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1,200 | Saks' research in computational complexity theory, combinatorics, and graph theory has contributed to the study of lower bounds in order theory, randomized computation, and space–time tradeoff. In 1984, Saks and Jeff Kahn showed that there exist a tight information-theoretical lower bound for sorting under partially or... | Michael Saks (mathematician) | 0.843647 |
1,201 | We may generalize Diophantus's solution to solve the problem for any given square, which we will represent algebraically as a2. Also, since Diophantus refers to an arbitrary multiple of x, we will take the arbitrary multiple to be tx. Then: ( t x − a ) 2 = a 2 − x 2 ⇒ t 2 x 2 − 2 a t x + a 2 = a 2 − x 2 ⇒ x 2 ( t 2 + 1... | Diophantus II.VIII | 0.843642 |
1,202 | The speed of light c can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the metre is currently defined in terms of the second, it has the exact value of 299 792 458 m/s. We would need a similar factor in Euclidean space if, for example, we measured wi... | Time in physics | 0.843642 |
1,203 | Different methods are used to reach that state such as vapor diffusion, microbatch, microdialysis, and free-interface diffusion. Developing protein crystals is a difficult process influenced by many factors, including pH, temperature, ionic strength in the crystallization solution, and even gravity. Once formed, these ... | Protein crystal | 0.843637 |
1,204 | Theorem 2. If A {\displaystyle A} and B {\displaystyle B} are C*-algebras and π: A → M ( B ) {\displaystyle \pi :A\to M(B)} is a non-degenerate *-homomorphism (i.e., π B {\displaystyle \pi B} is a dense subset of B {\displaystyle B} ), then we can uniquely extend π {\displaystyle \pi } to a *-homomorphism π ¯: M ( A )... | Locally compact quantum group | 0.843623 |
1,205 | The process of completing the square makes use of the algebraic identity x 2 + 2 h x + h 2 = ( x + h ) 2 , {\displaystyle x^{2}+2hx+h^{2}=(x+h)^{2},} which represents a well-defined algorithm that can be used to solve any quadratic equation. : 207 Starting with a quadratic equation in standard form, ax2 + bx + c = 0 Di... | Quadratic equations | 0.843614 |
1,206 | Other examples of emerging RNA-Seq applications due to the advancement of bioinformatics algorithms are copy number alteration, microbial contamination, transposable elements, cell type (deconvolution) and the presence of neoantigens.Prior to RNA-Seq, gene expression studies were done with hybridization-based microarra... | RNA sequencing | 0.84361 |
1,207 | Level 4, with its special construction and biosafety suits, is necessary to work with the most serious of pathogens including Ebola, Nipah, and Marburg.Following the SARS outbreak in 2003, lessons learned resulted in a number of changes to public health in Canada. Among those were the creation of the Public Health Agen... | Canadian Science Centre for Human and Animal Health | 0.843608 |
1,208 | 1938 – Nobel Prize winner (1920) Walther Nernst reestimates the cosmic ray temperature as 0.75 K. 1946 – Robert Dicke predicts "... radiation from cosmic matter" at < 20 K, but did not refer to background radiation. 1946 – George Gamow calculates a temperature of 50 K (assuming a 3-billion year old universe), commentin... | Cosmic Microwave Background Radiation | 0.843607 |
1,209 | Algebraic combinatorics, in which algebraic methods are used to study combinatorial questions. Relational algebra: a set of finitary relations that is closed under certain operators.Many mathematical structures are called algebras: Algebra over a field or more generally algebra over a ring.Many classes of algebras over... | Algebra | 0.843603 |
1,210 | Electrostatic analyzers are designed in different configurations. A simple version is a radial cylindrical analyzer, which consists of two curved parallel plates at different potentials. Ions or electrons enter the analyzer at one end and either pass through the other end or collide with the walls of the analyzer, depe... | Electron analyzer | 0.843603 |
1,211 | The nonexistence of an asymptotically optimal algorithm is called speedup. Blum's speedup theorem shows that there exist artificially constructed problems with speedup. However, it is an open problem whether many of the most well-known algorithms today are asymptotically optimal or not. | Asymptotic optimality | 0.843599 |
1,212 | For example, quantum mechanics and solid state physics might be relevant to an engineer working on VLSI (the design of integrated circuits), but are largely irrelevant to engineers working with macroscopic electrical systems. Even circuit theory may not be relevant to a person designing telecommunication systems that u... | Electrical engineering | 0.843595 |
