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9,700 | The Method of Mechanical Theorems (Greek: Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving works of the ancient Greek polymath Archimedes. The Method takes the form of a letter from Archimedes to Eratosthenes, the chief librarian at the Library of Alexandr... | Method of Mechanical Theorems | 0.819874 |
9,701 | {\displaystyle c_{1},c_{2},...} of positive real numbers (the weights) such that μ = ∑ k = 1 ∞ c k δ x k {\textstyle \mu =\sum _{k=1}^{\infty }c_{k}\delta _{x_{k}}} , which means that μ ( A ) = ∑ k = 1 ∞ c k δ x k ( A ) {\textstyle \mu (A)=\sum _{k=1}^{\infty }c_{k}\delta _{x_{k}}(A)} for every A ∈ Σ {\displaystyle A\i... | Atomic measure | 0.81987 |
9,702 | It is reminiscent of the intermediate value theorem for continuous functions. Sketch of proof of Sierpiński's theorem on non-atomic measures. A slightly stronger statement, which however makes the proof easier, is that if ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} is a non-atomic measure space and μ ( X ) = c , {\d... | Atomic measure | 0.81987 |
9,703 | A measure which has no atoms is called non-atomic measure or a diffuse measure. In other words, a measure μ {\displaystyle \mu } is non-atomic if for any measurable set A {\displaystyle A} with μ ( A ) > 0 {\displaystyle \mu (A)>0} there exists a measurable subset B {\displaystyle B} of A {\displaystyle A} such that A ... | Atomic measure | 0.81987 |
9,704 | In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proof complexity is predominantly concerned with proving p... | Proof complexity | 0.819868 |
9,705 | Mertz, Pitassi and Wei (2019) proved that tree-like Resolution and Resolution are not automatable even in certain quasi-polynomial time assuming the exponential time hypothesis. Atserias and Müller (2019) proved that Resolution is not automatable unless P=NP. This was extended by de Rezende, Göös, Nordström, Pitassi, R... | Proof complexity | 0.819868 |
9,706 | Propositional proof systems can be interpreted as nonuniform equivalents of theories of higher order. The equivalence is most often studied in the context of theories of bounded arithmetic. For example, the Extended Frege system corresponds to Cook's theory P V 1 {\displaystyle \mathrm {PV} _{1}} formalizing polynomial... | Proof complexity | 0.819868 |
9,707 | For example, sequent calculus is p-equivalent to (every) Frege system.A proof system is p-optimal if it p-simulates all other proof systems, and it is optimal if it simulates all other proof systems. It is an open problem whether such proof systems exist: Problem (Optimality) Does there exist a p-optimal or optimal pro... | Proof complexity | 0.819868 |
9,708 | This was extended by Bonet, Domingo, Gavaldá, Maciel and Pitassi (2004) who proved that constant-depth Frege systems of depth at least 2 are not weakly automatable unless the Diffie–Helman scheme is not secure against nonuniform adversaries working in subexponential time. Alekhnovich and Razborov (2008) proved that tre... | Proof complexity | 0.819868 |
9,709 | A propositional proof system is given as a proof-verification algorithm P(A,x) with two inputs. If P accepts the pair (A,x) we say that x is a P-proof of A. P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if A is a tautology. Examples of propositional proof systems i... | Proof complexity | 0.819868 |
9,710 | The plot on the right shows the following problem. max y − x + y ≤ 1 3 x + 2 y ≤ 12 2 x + 3 y ≤ 12 x , y ≥ 0 x , y ∈ Z {\displaystyle {\begin{aligned}\max &{\text{ }}y\\-x+y&\leq 1\\3x+2y&\leq 12\\2x+3y&\leq 12\\x,y&\geq 0\\x,y&\in \mathbb {Z} \end{aligned}}} The feasible integer points are shown in red, and the red da... | Integer programming | 0.819862 |
9,711 | An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are lin... | Integer programming | 0.819862 |
9,712 | Short-term memory can consist of previously tried solutions while medium-term memory can consist of values for the integer constrained variables that have resulted in high objective values (assuming the ILP is a maximization problem). Finally, long-term memory can guide the search towards integer values that have not p... | Integer programming | 0.819862 |
9,713 | In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these ax... | Three dimensional space | 0.819862 |
9,714 | Different materials require different processing or synthesis methods. For example, the processing of metals has historically defined eras such as the Bronze Age and Iron Age and is studied under the branch of materials science named physical metallurgy. Chemical and physical methods are also used to synthesize other m... | Material chemistry | 0.819858 |
9,715 | Synthesis and processing involves the creation of a material with the desired micro-nanostructure. A material cannot be used in industry if no economically viable production method for it has been developed. Therefore, developing processing methods for materials that are reasonably effective and cost-efficient is vital... | Material chemistry | 0.819858 |
