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2,900 | Whole genome bisulfite sequencing has also been applied to developmental biology studies in which non-CG methylation was discovered prevalent in pluripotent stem cells and oocytes. This technique helped researchers discover that non-CG methylation accumulated during oocyte growth and covered over half of all methylation in mouse germinal vesicle oocytes. Similarly, in plants, whole genome bisulfite sequencing was used to examine CG, CHH, and CHG methylation. It was then discovered that the plant germline conserved CG and CHG methylation while mammals lost CHH methylation in microspores and sperm cells. | Whole genome bisulfite sequencing | 0.83249 |
2,901 | In order to amplify the epigenome library, bisulfite-treated DNA is primed to generate DNA with a specific tagging sequence. The 3' end of this sequence is then tagged again, creating DNA fragments with markers on either end. These fragments are amplified in a final polymerase chain reaction reaction, after which the library is prepped for sequencing-by-synthesis. This is demonstrated in Figure 2, in which high-throughput sequencing system developed by biotechnology company, Illumina, perform comprehensive assays based on sequencing-by-synthesis of base pairs. | Whole genome bisulfite sequencing | 0.83249 |
2,902 | Consequently, large-scale studies for genomic-wide methylation profiling remain less cost-effective, often requiring multiple re-sequences of the entire genome multiple times for every experiment. Current studies are being conducted to reduce the conventional minimum coverage requirements while maintaining mapping accuracy. Finally, the technique is also limited the complexity of data and lack of sufficiently advanced analytical tools for downstream computational requirements. The current bioinformatics requirements for accurate data interpretation are ahead of existing technology, which stalls the accessibility of sequencing results to the general public. | Whole genome bisulfite sequencing | 0.83249 |
2,903 | The following steps are derived from one potential workflow of conventional whole genome bisulfite sequencing: target DNA extraction, bisulfite conversion, library amplification, and bioinformatics analysis. However, various sequencing systems and analysis tools often adapt the technical parameters and order of the following step processes in order to optimize assay coverage and efficacy. | Whole genome bisulfite sequencing | 0.83249 |
2,904 | Additionally, there are biological limitations concerning various steps in the standard protocol, particularly in the library preparation method. One of the biggest concerns is the potential of bias in the base composition of sequences and over-representation of methylated DNA data following bioinformatics analyses. Bias can arise from multiple unintended effects of bisulfite conversion including DNA degradation. This degradation can cause uneven sequence coverage by misrepresenting genomic sequences and overestimating 5-methylcytosine values. | Whole genome bisulfite sequencing | 0.83249 |
2,905 | In her review of the first edition, Mary Ellen Rudin wrote: In other mathematical fields one restricts one's problem by requiring that the space be Hausdorff or paracompact or metric, and usually one doesn't really care which, so long as the restriction is strong enough to avoid this dense forest of counterexamples. A usable map of the forest is a fine thing...In his submission to Mathematical Reviews C. Wayne Patty wrote: ...the book is extremely useful, and the general topology student will no doubt find it very valuable. In addition it is very well written.When the second edition appeared in 1978 its review in Advances in Mathematics treated topology as territory to be explored: Lebesgue once said that every mathematician should be something of a naturalist. This book, the updated journal of a continuing expedition to the never-never land of general topology, should appeal to the latent naturalist in every mathematician. | Counterexamples in Topology | 0.832481 |
2,906 | For instance, an example of a first-countable space which is not second-countable is counterexample #3, the discrete topology on an uncountable set. This particular counterexample shows that second-countability does not follow from first-countability. Several other "Counterexamples in ..." books and papers have followed, with similar motivations. | Counterexamples in Topology | 0.832481 |
2,907 | One of the easiest ways of doing this is to find a counterexample which exhibits one property but not the other. In Counterexamples in Topology, Steen and Seebach, together with five students in an undergraduate research project at St. Olaf College, Minnesota in the summer of 1967, canvassed the field of topology for such counterexamples and compiled them in an attempt to simplify the literature. | Counterexamples in Topology | 0.832481 |
2,908 | Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties. It is often useful in the study and understanding of abstracts such as topological spaces to determine that one property does not follow from another. | Counterexamples in Topology | 0.832481 |
2,909 | Several of the naming conventions in this book differ from more accepted modern conventions, particularly with respect to the separation axioms. The authors use the terms T3, T4, and T5 to refer to regular, normal, and completely normal. They also refer to completely Hausdorff as Urysohn. This was a result of the different historical development of metrization theory and general topology; see History of the separation axioms for more. The long line in example 45 is what most topologists nowadays would call the 'closed long ray'. | Counterexamples in Topology | 0.832481 |
2,910 | In machine learning, this is typically done by cross-validation. In statistics, some criteria are optimized. This leads to the inherent problem of nesting. More robust methods have been explored, such as branch and bound and piecewise linear network. | Variable selection | 0.832479 |
2,911 | Let xi be the set membership indicator function for feature fi; then the above can be rewritten as an optimization problem: C F S = max x ∈ { 0 , 1 } n . {\displaystyle \mathrm {CFS} =\max _{x\in \{0,1\}^{n}}\left.} The combinatorial problems above are, in fact, mixed 0–1 linear programming problems that can be solved by using branch-and-bound algorithms. | Variable selection | 0.832479 |
2,912 | Different flooding algorithms can be applied for different problems, and run with different time complexities. For example, the flood fill algorithm is a simple but relatively robust algorithm that works for intricate geometries and can determine which part of the (target) area that is connected to a given (source) node in a multi-dimensional array, and is trivially generalized to arbitrary graph structures. If there instead are several source nodes, there are no obstructions in the geometry represented in the multi-dimensional array, and one wishes to segment the area based on which of the source nodes the target nodes are closest to, while the flood fill algorithm can still be used, the jump flooding algorithm is potentially much faster as it has a lower time complexity. Unlike the flood fill algorithm, however, the jump flooding algorithm cannot trivially be generalized to unstructured graphs. | Flooding algorithm | 0.832457 |
