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1,600 | A problem is called 3SUM-hard if solving it in subquadratic time implies a subquadratic-time algorithm for 3SUM. The concept of 3SUM-hardness was introduced by Gajentaan & Overmars (1995). They proved that a large class of problems in computational geometry are 3SUM-hard, including the following ones. | 3SUM | 0.841109 |
1,601 | AQA's syllabus also includes a wide selection of matrices work, which is an AS Further Mathematics topic. AQA's syllabus is much more famous than Edexcel's, mainly for its controversial decision to award an A* with Distinction (A^), a grade higher than the maximum possible grade in any Level 2 qualification; it is know... | Additional Mathematics | 0.841105 |
1,602 | : 49–50 Finite abelian groups and torsion groups have rank zero, and every abelian group of rank zero is a torsion group. The integers and the rational numbers have rank one, as well as every nonzero additive subgroup of the rationals. On the other hand, the multiplicative group of the nonzero rationals has an infinite... | Fundamental theorem of finite abelian groups | 0.841092 |
1,603 | There are also the related U50, UL50, UG50, UG50%, N90, NG50, and D50 statistics. To provide a better assessment of assembly output for viral and microbial datasets, a new metric called U50 should be used. The U50 identifies unique, target-specific contigs by using a reference genome as baseline, aiming at circumventin... | N50, L50, and related statistics | 0.841087 |
1,604 | An electric generator is mechanically identical to an electric motor, but operates in the reverse direction, converting mechanical energy into electrical energy. Electrical engineering – Electrical engineering is an engineering discipline concerned with the study, design and application of equipment, devices and system... | Glossary of mechanical engineering | 0.841086 |
1,605 | The book outlines five approaches of machine learning: inductive reasoning, connectionism, evolutionary computation, Bayes' theorem and analogical modelling. The author explains these tribes to the reader by referring to more understandable processes of logic, connections made in the brain, natural selection, probabili... | The Master Algorithm | 0.841081 |
1,606 | The GRE subject test in biology was a standardized test in the United States created by the Educational Testing Service, and is designed to assess a candidate's potential for graduate or post-graduate study in the field of biology. The test is comprehensive and covers—in equal proportions—molecular biology, organismal ... | GRE Biology Test | 0.841078 |
1,607 | Theorem: If M and N are two simple modules over a ring R, then any homomorphism f: M → N of R-modules is either invertible or zero. In particular, the endomorphism ring of a simple module is a division ring.The condition that f is a module homomorphism means that f ( r m ) = r f ( m ) for all m ∈ M and r ∈ R . {\displa... | Schur lemma | 0.841048 |
1,608 | The question "is weakly learnability equivalent to strong learnability?" posed by Kearns and Valiant (Unpublished manuscript 1988, ACM Symposium on Theory of Computing 1989) is the origin of boosting machine learning algorithms, which got a positive answer by Robert Schapire (1990, proof by construction, not practical)... | Michael Kearns (computer scientist) | 0.841044 |
1,609 | Application: in biomedicine, nanotechnology, environmental sciences and many other fields. The planned research will allow, among other things, to direct the synthesis of potential drugs and their design. | Solaris synchrotron | 0.841042 |
1,610 | 3. In computer science, denotes the (unknown) greatest lower bound for the exponent of the computational complexity of matrix multiplication. | Glossary of mathematical symbols | 0.841039 |
1,611 | Exome sequencing is only able to identify those variants found in the coding region of genes which affect protein function. It is not able to identify the structural and non-coding variants associated with the disease, which can be found using other methods such as whole genome sequencing. There remains 99% of the huma... | Whole exome sequencing | 0.84103 |
1,612 | Several very similar statements of the theorem can be given. A slightly more involved one, based on semi-rings of sets, is given further down below. A shorter, simpler statement is as follows. | Carathéodory extension theorem | 0.841023 |
1,613 | In the mid-1970s, H. Garth Dales and J. Esterle independently proved that, if one furthermore assumes the validity of the continuum hypothesis, there exist compact Hausdorff spaces X and discontinuous homomorphisms from C(X) to some Banach algebra, giving counterexamples to the conjecture. In 1976, R. M. Solovay (build... | Kaplansky's conjectures | 0.841023 |