1,213 | In physics, Maxwell's equations imply that the (possibly time-varying) distributions of charges and currents are related to the electric and magnetic fields by a linear transformation. Thus, the superposition principle can be used to simplify the computation of fields that arise from a given charge and current distribu... | Wave superposition | 0.843593 |
1,214 | The following hierarchy is an example of a cognitive model task performance for the knowledge and skills in the areas of ratio, factoring, function, and substitution (called the Ratios and Algebra hierarchy). This hierarchy is divergent and composed of nine attributes which are described below. If the cognitive model i... | Attribute hierarchy method | 0.843573 |
1,215 | Other names for a double layer are electrostatic double layer, electric double layer, plasma double layers. The term ‘electrostatic shock’ in the magnetosphere has been applied to electric fields oriented at an oblique angle to the magnetic field in such a way that the perpendicular electric field is much stronger than... | Double layer (plasma physics) | 0.843572 |
1,216 | Attribute A8 also represents the skills of advanced substitution. However, what makes attribute A8 more difficult than attribute A7 is that algebraic expressions, rather than numbers, need to be substituted into another algebraic expression. The last branch in the sub-hierarchy contains only one additional attribute, A... | Attribute hierarchy method | 0.843571 |
1,217 | Loosening the error requirements further to allow for two-sided error yields the class BPP (bounded-error probabilistic polynomial time), the class of problems solvable in polynomial time by a probabilistic Turing machine with error probability less than 1/3 (for both strings in the language and not in the language). B... | Class (complexity theory) | 0.843562 |
1,218 | receiver – Superposition theorem – Surge arrester – Surge protection – Switch – Switched reluctance motor – Switched-mode power supply – Switchgear – Symbolic circuit analysis – Symmetrical components – Synchro – Synchronization (alternating current) – Synchronous circuit – Synchronous motor – Synchronous rectification... | Index of electrical engineering articles | 0.843526 |
1,219 | The group of non-zero real numbers with multiplication (R*,•) has two components and the group of components is ({1,−1},•). Consider the group of units U in the ring of split-complex numbers. In the ordinary topology of the plane {z = x + j y: x, y ∈ R}, U is divided into four components by the lines y = x and y = − x ... | Component group | 0.843508 |
1,220 | A similar effect is the proximity effect, which is caused by externally induced eddy currents.An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where... | Eddy currents | 0.843503 |
1,221 | Macromolecular structures can be determined from protein crystal using a variety of methods, including X-Ray Diffraction/X-ray crystallography, Cryogenic Electron Microscopy (CryoEM) (including Electron Crystallography and Microcrystal Electron Diffraction (MicroED)), Small-angle X-ray scattering, and Neutron diffracti... | Crystal protein | 0.843501 |
1,222 | Accumulation point Addition in N associativity of addition in N commutativity of addition in N uniqueness of addition in N Algorithmic information theory Boolean ring commutativity of a boolean ring Boolean satisfiability problem NP-completeness of the Boolean satisfiability problem Cantor's diagonal argument set is sm... | List of mathematical proofs | 0.8435 |
1,223 | The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of N electrons constrained to the surface of a unit sphere that repel each other with a force given by Coulomb's law. The physicist J. J. Thomson posed the problem in 1904 after proposing an atomic model, later... | Thomson Problem | 0.843497 |
1,224 | Berkeley Physics Course. Mechanics. Vol. | Charles Kittel | 0.843486 |
1,225 | Today, the terms threading and fold recognition are frequently (though somewhat incorrectly) used interchangeably. Fold recognition methods are widely used and effective because it is believed that there are a strictly limited number of different protein folds in nature, mostly as a result of evolution but also due to ... | Threading (protein sequence) | 0.84348 |
1,226 | Rosetta Genomics Ltd. was a molecular diagnostics company with offices in Israel and the United States that uses micro-ribonucleic acid (microRNA) biomarkers to develop diagnostic tests designed to differentiate between various types of cancer. The company expects the first three tests based on its technology to be sub... | Rosetta Genomics | 0.843477 |
1,227 | Machine Learning. 46: 225–254. doi:10.1023/A:1012470815092. | Machine Learning (journal) | 0.84347 |