2,913 | A flooding algorithm is an algorithm for distributing material to every part of a graph. The name derives from the concept of inundation by a flood. Flooding algorithms are used in computer networking and graphics. Flooding algorithms are also useful for solving many mathematical problems, including maze problems and many problems in graph theory. | Flooding algorithm | 0.832457 |
2,914 | The concept of NP-completeness was introduced in 1971 (see Cook–Levin theorem), though the term NP-complete was introduced later. At the 1971 STOC conference, there was a fierce debate between the computer scientists about whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine. John Hopcroft brought everyone at the conference to a consensus that the question of whether NP-complete problems are solvable in polynomial time should be put off to be solved at some later date, since nobody had any formal proofs for their claims one way or the other. This is known as "the question of whether P=NP". | NP completeness | 0.832448 |
2,915 | Nobody has yet been able to determine conclusively whether NP-complete problems are in fact solvable in polynomial time, making this one of the great unsolved problems of mathematics. The Clay Mathematics Institute is offering a US$1 million reward to anyone who has a formal proof that P=NP or that P≠NP.The existence of NP-complete problems is not obvious. The Cook–Levin theorem states that the Boolean satisfiability problem is NP-complete, thus establishing that such problems do exist. In 1972, Richard Karp proved that several other problems were also NP-complete (see Karp's 21 NP-complete problems); thus, there is a class of NP-complete problems (besides the Boolean satisfiability problem). Since the original results, thousands of other problems have been shown to be NP-complete by reductions from other problems previously shown to be NP-complete; many of these problems are collected in Garey and Johnson's 1979 book Computers and Intractability: A Guide to the Theory of NP-Completeness. | NP completeness | 0.832448 |
2,916 | A partially ordered group G is called integrally closed if for all elements a and b of G, if an ≤ b for all natural n then a ≤ 1.This property is somewhat stronger than the fact that a partially ordered group is Archimedean, though for a lattice-ordered group to be integrally closed and to be Archimedean is equivalent. There is a theorem that every integrally closed directed group is already abelian. This has to do with the fact that a directed group is embeddable into a complete lattice-ordered group if and only if it is integrally closed. | Ordered group | 0.832444 |
2,917 | EXPTIME can also be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space. EXPTIME relates to the other basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthemore, by the time hierarchy theorem and the space hierarchy theorem, it is known that P ⊊ EXPTIME, NP ⊊ NEXPTIME and PSPACE ⊊ EXPSPACE. | Exponential running time | 0.832437 |
2,918 | A decision problem is EXPTIME-complete if it is in EXPTIME and every problem in EXPTIME has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances of one to instances of the other with the same answer. Problems that are EXPTIME-complete might be thought of as the hardest problems in EXPTIME. Notice that although it is unknown whether NP is equal to P, we do know that EXPTIME-complete problems are not in P; it has been proven that these problems cannot be solved in polynomial time, by the time hierarchy theorem. | Exponential running time | 0.832437 |
2,919 | It is known that and also, by the time hierarchy theorem and the space hierarchy theorem, that In the above expressions, the symbol ⊆ means "is a subset of", and the symbol ⊊ means "is a strict subset of". so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are. Most experts believe all the inclusions are proper. | Exponential running time | 0.832437 |
2,920 | A circle is a simple shape of two-dimensional geometry that is the set of all points in a plane that are at a given distance from a given point, the center.The distance between any of the points and the center is called the radius. It can also be defined as the locus of a point equidistant from a fixed point. A perimeter is a path that surrounds a two-dimensional shape. | Elementary mathematics | 0.832428 |
2,921 | Two-dimensional geometry is a branch of mathematics concerned with questions of shape, size, and relative position of two-dimensional figures. Basic topics in elementary mathematics include polygons, circles, perimeter and area. A polygon is a shape that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. | Elementary mathematics | 0.832428 |
2,922 | The slope of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m.Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies. The slope is studied in grade 8. | Elementary mathematics | 0.832428 |
2,923 | Elementary mathematics, also known as primary or secondary school school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense, algebra, geometry, measurement, and data analysis. These concepts and skills form the foundation for more advanced mathematical study and are essential for success in many fields and everyday life. The study of elementary mathematics is a crucial part of a student's education and lays the foundation for future academic and career success. | Elementary mathematics | 0.832428 |
2,924 | Compass-and-straightedge, also known as ruler-and-compass construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass, see compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates. | Elementary mathematics | 0.832428 |
2,925 | Geometrically, one studies the Euclidean plane (2 dimensions) and Euclidean space (3 dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. Transformations are ways of shifting and scaling functions using different algebraic formulas. | Elementary mathematics | 0.832428 |
2,926 | A formula is an entity constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion; but, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume. An equation is a formula of the form A = B, where A and B are expressions that may contain one or several variables called unknowns, and "=" denotes the equality binary relation. Although written in the form of proposition, an equation is not a statement that is either true or false, but a problem consisting of finding the values, called solutions, that, when substituted for the unknowns, yield equal values of the expressions A and B. For example, 2 is the unique solution of the equation x + 2 = 4, in which the unknown is x. | Elementary mathematics | 0.832428 |
