id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
32,600 | Note the previous construction can be proven in algebraic geometry using the affine cone of a projective variety X {\displaystyle X} using Local cohomology. | Local homology | 0.803825 |
32,601 | NTL is a C++ library for doing number theory. NTL supports arbitrary length integer and arbitrary precision floating point arithmetic, finite fields, vectors, matrices, polynomials, lattice basis reduction and basic linear algebra. NTL is free software released under the GNU Lesser General Public License v2.1. | Number Theory Library | 0.803824 |
32,602 | In Africa, Kenya leads the AF-HOU part of the program, and they have even begun a new project at a high school in Nairobi. This project is focused on astronomy and astrophysics and it aims to teach students how scientific research works. In Europe, Dr. Ferlet and Dr. A.-L. | Hands-on universe | 0.803824 |
32,603 | An Fσ-set in a collectionwise normal space is also collectionwise normal in the subspace topology. In particular, this holds for closed subsets. The Moore metrization theorem states that a collectionwise normal Moore space is metrizable. | Collectionwise normal space | 0.803823 |
32,604 | A collectionwise normal space is collectionwise Hausdorff. A collectionwise normal space is normal. A Hausdorff paracompact space is collectionwise normal.Note: The Hausdorff condition is necessary here, since for example an infinite set with the cofinite topology is compact, hence paracompact, and T1, but is not even ... | Collectionwise normal space | 0.803823 |
32,605 | In mathematics, a topological space X {\displaystyle X} is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X {\displaystyle X} there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. Here a family F {\displaystyle {\mathcal {F}}} of subsets of X {\di... | Collectionwise normal space | 0.803823 |
32,606 | A path in Γ e ( V ) {\displaystyle \textstyle \Gamma _{\mathrm {e} }(V)} or Γ f ( V ) {\displaystyle \textstyle \Gamma _{\mathrm {f} }(V)} associated with such a path is also said to be periodic, with the same period matrix. The generalized Lagrange theorem states that for an irrational simplicial cone C ⊆ R n {\displa... | Klein polyhedron | 0.803823 |
32,607 | Lagrange proved that for an irrational real number α {\displaystyle \textstyle \alpha } , the continued-fraction expansion of α {\displaystyle \textstyle \alpha } is periodic if and only if α {\displaystyle \textstyle \alpha } is a quadratic irrational. Klein polyhedra allow us to generalize this result. Let K ⊆ R {\di... | Klein polyhedron | 0.803823 |
32,608 | In the geometry of numbers, the Klein polyhedron, named after Felix Klein, is used to generalize the concept of continued fractions to higher dimensions. | Klein polyhedron | 0.803823 |
32,609 | However, in some cases a compiler optimization is possible, namely performing escape analysis and proving that escape is not possible, and thus the object can be allocated on the stack; this is significant in Java. In this case object destruction will occur promptly – possibly even during the variable's lifetime (befor... | Object creation | 0.803821 |
32,610 | There are several methods for reverse engineering gene regulatory networks by using molecular biology and data science methods. They have been generally divided into six classes: Coexpression methods are based on the notion that if two genes exhibit a similar expression profile, they may be related although no causatio... | Reverse Engineering | 0.80382 |
32,611 | Reverse engineering concepts have been applied to biology as well, specifically to the task of understanding the structure and function of gene regulatory networks. They regulate almost every aspect of biological behavior and allow cells to carry out physiological processes and responses to perturbations. Understanding... | Reverse Engineering | 0.80382 |
32,612 | Modeling refers to the practice of combining the gathered information into an abstract model, which can be used as a guide for designing the new object or system. Review refers to the testing of the model to ensure the validity of the chosen abstract. Reverse engineering is applicable in the fields of computer engineer... | Reverse Engineering | 0.80382 |
32,613 | Nimonic 105 was used on the Rolls-Royce Spey. Nimonic 263 was used in the combustion chambers of the Bristol Olympus used on the Concorde supersonic airliner. 3D printed thermoplastic resin to create wind turbine blades is in development in a partnership between ORNL, NREL, and GE Renewable Energy. | Turbine blades | 0.80382 |
32,614 | The HLA Informatics Group (HIG) is a research group led by Professor Steven Marsh at the Anthony Nolan Research Institute that develops, runs and maintains the IMGT (immunogenetics)/HLA (Human leukocyte antigen) Database and the IPD (immuno polymorphism database). The IMGT/HLA database originated as part of IMGT and wa... | HLA Informatics Group | 0.803818 |