1,614 | Specifically, the members of the universal set of a Boolean algebra or group need not be numbers. Moreover, a fair bit of philosophy and theoretical science can be formalized as axiomatic theories embodying first-order logic and set theory. Note also how model theory has been employed to formalize and reason about such... | Universal characteristic | 0.84102 |
1,615 | "Corollary: A 2CM can compute any partial recursive function of one argument, provided the input is coded as 2N and the output (if the machine halts) is coded as 2answer." (p. 3) "Theorem: There is no two counter machine that calculates 2N ." | Counter machine | 0.841012 |
1,616 | In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is ... | Offline algorithm | 0.841009 |
1,617 | Each time the gambler plays the slots, there is a one in n chance of winning. Playing n times is modeled by the binomial distribution, which is closely related to the binomial theorem and Pascal's triangle. The probability of winning k times out of n trials is: ( n k ) ( 1 n ) k ( 1 − 1 n ) n − k . | E (mathematical constant) | 0.840988 |
1,618 | Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many opt... | Travelling salesman problem | 0.840986 |
1,619 | This was a standard technique also used by other memory optimization tools. SoftRAM also claimed to increase the amount of virtual memory available by compressing the pages of virtual memory stored in the swap file on the hard disk, which has the added effect of reducing the number of swap file reads and writes. The so... | SoftRAM | 0.840985 |
1,620 | PCR has been applied to many areas of research in molecular genetics: PCR allows rapid production of short pieces of DNA, even when not more than the sequence of the two primers is known. This ability of PCR augments many methods, such as generating hybridization probes for Southern or northern blot hybridization. PCR ... | PCR test | 0.840984 |
1,621 | "Experiments on Plant Hybridization" (German: "Versuche über Pflanzen-Hybriden") is a seminal paper written in 1865 and published in 1866 by Gregor Mendel, an Augustinian friar considered to be the founder of modern genetics. The paper was the result after years spent studying genetic traits in Pisum sativum, the pea p... | Experiments on Plant Hybridization | 0.840983 |
1,622 | This is then repeated for I13 and V42, P. As before, we can take advantage of the reciprocity theorem to provide a check on the accuracy of these measurements. If we reverse the direction of the currents (i.e. apply the current I42 and measure V31, P, and repeat for I31 and V24, P), then V13, P should be the same as V3... | Van der Pauw method | 0.840978 |
1,623 | A function has a left inverse or a right inverse if and only it is injective or surjective, respectively. An homomorphism of algebraic structures that has a left inverse or a right inverse is respectively injective or surjective, but the converse is not true in some algebraic structures. For example, the converse is tr... | Left inverse element | 0.840975 |
1,624 | Guess the Correlation is a game with a purpose challenging players to guess the true Pearson correlation coefficient in scatter plots. The collected data is used to study what features in scatter plots skew human perception of the true correlation. The game was developed by Omar Wagih at the European Bioinformatics Ins... | Human-based computation game | 0.840972 |
1,625 | In electromagnetism, surface equivalence principle or surface equivalence theorem relates an arbitrary current distribution within an imaginary closed surface with an equivalent source on the surface. It is also known as field equivalence principle, Huygens' equivalence principle or simply as the equivalence principle.... | Surface equivalence principle | 0.840962 |
1,626 | If most of the time the substantial portion of the references aggregate into clusters, and if the shape of this system of clusters can be well predicted, then it can be used for performance optimization. There are several ways to benefit from locality using optimization techniques. Common techniques are: Increasing the... | Memory locality | 0.840957 |
1,627 | If S and T are subgroups of G, their product need not be a subgroup (for example, two distinct subgroups of order 2 in the symmetric group on 3 symbols). This product is sometimes called the Frobenius product. In general, the product of two subgroups S and T is a subgroup if and only if ST = TS, and the two subgroups a... | Product of subgroups | 0.840953 |
1,628 | The facility uses conventional capillary Sanger sequencing on Applied Biosystems 3730xl instruments, governed by a Laboratory Information Management System (LIMS). Additionally, next-generation sequencing (NGS) using Illumina HiSeq 2500 and HiScan SQ instruments, Life Technologies Ion Proton and Applied Biosystems SOLi... | Centre for Applied Genomics | 0.840948 |