1,228 | Often, such identification is made with the aim of better understanding the genetic basis of disease, unique adaptations, desirable properties (esp. in agricultural species), or differences between populations. In a less formal way, bioinformatics also tries to understand the organizational principles within nucleic ac... | Medical electronics | 0.84347 |
1,229 | Plant genetics played a key role in the modern-day theories of heredity, beginning with Gregor Mendel's study of pea plants in the 19th century. The occupation has since grown to encompass advancements in biotechnology that have led to greater understanding of plant breeding and hybridization. Commercially, plant genet... | Plant geneticist | 0.843464 |
1,230 | Finding the structure of proteins important application of bioinformatics. The Critical Assessment of Protein Structure Prediction (CASP) is an open competition where worldwide research groups submit protein models for evaluating unknown protein models. | Bio informatics | 0.84346 |
1,231 | "This is a lighthouse project, our first major investment in terms of people and resources into a fundamental, very important, real-world scientific problem", Hassabis said to The Guardian. In November 2020, DeepMind again announced world-beating results in the CASP14 edition of the competition, with a median global di... | Demis Hassabis | 0.843452 |
1,232 | This cube can used for organizing major subjects within physics as occupying each of the eight corners. The eight corners of the cGh physics cube are: Classical mechanics (_, _, _) Special relativity (c, _, _), gravitation (_, G, _), quantum mechanics (_, _, h) General relativity (c, G, _), quantum field theory (c, _, ... | CGh physics | 0.843433 |
1,233 | Electrodynamic fields are electric fields which do change with time, for instance when charges are in motion. In this case, a magnetic field is produced in accordance with Ampère's circuital law (with Maxwell's addition), which, along with Maxwell's other equations, defines the magnetic field, B {\displaystyle \mathbf ... | Electrical field | 0.843415 |
1,234 | There are many binary operations that can be viewed as generalizations of the addition operation on the real numbers. The field of abstract algebra is centrally concerned with such generalized operations, and they also appear in set theory and category theory. | Addition of natural numbers | 0.843413 |
1,235 | The test can be extended to include video input, as well as a "hatch" through which objects can be passed: this would force the machine to demonstrate skilled use of well designed vision and robotics as well. Together, these represent almost all of the major problems that artificial intelligence research would like to ... | Imitation game | 0.843409 |
1,236 | Primer-BLAST is widely used, and freely accessible from the National Center for Biotechnology Information (NCBI) website. On the other hand, FastPCR, a commercial application, allows simultaneous testing of a single primer or a set of primers designed for multiplex target sequences. | In silico PCR | 0.843402 |
1,237 | Cryptographic limitations on learning Boolean formulae and finite automata. (with Leslie Valiant) Proceedings of the twenty-first annual ACM symposium on Theory of computing (STOC'89).The open question: is weakly learnability equivalent to strong learnability? ; The origin of boosting algorithms; Important publication ... | Michael Kearns (computer scientist) | 0.843384 |
1,238 | The 4273π project or 4273pi project also offers open source educational materials for free. The course runs on low cost Raspberry Pi computers and has been used to teach adults and school pupils. 4283 is actively developed by a consortium of academics and research staff who have run research level bioinformatics using ... | Bio informatics | 0.843382 |
1,239 | "I would study weak noncovalent bonds in the most challenging of solvents, water. Therefore, the ‘synthetic objective’ would be the three-dimensional assembly of multiple specific noncovalent bonds in aqueous media. Biological molecules, such as proteins or nucleic acids, would be my target and small molecule synthesis... | Peter Dervan | 0.843378 |
1,240 | In group and set theory, many algebraic structures are called commutative when certain operands satisfy the commutative property. In higher branches of mathematics, such as analysis and linear algebra the commutativity of well-known operations (such as addition and multiplication on real and complex numbers) is often u... | Commutative law | 0.843369 |
1,241 | Any finite abelian group, with the discrete topology. By the structure theorem for finite abelian groups, all such groups are products of cyclic groups. The integers Z {\displaystyle \mathbb {Z} } under addition, again with the discrete topology. | Locally compact abelian group | 0.843365 |
