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18,900 | In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts: | Sum of squares | 0.811893 |
18,901 | For representing a polynomial as the sum of squares of polynomials, see Polynomial SOS. For computational optimization, see Sum-of-squares optimization. For representing a multivariate polynomial that takes only non-negative values over the reals as a sum of squares of rational functions, see Hilbert's seventeenth prob... | Sum of squares | 0.811893 |
18,902 | The Pythagorean theorem says that the square on the hypotenuse of a right triangle is equal in area to the sum of the squares on the legs. The sum of squares is not factorable. The Squared Euclidean distance (SED) is defined as the sum of squares of the differences between coordinates. Heron's formula for the area of a... | Sum of squares | 0.811893 |
18,903 | 2019 2 Basel Computational Biology Conference "Big Data in Molecular Medicine" in association with BASEL LIFE 2017 2 Basel Computational Biology Conference 2015 2 Basel Computational Biology Conference. 2013 "Genetic Variation + Human Health" 2012 "ECCB'12, 11th European Conference on Computational Biology" in associat... | Basel Computational Biology Conference | 0.811891 |
18,904 | The Basel Computational Biology Conference (stylized as 2) is a scientific meeting on the subjects of bioinformatics and computational biology. It covers a wide spectrum of disciplines, including bioinformatics, computational biology, genomics, computational structural biology, and systems biology. The conference is or... | Basel Computational Biology Conference | 0.811891 |
18,905 | One can extend the definition of spectrum to unbounded operators on a Banach space X. These operators which are no longer elements in the Banach algebra B(X). | Point spectrum | 0.81189 |
18,906 | Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ(x) (or more explicitly σB(x)) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B. This extends the definition for bounded linear operators B(X) on a Banach space X, since B(X) is a uni... | Point spectrum | 0.81189 |
18,907 | Heyting algebras are always distributive. Specifically, we always have the identities a ∧ ( b ∨ c ) = ( a ∧ b ) ∨ ( a ∧ c ) {\displaystyle a\wedge (b\vee c)=(a\wedge b)\vee (a\wedge c)} a ∨ ( b ∧ c ) = ( a ∨ b ) ∧ ( a ∨ c ) {\displaystyle a\vee (b\wedge c)=(a\vee b)\wedge (a\vee c)} The distributive law is sometimes st... | Heyting algebra | 0.811888 |
18,908 | In order to prove that some formula F ( A 1 , A 2 , … , A n ) {\displaystyle F(A_{1},A_{2},\ldots ,A_{n})} is not provable, it is enough to exhibit a Heyting algebra H and elements a 1 , a 2 , … , a n ∈ H {\displaystyle a_{1},a_{2},\ldots ,a_{n}\in H} such that F ( a 1 , a 2 , … , a n ) ≠ 1 {\displaystyle F(a_{1},a_{2}... | Heyting algebra | 0.811888 |
18,909 | For example, let us choose the system of proof having modus ponens as its sole rule of inference, and whose axioms are the Hilbert-style ones given at Intuitionistic logic#Axiomatization. Then the facts to be verified follow immediately from the axiom-like definition of Heyting algebras given above. 1 ⇒ 2 also provides... | Heyting algebra | 0.811888 |
18,910 | (It follows from the deduction theorem that F→G is provable (unconditionally) if and only if G is provable from F, that is, if G is a provable consequence of F.) In particular, if F and G are provably equivalent, then F ( a 1 , a 2 , … , a n ) = G ( a 1 , a 2 , … , a n ) {\displaystyle F(a_{1},a_{2},\ldots ,a_{n})=G(a_... | Heyting algebra | 0.811888 |
18,911 | Given a formula F ( A 1 , A 2 , … , A n ) {\displaystyle F(A_{1},A_{2},\ldots ,A_{n})} of propositional calculus (using, in addition to the variables, the connectives ∧ , ∨ , ¬ , → {\displaystyle \land ,\lor ,\lnot ,\to } , and the constants 0 and 1), it is a fact, proved early on in any study of Heyting algebras, that... | Heyting algebra | 0.811888 |
18,912 | We show that 6 ⇒ 7 by taking ¬x and ¬¬x in place of x and y in 6 and using the identity a ∧ ¬a = 0. Notice that 2 ⇒ 1 follows from the first De Morgan law, and 7 ⇒ 6 results from the fact that the join operation ∨ on the subalgebra Hcomp is just the restriction of ∨ to Hcomp, taking into account the characterizations w... | Heyting algebra | 0.811888 |