9,716 | In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Being a primitive notion means that a point cannot be defined in terms of previous... | Euclidean point | 0.819854 |
9,717 | This is easily confirmed under modern extensions of Euclidean geometry, and had lasting consequences at its introduction, allowing the construction of almost all the geometric concepts known at the time. However, Euclid's postulation of points was neither complete nor definitive, and he occasionally assumed facts about... | Euclidean point | 0.819854 |
9,718 | Points, considered within the framework of Euclidean geometry, are one of the most fundamental objects. Euclid originally defined the point as "that which has no part". In the two-dimensional Euclidean plane, a point is represented by an ordered pair (x, y) of numbers, where the first number conventionally represents t... | Euclidean point | 0.819854 |
9,719 | Often in physics and mathematics, it is useful to think of a point as having non-zero mass or charge (this is especially common in classical electromagnetism, where electrons are idealized as points with non-zero charge). The Dirac delta function, or δ function, is (informally) a generalized function on the real number... | Euclidean point | 0.819854 |
9,720 | Stacks were first defined by Giraud (1966, 1971), and the term "stack" was introduced by Deligne & Mumford (1969) for the original French term "champ" meaning "field". In this paper they also introduced Deligne–Mumford stacks, which they called algebraic stacks, though the term "algebraic stack" now usually refers to t... | Stack associated to a scheme | 0.819854 |
9,721 | Since the inception of algebraic stacks it was expected that they are locally quotient stacks of the form {\displaystyle } where G {\displaystyle G} is a linearly reductive algebraic group. This was recently proved to be the case: given a quasi-separated algebraic stack X {\displaystyle {\mathfrak {X}}} locally of fin... | Stack associated to a scheme | 0.819854 |
9,722 | If X {\displaystyle X} is a scheme ( S c h / S ) {\displaystyle (Sch/S)} and G {\displaystyle G} is a smooth affine group scheme acting on X {\displaystyle X} , then there is a quotient algebraic stack {\displaystyle } , taking a scheme Y → S {\displaystyle Y\to S} to the groupoid of G {\displaystyle G} -torsors over ... | Stack associated to a scheme | 0.819854 |
9,723 | Behrend, Kai; Conrad, Brian; Edidin, Dan; Fulton, William; Fantechi, Barbara; Göttsche, Lothar; Kresch, Andrew (2006), Algebraic stacks, archived from the original on 2008-05-05 Goméz, Tomás (1999), Algebraic stacks, arXiv:math/9911199, Bibcode:1999math.....11199G is an expository article describing the basics of stack... | Stack associated to a scheme | 0.819854 |
9,724 | The category c is called a stack over the category C with a Grothendieck topology if it is a prestack over C and every descent datum is effective. A descent datum consists roughly of a covering of an object V of C by a family Vi, elements xi in the fiber over Vi, and morphisms fji between the restrictions of xi and xj ... | Stack associated to a scheme | 0.819854 |
9,725 | A category c {\displaystyle c} with a functor to a category C {\displaystyle C} is called a fibered category over C {\displaystyle C} if for any morphism F: X → Y {\displaystyle F:X\to Y} in C {\displaystyle C} and any object y {\displaystyle y} of c {\displaystyle c} with image Y {\displaystyle Y} (under the functor),... | Stack associated to a scheme | 0.819854 |
9,726 | The interaction information is a generalization of the mutual information for more than two variables. There are many names for interaction information, including amount of information, information correlation, co-information, and simply mutual information. Interaction information expresses the amount of information (r... | Interaction information | 0.819842 |
9,727 | Jakulin and Bratko (2003b) provide a machine learning algorithm which uses interaction information. Killian, Kravitz and Gilson (2007) use mutual information expansion to extract entropy estimates from molecular simulations. LeVine and Weinstein (2014) use interaction information and other N-body information measures t... | Interaction information | 0.819842 |
9,728 | Physical quantities that have different dimensions (such as time and length) cannot be equated even if they are numerically equal (e.g., 1 second is not the same as 1 metre). In theoretical physics, however, this scruple may be set aside, by a process called nondimensionalization. The effective result is that many fund... | Planck density | 0.819836 |
9,729 | The competition started in 2008 and was won in 2012. A new competition is planned for 2014.The Google AI Challenge was a bi-annual online contest organized by the University of Waterloo Computer Science Club and sponsored by Google that ran from 2009 to 2011. Each year a game was chosen and contestants submitted specia... | Competitions and prizes in artificial intelligence | 0.819836 |