32,615 | The older usage is now rarely seen. Early editions of Silvanus P. Thompson's Calculus Made Easy use the older term. In his 1998 update of this text, Martin Gardner lets the first use of "differential coefficient" stand, along with Thompson's criticism of the term as a needlessly obscure phrase that should not intimidat... | Differential coefficient | 0.803816 |
32,616 | In physics, the differential coefficient of a function f(x) is what is now called its derivative df(x)/dx, the (not necessarily constant) multiplicative factor or coefficient of the differential dx in the differential df(x). A coefficient is usually a constant quantity, but the differential coefficient of f is a consta... | Differential coefficient | 0.803816 |
32,617 | Similar to other ion channels, MscLs are organized as symmetric oligomers with the permeation pathway formed by the packing of subunits around the axis of rotational symmetry. Unlike MscS, which is heptameric, MscL is likely pentameric; although the Sa-MscL appears to be a tetramer in a crystal structure, this may be a... | Large-conductance mechanosensitive channel | 0.803812 |
32,618 | During the conference on Neutron Physics by Time-of-Flight, held at Gatlinburg, Tennessee, November 1 and 2, 1956, Wigner delivered a presentation on the theoretical arrangement of neighboring neutron resonances (with matching spin and parity) in heavy nuclei. In the presentation he gave the following guess:Perhaps I a... | Wigner surmise | 0.803811 |
32,619 | In mathematical physics, the Wigner surmise is a statement about the probability distribution of the spaces between points in the spectra of nuclei of heavy atoms, which have many degrees of freedom, or quantum systems with few degrees of freedom but chaotic classical dynamics. It was proposed by Eugene Wigner in proba... | Wigner surmise | 0.803811 |
32,620 | In an order complete vector lattice X {\displaystyle X} whose order is regular, X {\displaystyle X} is of minimal type if and only if every order convergent filter in X {\displaystyle X} converges when X {\displaystyle X} is endowed with the order topology. | Order convergence | 0.80381 |
32,621 | In mathematics, specifically in order theory and functional analysis, a filter F {\displaystyle {\mathcal {F}}} in an order complete vector lattice X {\displaystyle X} is order convergent if it contains an order bounded subset (that is, is contained in an interval of the form := { x ∈ X: a ≤ x and x ≤ b } {\displaysty... | Order convergence | 0.80381 |
32,622 | He said the long-term goal is to achieve "symbiosis with artificial intelligence", which he perceives as an existential threat to humanity if it goes unchecked. He believes the device will be "something analogous to a video game, like a saved game situation, where you are able to resume and upload your last state" and ... | Neuralink | 0.803807 |
32,623 | Neuralink was founded in 2016 by Elon Musk and a founding team of seven scientists and engineers. The group of initial hires consisted of experts in areas such as neuroscience, biochemistry and robotics. The trademark "Neuralink" was purchased from its previous owners in January 2017.In April 2017, Neuralink announced ... | Neuralink | 0.803807 |
32,624 | The growing acceptance of design-based research methodology as a means for study is often viewed as a significant factor that distinguishes LS from many of the fields that contribute to it. By including design-based research within its methodological toolkit, learning sciences qualifies as a "design science", sharing c... | Learning Sciences | 0.803803 |
32,625 | Learning sciences (LS) is an interdisciplinary field that works to further scientific, humanistic, and critical theoretical understanding of learning as well as to engage in the design and implementation of learning innovations, and the improvement of instructional methodologies. LS research traditionally focuses on co... | Learning Sciences | 0.803803 |
32,626 | A marginal likelihood is a likelihood function that has been integrated over the parameter space. In Bayesian statistics, it represents the probability of generating the observed sample from a prior and is therefore often referred to as model evidence or simply evidence. | Marginal likelihood | 0.803803 |
32,627 | Plasma Physics and Controlled Fusion is a monthly peer-reviewed scientific journal covering plasma physics. It is published by the Institute of Physics and the editor-in-chief is R.O. Dendy (Euratom/UKAEA Fusion Association). The journal was established in 1960 as Plasma Physics, obtaining its current title in 1984. | Plasma Physics and Controlled Fusion | 0.803802 |