1,629 | Additional studies suggest that other factors may further complicate the obstetrical dilemma hypothesis. One of these is dietary shifts, possibly due to the emergence of agriculture. This can be both due to change in diet as well as the increase in population density since agriculture was developed; more people leads t... | Obstetrical dilemma | 0.840948 |
1,630 | His motivation to develop the game was to expose non-physicists to the world of quantum mechanics.The game utilizes the same pieces as classical chess (8 pawns, 2 knights, 2 bishops, 2 rooks, 1 queen, 1 king) and is won in the same manner (by capturing the opponent's king). However, the pieces are allowed to obey laws ... | Quantum game theory | 0.840942 |
1,631 | Research goes beyond just sequencing to include therapeutic biomarker discoveries made utilizing bioinformatics programs. Among these discoveries are drug sensitivity biomarkers and inhibitor biomarkers. These discoveries paired with the evolution of DNA sequencing technologies to next-generation sequencing techniques,... | Cancer Genome Project | 0.840937 |
1,632 | In Typographical Number Theory, the usual symbols of "+" for additions, and "·" for multiplications are used. Thus to write "b plus c" is to write (b + c)and "a times d" is written as (a·d)The parentheses are required. Any laxness would violate TNT's formation system (although it is trivially proved this formalism is u... | Typographical Number Theory | 0.840934 |
1,633 | This is a somewhat larger application of the optimization of a cantilevered wing structure to maximize lift, subject to structure and weight constraints. In this case there are ten coordinate dimensions of the optimization unknowns that are being searched by the outer holon solver. The two outer holons each has a hidde... | PROSE modeling language | 0.840921 |
1,634 | According to the Classical Theory of Radiation, if each Fourier mode of the equilibrium radiation (in an otherwise empty cavity with perfectly reflective walls) is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal a... | Black body spectrum | 0.840919 |
1,635 | Machine learning in bioinformatics is the application of machine learning algorithms to bioinformatics, including genomics, proteomics, microarrays, systems biology, evolution, and text mining.Prior to the emergence of machine learning, bioinformatics algorithms had to be programmed by hand; for problems such as protei... | Machine learning in bioinformatics | 0.840906 |
1,636 | This is the origin of the term linear for describing this type of equations. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n. Linear equations occur frequently in all mathematics and their applications in physics a... | First degree equation | 0.840897 |
1,637 | This can be done using machine learning approaches that can reach an accuracy at genus-level of about 80%. Other popular analysis packages provide support for taxonomic classification using exact matches to reference databases and should provide greater specificity, but poor sensitivity. Unclassified microorganism shou... | Human microbiome | 0.840891 |
1,638 | Simplified models of friction applied to fully rigid bodies are extremely useful for a basic understanding of physical principles, or when modelling systems for applications such as animation, robotics and bio-mechanics. However, they are only an approximation to a full elastic model requiring complex systems of partia... | Painlevé paradox | 0.840888 |
1,639 | 1. Set the initial kinetic energy and all nodal velocity components to zero: E k ( t = 0 ) = 0 {\displaystyle E_{k}(t=0)=0{\frac {}{}}} V i ( t = 0 ) = 0 {\displaystyle V_{i}(t=0)=0{\frac {}{}}} 2. Compute the geometry set and the applied load component: X i ( t = 0 ) {\displaystyle X_{i}(t=0){\frac {}{}}} P i ( t = 0 ... | Dynamic relaxation | 0.840878 |
1,640 | The history of learning vector-valued functions is closely linked to transfer learning- storing knowledge gained while solving one problem and applying it to a different but related problem. The fundamental motivation for transfer learning in the field of machine learning was discussed in a NIPS-95 workshop on “Learnin... | Kernel methods for vector output | 0.840875 |
1,641 | 205ff and reference on p. 401 ibid: Greibach "The undecidability of the ambiguity problem for minimal lineal grammars," Information and Control 6:2, 117–125, also reference on p. 402 ibid: Greibach "A note on undecidable properties of formal languages", Math Systems Theory 2:1, 1–6.) Penrose tiling questions. Questio... | Proof of impossibility | 0.840874 |
1,642 | "Method 2" is the only solution that fulfills the transformation invariants that are present in certain physical systems—such as in statistical mechanics and gas physics—in the specific case of Jaynes's proposed experiment of throwing straws from a distance onto a small circle. Nevertheless, one can design other practi... | Bertrand paradox (probability) | 0.840872 |