9,730 | Concretely, it tackles the problem of devising an algorithm that is able to play any game it is given, even if the game is not known a priori. Additionally, the contests poses the challenge of creating level and rule generators for any game is given. This area of study can be seen as an approximation of General Artific... | Competitions and prizes in artificial intelligence | 0.819836 |
9,731 | The Pittsburgh Brain Activity Interpretation Competition will reward analysis of fMRI data "to predict what individuals perceive and how they act and feel in a novel Virtual Reality world involving searching for and collecting objects, interpreting changing instructions, and avoiding a threatening dog." The prize in 20... | Competitions and prizes in artificial intelligence | 0.819836 |
9,732 | The International Aerial Robotics Competition is a long-running event begun in 1991 to advance the state of the art in fully autonomous air vehicles. This competition is restricted to university teams (although industry and governmental sponsorship of teams is allowed). Key to this event is the creation of flying robot... | Competitions and prizes in artificial intelligence | 0.819836 |
9,733 | There are two age brackets in this competition, 13-18 Age Group, and 18 and Above Age Group. The IJCAI Award for Research Excellence is a biannual award given at the IJCAI conference to researcher in artificial intelligence as a recognition of excellence of their career. The 2011 Federal Virtual World Challenge, advert... | Competitions and prizes in artificial intelligence | 0.819836 |
9,734 | Entries are required to use evolutionary computing. The Intel AI Global Impact Festival is an international annual competition held by Intel Corporation for school, and college students with prizes upwards of $15,000. It is about artificial intelligence technology. | Competitions and prizes in artificial intelligence | 0.819836 |
9,735 | There are a number of competitions and prizes to promote research in artificial intelligence. | Competitions and prizes in artificial intelligence | 0.819836 |
9,736 | Since the game is not known in advance the competitors cannot especially adapt their programs to a particular scenario. The prize in 2006 and 2007 was $10,000. The General Video Game AI Competition (GVGAI) poses the problem of creating artificial intelligence that can play a wide, and in principle unlimited, range of g... | Competitions and prizes in artificial intelligence | 0.819836 |
9,737 | The Herbrand Award is a prize given by CADE Inc. to honour persons or groups for important contributions to the field of automated deduction. The prize is $1000. The CADE ATP System Competition (CASC) is a yearly competition of fully automated theorem provers for classical first order logic associated with the CADE and... | Competitions and prizes in artificial intelligence | 0.819836 |
9,738 | A perfect vacuum is itself only attainable in principle. It is an idealization, like absolute zero for temperature, that can be approached, but never actually realized: One reason is that the walls of a vacuum chamber emit light in the form of black-body radiation...If this soup of photons is in thermodynamic equilibr... | QED vacuum | 0.819835 |
9,739 | Metabolite pool is a collective term for all of the substances involved in the metabolic process in a biological system. Metabolic pools are within cells (or organelles such as chloroplasts) and refer to the reservoir of molecules upon which enzymes can operate. The size of the reservoir is referred to as its "metaboli... | Metabolite pool | 0.819834 |
9,740 | At this conference, Soviet scientists announced that they had achieved electron temperatures of over 1000 eV in a tokamak device (T-3). This same year, Coppi was named a full professor in the MIT Department of Physics. He immediately collaborated with engineers at the Francis Bitter Magnet Laboratory, led by Bruce Mont... | Lower Hybrid Current Drive | 0.819827 |
9,741 | In the late 1960s, magnetic-confinement fusion research at MIT was carried out on small-scale "table-top" experiments at the Research Laboratory for Electronics and the Francis Bitter Magnet Laboratory. At this time, the Soviet Union was developing a tokamak (though this was unknown in the United States), and Princeton... | Lower Hybrid Current Drive | 0.819827 |
9,742 | Modelling attempts to replicate laws of physics that govern sound production, and will typically have several parameters, some of which are constants that describe the physical materials and dimensions of the instrument, while others are time-dependent functions describing the player's interaction with the instrument, ... | Physical modeling | 0.819826 |
9,743 | The study of network topology recognizes eight basic topologies: point-to-point, bus, star, ring or circular, mesh, tree, hybrid, or daisy chain. | Logical topology | 0.819825 |