1,242 | If the application is of an abstraction to a value, however, it will result in a lambda calculus expression that may itself be an application (rather than a value), and so cannot be pushed onto the stack. In this case, the current contents of S, E, and C are pushed onto the dump D (which is a stack of these triples), S... | SECD machine | 0.843364 |
1,243 | There are several properties that may be familiar from ring theory, or from associative algebras, which are not always true for non-associative algebras. Unlike the associative case, elements with a (two-sided) multiplicative inverse might also be a zero divisor. For example, all non-zero elements of the sedenions have... | Non-associative algebra | 0.843356 |
1,244 | During the earlier times when genomics was being studied, scientists found it challenging to sequence genetic information. The field began to explode in 1977 when Fred Sanger, PhD, along with his colleagues, sequenced the DNA-based genome of a bacteriophage, using a method now known as the Sanger Method. The Sanger Met... | Pathogenomics | 0.843349 |
1,245 | Therefore, if (1) concludes that N is composite, it truly is composite. (2) and (3) check if Q has order 2 k {\displaystyle 2^{k}} . Thus, if (2) or (3) conclude N is composite, it is composite. Now, if the algorithm concludes that N is prime, then that means S 1 {\displaystyle S_{1}} satisfies the condition of Theorem... | Elliptic curve primality | 0.843325 |
1,246 | Fluid Phase Equilibria is a peer-reviewed scientific journal on physical chemistry and thermodynamics that is published by Elsevier. The articles deal with experimental, theoretical and applied research related to properties of pure components and mixtures, especially phase equilibria, caloric and transport properties ... | Fluid Phase Equilibria | 0.843317 |
1,247 | In order to calculate the phase equilibrium, it is necessary to use a thermodynamic model such as NRTL, UNIQUAC, etc. The corresponding parameters of these models can be obtained from literature (e.g. Dechema Chemistry Data Series, Dortmund Data Bank, etc.) or by a correlation process of experimental data. | Countercurrent solvent extraction | 0.84331 |
1,248 | In physics and metrology, the standard definition of measurement is the estimation of the ratio between a magnitude of a continuous quantity and a unit magnitude of the same kind (de Boer, 1994/95; Emerson, 2008). For example, the statement "Peter's hallway is 4 m long" expresses a measurement of an hitherto unknown le... | Theory of conjoint measurement | 0.84328 |
1,249 | In general, there is no known characterization (i.e., a necessary and sufficient condition) for the existence of semidirect products in groups. However, some sufficient conditions are known, which guarantee existence in certain cases. For finite groups, the Schur–Zassenhaus theorem guarantees existence of a semidirect ... | Semi-direct product | 0.843277 |
1,250 | Replication of DNA and transcription from DNA to mRNA occurs in the nucleus while translation from RNA to proteins occurs in the ribosome. The genetic code is made of four base pairs: adenine, cytosine, uracil, and guanine and is redundant meaning multiple combinations of these base pairs (which are read in triplicate)... | Molecular Genetics | 0.843264 |
1,251 | Dominance is a key concept in Mendelian inheritance and classical genetics. Letters and Punnett squares are used to demonstrate the principles of dominance in teaching, and the use of upper-case letters for dominant alleles and lower-case letters for recessive alleles is a widely followed convention. A classic example ... | Autosomal Recessive | 0.843257 |
1,252 | Nor are more sophisticated methods foolproof: students who are fully capable of applying rigorous definitions may still fall back on intuitive images when they are surprised by a result in advanced mathematics, including 0.999.... For example, one real analysis student was able to prove that 0.333... = 1⁄3 using a supr... | 0.999... | 0.843256 |
1,253 | In the absence of empirical algorithmics, analyzing the complexity of an algorithm can involve various theoretical methods applicable to various situations in which the algorithm may be used. Memory and cache considerations are often significant factors to be considered in the theoretical choice of a complex algorithm,... | Empirical algorithmics | 0.843252 |
1,254 | The tasks that lie in the space of sequence analysis are often non-trivial to resolve and require the use of relatively complex approaches. Of the many types of methods used in practice, the most popular include: Dynamic programming Artificial Neural Network Hidden Markov Model Support Vector Machine Clustering Bayesia... | Sequence analysis | 0.843236 |
1,255 | In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for el... | Coupling strength | 0.843233 |
1,256 | Many key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to enco... | Neuro-symbolic AI | 0.843232 |