18,913 | Condition 2 is the other De Morgan law. Condition 6 says that the join operation ∨reg on the Boolean algebra Hreg of regular elements of H coincides with the operation ∨ of H. Condition 7 states that every regular element is complemented, i.e., Hreg = Hcomp. | Heyting algebra | 0.811888 |
18,914 | {\displaystyle \forall x,y\in H:\qquad \lnot (x\wedge y)=\lnot \lnot (\lnot x\vee \lnot y).} The following statements are equivalent for all Heyting algebras H: H satisfies both De Morgan laws, ¬ ( x ∧ y ) = ¬ x ∨ ¬ y for all x , y ∈ H , {\displaystyle \lnot (x\wedge y)=\lnot x\vee \lnot y{\mbox{ for all }}x,y\in H,} ¬... | Heyting algebra | 0.811888 |
18,915 | One of the two De Morgan laws is satisfied in every Heyting algebra, namely ∀ x , y ∈ H: ¬ ( x ∨ y ) = ¬ x ∧ ¬ y . {\displaystyle \forall x,y\in H:\qquad \lnot (x\vee y)=\lnot x\wedge \lnot y.} However, the other De Morgan law does not always hold. We have instead a weak de Morgan law: ∀ x , y ∈ H: ¬ ( x ∧ y ) = ¬ ¬ ( ... | Heyting algebra | 0.811888 |
18,916 | In particular, 0 and 1 are always regular. For any Heyting algebra H, the following conditions are equivalent: H is a Boolean algebra; every x in H is regular; every x in H is complemented.In this case, the element a→b is equal to ¬a ∨ b. The regular (respectively complemented) elements of any Heyting algebra H constit... | Heyting algebra | 0.811888 |
18,917 | In any Heyting algebra, the elements 0 and 1 are complements to each other. For instance, it is possible that ¬x is 0 for every x different from 0, and 1 if x = 0, in which case 0 and 1 are the only regular elements. Any complemented element of a Heyting algebra is regular, though the converse is not true in general. | Heyting algebra | 0.811888 |
18,918 | An element x of a Heyting algebra H is called regular if either of the following equivalent conditions hold: x = ¬¬x. x = ¬y for some y in H.The equivalence of these conditions can be restated simply as the identity ¬¬¬x = ¬x, valid for all x in H. Elements x and y of a Heyting algebra H are called complements to each ... | Heyting algebra | 0.811888 |
18,919 | The constructions we have just given play an entirely analogous role with respect to Heyting algebras to that of Lindenbaum algebras with respect to Boolean algebras. In fact, The Lindenbaum algebra BT in the variables {Ai} with respect to the axioms T is just our HT∪T1, where T1 is the set of all formulas of the form ... | Heyting algebra | 0.811888 |
18,920 | It is a filter on H1. (Care should be taken because this definition, if applied to a morphism of Boolean algebras, is dual to what would be called the kernel of the morphism viewed as a morphism of rings.) By the foregoing, f induces a morphism f′: H1/(ker f) → H2. It is an isomorphism of H1/(ker f) onto the subalgebra... | Heyting algebra | 0.811888 |
18,921 | We call the Heyting algebra H/F the quotient of H by F. Let S be a subset of a Heyting algebra H and let F be the filter generated by S. Then H/F satisfies the following universal property: Given any morphism of Heyting algebras f: H → H′ satisfying f(y) = 1 for every y ∈ S, f factors uniquely through the canonical sur... | Heyting algebra | 0.811888 |
18,922 | Therefore, given any subset S of H there is a smallest filter containing S. We call it the filter generated by S. If S is empty, F = {1}. Otherwise, F is equal to the set of x in H such that there exist y1, y2, ..., yn ∈ S with y1 ∧ y2 ∧ ... ∧ yn ≤ x. If H is a Heyting algebra and F is a filter on H, we define a relati... | Heyting algebra | 0.811888 |
18,923 | Let H be a Heyting algebra, and let F ⊆ H. We call F a filter on H if it satisfies the following properties: 1 ∈ F , {\displaystyle 1\in F,} If x , y ∈ F then x ∧ y ∈ F , {\displaystyle {\mbox{If }}x,y\in F{\mbox{ then }}x\land y\in F,} If x ∈ F , y ∈ H , and x ≤ y then y ∈ F . {\displaystyle {\mbox{If }}x\in F,\ y\in ... | Heyting algebra | 0.811888 |
18,924 | It follows that even among the finite Heyting algebras there exist infinitely many that are subdirectly irreducible, no two of which have the same equational theory. Hence no finite set of finite Heyting algebras can supply all the counterexamples to non-laws of Heyting algebra. This is in sharp contrast to Boolean alg... | Heyting algebra | 0.811888 |
