id int32 0 100k | text stringlengths 20 3.54k | source stringlengths 1 104 | similarity float32 0.8 0.91 |
|---|---|---|---|
3,400 | However, this optimization makes it impossible to read off the minimal series of edit operations. A linear-space solution to this problem is offered by Hirschberg's algorithm. : 634 A general recursive divide-and-conquer framework for solving such recurrences and extracting an optimal sequence of operations cache-effic... | Edit distance | 0.834798 |
3,401 | The techniques of modern algebraic geometry, and in particular intersection theory, can be used to solve Apollonius's problem. In this approach, the problem is reinterpreted as a statement about circles in the complex projective plane. Solutions involving complex numbers are allowed and degenerate situations are counte... | Problem of Apollonius | 0.834794 |
3,402 | In topology, quantum mechanics and geometrodynamics, rolling-ball arguments are used to describe how the perceived geometry and connectedness of a surface can be scale-dependent. If a researcher probes the shape of an intricately curved surface by rolling a ball across it, then features that are continually curved but ... | Rolling ball argument | 0.834793 |
3,403 | The isomorphism theorems from ordinary group theory are not always true in the topological setting. This is because a bijective homomorphism need not be an isomorphism of topological groups. For example, a native version of the first isomorphism theorem is false for topological groups: if f: G → H {\displaystyle f:G\to... | Quasitopological group | 0.834792 |
3,404 | In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton iteration. Intersection problems between a line and a conic section (circle, ellipse, parabola, etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations th... | Intersection (geometry) | 0.834789 |
3,405 | Expressed protein ligation, has proven to be successful techniques for synthetically producing proteins that contain phosphomimetic molecules at either terminus. In addition, researchers have used unnatural amino acid mutagenesis at targeted sites within a peptide sequence.Advances in chemical biology have also improve... | Chemical Biology | 0.834789 |
3,406 | Since each insertion and deletion requires O(1) amortized time, the total deterministic time is T(n) = T(2n/3) + O(n). Using case 3 of the master theorem for divide-and-conquer recurrences (with ε=1 and c=2/3), we know that T(n) = Θ(n). The final algorithm looks like this: function softHeapSelect(a, k) if k = 1 then re... | Soft heap | 0.834783 |
3,407 | A group-contribution method in chemistry is a technique to estimate and predict thermodynamic and other properties from molecular structures. | Group-contribution method | 0.834777 |
3,408 | A parabola can be considered as the affine part of a non-degenerated projective conic with a point Y ∞ {\displaystyle Y_{\infty }} on the line of infinity g ∞ {\displaystyle g_{\infty }} , which is the tangent at Y ∞ {\displaystyle Y_{\infty }} . The 5-, 4- and 3- point degenerations of Pascal's theorem are properties ... | Parabolic curve | 0.834777 |
3,409 | The number of instructions to perform the above basic "loop" (Fetch/Execute/calculate new address) depends on hardware but it could be accomplished on IBM S/360/370/390/ES9000 range of machines in around 12 or 13 instructions for many instruction types. Checking for valid memory locations or for conditional "pause"s ad... | Instruction Set Simulator | 0.834775 |
3,410 | Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Such probes include effects of electric and magnetic fields, measuring response functions, transport properties and thermometry. Commonly used experimental methods include spectroscopy, with pro... | Condensed matter physicist | 0.834772 |
3,411 | The restrictions above (CNF, 2CNF, 3CNF, Horn, XOR-SAT) bound the considered formulae to be conjunctions of subformulae; each restriction states a specific form for all subformulae: for example, only binary clauses can be subformulae in 2CNF. Schaefer's dichotomy theorem states that, for any restriction to Boolean func... | Boolean satisfiability problem | 0.83477 |
3,412 | Applications of control methodology have helped to make possible space travel and communication satellites, safer and more efficient aircraft, cleaner automobile engines, and cleaner and more efficient chemical processes. Before it emerged as a unique discipline, control engineering was practiced as a part of mechanica... | Control Engineering | 0.834769 |