9,744 | A linear topology puts a two-way link between one computer and the next. However, this was expensive in the early days of computing, since each computer (except for the ones at each end) required two receivers and two transmitters. By connecting the computers at each end of the chain, a ring topology can be formed. | Logical topology | 0.819825 |
9,745 | A distributed star is a network topology that is composed of individual networks that are based upon the physical star topology connected in a linear fashion – i.e., 'daisy-chained' – with no central or top level connection point (e.g., two or more 'stacked' hubs, along with their associated star connected nodes or 'sp... | Logical topology | 0.819825 |
9,746 | The output of any general continuous-time linear system is related to the input by an integral which may be written over a doubly infinite range because of the causality condition: If the properties of the system do not depend on the time at which it is operated then it is said to be time-invariant and h is a function ... | Linear system | 0.819824 |
9,747 | This is usually done for mathematical convenience. The previous definition of a linear system is applicable to SISO (single-input single-output) systems. For MIMO (multiple-input multiple-output) systems, input and output signal vectors ( x 1 ( t ) {\displaystyle {\mathbf {x} }_{1}(t)} , x 2 ( t ) {\displaystyle {\math... | Linear system | 0.819824 |
9,748 | This mathematical property makes the solution of modelling equations simpler than many nonlinear systems. For time-invariant systems this is the basis of the impulse response or the frequency response methods (see LTI system theory), which describe a general input function x(t) in terms of unit impulses or frequency co... | Linear system | 0.819824 |
9,749 | Lion algorithm (LA) is one among the bio-inspired (or) nature-inspired optimization algorithms (or) that are mainly based on meta-heuristic principles. It was first introduced by B. R. Rajakumar in 2012 in the name, Lion’s Algorithm.. It was further extended in 2014 to solve the system identification problem. This vers... | Lion algorithm | 0.819822 |
9,750 | In the LA, the terms that are associated with lion’s social system are mapped to the terminology of optimization problems. Few of such notable terms are related here. Lion: A potential solution to be generated or determined as optimal (or) near-optimal solution of the problem. | Lion algorithm | 0.819822 |
9,751 | Also known as rebatement and rabattement, rabatment means the rotation of a plane into another plane about their line of intersection, as in closing an open hinge. In two dimensions, it means to rotate a line about a point until the line coincides with another sharing the same point. The term is used in geometry, art a... | Rabatment of the rectangle | 0.819815 |
9,752 | In mathematics, a bump function (also called a test function) is a function f: R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } on a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} which is both smooth (in the sense of having continuous derivatives of all orders) and compactly supported. The set of all b... | Test function | 0.81981 |
9,753 | A related statistical concept, the notion of E-statistic or energy-statistic was introduced by Gábor J. Székely in the 1980s when he was giving colloquium lectures in Budapest, Hungary and at MIT, Yale, and Columbia. This concept is based on the notion of Newton’s potential energy. The idea is to consider statistical o... | Energy distance | 0.819806 |
9,754 | Applications include: Hierarchical clustering (a generalization of Ward's method) Testing multivariate normality Testing the multi-sample hypothesis of equal distributions, Change point detection Multivariate independence: distance correlation, Brownian covariance. Scoring rules:Gneiting and Raftery apply energy distan... | Energy distance | 0.819805 |
9,755 | (in Russian), English Translation: A characterization of distributions by mean values of statistics and certain probabilistic metrics A. A. Zinger, A. V. Kakosyan, L. B. Klebanov in Journal of Soviet Mathematics (1992). In the same paper there was given a definition of strongly negative definite kernel, and provided a ... | Energy distance | 0.819805 |
9,756 | Energy distance and E-statistic were considered as N-distances and N-statistic in Zinger A.A., Kakosyan A.V., Klebanov L.B. Characterization of distributions by means of mean values of some statistics in connection with some probability metrics, Stability Problems for Stochastic Models. Moscow, VNIISI, 1989,47-55. | Energy distance | 0.819805 |
9,757 | An example of a metric of negative type but not of strong negative type is the plane with the taxicab metric. All Euclidean spaces and even separable Hilbert spaces have strong negative type.In the literature on kernel methods for machine learning, these generalized notions of energy distance are studied under the name... | Energy distance | 0.819805 |