18,925 | The internal logic of an elementary topos is based on the Heyting algebra of subobjects of the terminal object 1 ordered by inclusion, equivalently the morphisms from 1 to the subobject classifier Ω. The open sets of any topological space form a complete Heyting algebra. Complete Heyting algebras thus become a central ... | Heyting algebra | 0.811888 |
18,926 | It can further be shown that a ≤ ¬¬a, although the converse, ¬¬a ≤ a, is not true in general, that is, double negation elimination does not hold in general in a Heyting algebra. Heyting algebras generalize Boolean algebras in the sense that Boolean algebras are precisely the Heyting algebras satisfying a ∨ ¬a = 1 (excl... | Heyting algebra | 0.811888 |
18,927 | As lattices, Heyting algebras are distributive. Every Boolean algebra is a Heyting algebra when a → b is defined as ¬a ∨ b, as is every complete distributive lattice satisfying a one-sided infinite distributive law when a → b is taken to be the supremum of the set of all c for which c ∧ a ≤ b. In the finite case, every... | Heyting algebra | 0.811888 |
18,928 | In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that (c ∧ a) ≤ b is equivalent to c ≤ (a → b). From a logical standpoin... | Heyting algebra | 0.811888 |
18,929 | Algebraically, this corresponds to the action of S3 on the 2-cycles (its Sylow 2-subgroups) by conjugation and realizes the isomorphism with the group of inner automorphisms, S 3 → ∼ Inn ( S 3 ) ≅ S 3 . {\textstyle \mathrm {S} _{3}\mathrel {\overset {\sim }{\to }} \operatorname {Inn} (\mathrm {S} _{3})\cong \mathrm {... | Six cross-ratios | 0.811888 |
18,930 | On the other hand, the latter notation is coherent with the fact that the prime factorization of a positive integer is a uniquely defined multiset, as asserted by the fundamental theorem of arithmetic. Also, a monomial is a multiset of indeterminates; for example, the monomial x3y2 corresponds to the multiset {x, x, x,... | Multiset | 0.811886 |
18,931 | The fact that its solution is an implicit function is revealing in itself. One of the successes of theoretical physics is not simply a matter that it is amenable to a mathematical treatment but that the algebraic equations involved can be symbolically manipulated until an analytical solution, preferably a closed form s... | Euler's three-body problem | 0.811884 |
18,932 | Therefore, according to Bonnet's theorem, the same ellipses are the solutions for the Euler problem. Introducing elliptic coordinates, x = a cosh ξ cos η , {\displaystyle \,x=\,a\cosh \xi \cos \eta ,} y = a sinh ξ sin η , {\displaystyle \,y=\,a\sinh \xi \sin \eta ,} the potential energy can be written as V ( ξ ... | Euler's three-body problem | 0.811884 |
18,933 | However, solutions required series expansions from basis sets. Nonetheless, through experimental mathematics, it was found that the energy eigenvalue was mathematically a generalization of the Lambert W function (see Lambert W function and references therein for more details). The hydrogen molecular ion in the case of ... | Euler's three-body problem | 0.811884 |
18,934 | A special case of the quantum mechanical three-body problem is the hydrogen molecule ion, H+2. Two of the three bodies are nuclei and the third is a fast moving electron. The two nuclei are 1800 times heavier than the electron and thus modeled as fixed centers. It is well known that the Schrödinger wave equation is sep... | Euler's three-body problem | 0.811884 |
18,935 | In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are fixed in space. This problem is exactly solvable, and yields an approximate solution for particles moving in the gravitational fields of prolate ... | Euler's three-body problem | 0.811884 |
18,936 | Mathematics and geometry describe abstract objects that sometimes correspond to familiar shapes, and sometimes do not. Circles, triangles, rectangles, and so forth describe two-dimensional shapes that are often found in the real world. However, mathematical formulas do not describe individual physical circles, triangle... | Intentional objects | 0.81188 |