32,628 | The back end is responsible for the CPU architecture specific optimizations and for code generation. The main phases of the back end include the following: Machine dependent optimizations: optimizations that depend on the details of the CPU architecture that the compiler targets. A prominent example is peephole optimiz... | Semantic analysis (computer science) | 0.803801 |
32,629 | It can be difficult to count exactly how many passes an optimizing compiler makes. For instance, different phases of optimization may analyse one expression many times but only analyse another expression once. Splitting a compiler up into small programs is a technique used by researchers interested in producing provabl... | Semantic analysis (computer science) | 0.803801 |
32,630 | In this case, the first pass needs to gather information about declarations appearing after statements that they affect, with the actual translation happening during a subsequent pass. The disadvantage of compiling in a single pass is that it is not possible to perform many of the sophisticated optimizations needed to ... | Semantic analysis (computer science) | 0.803801 |
32,631 | The back end generates the target-dependent assembly code, performing register allocation in the process. The back end performs instruction scheduling, which re-orders instructions to keep parallel execution units busy by filling delay slots. Although most optimization problems are NP-hard, heuristic techniques for sol... | Semantic analysis (computer science) | 0.803801 |
32,632 | Examples of middle end optimizations are removal of useless (dead-code elimination) or unreachable code (reachability analysis), discovery and propagation of constant values (constant propagation), relocation of computation to a less frequently executed place (e.g., out of a loop), or specialization of computation base... | Semantic analysis (computer science) | 0.803801 |
32,633 | This IR is usually a lower-level representation of the program with respect to the source code. The middle end performs optimizations on the IR that are independent of the CPU architecture being targeted. This source code/machine code independence is intended to enable generic optimizations to be shared between version... | Semantic analysis (computer science) | 0.803801 |
32,634 | In physics, an atomic mirror is a device which reflects neutral atoms in a way similar to the way a conventional mirror reflects visible light. Atomic mirrors can be made of electric fields or magnetic fields, electromagnetic waves or just silicon wafer; in the last case, atoms are reflected by the attracting tails of ... | Atomic mirror | 0.8038 |
32,635 | Some programming languages support array programming, where operations and functions defined for certain data types are implicitly extended to arrays of elements of those types. Thus one can write A+B to add corresponding elements of two arrays A and B. Usually these languages provide both the element-by-element multip... | Multidimensional array | 0.803797 |
32,636 | Vorlesungen über Zahlentheorie (German for Lectures on Number Theory) is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund Landau, and Helmut Hasse. They all... | Vorlesungen über Zahlentheorie | 0.803795 |
32,637 | Helmut Hasse's book Vorlesungen über Zahlentheorie was published in 1950, and is different from and more elementary than his book Zahlentheorie. It covers elementary number theory, Dirichlet's theorem, and quadratic fields. | Vorlesungen über Zahlentheorie | 0.803795 |
32,638 | Volume 1 on elementary and additive number theory includes the topics such as Dirichlet's theorem, Brun's sieve, binary quadratic forms, Goldbach's conjecture, Waring's problem, and the Hardy–Littlewood work on the singular series. Volume 2 covers topics in analytic number theory, such as estimates for the error in the... | Vorlesungen über Zahlentheorie | 0.803795 |
32,639 | Edmund Landau's book Vorlesungen über Zahlentheorie was first published as a 3-volume set in 1927. The first half of volume 1 was published as Vorlesungen über Zahlentheorie. Aus der elementare Zahlentheorie in 1950, with an English translation in 1958 under the title Elementary number theory. In 1969 Chelsea republish... | Vorlesungen über Zahlentheorie | 0.803795 |
32,640 | Based on Dirichlet's number theory course at the University of Göttingen, the Vorlesungen were edited by Dedekind and published after Lejeune Dirichlet's death. Dedekind added several appendices to the Vorlesungen, in which he collected further results of Lejeune Dirichlet's and also developed his own original mathemat... | Vorlesungen über Zahlentheorie | 0.803795 |