3,413 | In either the coordinate or vector formulations, one may verify that the given point lies on the given plane by plugging the point into the equation of the plane. To see that it is the closest point to the origin on the plane, observe that p {\displaystyle \mathbf {p} } is a scalar multiple of the vector v {\displaysty... | Point-plane distance | 0.834765 |
3,414 | With the dimensions shown, the mechanical advantage, W/F can be calculated as 10/3 × 9/4 = 7.5, meaning that an applied force of 1 pound (or 1 kg) could lift a weight of 7.5 lb (or 7.5 kg). Alternatively, if the position of the fulcrum on lever AA' were moved so that A1 = 4 units and A2 = 9 units, then the mechanical a... | Compound lever | 0.834762 |
3,415 | Further speed-up is gained by the auto-management of the memory of large array objects. Numerical operations are parallelized on multicore systems. Linear algebra routines rely on processor specific optimized versions of LAPACK and BLAS. ILNumerics arrays utilize the unmanaged heap for storing data. This way, the size ... | ILNumerics | 0.834759 |
3,416 | (PM 1962:188) α ∪ –α = V The union of a set and its inverse is the universal (completed) set. α ∩ –α = Λ The intersection of a set and its inverse is the null (empty) set.When applied to relations in section ✸23 CALCULUS OF RELATIONS, the symbols "⊂", "∩", "∪", and "–" acquire a dot: for example: "⊍", "∸".The notion, a... | Ramified type theory | 0.834758 |
3,417 | Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a collection of mathematical lemmas on "the method of first and last ratios", a geometrical form of infinitesimal calculus. The second section establishes relationships between centripetal ... | Philosophiæ Naturalis Principia Mathematica | 0.834755 |
3,418 | Putting it another way, according to the Rouché–Capelli theorem, any system of equations (overdetermined or otherwise) is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two matrices are equal, the system must have at least o... | Linear equation system | 0.834753 |
3,419 | If the division algebra is not assumed to be associative, usually some weaker condition (such as alternativity or power associativity) is imposed instead. See algebra over a field for a list of such conditions. Over the reals there are (up to isomorphism) only two unitary commutative finite-dimensional division algebra... | Division algebra | 0.834751 |
3,420 | Integer1 -eq Integer2 - Integer1 and Integer2 variables are algebraically equal -ne - not equal -gt - greater than -ge - greater or equal -lt - less than -le - less or equal | Test (Unix) | 0.834747 |
3,421 | When n = 2, the inequalities become 2 1 x 1 + 1 x 2 ≤ x 1 x 2 ≤ x 1 + x 2 2 ≤ x 1 2 + x 2 2 2 {\displaystyle {\frac {2}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}}}\leq {\sqrt {x_{1}x_{2}}}\leq {\frac {x_{1}+x_{2}}{2}}\leq {\sqrt {\frac {x_{1}^{2}+x_{2}^{2}}{2}}}} for all x 1 , x 2 > 0 , {\displaystyle x_{1},x_{2}>0,} which... | HM-GM-AM-QM inequalities | 0.834747 |
3,422 | The classical problem in computer vision, image processing, and machine vision is that of determining whether or not the image data contains some specific object, feature, or activity. Different varieties of recognition problem are described in the literature. Object recognition (also called object classification) – on... | Computer Vision | 0.834747 |
3,423 | This method permits amplification of genes for which only a partial sequence information is available, and allows unidirectional genome walking from known into unknown regions of the chromosome. Solid Phase PCR: encompasses multiple meanings, including Polony Amplification (where PCR colonies are derived in a gel matri... | Single Specific Primer-PCR | 0.834742 |
3,424 | For example, although the support-vector machine (SVM) yielded the best result in landslide susceptibility assessment accuracy, the result cannot be rewritten in the form of expert rules that explain how and why an area was classified as that specific class. In contrast, the decision tree has a transparent model that c... | Machine learning in earth sciences | 0.834737 |
3,425 | GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory. | GAP computer algebra system | 0.834737 |
3,426 | Activities of food scientists include the development of new food products, design of processes to produce and conserve these foods, choice of packaging materials, shelf-life studies, study of the effects of food on the human body, sensory evaluation of products using panels or potential consumers, as well as microbiol... | Life science | 0.83473 |