1,643 | This bound is sharp. If all the degrees are equal to d, this bound becomes dn and is exponential in the number of variables. (The fundamental theorem of algebra is the special case n = 1.) This exponential behavior makes solving polynomial systems difficult and explains why there are few solvers that are able to automa... | Polynomial system | 0.840872 |
1,644 | (The last case has no analogue in planar trigonometry.) No single method solves all cases. The figure below shows the seven non-trivial cases: in each case the given sides are marked with a cross-bar and the given angles with an arc. | Spherical triangles | 0.840871 |
1,645 | Using the language of category theory, many areas of mathematical study can be categorized. Categories include sets, groups and topologies. Each category is distinguished by properties that all its objects have in common, such as the empty set or the product of two topologies, yet in the definition of a category, objec... | Category theory | 0.84087 |
1,646 | In fact, this example shows that the hyperbolic quaternions are not even an alternative algebra. The first three relations show that products of the (non-real) basis elements are anti-commutative. Although this basis set does not form a group, the set { 1 , i , j , k , − 1 , − i , − j , − k } {\displaystyle \{1,i,j,k,-... | Hyperbolic quaternion | 0.840857 |
1,647 | The uses that have been derived from Vectorette PCR are many and have been useful to the science of biology. For example, it gives rise to methods that can help during the outbreaks of diseases by making it easier to subtype pathogens that are similar or closely related. It can also be used to help diagnose certain dis... | Vectorette PCR | 0.840857 |
1,648 | Systems of the form Ax = b with A symmetric and positive definite arise quite often in applications. For instance, the normal equations in linear least squares problems are of this form. It may also happen that matrix A comes from an energy functional, which must be positive from physical considerations; this happens f... | LDL decomposition | 0.840855 |
1,649 | Genetics stimulated research to improve crop production through plant breeding. Modern plant breeding is applied genetics, but its scientific basis is broader, covering molecular biology, cytology, systematics, physiology, pathology, entomology, chemistry, and statistics (biometrics). It has also developed its own tech... | Pest resistance | 0.840851 |
1,650 | An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p(x, y) = 0. This equation is often called the implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x. Wi... | Rational curve | 0.840846 |
1,651 | The term phase may have several different uses in chemistry contexts; colloquially, it is often used interchangeably with state of matter, but many distinct phases may exist within a single state of matter. phase diagram A graphical representation of the equilibrium relationships between thermodynamically distinct phas... | Glossary of chemistry terms | 0.840842 |
1,652 | The Church lab works on research projects that are distributed in diverse areas of modern biology like developmental biology, neurobiology, info processing, medical genetics, genomics, gene therapy, diagnostics, chemistry & bioengineering, space biology & space genetics, and ecosystem. Research and technology developme... | George Church (geneticist) | 0.840841 |
1,653 | Absorption spectroscopy – Anders Jonas Ångström – Astronomical spectroscopy – Astronomy – Black body – Blazar – Bremsstrahlung – Caesium – Cherenkov radiation – Color – Diffraction – Digital signal processing – Direct-sequence spread spectrum – Dispersion (optics) – Eigenstate – Eigenvalue – Electromagnetic radiation –... | List of cycles | 0.840834 |
1,654 | They often played bridge and golf together. : 77 Bardeen was a quantum physicist, Brattain a gifted experimenter in materials science, and Shockley, the leader of their team, was an expert in solid-state physics. According to theories of the time, Shockley's field effect transistor, a cylinder coated thinly with silico... | Walter Houser Brattain | 0.840832 |
1,655 | In the context of group theory, a sequence G 0 → f 1 G 1 → f 2 G 2 → f 3 ⋯ → f n G n {\displaystyle G_{0}\;{\xrightarrow {f_{1}}}\;G_{1}\;{\xrightarrow {f_{2}}}\;G_{2}\;{\xrightarrow {f_{3}}}\;\cdots \;{\xrightarrow {f_{n}}}\;G_{n}} of groups and group homomorphisms is called exact, if the image (or range) of each homo... | Numerical order | 0.84083 |
1,656 | In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates. Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on the choice of the initial point of origin. There are a variety of coo... | Analytical geometry | 0.840826 |