32,641 | The German titles of supplements X and XI are: Supplement X: Über die Composition der binären quadratische Formen (On the composition of binary quadratic forms) Supplement XI: Über die Theorie der ganzen algebraischen Zahlen (On the theory of algebraic integers)Chapters 1 to 4 cover similar ground to Gauss' Disquisitio... | Vorlesungen über Zahlentheorie | 0.803795 |
32,642 | Some theorems from the theory of circle division Supplement VIII. On the Pell equation Supplement IX. Convergence and continuity of some infinite seriesThis translation does not include Dedekind's Supplements X and XI in which he begins to develop the theory of ideals. | Vorlesungen über Zahlentheorie | 0.803795 |
32,643 | A geometric theorem Supplement IV. Genera of quadratic forms Supplement V. Power residues for composite moduli Supplement VI. Primes in arithmetic progressions Supplement VII. | Vorlesungen über Zahlentheorie | 0.803795 |
32,644 | On quadratic forms Chapter 5. Determination of the class number of binary quadratic forms Supplement I. Some theorems from Gauss's theory of circle division Supplement II. On the limiting value of an infinite series Supplement III. | Vorlesungen über Zahlentheorie | 0.803795 |
32,645 | The Vorlesungen cover topics in elementary number theory, algebraic number theory and analytic number theory, including modular arithmetic, quadratic congruences, quadratic reciprocity and binary quadratic forms. | Vorlesungen über Zahlentheorie | 0.803795 |
32,646 | The Vorlesungen can be seen as a watershed between the classical number theory of Fermat, Jacobi and Gauss, and the modern number theory of Dedekind, Riemann and Hilbert. Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understan... | Vorlesungen über Zahlentheorie | 0.803795 |
32,647 | Leopold Kronecker's book was first published in 1901 in 2 parts and reprinted by Springer in 1978. It covers elementary and algebraic number theory, including Dirichlet's theorem. | Vorlesungen über Zahlentheorie | 0.803795 |
32,648 | The Focus section of Physics continues to produce the same style of articles that were previously published in Physical Review Focus. The content is available without payment. The name came from the service's connection to the Physical Review, a suite of scientific journals published by the American Physical Society. | Physical Review Focus | 0.803795 |
32,649 | Physical Review Focus was an internet service of the American Physical Society that began in 1998, aiming to explain new developments in physics in a language understandable to the educated non-physicist. One or two short articles were published weekly. In 2011, it merged with the magazine Physics (physics.aps.org) and... | Physical Review Focus | 0.803795 |
32,650 | In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way. The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of house... | Tobit model | 0.803795 |
32,651 | The central limit theorem states that the distribution of an average of many independent, identically distributed random variables tends toward the famous bell-shaped normal distribution with a probability density function of where μ is the expected value of the random variables, σ equals their distribution's standard ... | Sample standard deviation | 0.803792 |
32,652 | In physics, the vacuum level refers to the energy of a free stationary electron that is outside of any material (it is in a perfect vacuum). It may be taken as infinitely far away from a solid, or, defined to be near a surface. Its definition and measurement are often discussed in UPS literature, for example As the vac... | Vacuum level | 0.803791 |
32,653 | A wireless mesh network (WMN) is a network made up of radio nodes organized in a mesh topology. It can also be a form of wireless ad hoc network. | Mesh topology | 0.80379 |
32,654 | The ability to self-configure enables dynamic distribution of workloads, particularly in the event a few nodes should fail. This in turn contributes to fault-tolerance and reduced maintenance costs.Mesh topology may be contrasted with conventional star/tree local network topologies in which the bridges/switches are dir... | Mesh topology | 0.80379 |
32,655 | A mesh network is a local area network topology in which the infrastructure nodes (i.e. bridges, switches, and other infrastructure devices) connect directly, dynamically and non-hierarchically to as many other nodes as possible and cooperate with one another to efficiently route data to and from clients. This lack of ... | Mesh topology | 0.80379 |
32,656 | Negative feedback loops in which just the right amount of correction is applied with optimum timing can be very stable, accurate, and responsive. Negative feedback is widely used in mechanical and electronic engineering, and also within living organisms, and can be seen in many other fields from chemistry and economics... | Negative feedback loop | 0.803788 |