3,427 | Below we present four theorems, labelled A, B, C and D. They are often numbered as "First isomorphism theorem", "Second..." and so on; however, there is no universal agreement on the numbering. Here we give some examples of the group isomorphism theorems in the literature. Notice that these theorems have analogs for ri... | First ring isomorphism theorem | 0.834729 |
3,428 | In the 3D ideal chain model in chemistry, two angles are necessary to describe the orientation of each monomer. It is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the system. Depending on what one is counting, there are sever... | Degrees of freedom (physics) | 0.834727 |
3,429 | Originally, in the actual data transfer each set of resource records for a single domain name and type was transferred in a separate response message from the server to the client. However, this is inefficient, and some DNS server software implemented optimizations, geared at allowing the response compression mechanism... | Zone transfer | 0.834715 |
3,430 | The idea of describing algebraic structures with finite-automata can be generalized from groups to other structures. For instance, it generalizes naturally to automatic semigroups. | Automatic group | 0.834715 |
3,431 | In mathematics, a ternary operation is an n-ary operation with n = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A. In computer science, a ternary operator is an operator that takes three arguments as input and returns one output. | Ternary operation | 0.834714 |
3,432 | This geometry ensures that, per rotation, a constant flow volume proportional to rotary angle is always produced. The flow direction is reversed by changing the direction of rotation. Volume is therefore clearly determined by degree angle. | Endless-piston principle | 0.834714 |
3,433 | The title of her diploma thesis was "Estimating the absolute entropy of a liquid based on a single molecular dynamics simulation under periodic boundary conditions." In 2005, she started her PhD studies in Chemistry at ETH Zürich. | Bettina G. Keller | 0.834709 |
3,434 | For example, the standard signature for groups in universal algebra is (•, −1, 1). (Inversion and unit are needed to get the right notions of homomorphism and so that the group laws can be expressed as equations.) Therefore, a subgroup of a group G is a subset S of G such that: the identity e of G belongs to S (so that... | Subalgebra | 0.834706 |
3,435 | 755–772. 1985. How biology differs from the physical sciences. | Ernst Mayr | 0.834702 |
3,436 | Between 2009 and 2012, recurrent neural networks and deep feedforward neural networks developed in Schmidhuber's research group won eight international competitions in pattern recognition and machine learning. For example, the bi-directional and multi-dimensional long short-term memory (LSTM) of Graves et al. won three... | History of artificial neural networks | 0.834697 |
3,437 | In addition to points for pieces, most handcrafted evaluation functions take many factors into account, such as pawn structure, the fact that a pair of bishops are usually worth more, centralized pieces are worth more, and so on. The protection of kings is usually considered, as well as the phase of the game (opening, ... | Chess-playing program | 0.834696 |
3,438 | In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. | Units of measure | 0.834695 |
3,439 | These molecules alter the biology of protein folding and/or degradation by altering the stoichiometry of the proteostasis network components in a given sub cellular compartment. For example, some proteostasis regulators initiate stress responsive signaling, such as the unfolded protein response, which transcriptionally... | Proteostasis | 0.834694 |
3,440 | The Entscheidungsproblem (German for 'decision problem') is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for an algorithm that takes as input a statement of a first-order logic (possibly with a finite number of axioms beyond the usual axioms of first-order logic) and answers "Yes" or "No" a... | Metamathematics | 0.834691 |
3,441 | An example would be ChatGPT using a plugin to query Wolfram Alpha.These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that considered, e.g., whether the use of symbols included logic or not and if it did, whether the l... | Neuro-symbolic AI | 0.83469 |
3,442 | The idea of motion may not be applied to it." Hence it was made clear that in the case of electromagnetism there is no underlying material through which the forces must propagate. In these cases there can be no distinction made between the effects of a field arising through a potential and the effects of an "action at ... | History of the philosophy of field theory | 0.834685 |