9,758 | One can generalize the notion of energy distance to probability distributions on metric spaces. Let ( M , d ) {\displaystyle (M,d)} be a metric space with its Borel sigma algebra B ( M ) {\displaystyle {\mathcal {B}}(M)} . Let P ( M ) {\displaystyle {\mathcal {P}}(M)} denote the collection of all probability measures o... | Energy distance | 0.819805 |
9,759 | The derivation of this formula is given below. When a light ray is incident from a medium of refractive index n to the core of index ncore at the maximum acceptance angle, Snell's law at the medium–core interface gives n sin θ max = n core sin θ r . {\displaystyle n\sin \theta _{\max }=n_{\text{core}}\sin \theta _{... | Numerical apertures | 0.819804 |
9,760 | The roots of FKS date back to 1985, when Ján Pišút, a university professor inspired by emerging mathematical correspondence seminars throughout Slovakia and Central Europe, founded a similar competition for physics enthusiasts. FKS, as well as other correspondence seminars, were created in the 1980s in order to provide... | Physics Correspondence Seminar | 0.819798 |
9,761 | The FKS Summer School is a two-week summer camp organised at FMFI, Comenius University, Slovakia. The aim of FKS Summer School is primarily to broaden the physics knowledge of a large number of motivated students, not necessarily the participants of the correspondence seminars, and thus increasing the competition in ph... | Physics Correspondence Seminar | 0.819798 |
9,762 | Trojsten Academy serves as a one-day event of Trojsten annually organized in December, where university professors and prominent scientists deliver lectures on quantum mechanics, quantum information, condensed matter, etc. Trojsten Club is a one-day companion event to the Academy, Mathematics Náboj and Physics Náboj. D... | Physics Correspondence Seminar | 0.819798 |
9,763 | FX is a special category designed for most passionate students, who aspire to become professional researchers. The problems often involve advanced mathematical methods, such as differentiation or integration, and concepts from undergraduate physics curricula, and require intense self-study prior to submission. The part... | Physics Correspondence Seminar | 0.819798 |
9,764 | The first Physics Náboj was held in 1998. In 2015, Náboj was organized internationally for the first time (alongside Bratislava in Prague and Budapest) with the help of local educational organizations. The future plans are to increase this unique international collaboration by expanding to other countries in the region... | Physics Correspondence Seminar | 0.819798 |
9,765 | Physics Náboj (Bullet) is a team competition for high school students held each year in November. Teams representing high schools consisting of up to five students compete in a time limit of about 90 minutes in solving as many problems as possible. Each team starts with eight problems; after the successful submission o... | Physics Correspondence Seminar | 0.819798 |
9,766 | Physics Correspondence Seminar (FKS) is a correspondence competition primarily aimed at high school students in Slovakia. Its purpose is to provide an outlet for talented individuals by creating challenging problems and organising academic camps. The seminar organisers are mostly undergraduate students from the FMFI, C... | Physics Correspondence Seminar | 0.819798 |
9,767 | "In response, some politicians expressed skepticism about the wisdom of regulating a technology that is still in development. Responding both to Musk and to February 2017 proposals by European Union lawmakers to regulate AI and robotics, Intel CEO Brian Krzanich has argued that artificial intelligence is in its infancy... | Regulation of algorithms | 0.819793 |
9,768 | In 2016, Joy Buolamwini founded Algorithmic Justice League after a personal experience with biased facial detection software in order to raise awareness of the social implications of artificial intelligence through art and research.In 2017 Elon Musk advocated regulation of algorithms in the context of the existential r... | Regulation of algorithms | 0.819793 |
9,769 | However, in Frank Herbert's Dune universe, thinking machines is a collective term for artificial intelligence, which were completely destroyed and banned after a revolt known as the Butlerian Jihad: JIHAD, BUTLERIAN: (see also Great Revolt) — the crusade against computers, thinking machines, and conscious robots begun ... | Regulation of algorithms | 0.819793 |
9,770 | In 1942, author Isaac Asimov addressed regulation of algorithms by introducing the fictional Three Laws of Robotics: A robot may not injure a human being or, through inaction, allow a human being to come to harm. A robot must obey the orders given it by human beings except where such orders would conflict with the Firs... | Regulation of algorithms | 0.819793 |
9,771 | In the United States, steering on regulating security-related AI is provided by the National Security Commission on Artificial Intelligence.In 2017, the U.K. Vehicle Technology and Aviation Bill imposes liability on the owner of an uninsured automated vehicle when driving itself and makes provisions for cases where the... | Regulation of algorithms | 0.819793 |