32,657 | In it Hawking explains to a general audience various matters relating to the Lucasian professor's work, such as Gödel's Incompleteness Theorem and P-branes (part of superstring theory in quantum mechanics). He tells the history and principles of modern physics. He seeks to "combine Einstein's General Theory of Relativi... | The Universe in a Nutshell | 0.803787 |
32,658 | The Universe in a Nutshell is a 2001 book about theoretical physics by Stephen Hawking. It is generally considered a sequel and was created to update the public concerning developments since the multi-million-copy bestseller A Brief History of Time was published in 1988. | The Universe in a Nutshell | 0.803787 |
32,659 | The standard definition of lambda calculus uses some definitions which may be considered as theorems, which can be proved based on the definition as mathematical formulas. The canonical naming definition deals with the problem of variable identity by constructing a unique name for each variable based on the position of... | Weak head normal form | 0.803787 |
32,660 | The purpose of β-reduction is to calculate a value. A value in lambda calculus is a function. So β-reduction continues until the expression looks like a function abstraction. A lambda expression that cannot be reduced further, by either β-redex, or η-redex is in normal form. | Weak head normal form | 0.803787 |
32,661 | Lambda calculus is a formal mathematical system based on lambda abstraction and function application. Two definitions of the language are given here: a standard definition, and a definition using mathematical formulas. | Weak head normal form | 0.803787 |
32,662 | Hence, the set of real numbers consists of non-overlapping rational, algebraic non-rational and transcendental real numbers. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted φ {\displaystyle ... | Transcendental number | 0.803787 |
32,663 | In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are π and e.Though only a few classes of transcendental numbers are known – partly because it can ... | Transcendental number | 0.803787 |
32,664 | The cube super-root of any natural number is either an integer or irrational (by the Gelfond–Schneider theorem). However, it is still unclear if the irrational numbers in the later case are all transcendental. The second and later eigenvalues of the Gauss-Kuzmin-Wirsing operator, also not proven to be irrational. | Transcendental number | 0.803787 |
32,665 | Numbers which have yet to be proven to be either transcendental or algebraic: Most sums, products, powers, etc. of the number π and the number e, e.g. eπ, e + π, π − e, π/e, ππ, ee, πe, π√2, eπ2 are not known to be rational, algebraic, irrational or transcendental. A notable exception is eπ√n (for any positive integer ... | Transcendental number | 0.803787 |
32,666 | In biology inputs are time dependent. Moreover, dendrites are not always linear. Compartmental models enable to include nonlinearities via ion channels positioned at arbitrary locations along the dendrites. For static inputs, it is sometimes possible to reduce the number of compartments (increase the computational spee... | Biological neuron model | 0.803785 |
32,667 | For an entire neuron in which the cell body conductance is GS and the membrane conductance per unit area is Gmd = Gm / A, we find the total neuron conductance GN for n dendrite trees by adding up all tree and soma conductances, given by G N = G S + ∑ j = 1 n A D j F d g a j , {\displaystyle G_{N}=G_{S}+\sum _{j=1}^{n}A... | Biological neuron model | 0.803785 |
32,668 | Sweeping simplifications to Hodgkin–Huxley were introduced by FitzHugh and Nagumo in 1961 and 1962. Seeking to describe "regenerative self-excitation" by a nonlinear positive-feedback membrane voltage and recovery by a linear negative-feedback gate voltage, they developed the model described by d V d t = V − V 3 / 3 − ... | Biological neuron model | 0.803785 |
32,669 | Typically, differential equations describing the i-th moment will depend on the (i + 1)-st moment. To use moment closure, a level is chosen past which all cumulants are set to zero. This leaves a resulting closed system of equations which can be solved for the moments. The approximation is particularly useful in models... | Moment closure | 0.803785 |
32,670 | In probability theory, moment closure is an approximation method used to estimate moments of a stochastic process. | Moment closure | 0.803785 |
32,671 | The NASA Infrared Telescope Facility (NASA IRTF) is a 3-meter (9.8 ft) telescope optimized for use in infrared astronomy and located at the Mauna Kea Observatory in Hawaii. It was first built to support the Voyager missions and is now the US national facility for infrared astronomy, providing continued support to plane... | NASA Infrared Telescope Facility | 0.803785 |