3,443 | The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used. The problem has many applications, such as filling up containers, loading trucks with weight c... | Bin packing problem | 0.834685 |
3,444 | Through iterative optimization of an objective function, supervised learning algorithms learn a function that can be used to predict the output associated with new inputs. An optimal function will allow the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm th... | Statistical learning | 0.834685 |
3,445 | In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all points experience the same physics). A material constructed wit... | Homogeneity (physics) | 0.834684 |
3,446 | Isabella A. Abbott (1997) For her comprehensive investigations of the biogeography and systematics of marine algae in the eastern and central Pacific, with emphasis on Rhodophyta, the red algae. Elisabeth Gantt (1994) For her pioneering work in elucidating the supramolecular structure of the light-harvesting complexes ... | Gilbert Morgan Smith Medal | 0.83468 |
3,447 | Fibonacci nim is an impartial game in that the moves that are available from any position do not depend on the identity of the player who is about to move. Therefore, the Sprague–Grundy theorem can be used to analyze an extension of the game in which there are multiple piles of coins, and each move removes coins from o... | Fibonacci nim | 0.83468 |
3,448 | Consequently, electromagnetic quantities in the Heaviside–Lorentz system differ by factors of √4π in the definitions of the electric and magnetic fields and of electric charge. It is often used in relativistic calculations, and are used in particle physics. They are particularly convenient when performing calculations ... | Heaviside–Lorentz units | 0.834679 |
3,449 | The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science, and engineering. List of algorithm general topics List of computability and complexity topi... | Lists of mathematics topics | 0.834679 |
3,450 | Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set th... | Open problem in mathematics | 0.834679 |
3,451 | A particularly important development here is the work of Gromov who used probabilistic methods to prove the existence of a finitely generated group that is not uniformly embeddable into a Hilbert space. Other notable developments include introduction and study of the notion of generic-case complexity for group-theoreti... | Geometric group theory | 0.834677 |
3,452 | Supervised learning (SL) is a paradigm in machine learning where input objects (for example, a vector of predictor variables) and a desired output value (also known as human-labeled supervisory signal) train a model. The training data is processed, building a function that maps new data on expected output values. An op... | Supervised classification | 0.834676 |
3,453 | Plants are the eukaryotes that form the kingdom Plantae; they are predominantly photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with cyanobacteria to produce sugars from carbon dioxide and water, using the green pigment chlorophyll. Exceptions are pa... | Plant | 0.834673 |
3,454 | Detection of the marker can be direct by RNA sequencing, or indirect using allozymes. Some of the methods used to study the genome or phylogenetics are RFLP, AFLP, RAPD, SSR. | Genetic markers | 0.834669 |
3,455 | After tearing a partitioning algorithm is reapplied. Minimizing feedback loops gets the best results for Binary DSM, but not always for Numeric DSM or Probability DSM. Sequencing algorithms (using optimization, genetic algorithms) are typically trying to minimize the number of feedback loops and also to reorder coupled... | Design Structure Matrix | 0.834667 |
3,456 | However if we extend the group G {\displaystyle G\ } to the group H {\displaystyle H\ } with the adjacent multiplication table: Then the conditions have two solutions, namely x = b {\displaystyle x=b\ } and x = c {\displaystyle x=c\ } . Thus there are three possibilities regarding such conditions: They may be inconsist... | Algebraically closed group | 0.834665 |
3,457 | In justifying the deprecation of the term "field quantity" and instead using "root-power quantity" in the context of levels, ISO 80000 draws attention to the conflicting use of the former term to mean a quantity that depends on the position, which in physics is called a field. Such a field is often called a field quant... | Field and power quantities | 0.834664 |