2,927 | Solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, cylinders, cones, truncated cones, spheres, and prisms. | Elementary mathematics | 0.832428 |
2,928 | Analytic geometry is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. | Elementary mathematics | 0.832428 |
2,929 | Number Sense is an understanding of numbers and operations. In the 'Number Sense and Numeration' strand students develop an understanding of numbers by being taught various ways of representing numbers, as well as the relationships among numbers.Properties of the natural numbers such as divisibility and the distribution of prime numbers, are studied in basic number theory, another part of elementary mathematics. Elementary Focus Abacus LCM and GCD Fractions and Decimals Place Value & Face Value Addition and subtraction Multiplication and Division Counting Counting Money Algebra Representing and ordering numbers Estimating Approximating Problem SolvingTo have a strong foundation in mathematics and to be able to succeed in the other strands students need to have a fundamental understanding of number sense and numeration. | Elementary mathematics | 0.832428 |
2,930 | Euclid used a restricted version of the fundamental theorem and some careful argument to prove the theorem. His proof is in Euclid's Elements Book X Proposition 9.The fundamental theorem of arithmetic is not actually required to prove the result, however. There are self-contained proofs by Richard Dedekind, among others. | Quadratic irrational numbers | 0.832427 |
2,931 | Many proofs of the irrationality of the square roots of non-square natural numbers implicitly assume the fundamental theorem of arithmetic, which was first proven by Carl Friedrich Gauss in his Disquisitiones Arithmeticae. This asserts that every integer has a unique factorization into primes. For any rational non-integer in lowest terms there must be a prime in the denominator which does not divide into the numerator. | Quadratic irrational numbers | 0.832427 |
2,932 | Theodorus of Cyrene proved the irrationality of the square roots of non-square natural numbers up to 17, but stopped there, probably because the algebra he used could not be applied to the square root of numbers greater than 17. Euclid's Elements Book 10 is dedicated to classification of irrational magnitudes. The original proof of the irrationality of the non-square natural numbers depends on Euclid's lemma. | Quadratic irrational numbers | 0.832427 |
2,933 | The property of being conjugacy-closed is transitive, that is, every conjugacy-closed subgroup of a conjugacy-closed subgroup is conjugacy-closed.The property of being conjugacy-closed is sometimes also termed as being conjugacy stable. It is a known result that for finite field extensions, the general linear group of the base field is a conjugacy-closed subgroup of the general linear group over the extension field. This result is typically referred to as a stability theorem. A subgroup is said to be strongly conjugacy-closed if all intermediate subgroups are also conjugacy-closed. | Conjugacy-closed subgroup | 0.832413 |
2,934 | In mathematics, the connective constant is a numerical quantity associated with self-avoiding walks on a lattice. It is studied in connection with the notion of universality in two-dimensional statistical physics models. While the connective constant depends on the choice of lattice so itself is not universal (similarly to other lattice-dependent quantities such as the critical probability threshold for percolation), it is nonetheless an important quantity that appears in conjectures for universal laws. Furthermore, the mathematical techniques used to understand the connective constant, for example in the recent rigorous proof by Duminil-Copin and Smirnov that the connective constant of the hexagonal lattice has the precise value 2 + 2 {\displaystyle {\sqrt {2+{\sqrt {2}}}}} , may provide clues to a possible approach for attacking other important open problems in the study of self-avoiding walks, notably the conjecture that self-avoiding walks converge in the scaling limit to the Schramm–Loewner evolution. | Connective constant | 0.832411 |
2,935 | It has not been shown to be curl-free, but this would solve several open problems (see conjectures). The proof of this lemma is a clever computation that relies heavily on the geometry of the hexagonal lattice. | Connective constant | 0.83241 |
2,936 | An extension of the notion of integrability is also applicable to discrete systems such as lattices. This definition can be adapted to describe evolution equations that either are systems of differential equations or finite difference equations. The distinction between integrable and nonintegrable dynamical systems has the qualitative implication of regular motion vs. chaotic motion and hence is an intrinsic property, not just a matter of whether a system can be explicitly integrated in an exact form. | Exactly solved model | 0.832408 |
2,937 | In general, epistasis is used to denote the departure from 'independence' of the effects of different genetic loci. Confusion often arises due to the varied interpretation of 'independence' among different branches of biology. The classifications below attempt to cover the various terms and how they relate to one another. | Genetic interactions | 0.832408 |
2,938 | Terminology about epistasis can vary between scientific fields. Geneticists often refer to wild type and mutant alleles where the mutation is implicitly deleterious and may talk in terms of genetic enhancement, synthetic lethality and genetic suppressors. Conversely, a biochemist may more frequently focus on beneficial mutations and so explicitly state the effect of a mutation and use terms such as reciprocal sign epistasis and compensatory mutation. Additionally, there are differences when looking at epistasis within a single gene (biochemistry) and epistasis within a haploid or diploid genome (genetics). | Genetic interactions | 0.832408 |
2,939 | This problem arises frequently in practice. In computational geometry, polynomials are used to compute function approximations using Taylor polynomials. In cryptography and hash tables, polynomials are used to compute k-independent hashing. In the former case, polynomials are evaluated using floating-point arithmetic, which is not exact. Thus different schemes for the evaluation will, in general, give slightly different answers. In the latter case, the polynomials are usually evaluated in a finite field, in which case the answers are always exact. | Polynomial evaluation | 0.832386 |