9,772 | In response, the National Institute of Standards and Technology has released a position paper, the National Security Commission on Artificial Intelligence has published an interim report, and the Defense Innovation Board has issued recommendations on the ethical use of AI.In April 2016, for the first time in more than ... | Regulation of algorithms | 0.819793 |
9,773 | AI law and regulations can be divided into three main topics, namely governance of autonomous intelligence systems, responsibility and accountability for the systems, and privacy and safety issues. The development of public sector strategies for management and regulation of AI has been increasingly deemed necessary at ... | Regulation of algorithms | 0.819793 |
9,774 | Another emerging topic is the regulation of blockchain algorithms (Use of the smart contracts must be regulated) and is mentioned along with regulation of AI algorithms. Many countries have enacted regulations of high frequency trades, which is shifting due to technological progress into the realm of AI algorithms.The ... | Regulation of algorithms | 0.819793 |
9,775 | Regulation of algorithms, or algorithmic regulation, is the creation of laws, rules and public sector policies for promotion and regulation of algorithms, particularly in artificial intelligence and machine learning. For the subset of AI algorithms, the term regulation of artificial intelligence is used. The regulatory... | Regulation of algorithms | 0.819793 |
9,776 | A probability distribution can be described in various forms, such as by a probability mass function or a cumulative distribution function. One of the most general descriptions, which applies for absolutely continuous and discrete variables, is by means of a probability function P: A → R {\displaystyle P\colon {\mathca... | Probability distribution | 0.819792 |
9,777 | This is a key principle of quantum mechanics. Probabilistic load flow in power-flow study explains the uncertainties of input variables as probability distribution and provides the power flow calculation also in term of probability distribution. Prediction of natural phenomena occurrences based on previous frequency di... | Probability distribution | 0.819792 |
9,778 | The cache language models and other statistical language models used in natural language processing to assign probabilities to the occurrence of particular words and word sequences do so by means of probability distributions. In quantum mechanics, the probability density of finding the particle at a given point is prop... | Probability distribution | 0.819792 |
9,779 | Mass spectrometry has both qualitative and quantitative uses. These include identifying unknown compounds, determining the isotopic composition of elements in a molecule, and determining the structure of a compound by observing its fragmentation. Other uses include quantifying the amount of a compound in a sample or st... | Mass Spectrometry | 0.819788 |
9,780 | Most NMR-based structure validation protocols primarily use NOE (Nuclear Overhauser Enhancement), J-coupling or residual dipolar coupling (RDC ) data to assess or validate structures. In particular, they try to assess the agreement between the experimentally observed and the calculated NOEs, RDCs and/or J-couplings. Go... | Protein Structure Evaluation Suite & Server | 0.819786 |
9,781 | Since 1986, (Reduced ordered) binary decision diagrams have also been used for SAT solving. In 1989-1990, Stålmarck's method for formula verification was presented and patented. It has found some use in industrial applications.DPLL has been extended for automated theorem proving for fragments of first-order logic by wa... | DPLL algorithm | 0.81978 |
9,782 | In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem. It was introduced in 1961 by Martin Davis, George Logema... | DPLL algorithm | 0.81978 |
9,783 | The SAT problem is important both from theoretical and practical points of view. In complexity theory it was the first problem proved to be NP-complete, and can appear in a broad variety of applications such as model checking, automated planning and scheduling, and diagnosis in artificial intelligence. As such, writing... | DPLL algorithm | 0.81978 |
9,784 | This formalizes what is meant by R n {\displaystyle \mathbf {R} ^{n}} being or the standard simplex being model spaces, and such observations as that every bounded convex polytope is the image of a simplex. Here suboperads correspond to more restricted operations and thus more general theories. From this point of view,... | Linear combinations | 0.819779 |
9,785 | More abstractly, in the language of operad theory, one can consider vector spaces to be algebras over the operad R ∞ {\displaystyle \mathbf {R} ^{\infty }} (the infinite direct sum, so only finitely many terms are non-zero; this corresponds to only taking finite sums), which parametrizes linear combinations: the vector... | Linear combinations | 0.819779 |