18,937 | The International Journal of Geometry is a peer-reviewed academic journal that covers Euclidean, Non-Euclidean and Discrete geometry. It was established in 2012 with two volumes per year, and as of 2021 is published quarterly by the Department of Mathematics of the Vasile Alecsandri National College of Bacău. It is abs... | International Journal of Geometry | 0.811879 |
18,938 | And engineering ethics deals with the professional standards of engineers, including software engineers and their moral responsibilities to the public.A wide branch of technology ethics is concerned with the ethics of artificial intelligence: it includes robot ethics, which deals with ethical issues involved in the des... | Virtual technology | 0.811874 |
18,939 | Computer ethics focuses on issues related to computing. Cyberethics explores internet-related issues like intellectual property rights, privacy, and censorship. Nanoethics examines issues surrounding the alteration of matter at the atomic and molecular level in various disciplines including computer science, engineerin... | Virtual technology | 0.811874 |
18,940 | ; by 1989, this increased to an average of one citation per patent. The average was skewed upwards by patents related to the pharmaceutical industry, chemistry, and electronics. A 2021 analysis shows that patents that are based on scientific discoveries are on average 26% more valuable than equivalent non-science-based... | Virtual technology | 0.811874 |
18,941 | Autonomous robots have undergone rapid progress, and are expected to replace humans at many dangerous tasks, including search and rescue, bomb disposal, firefighting, and war.Estimates on the advent of artificial general intelligence vary, but half of machine learning experts surveyed in 2018 believe that AI will "acco... | Virtual technology | 0.811874 |
18,942 | Some thinkers believe that this may shatter our sense of self, and have urged for renewed public debate exploring the issue more thoroughly; others fear that directed evolution could lead to eugenics or extreme social inequality. Nanotechnology will grant us the ability to manipulate matter "at the molecular and atomic... | Virtual technology | 0.811874 |
18,943 | Emerging technologies are novel technologies whose development or practical applications are still largely unrealized. They include nanotechnology, biotechnology, robotics, 3D printing, blockchains, and artificial intelligence. In 2005, futurist Ray Kurzweil claimed the next technological revolution would rest upon adv... | Virtual technology | 0.811874 |
18,944 | The Space Age began with the launch of Sputnik 1 in 1957, and later the launch of crewed missions to the moon in the 1960s. Organized efforts to search for extraterrestrial intelligence have used radio telescopes to detect signs of technology use, or technosignatures, given off by alien civilizations. In medicine, new ... | Virtual technology | 0.811874 |
18,945 | In physics, the discovery of nuclear fission in the Atomic Age led to both nuclear weapons and nuclear power. Computers were invented and later shifted from analog to digital in the Digital Revolution. Information technology, particularly optical fiber and optical amplifiers led to the birth of the Internet, which ushe... | Virtual technology | 0.811874 |
18,946 | These technological advances led to significant developments in medicine, chemistry, physics, and engineering. They were accompanied by consequential social change, with the introduction of skyscrapers accompanied by rapid urbanization. Communication improved with the invention of the telegraph, the telephone, the radi... | Virtual technology | 0.811874 |
18,947 | Since the invention of the wheel, technologies have helped increase humans' economic output. Past automation has both substituted and complemented labor; machines replaced humans at some lower-paying jobs (for example in agriculture), but this was compensated by the creation of new, higher-paying jobs. Studies have fou... | Virtual technology | 0.811874 |
18,948 | Metre per hour (American spelling: meter per hour) is a metric unit of both speed (scalar) and velocity (Vector (geometry)). Its symbol is m/h or m·h−1 (not to be confused with the imperial unit symbol mph). By definition, an object travelling at a speed of 1 m/h for an hour would move 1 metre. The term is rarely used ... | Metre per hour | 0.811871 |