2,940 | Because of how m 0 {\displaystyle m_{0}} and m 1 {\displaystyle m_{1}} were defined, we have R 0 ( x i ) = P ( x i ) for i ≤ n / 2 and R 1 ( x i ) = P ( x i ) for i > n / 2. {\displaystyle {\begin{aligned}R_{0}(x_{i})&=P(x_{i})\quad {\text{for }}i\leq n/2\quad {\text{and}}\\R_{1}(x_{i})&=P(x_{i})\quad {\text{for }}i>n/2.\end{aligned}}} Thus to compute P {\displaystyle P} on all n {\displaystyle n} of the x i {\displaystyle x_{i}} , it suffices to compute the smaller polynomials R 0 {\displaystyle R_{0}} and R 1 {\displaystyle R_{1}} on each half of the points. This gives us a divide-and-conquer algorithm with T ( n ) = 2 T ( n / 2 ) + n log n {\displaystyle T(n)=2T(n/2)+n\log n} , which implies T ( n ) = O ( n ( log n ) 2 ) {\displaystyle T(n)=O(n(\log n)^{2})} by the master theorem. | Polynomial evaluation | 0.832386 |
2,941 | The idea is to define two polynomials that are zero in respectively the first and second half of the points: m 0 ( x ) = ( x − x 1 ) ⋯ ( x − x n / 2 ) {\displaystyle m_{0}(x)=(x-x_{1})\cdots (x-x_{n/2})} and m 1 ( x ) = ( x − x n / 2 + 1 ) ⋯ ( x − x n ) {\displaystyle m_{1}(x)=(x-x_{n/2+1})\cdots (x-x_{n})} . We then compute R 0 = P mod m 0 {\displaystyle R_{0}=P{\bmod {m}}_{0}} and R 1 = P mod m 1 {\displaystyle R_{1}=P{\bmod {m}}_{1}} using the Polynomial remainder theorem, which can be done in O ( n log n ) {\displaystyle O(n\log n)} time using a fast Fourier transform. This means P ( x ) = Q ( x ) m 0 ( x ) + R 0 ( x ) {\displaystyle P(x)=Q(x)m_{0}(x)+R_{0}(x)} and P ( x ) = Q ( x ) m 1 ( x ) + R 1 ( x ) {\displaystyle P(x)=Q(x)m_{1}(x)+R_{1}(x)} by construction, where R 0 {\displaystyle R_{0}} and R 1 {\displaystyle R_{1}} are polynomials of degree at most n / 2 {\displaystyle n/2} . | Polynomial evaluation | 0.832386 |
2,942 | That means we can compute and store f {\displaystyle f} on all the possible values in T = ( log log q ) m {\displaystyle T=(\log \log q)^{m}} time and space. If we take d = log q {\displaystyle d=\log q} , we get m = log n log log q {\displaystyle m={\tfrac {\log n}{\log \log q}}} , so the time/space requirement is just n log log q log log log q . {\displaystyle n^{\frac {\log \log q}{\log \log \log q}}.} Kedlaya and Umans further show how to combine this preprocessing with fast (FFT) multipoint evaluation. This allows optimal algorithms for many important algebraic problems, such as polynomial modular composition. | Polynomial evaluation | 0.832386 |
2,943 | Using the Chinese remainder theorem, it suffices to evaluate f {\displaystyle f} modulo different primes p 1 , … , p ℓ {\displaystyle p_{1},\dots ,p_{\ell }} with a product at least M {\displaystyle M} . Each prime can be taken to be roughly log M = O ( d m log q ) {\displaystyle \log M=O(dm\log q)} , and the number of primes needed, ℓ {\displaystyle \ell } , is roughly the same. Doing this process recursively, we can get the primes as small as log log q {\displaystyle \log \log q} . | Polynomial evaluation | 0.832386 |
2,944 | In mathematics and computer science, polynomial evaluation refers to computation of the value of a polynomial when its indeterminates are substituted for some values. In other words, evaluating the polynomial P ( x 1 , x 2 ) = 2 x 1 x 2 + x 1 3 + 4 {\displaystyle P(x_{1},x_{2})=2x_{1}x_{2}+x_{1}^{3}+4} at x 1 = 2 , x 2 = 3 {\displaystyle x_{1}=2,x_{2}=3} consists of computing P ( 2 , 3 ) = 2 ⋅ 2 ⋅ 3 + 2 3 + 4 = 24. {\displaystyle P(2,3)=2\cdot 2\cdot 3+2^{3}+4=24.} | Polynomial evaluation | 0.832386 |
2,945 | An electrostatic vaneless ion wind generator, the EWICON, has been developed by The School of Electrical Engineering, Mathematics and Computer Science at Delft University of Technology (TU Delft). Its stands near Mecanoo, an architecture firm. The main developers were Johan Smit and Dhiradj Djairam. | Electrostatic generator | 0.832386 |
2,946 | This type of Van de Graaff particle accelerator is still used in medicine and research. Other variations were also invented for physics research, such as the Pelletron, that uses a chain with alternating insulating and conducting links for charge transport. Small Van de Graaff generators are commonly used in science museums and science education to demonstrate the principles of static electricity. A popular demonstration is to have a person touch the high voltage terminal while standing on an insulated support; the high voltage charges the person's hair, causing the strands to stand out from the head. | Electrostatic generator | 0.832386 |
2,947 | There are two principle classes of analogy in use. The impedance analogy (also called the Maxwell analogy) preserves the analogy between mechanical, acoustical and electrical impedance but does not preserve the topology of networks. The mechanical network is arranged differently to its analogous electrical network. The mobility analogy (also called the Firestone analogy) preserves network topologies at the expense of losing the analogy between impedances across energy domains. | Mechanical-electrical analogy | 0.832381 |
2,948 | As electrical phenomena became better understood the reverse of this analogy, using electrical analogies to explain mechanical systems, started to become more common. Indeed, the lumped element abstract topology of electrical analysis has much to offer problems in the mechanical domain, and other energy domains for that matter. By 1900 the electrical analogy of the mechanical domain was becoming commonplace. | Mechanical-electrical analogy | 0.832381 |
2,949 | The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification. Thus the "symmetric double-well potential" served for many years as a model to illustrate the concept of instantons as a pseudo-classical configuration in a Euclideanised field theory. In the simpler quantum mechanical context this potential served as a model for the evaluation of Feynman path integrals. or the solution of the Schrödinger equation by various methods for the purpose of obtaining explicitly the energy eigenvalues. | Double-well potential | 0.832365 |
2,950 | The above results for the double-well and the inverted double-well can also be obtained by the path integral method (there via periodic instantons, cf. instantons), and the WKB method, though with the use of elliptic integrals and the Stirling approximation of the gamma function, all of which make the calculation more difficult. The symmetry property of the perturbative part in changes q → -q, h 2 {\displaystyle h^{2}} → - h 2 {\displaystyle h^{2}} of the results can only be obtained in the derivation from the Schrödinger equation which is therefore the better and correct way to obtain the result. This conclusion is supported by investigations of other second-order differential equations like the Mathieu equation and the Lamé equation which exhibit similar properties in their eigenvalue equations. Moreover in each of these cases (double-well, inverted double-well, cosine potential) the equation of small fluctuations about the classical configuration is a Lamé equation. == References == | Double-well potential | 0.832365 |