3,458 | Świerczkowski (1959a) built upon Rieger's results in another direction. Given a cyclically ordered group K and an ordered group L, the product K × L is a cyclically ordered group. In particular, if T is the circle group and L is an ordered group, then any subgroup of T × L is a cyclically ordered group. Moreover, every... | Cyclically ordered group | 0.834663 |
3,459 | GeneMapper A commercial software for normalisation and size calling of peaks from a certain brand of capillary electrophoresis machines. BioNumerics A commercial bioinformatics solution to store and analyze a large panel of biological data, including MLVA, and more generally character datasets. Normalisation, size call... | Multiple loci VNTR analysis | 0.834661 |
3,460 | Roots, rodents, worms, and freezing-thawing cycles further break the peds into smaller peds of a more or less spherical shape.At a smaller scale, plant roots extend into voids (macropores) and remove water causing macroporosity to increase and microporosity to decrease, thereby decreasing aggregate size. At the same ti... | Physical properties of soil | 0.83466 |
3,461 | In Scotland the subjects split into chemistry, physics and biology at the age of 13–15 for National 4/5s in these subjects, and there is also a combined science standard grade qualification which students can sit, provided their school offers it. In September 2006 a new science program of study known as 21st Century Sc... | Biology education | 0.834659 |
3,462 | Other, comparable solutions were subsequently developed. Notably, all closed-form solutions were found a decade or more after the GPS program was initiated using iterative methods. The solution for the position of an aircraft having a known altitude using 3 TOA measurements requires solving a quartic (fourth-order) pol... | Pseudo-range multilateration | 0.834658 |
3,463 | 5. A boolean algebra is orthomodular. | Map of lattices | 0.834656 |
3,464 | The major advantage of the TI-89 over other TI calculators is its built-in computer algebra system, or CAS. The calculator can evaluate and simplify algebraic expressions symbolically. For example, entering x^2-4x+4 returns x 2 − 4 x + 4 {\displaystyle x^{2}-4x+4} . The answer is "prettyprinted" by default; that is, di... | TI-89 series | 0.834655 |
3,465 | Historically, each volume has centered on a specific topic of biochemistry, such as DNA repair, yeast genetics, or the biology of nitric oxide. In recent years, however, the range of topics covered has broadened to also include biotechnology-oriented areas of research. Each Volume and Chapter includes not only backgrou... | Methods in Enzymology | 0.834652 |
3,466 | This finding explained how kinesin could carry cargos long distances in the axons of nerve cells. This work also helped to establish the field of single-molecule biophysics. In 1989, Howard set up his own lab at the University of Washington, where his research focused on how motor proteins convert chemical energy deriv... | Jonathon Howard | 0.834651 |
3,467 | In computational biology, de novo protein structure prediction refers to an algorithmic process by which protein tertiary structure is predicted from its amino acid primary sequence. The problem itself has occupied leading scientists for decades while still remaining unsolved. According to Science, the problem remains ... | De novo protein structure prediction | 0.83465 |
3,468 | The equation defining an algebraic curve expressed in polar coordinates is known as a polar equation. In many cases, such an equation can simply be specified by defining r as a function of φ. The resulting curve then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r. Note... | Radial distance (geometry) | 0.834645 |
3,469 | The behavior of ions in a homogeneous, linear, static electric or magnetic field (separately) as is found in a sector instrument is simple. The physics are described by a single equation called the Lorentz force law. This equation is the fundamental equation of all mass spectrometric techniques and applies in non-linea... | Bainbridge mass spectrometer | 0.834642 |
3,470 | The selection algorithms evaluate components of random sets of solutions to a problem. The solutions that come out on top are then recombined and mutated and run through the process again. This happens over and over until the proper solution is discovered. They are functionally similar to neural networks in that they a... | Clinical decision support system | 0.834641 |
3,471 | Consider a three-dimensional space with unit basis vectors A, B, and C. The sphere in the figure below is used to show the scale of the reference frame for context and the box is used to provide a rotational context. Typically, in electrical engineering (or any other context that uses three-phase systems), the three-ph... | Direct-quadrature-zero transformation | 0.834641 |