18,949 | In organic chemistry, tolyl groups are functional groups related to toluene. They have the general formula CH3C6H4−R, the change of the relative position of the methyl and the R substituent on the aromatic ring can generate three possible structural isomers 1,2 (ortho), 1,3 (meta), and 1,4 (para). Tolyl groups are aryl... | Tolyl groups | 0.811869 |
18,950 | Properties of the adjacency algebra of G are associated with various spectral, adjacency and connectivity properties of G. Statement. The number of walks of length d between vertices i and j is equal to the (i, j)-th element of Ad.Statement. The dimension of the adjacency algebra of a connected graph of diameter d is a... | Adjacency algebra | 0.811867 |
18,951 | In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an example of a matrix algebra and is the set of the linear combinations of powers of A.Some other similar mathematical objects are also called "adjacency algebra". | Adjacency algebra | 0.811867 |
18,952 | This allows an extension of the Kirby calculus to rational surgeries. There are also various tricks to modify surgery diagrams. | Kirby calculus | 0.811861 |
18,953 | Different presentations of "Kirby calculus" have a different set of moves and these are sometimes called Kirby moves. Kirby's original formulation involved two kinds of move, the "blow-up" and the "handle slide"; Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn–Rourke... | Kirby calculus | 0.811861 |
18,954 | In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J resp... | Kirby calculus | 0.811861 |
18,955 | It is first mentioned in Section II of Groundworks of the Metaphysics of Morals. Kant defined it as the formula of the command of reason that represents an objective principle "in so far as it is necessitating for a will", in other words, imperatives act as the empirical formulas for knowing and enacting with reason. H... | Hypothetical imperative | 0.811859 |
18,956 | In physics, persistent current refers to a perpetual electric current, not requiring an external power source. Such a current is impossible in normal electrical devices, since all commonly-used conductors have a non-zero resistance, and this resistance would rapidly dissipate any such current as heat. However, in super... | Persistent current | 0.811854 |
18,957 | By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra. Structuralism is an epistemologically realistic view in that it holds that mathemati... | Mathematical structuralism | 0.811846 |
18,958 | In computer science, computer engineering and programming language implementations, a stack machine is a computer processor or a virtual machine in which the primary interaction is moving short-lived temporary values to and from a push down stack. In the case of a hardware processor, a hardware stack is used. The use o... | Stack machines | 0.811846 |
18,959 | In register machines, a common subexpression (a subexpression which is used multiple times with the same result value) can be evaluated just once and its result saved in a fast register. The subsequent reuses have no time or code cost, just a register reference. This optimization speeds simple expressions (for example,... | Stack machines | 0.811846 |
18,960 | After another chapter on the linear transformations of lattices, the book studies the problem of finding the smallest nonzero values of quadratic forms, and Lagrange's four-square theorem, the theorem that every non-negative integer can be represented as a sum of four squares of integers. The final two chapters concern... | The Geometry of Numbers | 0.811845 |
18,961 | The Geometry of Numbers is relatively short, and is divided into two parts. The first part applies number theory to the geometry of lattices, and the second applies results on lattices to number theory. Topics in the first part include the relation between the maximum distance between parallel lines that are not separa... | The Geometry of Numbers | 0.811845 |