2,951 | The classic applications of elliptic coordinates are in solving partial differential equations, e.g., Laplace's equation or the Helmholtz equation, for which elliptic coordinates are a natural description of a system thus allowing a separation of variables in the partial differential equations. Some traditional examples are solving systems such as electrons orbiting a molecule or planetary orbits that have an elliptical shape. The geometric properties of elliptic coordinates can also be useful. A typical example might involve an integration over all pairs of vectors p {\displaystyle \mathbf {p} } and q {\displaystyle \mathbf {q} } that sum to a fixed vector r = p + q {\displaystyle \mathbf {r} =\mathbf {p} +\mathbf {q} } , where the integrand was a function of the vector lengths | p | {\displaystyle \left|\mathbf {p} \right|} and | q | {\displaystyle \left|\mathbf {q} \right|} . (In such a case, one would position r {\displaystyle \mathbf {r} } between the two foci and aligned with the x {\displaystyle x} -axis, i.e., r = 2 a x ^ {\displaystyle \mathbf {r} =2a\mathbf {\hat {x}} } .) For concreteness, r {\displaystyle \mathbf {r} } , p {\displaystyle \mathbf {p} } and q {\displaystyle \mathbf {q} } could represent the momenta of a particle and its decomposition products, respectively, and the integrand might involve the kinetic energies of the products (which are proportional to the squared lengths of the momenta). | Elliptic coordinates | 0.832298 |
2,952 | The first ten volunteers were referred to as the "PGP-10". These volunteers were: Misha Angrist, Duke Institute for Genome Sciences and Policy Keith Batchelder, Genomic Healthcare Strategies, Esther Dyson, EDventure Holdings, Rosalynn Gill-Garrison, Sciona, John Halamka, Harvard Medical School, Stan Lapidus, Helicos BioSciences, Kirk Maxey, Cayman Chemical, James Sherley, Boston stem cell researcher, and Steven Pinker, HarvardIn order to enroll, each participant must pass a series of short online tests to ensure that they are providing informed consent. By 2012, 2000 participants had enrolled and by November 2017 10,000 had joined the project.In July 2014, at the 'Genetics, Genomics and Global Health—Inequalities, Identities and Insecurities' conference, Stephan Beck, the head of the UK arm of this project indicated that they had over 1000 volunteers, and had temporarily paused collection data due to lack of funding. | Personal Genome Project | 0.832274 |
2,953 | On March 9, 2017, producers of the popular online brain-training program Lumosity announced they would collaborate with Harvard researchers to investigate the relationship between genetics and memory, attention, and reaction speed.Scientists at the Wyss Institute for Biologically Inspired Engineering and the Harvard Medical School Personal Genome Project (PGP) planned to recruit 10,000 members from the PGP, to perform a set of cognitive tests from Lumos Labs’ NeuroCognitive Performance Test, a brief, repeatable, online assessment to evaluate participants’ memory functions, including object recall, object pattern memorization, and response times. The researchers would then correlate extremely high performance scores with naturally occurring variations in the participants’ genomes. To validate their findings, the team would sequence, edit, and visualize DNA, model neuronal development in 3-D brain organoids ex vivo, and finally test emerging hypotheses in experimental models of neurodegeneration. | Personal Genome Project | 0.832274 |
2,954 | These ideas had occurred to me earlier in 1955 when I coined the term "signalizing function", which is nowadays commonly known as "complexity measure". In 1967, Manuel Blum formulated a set of axioms (now known as Blum axioms) specifying desirable properties of complexity measures on the set of computable functions and proved an important result, the so-called speed-up theorem. The field began to flourish in 1971 when Stephen Cook and Leonid Levin proved the existence of practically relevant problems that are NP-complete. In 1972, Richard Karp took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its computational intractability, are NP-complete. | Complexity theory (computation) | 0.832256 |
2,955 | An early example of algorithm complexity analysis is the running time analysis of the Euclidean algorithm done by Gabriel Lamé in 1844. Before the actual research explicitly devoted to the complexity of algorithmic problems started off, numerous foundations were laid out by various researchers. Most influential among these was the definition of Turing machines by Alan Turing in 1936, which turned out to be a very robust and flexible simplification of a computer. The beginning of systematic studies in computational complexity is attributed to the seminal 1965 paper "On the Computational Complexity of Algorithms" by Juris Hartmanis and Richard E. Stearns, which laid out the definitions of time complexity and space complexity, and proved the hierarchy theorems. | Complexity theory (computation) | 0.832256 |
2,956 | A complexity class is a set of problems of related complexity. Simpler complexity classes are defined by the following factors: The type of computational problem: The most commonly used problems are decision problems. However, complexity classes can be defined based on function problems, counting problems, optimization problems, promise problems, etc. The model of computation: The most common model of computation is the deterministic Turing machine, but many complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc. The resource (or resources) that is being bounded and the bound: These two properties are usually stated together, such as "polynomial time", "logarithmic space", "constant depth", etc.Some complexity classes have complicated definitions that do not fit into this framework. Thus, a typical complexity class has a definition like the following: The set of decision problems solvable by a deterministic Turing machine within time f(n). | Complexity theory (computation) | 0.832256 |
2,957 | The P versus NP problem, one of the seven Millennium Prize Problems, is dedicated to the field of computational complexity.Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically. | Complexity theory (computation) | 0.832256 |
2,958 | In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. | Complexity theory (computation) | 0.832256 |
2,959 | Thus there are pairs of complexity classes such that one is properly included in the other. Having deduced such proper set inclusions, we can proceed to make quantitative statements about how much more additional time or space is needed in order to increase the number of problems that can be solved. More precisely, the time hierarchy theorem states that D T I M E ( o ( f ( n ) ) ) ⊊ D T I M E ( f ( n ) ⋅ log ( f ( n ) ) ) {\displaystyle {\mathsf {DTIME}}{\big (}o(f(n)){\big )}\subsetneq {\mathsf {DTIME}}{\big (}f(n)\cdot \log(f(n)){\big )}} .The space hierarchy theorem states that D S P A C E ( o ( f ( n ) ) ) ⊊ D S P A C E ( f ( n ) ) {\displaystyle {\mathsf {DSPACE}}{\big (}o(f(n)){\big )}\subsetneq {\mathsf {DSPACE}}{\big (}f(n){\big )}} .The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained in PSPACE. | Complexity theory (computation) | 0.832256 |