3,472 | This group was originally classified among the fungi (the name "oomycota" means "egg fungus") and later treated as protists, based on general morphology and lifestyle. A cladistic analysis based on modern discoveries about the biology of these organisms supports a relatively close relationship with some photosynthetic ... | Water mould | 0.83463 |
3,473 | The soundness of the optimal strategy described above was demonstrated by C. Bouton. Theorem. In a normal nim game, the player making the first move has a winning strategy if and only if the nim-sum of the sizes of the heaps is not zero. Otherwise, the second player has a winning strategy. | Nim | 0.834629 |
3,474 | The Sprague–Grundy theorem applies to impartial games (in which each move may be played by either player) and asserts that every such game has an equivalent Sprague–Grundy value, a "nimber", which indicates the number of pieces in an equivalent position in the game of nim. All second-player win games have a Sprague–Gru... | Zero game | 0.834627 |
3,475 | This example shows the Euler and Venn diagrams and Karnaugh map deriving and verifying the deduction "No Xs are Zs". In the illustration and table the following logical symbols are used: 1 can be read as "true", 0 as "false" ~ for NOT and abbreviated to ' when illustrating the minterms e.g. x' =defined NOT x, + for Boo... | Euler diagram | 0.834625 |
3,476 | Brailov (2021), Brailov (2022), Ehrenborg, Morel & Readdy (2022) extends this result to higher dimensions, i.e. for certain arrangements of hyperplanes, the alternating sum of volumes cut out by the hyperplanes is zero. Compare with the ham sandwich theorem, a result about slicing n-dimensional objects. The two-dimensi... | Pizza theorem | 0.834623 |
3,477 | Mechatronics accentuates the intersection of both fields. Together, electronic and electric devices, their development, maintenance, and power supply comprise the subject of electrical engineering. The majority of electric devices in households is stationary and — due to their considerable power consumption — relies on... | Electric device | 0.834621 |
3,478 | Charge conservation can also be understood as a consequence of symmetry through Noether's theorem, a central result in theoretical physics that asserts that each conservation law is associated with a symmetry of the underlying physics. The symmetry that is associated with charge conservation is the global gauge invaria... | Charge conservation | 0.834619 |
3,479 | The Java virtual machine is an abstract (virtual) computer defined by a specification. It is a part of java runtime environment. The garbage collection algorithm used and any internal optimization of the Java virtual machine instructions (their translation into machine code) are not specified. | Java Virtual Machine | 0.834617 |
3,480 | An axiom of an algebraic structure often has the form of an identity, that is, an equation such that the two sides of the equals sign are expressions that involve operations of the algebraic structure and variables. If the variables in the identity are replaced by arbitrary elements of the algebraic structure, the equa... | Algebraic structure | 0.834613 |
3,481 | During this time the neural networks also resurfaced as it was shown that the limitations of the perceptrons can be overcome by Multi-layer perceptrons. Also in the early 1990s convolutional neural networks were born which showed great results on digit recognition but did not scale up well on harder problems. | Visual Turing Test | 0.834612 |
3,482 | Elements of parity 0 are said to be even and those of parity 1 to be odd. If x and y are both homogeneous then so is the product xy and | x y | = | x | + | y | {\displaystyle |xy|=|x|+|y|} . An associative superalgebra is one whose multiplication is associative and a unital superalgebra is one with a multiplicative ide... | Superalgebra | 0.834612 |
3,483 | Since live cells are not being used, the toxicity of the product protein is not a significant concern. These advantages enable numerous applications. A major application of CFPS is incorporation of unnatural amino acids into protein structures (see expanded genetic code). The openness of the reaction is ideal for inser... | Cell-free protein synthesis | 0.83461 |
3,484 | ALEKS (Assessment and Learning in Knowledge Spaces) is an online tutoring and assessment program that includes course material in mathematics, chemistry, introductory statistics, and business.Rather than being based on numerical test scores, ALEKS uses the theory of knowledge spaces to develop a combinatorial understan... | ALEKS | 0.834608 |