18,962 | The Geometry of Numbers is intended for secondary-school and undergraduate mathematics students, although it may be too advanced for the secondary-school students; it contains exercises making it suitable for classroom use. It has been described as "expository", "self-contained", and "readable".However, reviewer Henry ... | The Geometry of Numbers | 0.811845 |
18,963 | The Geometry of Numbers is based on a book manuscript that Carl D. Olds, a New Zealand-born mathematician working in California at San Jose State University, was still writing when he died in 1979. Anneli Cahn Lax, the editor of the New Mathematical Library of the Mathematical Association of America, took up the task o... | The Geometry of Numbers | 0.811845 |
18,964 | The Geometry of Numbers is a book on the geometry of numbers, an area of mathematics in which the geometry of lattices, repeating sets of points in the plane or higher dimensions, is used to derive results in number theory. It was written by Carl D. Olds, Anneli Cahn Lax, and Giuliana Davidoff, and published by the Mat... | The Geometry of Numbers | 0.811845 |
18,965 | Nowadays, after the first quantum revolution that brought us lasers, MRI imagers and transistors, a second wave of quantum technologies is expected to impact society in a similar way. This second quantum revolution makes use of quantum coherence and capitalizes on the great progress achieved in the last century in unde... | Quantum engineering | 0.811845 |
18,966 | Quantum engineering is the development of technology that capitalizes on the laws of quantum mechanics. Quantum engineering uses quantum mechanics as a toolbox for the development of quantum technologies, such as quantum sensors or quantum computers. There are many devices available which rely on quantum mechanical eff... | Quantum engineering | 0.811845 |
18,967 | Students are trained in signal and information processing, optoelectronics and photonics, integrated circuits (bipolar, CMOS) and electronic hardware architectures (VLSI, FPGA, ASIC). In addition, they are exposed to emerging applications such as quantum sensing, quantum communication and cryptography and quantum infor... | Quantum engineering | 0.811845 |
18,968 | Results show that companies often look for people that are familiar with quantum technologies and simultaneously possess excellent hands-on lab skills.Several technical universities have launched education programs in this domain. For example, ETH Zurich has initiated a Master of Science in Quantum Engineering, a joint... | Quantum engineering | 0.811845 |
18,969 | Quantum engineering is evolving into its own engineering discipline. The quantum industry requires a quantum-literate workforce, a missing resource at the moment. Currently, scientists in the field of quantum technology have mostly either a physics or engineering background and have acquired their ”quantum engineering ... | Quantum engineering | 0.811845 |
18,970 | The terminology may be due to Weil, who wrote his Basic Number Theory (1967) in part to work out the parallelism. It is usually easier to work in the function field case and then try to develop parallel techniques on the number field side. The development of Arakelov theory and its exploitation by Gerd Faltings in his ... | Global function field | 0.811841 |
18,971 | {\displaystyle \prod _{v}|x|_{v}=1.\ } The analogy between the two kinds of fields has been a strong motivating force in algebraic number theory. The idea of an analogy between number fields and Riemann surfaces goes back to Richard Dedekind and Heinrich M. Weber in the nineteenth century. The more strict analogy expre... | Global function field | 0.811841 |
18,972 | A global field is one of the following: An algebraic number fieldAn algebraic number field F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The function field of an algebraic curve... | Global function field | 0.811841 |
18,973 | The Earth's atmosphere is opaque over most of the far-infrared, so most far-infrared astronomy is performed by satellites such as the Herschel Space Observatory, Spitzer Space Telescope, IRAS, and Infrared Space Observatory. Upper-atmosphere observations are also possible, as conducted by the airborne SOFIA telescope. ... | Far infrared astronomy | 0.811838 |