1,257 | Smarter compilers (such as Glasgow Haskell Compiler) will track this, but naive inlining loses this information. A further benefit of inlining for the memory system is: Eliminating branches and keeping code that is executed close together in memory improves instruction cache performance by improving locality of referen... | Method inlining | 0.843222 |
1,258 | Both games involve asking yes/no questions, but Twenty Questions places a greater premium on efficiency of questioning. A limit on their likeness to the scientific process of trying hypotheses is that a hypothesis, because of its scope, can be harder to test for truth (test for a "yes") than to test for falsity (test f... | Twenty Questions | 0.843216 |
1,259 | The primary arithmetic suggests the following arithmetic axiomatization of 2: 1+1=1+0=0+1=1=~0, and 0+0=0=~1. The set B = { {\displaystyle \ B=\{} , {\displaystyle ,} } {\displaystyle \ \}} is the Boolean domain or carrier. In the language of universal algebra, the primary algebra is the algebraic structure ⟨ B , − − ,... | Boundary algebra | 0.843202 |
1,260 | Eventually, when no one could do (a) or (b), the code was considered optimized, and they moved on to other snippets. Small shops with only one analyst learned CICS optimization very slowly (or not at all). Because application programs could be shared by many concurrent threads, the use of static variables embedded with... | CICS | 0.843201 |
1,261 | In computer science and operations research, exact algorithms are algorithms that always solve an optimization problem to optimality. Unless P = NP, an exact algorithm for an NP-hard optimization problem cannot run in worst-case polynomial time. There has been extensive research on finding exact algorithms whose runnin... | Exact algorithm | 0.843197 |
1,262 | At the top level, 64 mathematical disciplines are labeled with a unique two-digit number. In addition to the typical areas of mathematical research, there are top-level categories for "History and Biography", "Mathematics Education", and for the overlap with different sciences. Physics (i.e. mathematical physics) is pa... | Mathematics Subject Classification | 0.843195 |
1,263 | Preface Advertisement Chapter 1: Vector Analysis Chapter 2: Electrostatics Chapter 3: Potentials Chapter 4: Electric Fields in Matter Chapter 5: Magnetostatics Chapter 6: Magnetic Fields in Matter Chapter 7: Electrodynamics Chapter 8: Conservation Laws Chapter 9: Electromagnetic Waves Chapter 10: Potentials and Fields ... | Introduction to Electrodynamics | 0.843186 |
1,264 | 2. β is the set of all subsets of a set α of cardinality β, or of an ordered set α of order type β 3. is the equivalence class of x { } 1. {a, b, ...} is the set with elements a, b, ... 2. {x: φ(x)} is the set of x such that φ(x) ⟨ ⟩ ⟨a,b⟩ is an ordered pair, and similarly for ordered n-tuples | X | {\displaystyle |X|... | Glossary of set theory | 0.843168 |
1,265 | Native-like conformations are then selected from these decoys using scoring functions as well as conformer clustering. High-resolution refinement is sometimes used as a final step to fine-tune native-like structures. There are two major classes of scoring functions. Physics-based functions are based on mathematical mod... | Ab initio structure prediction | 0.843145 |
1,266 | Ultraviolet astronomy employs ultraviolet wavelengths between approximately 100 and 3200 Å (10 to 320 nm). Light at those wavelengths is absorbed by the Earth's atmosphere, requiring observations at these wavelengths to be performed from the upper atmosphere or from space. Ultraviolet astronomy is best suited to the st... | Stellar astronomy | 0.843124 |
1,267 | Although every concrete Boolean algebra is a Boolean algebra, not every Boolean algebra need be concrete. Let n be a square-free positive integer, one not divisible by the square of an integer, for example 30 but not 12. The operations of greatest common divisor, least common multiple, and division into n (that is, ¬x ... | Boolean operator (Boolean algebra) | 0.843117 |
1,268 | It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with dynamical systems tools including differential equations, and recently, Lagrangians. Students are expected to understand the modeling tools as well as the mathematics, physics, circuit ... | Radio frequency signal | 0.843115 |
1,269 | Algebraic structures are so numerous today that this article will inevitably be incomplete. In addition to this, there are sometimes multiple names for the same structure, and sometimes one name will be defined by disagreeing axioms by different authors. | Outline of algebraic structures | 0.843114 |