32,672 | CSHELL also had an IR imaging mode for source acquisition which covers a 30" x 30" field. An internal CCD with a 1' FOV allows for guiding. NSFCAM2 was a 1-5 µm camera, built at the Institute for Astronomy, (IfA), for the NASA Infrared Telescope Facility (IRTF). | NASA Infrared Telescope Facility | 0.803785 |
32,673 | SpeX is a medium-resolution 0.8-5.4 µm spectrograph built at the Institute for Astronomy (IfA), for the NASA Infrared Telescope Facility (IRTF) on Mauna Kea. The primary scientific driver of SpeX was to provide maximum simultaneous wavelength coverage at a spectral resolving power which is well-matched to many planetar... | NASA Infrared Telescope Facility | 0.803785 |
32,674 | Glivenko's theorem states: If φ is a propositional formula, then φ is a classical tautology if and only if ¬¬φ is an intuitionistic tautology.Glivenko's theorem implies the more general statement: If T is a set of propositional formulas and φ a propositional formula, then T ⊢ φ in classical logic if and only if T ⊢ ¬¬φ... | Double-negation translation | 0.803783 |
32,675 | The easiest double-negation translation to describe comes from Glivenko's theorem, proved by Valery Glivenko in 1929. It maps each classical formula φ to its double negation ¬¬φ. | Double-negation translation | 0.803783 |
32,676 | And further, in intuitionistic propositional logic, the Kuroda- and Kolmogorov-translated formulas are equivalent also. The mere propositional mapping of φ to ¬¬φ does not extend to a sound translation of first-order logic, as the so called double negation shift ∀x ¬¬φ(x) → ¬¬∀x φ(x)is not a theorem of intuitionistic p... | Double-negation translation | 0.803783 |
32,677 | Let TN consist of the double-negation translations of the formulas in T. The fundamental soundness theorem (Avigad and Feferman 1998, p. 342; Buss 1998 p. 66) states: If T is a set of axioms and φ is a formula, then T proves φ using classical logic if and only if TN proves φN using intuitionistic logic. | Double-negation translation | 0.803783 |
32,678 | Secure multi-party computation (also known as secure computation, multi-party computation (MPC) or privacy-preserving computation) is a subfield of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private. Unlike traditional cryptograp... | Multi-party computation | 0.803783 |
32,679 | Using these resources they could evaluate the 4095-bit edit distance function, whose circuit comprises almost 6 billion gates. To accomplish this they developed a custom, better optimized circuit compiler than Fairplay and several new optimizations such as pipelining, whereby transmission of the garbled circuit across ... | Multi-party computation | 0.803783 |
32,680 | In theoretical computer science, Temporal Process Language (TPL) is a process calculus which extends Robin Milner's CCS with the notion of multi-party synchronization, which allows multiple process to synchronize on a global 'clock'. This clock measures time, though not concretely, but rather as an abstract signal whic... | Temporal Process Language | 0.803783 |
32,681 | In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity. It is an extension (suitable for the curved spacetimes of e.g. general relativity) of ... | Conformal boundary | 0.803783 |
32,682 | Online tutoring is one area for the application of various theories and implementations of tutoring provided to students by a computer. Companies involved in automated online tutoring include Wolfram Alpha, with its module called The Problem Generator (PG) Cognitive Tutor, and others. All automated tutoring involves an... | Online Tutoring | 0.803782 |
32,683 | Geometrically, this action can be understood via a biplane geometry, which is defined as follows. A biplane geometry is a symmetric design (a set of points and an equal number of "lines", or rather blocks) such that any set of two points is contained in two lines, while any two lines intersect in two points; this is si... | Projective group | 0.803781 |
32,684 | L2(11) is subtler, and elaborated below; it acts on the order 3 biplane.Further, L2(7) and L2(11) have two inequivalent actions on p points; geometrically this is realized by the action on a biplane, which has p points and p blocks – the action on the points and the action on the blocks are both actions on p points, bu... | Projective group | 0.803781 |
32,685 | PGL sends collinear points to collinear points (it preserves projective lines), but it is not the full collineation group, which is instead either PΓL (for n > 2) or the full symmetric group for n = 2 (the projective line). Every (biregular) algebraic automorphism of a projective space is projective linear. The biratio... | Projective group | 0.803781 |