18,974 | The Underground Area 9 (UA9) experiment is a high-energy physics experiment using particle beams from the Super Proton Synchrotron (SPS), at CERN. The purpose of the experiment is to investigate how using tiny bent crystals could allow the collimation of beams in modern hadron colliders to improve. UA9 was approved in ... | UA9 experiment | 0.811835 |
18,975 | Software engineering practitioners make use of diagrams for designing software. Formal standards and modeling languages such as Unified Modeling Language (UML) exist but most diagramming happens using informal ad hoc diagrams that illustrate a conceptual model.Practitioners reported that diagramming helped with analysi... | Technical drawing | 0.811832 |
18,976 | Some enzymes are inhibited by the product of their reaction binds to the enzyme and reduces its activity. This can be important in the regulation of metabolism as a form of negative feedback controlling metabolic pathways. Product inhibition is also an important topic in biotechnology, as overcoming this effect can inc... | Chemical products | 0.811832 |
18,977 | Additionally, the properties of a product can make it easier to extract and purify following a chemical reaction, especially if the product has a different state of matter than the reactants. Much of chemistry research is focused on the synthesis and characterization of beneficial products, as well as the detection and... | Chemical products | 0.811832 |
18,978 | Closely related to the brain simulator reply, this claims that a massively parallel connectionist architecture would be capable of understanding. Modern deep learning is massively parallel and has successfully displayed intelligent behavior in many domains. Nils Nilsson argues that modern AI is using digitized "dynamic... | Strong AI hypothesis | 0.811825 |
18,979 | Searle argues that no reasonable person should be satisfied with the reply, unless they are "under the grip of an ideology;" In order for this reply to be remotely plausible, one must take it for granted that consciousness can be the product of an information processing "system", and does not require anything resemblin... | Strong AI hypothesis | 0.811825 |
18,980 | The Chinese room has a design analogous to that of a modern computer. It has a Von Neumann architecture, which consists of a program (the book of instructions), some memory (the papers and file cabinets), a CPU that follows the instructions (the man), and a means to write symbols in memory (the pencil and eraser). A ma... | Strong AI hypothesis | 0.811825 |
18,981 | Searle's thought experiment begins with this hypothetical premise: suppose that artificial intelligence research has succeeded in constructing a computer that behaves as if it understands Chinese. It takes Chinese characters as input and, by following the instructions of a computer program, produces other Chinese chara... | Strong AI hypothesis | 0.811825 |
18,982 | Therefore no programs are minds.This much of the argument is intended to show that artificial intelligence can never produce a machine with a mind by writing programs that manipulate symbols. The remainder of the argument addresses a different issue. Is the human brain running a program? | Strong AI hypothesis | 0.811825 |
18,983 | Abu Kamil Shuja' wrote a book of algebra accompanied with geometrical illustrations and proofs. He also enumerated all the possible solutions to some of his problems. Abu al-Jud, Omar Khayyam, along with Sharaf al-Dīn al-Tūsī, found several solutions of the cubic equation. Omar Khayyam found the general geometric solut... | Islamic mathematics | 0.811823 |
18,984 | Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before." Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. | Islamic mathematics | 0.811823 |
18,985 | It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broade... | Islamic mathematics | 0.811823 |
18,986 | This was unlike the algebraic work of Diophantus, which was syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of Ibn al-Banna' al-Marrakushi and Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī.On the work done by Al-Khwarizmi, J. J. O'Connor and ... | Islamic mathematics | 0.811823 |