2,960 | For the complexity classes defined in this way, it is desirable to prove that relaxing the requirements on (say) computation time indeed defines a bigger set of problems. In particular, although DTIME(n) is contained in DTIME(n2), it would be interesting to know if the inclusion is strict. For time and space requirements, the answer to such questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined by constraining the respective resources. | Complexity theory (computation) | 0.832256 |
2,961 | Continuous complexity theory can refer to complexity theory of problems that involve continuous functions that are approximated by discretizations, as studied in numerical analysis. One approach to complexity theory of numerical analysis is information based complexity. Continuous complexity theory can also refer to complexity theory of the use of analog computation, which uses continuous dynamical systems and differential equations. Control theory can be considered a form of computation and differential equations are used in the modelling of continuous-time and hybrid discrete-continuous-time systems. | Complexity theory (computation) | 0.832256 |
2,962 | Negatively curved groups (hyperbolic or CAT(0) groups) are always of type F∞. Such a group is of type F if and only if it is torsion-free. As an example, cocompact S-arithmetic groups in algebraic groups over number fields are of type F∞. The Borel–Serre compactification shows that this is also the case for non-cocompact arithmetic groups. Arithmetic groups over function fields have very different finiteness properties: if Γ {\displaystyle \Gamma } is an arithmetic group in a simple algebraic group of rank r {\displaystyle r} over a global function field (such as F q ( t ) {\displaystyle \mathbb {F} _{q}(t)} ) then it is of type Fr but not of type Fr+1. | Finiteness properties of groups | 0.832241 |
2,963 | In mathematics, finiteness properties of a group are a collection of properties that allow the use of various algebraic and topological tools, for example group cohomology, to study the group. It is mostly of interest for the study of infinite groups. Special cases of groups with finiteness properties are finitely generated and finitely presented groups. | Finiteness properties of groups | 0.832241 |
2,964 | Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter, keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass M ( t ) {\displaystyle M(t)} , moving at velocity v → ( t ) {\displaystyle {\vec {v}}(t)} , ejects matter at a velocity u → {\displaystyle {\vec {u}}} relative to the rocket, then where F → {\displaystyle {\vec {F}}} is the net external force (e.g., a planet's gravitational pull). : 139 | Newtonian Mechanics | 0.832224 |
2,965 | Goddard's Heliophysics Science Division consists of four separate laboratories. | Heliophysics Science Division | 0.832212 |
2,966 | The unique instrument capabilities, coupled with state of the art 3-D modeling, will fill a large gap in our knowledge of this dynamic region of the solar atmosphere. The mission will extend the scientific output of existing heliophysics spacecraft that follow the effects of energy release processes from the sun to Earth. The IRIS mission launched June 27, 2013. | Heliophysics Science Division | 0.832212 |
2,967 | The Space Physics Data Facility (SPDF) is a project of the Heliospheric Science Division (HSD) at NASA's Goddard Space Flight Center. SPDF consists of web-based services for survey and high resolution data and trajectories. The Facility supports data from most NASA Heliophysics missions to promote correlative and collaborative research across discipline and mission boundaries. | Heliophysics Science Division | 0.832212 |
2,968 | The Solar Physics Laboratory works to understand the Sun as a star and as the primary driver of activity throughout the solar system. Their research expands knowledge of the Earth-Sun system and helps to enable robotic and human exploration. | Heliophysics Science Division | 0.832212 |
2,969 | The Reuven Ramaty High Energy Solar Spectroscopic Imager, or RHESSI, combines high-resolution imaging in hard X-rays and gamma rays with high-resolution spectroscopy to explore the basic physics of particle acceleration and energy release in solar flares. Such information improves our understanding of the fundamental processes that are involved in generating solar flares and coronal mass ejections. These super-energetic solar eruptive events are the most extreme drivers of space weather and present significant dangers in space and on Earth. | Heliophysics Science Division | 0.832212 |
2,970 | The Geospace Physics Laboratory focuses on processes occurring in the magnetospheres of magnetized planets and on the interaction of the solar wind with planetary magnetospheres. Researchers also study processes, such as magnetofluid turbulence, that permeate the heliosphere from the solar atmosphere to the edge of the Solar System. | Heliophysics Science Division | 0.832212 |
2,971 | This division of Goddard Space Flight Center has interests in various projects and missions. In addition to performing research based on NASA solar observatories in space, the division manages many heliophysics missions on behalf of the Science Mission Directorate at NASA headquarters. These include: | Heliophysics Science Division | 0.832212 |
2,972 | The Voyager missions (Voyager 1 and Voyager 2) are a part of NASA's Heliophysics System Observatory, sponsored by the Heliophysics Division of the Science Mission Directorate at NASA Headquarters in Washington. The Voyager spacecraft were built and continue to be operated by NASA's Jet Propulsion Laboratory, in Pasadena, Calif. On December 4, 2012, eleven billion miles from Earth, NASA's Voyager 1 spacecraft has entered a "magnetic highway" that connects our Solar System to interstellar space. The "magnetic highway" is a place in the far reaches of the Solar System where the sun's magnetic field connects to the magnetic field of interstellar space. In this region, the sun's magnetic field lines are connected to interstellar magnetic field lines, allowing particles from inside the heliosphere to zip away and particles from interstellar space to zoom in. In recent years, the speed of the solar wind around Voyager 1 has slowed to zero, and the intensity of the magnetic field has increased. | Heliophysics Science Division | 0.832212 |
2,973 | The Heliospheric Physics Laboratory develops instruments and models to investigate the origin and evolution of the solar wind, low-energy cosmic rays, and the interaction of the Sun's heliosphere with the local interstellar medium. The Laboratory designs and implements unique multi-mission and multidisciplinary data services to advance NASA's solar-terrestrial program and our understanding of the Sun-Earth system. | Heliophysics Science Division | 0.832212 |
