ives' criticism w... | E = mc2 | 0.822532 |
7,599 | Physics has two concepts of mass, the gravitational mass and the inertial mass. The gravitational mass is the quantity that determines the strength of the gravitational field generated by an object, as well as the gravitational force acting on the object when it is immersed in a gravitational field produced by other bo... | E = mc2 | 0.822532 |
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