1,657 | For the choice of the 4D coordinates to be valid descriptors of the original 3D space it must have the same number of degrees of freedom. Since four coordinates have four degrees of freedom it must have a constraint placed on it. We can choose a constraint such that Pythagorean theorem holds in the new 4D space. | Curved space | 0.840807 |
1,658 | In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the compl... | Bit complexity | 0.840801 |
1,659 | ```List of subjects in A Level Mathematics``` 1. Core Mathematics: Covers foundational topics like algebra, calculus, trigonometry, and coordinate geometry. 2. Further Mathematics: Expands upon Core Mathematics with additional areas such as complex numbers, matrices, differential equations, and numerical methods. | Advanced level mathematics | 0.840798 |
1,660 | Hence Q = g Q0 g−1. The condition QAQ=0 implies Q gt g−1 Q = 0 and hence that Q0 g−1 gt Q0 =0.There is another kinematic way of understanding parallel transport and geodesic curvature in terms of "rolling without slipping or twisting". Although well known to differential geometers since the early part of the twentieth ... | Riemannian connection on a surface | 0.84079 |
1,661 | In electric-field screening, screened Poisson equation for the electric potential ϕ ( r ) {\displaystyle \phi (\mathbf {r} )} is usually written as (SI units) where k 0 − 1 {\displaystyle k_{0}^{-1}} is the screening length, ρ e x t ( r ) {\displaystyle \rho _{\rm {ext}}(\mathbf {r} )} is the charge density produced by... | Screened Poisson equation | 0.840772 |
1,662 | A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem). There are four major issues to consider in supervised learning: | Supervised classification | 0.840761 |
1,663 | The real RAM closely resembles the later Blum–Shub–Smale machine. However, the real RAM is typically used for the analysis of concrete algorithms in computational geometry, while the Blum–Shub–Smale machine instead forms the basis for extensions of the theory of NP-completeness to real-number computation. An alternativ... | Real RAM | 0.840757 |
1,664 | In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D +... | Quadric | 0.840755 |
1,665 | Biochemistry is the study of the chemical processes in living organisms. It deals with the structure and function of cellular components such as proteins, carbohydrates, lipids, nucleic acids and other biomolecules. Articles related to biochemistry include: | Index of biochemistry articles | 0.840749 |
1,666 | Automation and programmed logical controls Power and driving electronics Modern and digital control systems Robotics systems Mechatronics systems Automated control Computer applications for mechatronics Calculus Electrical circuits Systems Dynamics Dynamics and vibrations Artificial Intelligence Engineering Mathematics... | Mechatronics | 0.840746 |
1,667 | Walter's theorem states that if G is a finite group whose 2-sylow subgroups are abelian, then G/O(G) has a normal subgroup of odd index that is a product of groups each of which is a 2-group or one of the simple groups PSL2(q) for q = 2n or q = 3 or 5 mod 8, or the Janko group J1, or Ree groups 2G2(32n+1). (Here O(G) d... | Walter theorem | 0.840736 |
1,668 | Many other less formal definitions have been proposed, often applying concepts from the differential geometry of curves, such as curvature and torsion. Structural biologists solving a new atomic-resolution structure will sometimes assign its secondary structure by eye and record their assignments in the corresponding P... | Primary sequence | 0.840735 |
1,669 | Bidirectional Encoder Representations from Transformers (BERT) is a family of language models introduced in 2018 by researchers at Google. A 2020 literature survey concluded that "in a little over a year, BERT has become a ubiquitous baseline in Natural Language Processing (NLP) experiments counting over 150 research p... | BERT (language model) | 0.840733 |
1,670 | In the following, the angle of two lines will be measured by the difference of the slopes of the line with respect to the directrix of the parabola. That is, for a parabola of equation y = a x 2 + b x + c , {\displaystyle y=ax^{2}+bx+c,} the angle between two lines of equations y = m 1 x + d 1 , y = m 2 x + d 2 {\displ... | Parabolic curve | 0.840725 |
1,671 | Revealing the evolution and genetic diversity of sequences and organisms Identification of molecular structure from sequence aloneIn chemistry, sequence analysis comprises techniques used to determine the sequence of a polymer formed of several monomers (see Sequence analysis of synthetic polymers). In molecular biolog... | Sequence analysis | 0.840721 |