9,786 | In arithmetic frameworks, the functions can be taken to be sequences of numbers. If a proof calculus includes the principle of excluded middle, then the notion of function predicate is a liberal one as well, and then the function comprehension principle grants existence of function objects incompatible with the constru... | Axiom of non-choice | 0.819774 |
9,787 | Unique choice is thus a theorem. Note that Z F {\displaystyle {\mathsf {ZF}}} does not adopt the axiom of choice. In intuitionistic Zermelo–Fraenkel set theory I Z F {\displaystyle {\mathsf {IZF}}} and some weaker theories, unique choice is also derivable. As in the case with theories of arithmetic, this then means tha... | Axiom of non-choice | 0.819774 |
9,788 | Pharmaceutical Biology is a monthly peer-reviewed medical journal that publishes research on natural product research related to pharmaceutical biology. The editor-in-chief is John M. Pezzuto (Western New England University). | Pharmaceutical Biology | 0.819766 |
9,789 | Quantitative biology is an umbrella term encompassing the use of mathematical, statistical or computational techniques to study life and living organisms. The central theme and goal of quantitative biology is the creation of predictive models based on fundamental principles governing living systems.The subfields of bio... | Quantitative biology | 0.819766 |
9,790 | It has been shown that one can crosslink the DNA strands at their base, and subsequently dissolve the inorganic core with KCN or I2 to create a core-less (hollow) form of SNA (Fig. 3, right), which exhibits many of the same properties as the original polyvalent DNA gold nanoparticle conjugate (Fig. 3, left). Due to the... | Spherical nucleic acid | 0.819759 |
9,791 | Scientists and engineers have been synthesizing and, in certain cases, mass-producing nucleic acids for decades to understand and exploit this elegant chemical recognition motif. The recognition abilities of nucleic acids can be enhanced when arranged in a spherical geometry, which allows for polyvalent interactions to... | Spherical nucleic acid | 0.819759 |
9,792 | In another research, researchers trained robots to learn behaviors such as pouring liquid from a cup; robots learned from videos of human demonstrations recorded from multiple viewpoints.Google Brain researchers have collaborated with other companies and academic institutions on robotics research. In 2016, the Google B... | Google Brain | 0.819759 |
9,793 | The different layers of neural networks, replicating the human brain, were able to link the corresponding parts and subsequently manipulate the audio waveform until it was transformed to English text. Another drawback of the GNMT model is that it causes the time of translation to increase exponentially with the number ... | Google Brain | 0.819759 |
9,794 | In October 2016, Google Brain designed an experiment to determine that neural networks are capable of learning secure symmetric encryption. In this experiment, three neural networks were created: Alice, Bob and Eve. Adhering to the idea of a generative adversarial network (GAN), the goal of the experiment was for Alice... | Google Brain | 0.819759 |
9,795 | Google Brain was a deep learning artificial intelligence research team under the umbrella of Google AI, a research division at Google dedicated to artificial intelligence. Formed in 2011, Google Brain combined open-ended machine learning research with information systems and large-scale computing resources. The team ha... | Google Brain | 0.819759 |
9,796 | Aiming to improve traditional robotics control algorithms where new skills of a robot need to be hand-programmed, robotics researchers at Google Brain are developing machine learning techniques to allow robots to learn new skills on their own. They also attempt to develop ways for information sharing between robots so ... | Google Brain | 0.819759 |
9,797 | This means that it is possible to translate speech in one language directly into text in another language, without first transcribing it to text. According to the Researchers at Google Brain, this intermediate step can be avoided using neural networks. In order for the system to learn this, they exposed it to many hour... | Google Brain | 0.819759 |
9,798 | Furthermore, it allows for Zero-Shot Translations, which are translations between two languages that the system has never explicitly seen before. Google announced that Google Translate can now also translate without transcribing, using neural networks. | Google Brain | 0.819759 |
9,799 | The Google Brain team contributed to the Google Translate project by employing a new deep learning system that combines artificial neural networks with vast databases of multilingual texts. In September 2016, Google Neural Machine Translation (GNMT) was launched, an end-to-end learning framework, able to learn from a l... | Google Brain | 0.819759 |
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