2,974 | The Heliophysics Science Division of the Goddard Space Flight Center (NASA) conducts research on the Sun, its extended Solar System environment (the heliosphere), and interactions of Earth, other planets, small bodies, and interstellar gas with the heliosphere. Division research also encompasses geospace—Earth's uppermost atmosphere, the ionosphere, and the magnetosphere—and the changing environmental conditions throughout the coupled heliosphere (solar system weather). Scientists in the Heliophysics Science Division develop models, spacecraft missions and instruments, and systems to manage and disseminate heliophysical data. They interpret and evaluate data gathered from instruments, draw comparisons with computer simulations and theoretical models, and publish the results. The Division also conducts education and public outreach programs to communicate the excitement and social value of NASA heliophysics. | Heliophysics Science Division | 0.832212 |
2,975 | Sleep has been described using Tinbergen's four questions as a framework (Bode & Kuula, 2021): Function: Energy restoration, metabolic regulation, thermoregulation, boosting immune system, detoxification, brain maturation, circuit reorganization, synaptic optimization, avoiding danger. Phylogeny: Sleep exists in invertebrates, lower vertebrates, and higher vertebrates. NREM and REM sleep exist in eutheria, marsupialiformes, and also evolved in birds. Mechanisms: Mechanisms regulate wakefulness, sleep onset, and sleep. | Tinbergen's four questions | 0.832202 |
2,976 | When asked about the purpose of sight in humans and animals, even elementary-school children can answer that animals have vision to help them find food and avoid danger (function/adaptation). Biologists have three additional explanations: sight is caused by a particular series of evolutionary steps (phylogeny), the mechanics of the eye (mechanism/causation), and even the process of an individual's development (ontogeny). This schema constitutes a basic framework of the overlapping behavioural fields of ethology, behavioural ecology, comparative psychology, sociobiology, evolutionary psychology, and anthropology. Julian Huxley identified the first three questions. Niko Tinbergen gave only the fourth question, as Huxley's questions failed to distinguish between survival value and evolutionary history; Tinbergen's fourth question helped resolve this problem. | Tinbergen's four questions | 0.832202 |
2,977 | The Four Areas of Biology pdf The Four Areas and Levels of Inquiry pdf Tinbergen's four questions within the "Fundamental Theory of Human Sciences" ppt Tinbergen's Four Questions, organized pdf | Tinbergen's four questions | 0.832202 |
2,978 | In such cases, genes determine the timing of the environmental impact. A related concept is labeled "biased learning" (Alcock 2001:101–103) and "prepared learning" (Wilson, 1998:86–87). For instance, after eating food that subsequently made them sick, rats are predisposed to associate that food with smell, not sound (Alcock 2001:101–103). Many primate species learn to fear snakes with little experience (Wilson, 1998:86–87).See developmental biology and developmental psychology. It corresponds to Aristotle's material cause. | Tinbergen's four questions | 0.832202 |
2,979 | The tabulated schema is used as the central organizing device in many animal behaviour, ethology, behavioural ecology and evolutionary psychology textbooks (e.g., Alcock, 2001) . One advantage of this organizational system, what might be called the "periodic table of life sciences," is that it highlights gaps in knowledge, analogous to the role played by the periodic table of elements in the early years of chemistry. This "biopsychosocial" framework clarifies and classifies the associations between the various levels of the natural and social sciences, and it helps to integrate the social and natural sciences into a "tree of knowledge" (see also Nicolai Hartmann's "Laws about the Levels of Complexity"). Especially for the social sciences, this model helps to provide an integrative, foundational model for interdisciplinary collaboration, teaching and research (see The Four Central Questions of Biological Research Using Ethology as an Example – PDF). | Tinbergen's four questions | 0.832202 |
2,980 | Galileo was the first to demonstrate and then formulate these equations. He used a ramp to study rolling balls, the ramp slowing the acceleration enough to measure the time taken for the ball to roll a known distance. He measured elapsed time with a water clock, using an "extremely accurate balance" to measure the amount of water.The equations ignore air resistance, which has a dramatic effect on objects falling an appreciable distance in air, causing them to quickly approach a terminal velocity. The effect of air resistance varies enormously depending on the size and geometry of the falling object—for example, the equations are hopelessly wrong for a feather, which has a low mass but offers a large resistance to the air. | Equations for a falling body | 0.832196 |
2,981 | Terminal velocity depends on atmospheric drag, the coefficient of drag for the object, the (instantaneous) velocity of the object, and the area presented to the airflow. Apart from the last formula, these formulas also assume that g negligibly varies with height during the fall (that is, they assume constant acceleration). The last equation is more accurate where significant changes in fractional distance from the centre of the planet during the fall cause significant changes in g. This equation occurs in many applications of basic physics. | Equations for a falling body | 0.832195 |
2,982 | Molecular breeding is the application of molecular biology tools, often in plant breeding and animal breeding. In the broad sense, molecular breeding can be defined as the use of genetic manipulation performed at the level of DNA to improve traits of interest in plants and animals, and it may also include genetic engineering or gene manipulation, molecular marker-assisted selection, and genomic selection. More often, however, molecular breeding implies molecular marker-assisted breeding (MAB) and is defined as the application of molecular biotechnologies, specifically molecular markers, in combination with linkage maps and genomics, to alter and improve plant or animal traits on the basis of genotypic assays.The areas of molecular breeding include: QTL mapping or gene discovery Marker assisted selection and genomic selection Genetic engineering Genetic transformation | Molecular breeding | 0.832182 |