1,672 | Combining Cases 1 and 2 proves the theorem by induction. It is also easy to the converse of Theorem 2 by induction. Proposition 8. A graph with a Henneberg construction is generically minimally rigid. | Geiringer–Laman theorem | 0.840717 |
1,673 | This is the "genotype–phenotype map". T2 is the transformation due to natural selection, T3 are epigenetic relations that predict genotypes based on the selected phenotypes and finally T4 the rules of Mendelian genetics. In practice, there are two bodies of evolutionary theory that exist in parallel, traditional popula... | Genotype–phenotype distinction | 0.840715 |
1,674 | The following is a list of common inductive biases in machine learning algorithms. Maximum conditional independence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditional independence. This is the bias used in the Naive Bayes classifier. Minimum cross-validation error: when trying to choose... | Inductive bias | 0.840713 |
1,675 | The first theoretical treatment of electrostatic screening, due to Peter Debye and Erich Hückel, dealt with a stationary point charge embedded in a fluid. Consider a fluid of electrons in a background of heavy, positively charged ions. For simplicity, we ignore the motion and spatial distribution of the ions, approxima... | Electric-field screening | 0.840712 |
1,676 | If the point is near the origin, the Pythagorean theorem shows that But if (x, y) is extremely close to the origin, since the x axis is a tangent to the circle, y is very small compared with x, so y2 is negligible compared with the other terms. Therefore, extremely close to the origin Compare this with the parabola whi... | Parabolic curve | 0.840708 |
1,677 | As Lipton states:This alone could be important and often is a great reason for finding such algorithms. For example, if tomorrow there were a discovery that showed there is a factoring algorithm with a huge but provably polynomial time bound, that would change our beliefs about factoring. The algorithm might never be u... | Galactic algorithm | 0.840707 |
1,678 | Simple probability theory helps the individual either estimate or calculate the probabilities involved with games of chance. However, most individuals fail to approximate, for example, the probability of being dealt a full-house in a game of poker. Not understanding these probabilities causes the individual to wager mo... | Statistical literacy | 0.840703 |
1,679 | Intended to be equivalent to an introductory college course in mechanics for physics or engineering majors, the course modules are: Kinematics Newton's laws of motion Work, energy and power Systems of particles and linear momentum Circular motion and rotation Oscillations and gravitation.Methods of calculus are used wh... | AP Physics C: Mechanics | 0.840703 |
1,680 | Radial basis function and wavelet networks have also been introduced. These can be shown to offer best approximation properties and have been applied in nonlinear system identification and classification applications.Deep learning feedforward networks alternate convolutional layers and max-pooling layers, topped by sev... | Neural networks | 0.840702 |
1,681 | AP Physics 2 covers the following topics: Unit 1: Fluids Unit 2: Thermodynamics Unit 3: Electric Force, Field, and Potential Unit 4: Electric Circuits Unit 5: Magnetism and Electromagnetic Induction Unit 6: Geometric and Physical Optics Unit 7: Quantum, Atomic, and Nuclear Physics | AP Physics | 0.840697 |
1,682 | Binary relation – Heterogeneous relation – Reflexive relation – Reflexive property of equality – Symmetric relation – Symmetric property of equality – Antisymmetric relation – Transitivity (mathematics) – Transitive closure – Transitive property of equality – Equivalence and identity Equivalence relation – Equivalence ... | Outline of discrete mathematics | 0.840687 |
1,683 | 388) To obtain a non-Euclidean geometry, the parallel postulate (or its equivalent) must be replaced by its negation. Negating the Playfair's axiom form, since it is a compound statement (... there exists one and only one ...), can be done in two ways. Either there will exist more than one line through the point parall... | Foundations of geometry | 0.840679 |
1,684 | MDL applies in machine learning when algorithms (machines) generate descriptions. Learning occurs when an algorithm generates a shorter description of the same data set. The theoretic minimum description length of a data set, called its Kolmogorov complexity, cannot, however, be computed. That is to say, even if by ran... | Minimum description length | 0.840673 |
1,685 | Every subgroup of a free abelian group is itself a free abelian group. This result of Richard Dedekind was a precursor to the analogous Nielsen–Schreier theorem that every subgroup of a free group is free, and is a generalization of the fact that every nontrivial subgroup of the infinite cyclic group is infinite cyclic... | Free abelian group | 0.840665 |