32,686 | PSL(2, q) and PGL(2, q) (for q > 2, and q odd for PSL) are two of the four families of Zassenhaus groups. PGL(n, K) is an algebraic group of dimension n2−1 and an open subgroup of the projective space Pn2−1. As defined, the functor PSL(n,K) does not define an algebraic group, or even an fppf sheaf, and its sheafificati... | Projective group | 0.803781 |
32,687 | The strain of E. coli Lenski chose to use in the long-term evolution experiment was derived from "strain B", as described in a 1966 paper by Seymour Lederberg (which incorrectly identified the strain as "Bc251", although later genetic analysis found it to be "B" instead), via Bruce Levin, who had used it in a bacterial... | E. coli long-term evolution experiment | 0.803781 |
32,688 | Moreover, due to the long use of E. coli as a principle model organism in molecular biology, a wide array of tools, protocols, and procedures were available for studying changes at the genetic, phenotypic, and physiological levels. The bacteria can also be frozen and preserved while remaining viable. This has permitted... | E. coli long-term evolution experiment | 0.803781 |
32,689 | The long-term evolution experiment was designed as an open-ended means of empirical examination of central features of evolution. The experiment was begun with three principal goals: To examine the dynamics of evolution, including the rate of evolutionary change. To examine the repeatability of evolution. To better und... | E. coli long-term evolution experiment | 0.803781 |
32,690 | Quandt et al. concluded that the dctA mutation was not involved in potentiation, but refinement. This led them to suggest that evolution of Cit+ in the Ara-3 population might have been contingent upon a genetic background and population-specific ecology that permitted the early, weak Cit+ variants to persist in the pop... | E. coli long-term evolution experiment | 0.803781 |
32,691 | Refinement: Once the trait exists, if it provides selective benefit, mutations will accumulate that improve the trait, making it effective. This phase is open-ended, and will continue so long as refining mutations arise and the trait remains beneficial.This model has seen acceptance in evolutionary biology. In 2015 pal... | E. coli long-term evolution experiment | 0.803781 |
32,692 | For example, all 12 populations showed a similar pattern of rapid improvement in fitness that decelerated over time, faster growth rates, and increased cell size. Half of the populations have evolved defects in DNA repair that have caused mutator phenotypes marked by elevated mutation rates. The most striking adaptatio... | E. coli long-term evolution experiment | 0.803781 |
32,693 | Järlström had begun investigating the matter after his wife received a ticket from a red light camera in 2013. After he published his findings, the state of Oregon fined him for practicing engineering without a license. Järlström, who has a degree in electrical engineering, filed suit in the federal District Court alle... | Signal timing | 0.803779 |
32,694 | A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe. T... | Hubble horizon | 0.803776 |
32,695 | Bilevel optimization problems are hard to solve. One solution method is to reformulate bilevel optimization problems to optimization problems for which robust solution algorithms are available. Extended Mathematical Programming (EMP) is an extension to mathematical programming languages that provides several keywords f... | Bilevel program | 0.80377 |
32,696 | Bilevel optimization problems are commonly found in a number of real-world problems. This includes problems in the domain of transportation, economics, decision science, business, engineering, environmental economics etc. Some of the practical bilevel problems studied in the literature are briefly discussed. | Bilevel program | 0.80377 |
32,697 | Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred to as the upper-level optimization task, and the inner optimization task is commonly referred to as the lower-level optimization task. These problems involve two... | Bilevel program | 0.80377 |
32,698 | For any given tax structure the highway users solve their own optimization problem, where they minimize their traveling costs by deciding between utilizing the highways or an alternative route. Under these circumstances, the government's problem needs to be formulated as a bilevel optimization problem. The upper level ... | Bilevel program | 0.80377 |
32,699 | In the field of transportation, bilevel optimization commonly appears in the toll-setting problem. Consider a network of highways that is operated by the government. The government wants to maximize its revenues by choosing the optimal toll setting for the highways. However, the government can maximize its revenues onl... | Bilevel program | 0.80377 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.