2,983 | In physics, field strength is the magnitude of a vector-valued field (e.g., in volts per meter, V/m, for an electric field E). For example, an electromagnetic field has both electric field strength and magnetic field strength. As an application, in radio frequency telecommunications, the signal strength excites a receiving antenna and thereby induces a voltage at a specific frequency and polarization in order to provide an input signal to a radio receiver. Field strength meters are used for such applications as cellular, broadcasting, wi-fi and a wide variety of other radio-related applications. | Field intensity | 0.832171 |
2,984 | Hugh's treatment somewhat elevates the mechanical arts as ordained to the improvement of humanity, a promotion which was to represent a growing trend among late medievals.The classification of the artes mechanicae as applied geometry was introduced to Western Europe by Dominicus Gundissalinus (12th century) under the influence of his readings in Arabic scholarship. In the 19th century, "mechanic arts" referred to some of the fields that are now known as engineering. Use of the term was apparently an attempt to distinguish these fields from creative and artistic endeavors like the performing arts and the fine arts, which were for the upper class of the time, and the intelligentsia. | Mechanical arts | 0.832167 |
2,985 | Combined the results from the use of the microscopic and PCR methods, it has been stated that the molecular biology methods can be executed as a supplementary method for PAP detection.For undercooked raw beef, in order to make sure a safe beef supply, sensitive and quick detection techniques for E. coli O157:H7 are important in the meat industry. Three different techniques can be used in raw ground beef: the VIDAS ultraperformance E. coli test (ECPT UP), a noncommercial real-time (RT) PCR method and the U.S. Department of Agriculture, Food Safety and Inspection Service (USDA-FSIS) reference method to detect E. coli O157:H7. | Protein detection | 0.832163 |
2,986 | During the last 30 years, broad methods and techniques were experimented to discover soybean protein. These methods and techniques can be conveyed to lab environment easily. The original and traditional methods were designed and tested in molecular biology spectrum. Enzyme‐Linked Immunosorbent Assay technique containing high susceptibility and specificity is reliable method to investigate soybean proteins through applying a protein which can identify a foreign molecule. | Protein detection | 0.832163 |
2,987 | Protein detection in cells from the human rectal mucous membrane can imply colorectal disease such as colon tumours, inflammatory bowel disease. Protein detection based on antibody microarrays can implicate life signature for example organics and biochemical compounds in the solar system in astrobiology field. Protein detection can monitor soybean protein labeling system in processed foods to protect consumers in a reliable way. The labeling for soybean protein declaimed by protein detection has indicated to be the most important solution. Detailed labeling description for the soybean ingredients in refined foods is required to protect the consumer. | Protein detection | 0.832163 |
2,988 | The following outline is provided as an overview of and topical guide to machine learning. Machine learning is a subfield of soft computing within computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. In 1959, Arthur Samuel defined machine learning as a "field of study that gives computers the ability to learn without being explicitly programmed". Machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from an example training set of input observations in order to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions. | Outline of machine learning | 0.832156 |
2,989 | History of machine learning Timeline of machine learning | Outline of machine learning | 0.832156 |
2,990 | Artificial neural network Feedforward neural network Extreme learning machine Convolutional neural network Recurrent neural network Long short-term memory (LSTM) Logic learning machine Self-organizing map | Outline of machine learning | 0.832156 |
2,991 | Apache Singa Apache MXNet Caffe PyTorch mlpack TensorFlow Torch CNTK Accord.Net Jax MLJ.jl – A machine learning framework for Julia | Outline of machine learning | 0.832156 |
2,992 | Anomaly detection Association rules Bias-variance dilemma Classification Multi-label classification Clustering Data Pre-processing Empirical risk minimization Feature engineering Feature learning Learning to rank Occam learning Online machine learning PAC learning Regression Reinforcement Learning Semi-supervised learning Statistical learning Structured prediction Graphical models Bayesian network Conditional random field (CRF) Hidden Markov model (HMM) Unsupervised learning VC theory | Outline of machine learning | 0.832156 |
2,993 | An academic discipline A branch of science An applied science A subfield of computer science A branch of artificial intelligence A subfield of soft computing Application of statistics | Outline of machine learning | 0.832156 |
2,994 | Supervised learning Averaged one-dependence estimators (AODE) Artificial neural network Case-based reasoning Gaussian process regression Gene expression programming Group method of data handling (GMDH) Inductive logic programming Instance-based learning Lazy learning Learning Automata Learning Vector Quantization Logistic Model Tree Minimum message length (decision trees, decision graphs, etc.) Nearest Neighbor Algorithm Analogical modeling Probably approximately correct learning (PAC) learning Ripple down rules, a knowledge acquisition methodology Symbolic machine learning algorithms Support vector machines Random Forests Ensembles of classifiers Bootstrap aggregating (bagging) Boosting (meta-algorithm) Ordinal classification Conditional Random Field ANOVA Quadratic classifiers k-nearest neighbor Boosting SPRINT Bayesian networks Naive Bayes Hidden Markov models Hierarchical hidden Markov model | Outline of machine learning | 0.832156 |
2,995 | Machine learning projects DeepMind Google Brain OpenAI Meta AI | Outline of machine learning | 0.832156 |
2,996 | Adversarial machine learning Predictive analytics Quantum machine learning Robot learning Developmental robotics | Outline of machine learning | 0.832156 |
2,997 | List of artificial intelligence projects List of datasets for machine learning research | Outline of machine learning | 0.832156 |
2,998 | In 2010, researchers from the Plant Stem Cell Institute (formerly Unhwa Institute of Science and Technology) presented their data to the world via Nature Biotechnology. Their research demonstrated the world's first cambial meristematic cell isolation. Due to the valuable and beneficial compounds for human health (i.e. paclitaxel) which are secreted by the CMC's, this technology is considered a serious breakthrough in plant biotechnology. | Plant stem cell | 0.832143 |
2,999 | Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem. | Theory of probabilities | 0.832141 |
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