1,270 | Whereas expressions denote mainly numbers in elementary algebra, in Boolean algebra, they denote the truth values false and true. These values are represented with the bits, 0 and 1. They do not behave like the integers 0 and 1, for which 1 + 1 = 2, but may be identified with the elements of the two-element field GF(2)... | Boolean Algebra | 0.843099 |
1,271 | In the algebraic theory of semigroups, in constructing special classes, attention is focused only on those properties, restrictions and conditions which can be expressed in terms of the binary operations in the semigroups and occasionally on the cardinality and similar properties of subsets of the underlying set. The u... | Completely simple semigroup | 0.843098 |
1,272 | Machine Learning. 27: 1–14. Robert E. Schapire and Yoram Singer (1999). | Machine Learning (journal) | 0.843089 |
1,273 | In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero. The fact that the additive identity (zero) is even, together with the evenness of sums and additive inverses of even numbers and the associativity of addition, means that the even integers form a group. Moreover... | Zero is even | 0.843085 |
1,274 | To find the radius of a fourth circle tangent to three given kissing circles, the quadratic equation can be solved as The ± {\displaystyle \pm } symbol indicates that in general this equation has two solutions, and any triple of tangent circles has two tangent circles (or degenerate straight lines). Problem-specific cr... | Soddy circles | 0.843073 |
1,275 | Nucleic acid sequence-based amplification, commonly referred to as NASBA, is a method in molecular biology which is used to produce multiple copies of single stranded RNA. NASBA is a two-step process that takes RNA and anneals specially designed primers, then utilizes an enzyme cocktail to amplify it. | NASBA (molecular biology) | 0.843067 |
1,276 | Elementary Classical Mechanics. figshare. (2017) Ordinary Differential Equations. figshare. | Stephen Wiggins | 0.843066 |
1,277 | If the values of the nonbasic variables are set to 0, then the values of the basic variables are easily obtained as entries in b and this solution is a basic feasible solution. The algebraic interpretation here is that the coefficients of the linear equation represented by each row are either 0 {\displaystyle 0} , 1 {\... | Simplex algorithm | 0.843061 |
1,278 | In 2010, the institute 500-node supercomputer processed 10 terabytes of raw sequencing data every 24 hours from 30 or so Genome Analyzers from Illumina. The annual budget for the computer center was US$9 million. In the same year, BGI's computational biologists developed the first successful algorithm, based on graph t... | BGI Group | 0.84306 |
1,279 | The situation is described by the following commutative diagram: h is injective if and only if N = ker(f). Therefore, by setting N = ker(f) we immediately get the first isomorphism theorem. We can write the statement of the fundamental theorem on homomorphisms of groups as "every homomorphic image of a group is isomorp... | Fundamental theorem on homomorphisms | 0.843056 |
1,280 | Mathematics: Higher Algebra (including certain topics from Linear Algebra), Combinatorics, Probability (including topics like Conditional probability, Law of total probability, Bayes theorem), Geometry, Coordinate system (Point and Lines, Circles, Parabolas, Ellipse and Hyperbola), Trigonometry (including the Inverse t... | Joint Entrance Examination – Advanced | 0.843055 |
1,281 | Set (mathematics) – Element (mathematics) – Venn diagram – Empty set – Subset – Union (set theory) – Disjoint union – Intersection (set theory) – Disjoint sets – Complement (set theory) – Symmetric difference – Ordered pair – Cartesian product – Power set – Simple theorems in the algebra of sets – Naive set theory – Mu... | Outline of discrete mathematics | 0.843055 |
1,282 | The last twenty years of the 20th century enjoyed the successes of over one hundred years of study in group theory. In finite groups, post classification results included the O'Nan–Scott theorem, the Aschbacher classification, the classification of multiply transitive finite groups, the determination of the maximal sub... | History of group theory | 0.84305 |
1,283 | For example, an algebra problem from the Chinese Arithmetic in Nine Sections, c. 200 BCE, begins "Three sheafs of good crop, two sheafs of mediocre crop, and one sheaf of bad crop are sold for 29 dou." We would write 3x + 2y + z = 29. | Polynomial curve | 0.843045 |
1,284 | Although some students take it as eighth graders, this class is most commonly taken in ninth or tenth grade, after the students have taken Pre-algebra. Students learn about real numbers and the order of operations (PEMDAS), functions, linear equations, graphs, polynomials, the factor theorem, radicals, and quadratic eq... | Mathematics education in the United States | 0.843031 |