1,686 | The transport of water along this pathway occurs in components, variously defined among scientific disciplines: Soil physics characterizes water in soil in terms of tension, Physiology of plants and animals characterizes water in organisms in terms of diffusion pressure deficit, and Meteorology uses vapour pressure or ... | Soil-plant-atmosphere continuum | 0.840664 |
1,687 | The word problem on free lattices and more generally free bounded lattices has a decidable solution. Bounded lattices are algebraic structures with the two binary operations ∨ and ∧ and the two constants (nullary operations) 0 and 1. The set of all well-formed expressions that can be formulated using these operations o... | Word problem (mathematics) | 0.840662 |
1,688 | The FAQ has become an important component of websites, either as a stand-alone page or as a website section with multiple subpages per question or topic. Embedded links to FAQ pages have become commonplace in website navigation bars, bodies, or footers. The FAQ page is an important consideration in web design, in order... | FAQ | 0.840662 |
1,689 | The spectral range covers visible to near-infrared wavelengths (450 nm – 950 nm). Advanced Small Analyzer for Neutrals (ASAN), is an energetic neutral atom analyzer provided by the Swedish Institute of Space Physics (IRF). It will reveal how solar wind interacts with the lunar surface, which may help determine the proc... | Yutu-2 | 0.84066 |
1,690 | In the tenth year, courses focused on geometry through algebraic uses. The eleventh year focused on a continuation of more advanced algebra topics. These topics were more advanced than those discussed in the ninth grade. However, if the student took an advanced algebra class during the ninth year, then he took two of t... | National Council of Teachers of Mathematics | 0.840658 |
1,691 | Dydrogesterone, also known as 6-dehydro-9β,10α-progesterone or as 9β,10α-pregna-4,6-diene-3,20-dione, is a synthetic pregnane steroid and a derivative of progesterone and retroprogesterone (9β,10α-progesterone). Retroprogesterone derivatives like dydrogesterone are analogues of progesterone in which the hydrogen atom a... | Dydrogesterone | 0.840654 |
1,692 | In the context of classical mechanics simulations and physics engines employed within video games, collision response deals with models and algorithms for simulating the changes in the motion of two solid bodies following collision and other forms of contact. | Collision response | 0.840645 |
1,693 | It was found that providing combined cytotoxic drugs is better than a single drug, a process called the combination therapy, which has an advantage in the statistics of survival and response to the tumor and in the progress of the disease. A Cochrane review concluded that combined therapy was more effective to treat me... | Malignant neoplasm | 0.840644 |
1,694 | Burnside's theorem in group theory 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. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes. | Finite group | 0.840641 |
1,695 | Binary relations over sets X and Y can be represented algebraically by logical matrices indexed by X and Y with entries in the Boolean semiring (addition corresponds to OR and multiplication to AND) where matrix addition corresponds to union of relations, matrix multiplication corresponds to composition of relations (o... | Mathematical relation | 0.840633 |
1,696 | They are roughly 0.5 µm by 1.1 µm. They have an unusual biology: they do not require organic carbon for growth, instead growing by coupling hydrogen oxidation with a form of Fe(III) oxide reduction. == References == | Geothermobacterium ferrireducens | 0.840627 |
1,697 | He is also well known for his work as a teacher of the "BIS 101" undergraduate genetics course and his use of whiteboard writing and his co-produced video series alongside the university. A collaboration between Comai's lab and Kyoto University in 2014 on the genetic sex reproduction of the persimmon species Diospyros ... | Luca Comai | 0.840625 |
1,698 | In computer science, a call stack is a stack data structure that stores information about the active subroutines of a computer program. This kind of stack is also known as an execution stack, program stack, control stack, run-time stack, or machine stack, and is often shortened to just "the stack". Although maintenance... | Run-time stack | 0.840624 |
1,699 | Metagenomics is the study of genetic material recovered directly from environmental or clinical samples by a method called sequencing. The broad field may also be referred to as environmental genomics, ecogenomics, community genomics or microbiomics. While traditional microbiology and microbial genome sequencing and ge... | Human metagenome | 0.84062 |
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