18,987 | The study of algebra, the name of which is derived from the Arabic word meaning completion or "reunion of broken parts", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a Persian scholar in the House of Wisdom in Baghdad was the founder of algebra, is along with the Greek mathematician Diophan... | Islamic mathematics | 0.811823 |
18,988 | The earliest implicit traces of mathematical induction can be found in Euclid's proof that the number of primes is infinite (c. 300 BCE). The first explicit formulation of the principle of induction was given by Pascal in his Traité du triangle arithmétique (1665). In between, implicit proof by induction for arithmetic... | Islamic mathematics | 0.811823 |
18,989 | 967) Ibn al-Haytham (c. 965–1040) Abū al-Rayḥān al-Bīrūnī (973–1048) (trigonometry) Ibn Maḍāʾ (c. 1116–1196) Jamshīd al-Kāshī (c. 1380–1429) (decimals and estimation of the circle constant) | Islamic mathematics | 0.811823 |
18,990 | A deductive system is used to demonstrate, on a purely syntactic basis, that one formula is a logical consequence of another formula. There are many such systems for first-order logic, including Hilbert-style deductive systems, natural deduction, the sequent calculus, the tableaux method, and resolution. These share th... | First-order logic | 0.81182 |
18,991 | Gödel's completeness theorem, proved by Kurt Gödel in 1929, establishes that there are sound, complete, effective deductive systems for first-order logic, and thus the first-order logical consequence relation is captured by finite provability. Naively, the statement that a formula φ logically implies a formula ψ depend... | First-order logic | 0.81182 |
18,992 | In geometry, an elongated octahedron is a polyhedron with 8 faces (4 triangular, 4 isosceles trapezoidal), 14 edges, and 8 vertices. | Elongated octahedron | 0.811814 |
18,993 | In the special case, where the trapezoid faces are squares or rectangles, the pairs of triangles becoming coplanar and the polyhedron's geometry is more specifically a right rhombic prism. This polyhedron has a highest symmetry as D2h symmetry, order 8, representing 3 orthogonal mirrors. Removing one mirror between the... | Elongated octahedron | 0.811814 |
18,994 | Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations. The samples are generated using some distribution over the input. The problem is easy to solve using ... | Parity learning | 0.811813 |
18,995 | Richard T. Cox showed that Bayesian updating follows from several axioms, including two functional equations and a hypothesis of differentiability. The assumption of differentiability or even continuity is controversial; Halpern found a counterexample based on his observation that the Boolean algebra of statements may ... | Bayesian probability theory | 0.81181 |
18,996 | Hysteresis is a commonly encountered phenomenon in ecology and epidemiology, where the observed equilibrium of a system can not be predicted solely based on environmental variables, but also requires knowledge of the system's past history. Notable examples include the theory of spruce budworm outbreaks and behavioral-e... | Tipping point (physics) | 0.811804 |
18,997 | In developmental biology, cell type diversity is regulated by long range-acting signaling molecules called morphogens that pattern uniform pools of cells in a concentration- and time-dependent manner. The morphogen sonic hedgehog (Shh), for example, acts on limb bud and neural progenitors to induce expression of a set ... | Tipping point (physics) | 0.811804 |
18,998 | The mechanisms are often elucidated by allowing independent control of the concentration of the key intermediate, for instance, by using an inducible promoter. Darlington in his classic works on genetics discussed hysteresis of the chromosomes, by which he meant "failure of the external form of the chromosomes to respo... | Tipping point (physics) | 0.811804 |
18,999 | Hysteresis in cell biology often follows bistable systems where the same input state can lead to two different, stable outputs. Where bistability can lead to digital, switch-like outputs from the continuous inputs of chemical concentrations and activities, hysteresis makes these systems more resistant to noise. These s... | Tipping point (physics) | 0.811804 |
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