3,485 | Case 2: g ∥ h {\displaystyle g\parallel h\ } (little theorem). In this case the coordinates are chosen such that c = ( 0 , 0 ) , b = ( 1 , 0 ) , A = ( 0 , 1 ) , B = ( γ , 1 ) , γ ≠ 0 {\displaystyle \;c=(0,0),\;b=(1,0),\;A=(0,1),\;B=(\gamma ,1),\;\gamma \neq 0} . From the parallelity of A b ∥ B a {\displaystyle Ab\paral... | Pappus's hexagon theorem | 0.834606 |
3,486 | An example would be ChatGPT using a plugin to query Wolfram Alpha.These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that considered, e.g., whether the use of symbols included logic and if it did, whether the logic wa... | Neuro-symbolic AI | 0.834601 |
3,487 | Elasticity – Elasticity tensor - Electric motor – Electrical engineering – Electrical circuit – Electrical network – Electromagnetism – Electronic circuit – Electronics – Energy – Engine – Engineering – Engineering cybernetics – Engineering drawing – Engineering economics – Engineering ethics – Engineering management –... | Index of mechanical engineering articles | 0.834601 |
3,488 | In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability spac... | Probability spaces | 0.834598 |
3,489 | These manually curated lineage designations, and the associated genome sequences, are the input into the machine learning model training. This model, both the training and the assignment, has been termed 'pangoLEARN'. The current version of pangoLEARN uses a classification tree, based on the scikit-learn implementation... | Phylogenetic Assignment of Named Global Outbreak Lineages | 0.834597 |
3,490 | Burnside's theorem states that if G is a finite group of order paqb where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. | Solvable subgroup | 0.834597 |
3,491 | Modulo 1 any two integers are congruent, i.e., there is only one congruence class, , coprime to 1. Therefore, ( Z / 1 Z ) × ≅ C 1 {\displaystyle (\mathbb {Z} /1\,\mathbb {Z} )^{\times }\cong \mathrm {C} _{1}} is the trivial group with φ(1) = 1 element. Because of its trivial nature, the case of congruences modulo 1 is ... | Multiplicative group of integers modulo n | 0.834593 |
3,492 | A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e an... | Mathematical constant | 0.834592 |
3,493 | In practice, it is difficult to use Kuratowski's criterion to quickly decide whether a given graph is planar. However, there exist fast algorithms for this problem: for a graph with n vertices, it is possible to determine in time O(n) (linear time) whether the graph may be planar or not (see planarity testing). For a s... | Maximal planar graph | 0.834588 |
3,494 | As many as 10 points may be awarded for 1–100 percent roof coverage with either vegetation or highly reflective materials or both. The basis in physics of a high emittance is quite questionable, since it merely describes a material which easily radiates infrared wavelength heat to the environment, contributing to the g... | Cool roofs | 0.834585 |
3,495 | In applying FEA, the complex problem is usually a physical system with the underlying physics such as the Euler–Bernoulli beam equation, the heat equation, or the Navier-Stokes equations expressed in either PDE or integral equations, while the divided small elements of the complex problem represent different areas in t... | Finite Element Method | 0.834584 |
3,496 | Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination of kernels as part of the algorithm. Reasons to use multiple kernel learning include a) the ability to select for an optimal kernel and parameters from a larger... | Multiple kernel learning | 0.834573 |
3,497 | Game theory Combinatorial game theory Combinatorial game theory (history) Combinatorial game theory (pedagogy) Star (game theory) Zero game, fuzzy game Dots and Boxes Impartial game Digital sum Nim Nimber Sprague–Grundy theorem Partizan game Solved board games Col game Sim (pencil game) Sprouts (game) Surreal numbers T... | Index of combinatorics articles | 0.834569 |
3,498 | Methods from empirical algorithmics complement theoretical methods for the analysis of algorithms. Through the principled application of empirical methods, particularly from statistics, it is often possible to obtain insights into the behavior of algorithms such as high-performance heuristic algorithms for hard combina... | Empirical algorithmics | 0.834569 |
3,499 | In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membershi... | Set (abstract data type) | 0.834566 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.