1,285 | The primary approximation is based on the assumption that the absorption coefficient, typically represented by an α ν {\displaystyle \alpha _{\nu }} , has no dependence on frequency ν {\displaystyle \nu } for the frequency range being worked in, e.g. α ν ⟶ α {\displaystyle \alpha _{\nu }\longrightarrow \alpha } . Typic... | Grey atmosphere | 0.843028 |
1,286 | The best choice of k depends upon the data; generally, larger values of k reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good k can be selected by various heuristic techniques (see hyperparameter optimization). The special case where the class is predicted to be ... | K-nearest neighbor algorithm | 0.843026 |
1,287 | Algebra began with computations similar to those of arithmetic, with letters standing for numbers. This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0,} a , b , c {\displaystyle a,b,c} can be any ... | Diagrammatic algebra | 0.843022 |
1,288 | The Sylow 2-subgroup is a dihedral group of order 8. It can be described as centralizer of any element from the conjugacy class 2A21. In the GL(3, 2) representation, a Sylow 2-subgroup consists of the upper triangular matrices. This group and its Sylow 2-subgroup provide a counter-example for various normal p-complemen... | PSL(2,7) | 0.843014 |
1,289 | This phenomenon can best be described using the vocabulary of abstract algebra. The congruence classes relatively prime to the modulus are a group under multiplication, called the group of units of the ring Z/nZ, and the squares are a subgroup of it. Different nonresidues may belong to different cosets, and there is no... | Modular square root | 0.843013 |
1,290 | Benner's approach opened new perspectives on how nucleic acids work, as well as tools for diagnostics and nanotechnology. The FDA has approved products that use AEGIS DNA in human diagnostics. These monitor the loads of virus in patients infected with hepatitis B, hepatitis C and HIV. AEGIS has been the basis of the de... | Steven A. Benner | 0.843011 |
1,291 | If time and aptitude permit, students might learn Heron's formula, how to calculate the determinant of a 3 × 3 {\displaystyle 3\times 3} matrix via the rule of Sarrus, and the vector cross product. Students are introduced to the use of a graphing calculator to help them visualize the plots of equations and to supplemen... | Mathematics education in the United States | 0.843009 |
1,292 | For many types of algebraic structure, the fundamental theorem on homomorphisms (or first isomorphism theorem) states that image of a homomorphism is isomorphic to the quotient by the kernel. The concept of a kernel has been extended to structures such that the inverse image of a single element is not sufficient for de... | Kernel (algebra) | 0.843007 |
1,293 | decision boundary In the case of backpropagation-based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it... | Glossary of artificial intelligence | 0.843007 |
1,294 | These puzzles are based on algebra with binary variables taking a pair of values, for example, (no, yes), (false, true), (not exists, exists), (0, 1). It invites the player quickly establish some equations, and inequalities for the solution. The partitioning can be used to reduce the complexity of the problem. Moreover... | Board puzzles with algebra of binary variables | 0.843003 |
1,295 | Classifying data is a common task in machine learning. Suppose some data points, each belonging to one of two sets, are given and we wish to create a model that will decide which set a new data point will be in. In the case of support vector machines, a data point is viewed as a p-dimensional vector (a list of p number... | Linearly separable | 0.842997 |
1,296 | In terms of phenotyping, optimization of the assay and antibodies also presents a potential problem if proteins of interest are not included in the currently available panels. Moreover, right now CITE-Seq is not able to detect intracellular proteins. With the current protocol, there are many challenges that would arise... | CITE-Seq | 0.842992 |
1,297 | {\displaystyle O(\log \,n).} An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed this line of work in computational materials, computational... | Level set (data structures) | 0.842988 |
1,298 | In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph. In other words, it asks whether the variables of a given Boolean formula—whose incidence graph consisting of variables and clauses c... | Planar SAT | 0.842977 |
1,299 | Calculus also demonstrates that there are functions and points on their graphs for which the limit determining the slope of the tangent line does not exist. For these points the function f is non-differentiable. There are two possible reasons for the method of finding the tangents based on the limits and derivatives to... | Tangent point | 0.842975 |
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