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19,400 | The frequentist interpretation is a philosophical approach to the definition and use of probabilities; it is one of several such approaches. It does not claim to capture all connotations of the concept 'probable' in colloquial speech of natural languages. As an interpretation, it is not in conflict with the mathematica... | Frequency probability | 0.811502 |
19,401 | Probability theory is a branch of mathematics. While its roots reach centuries into the past, it reached maturity with the axioms of Andrey Kolmogorov in 1933. The theory focuses on the valid operations on probability values rather than on the initial assignment of values; the mathematics is largely independent of any ... | Frequency probability | 0.811502 |
19,402 | 104) ... I assert that this is not so ... The essential distinction between the frequentists and the non-frequentists is, I think, that the former, in an effort to avoid anything savouring of matters of opinion, seek to define probability in terms of the objective properties of a population, real or hypothetical, where... | Frequency probability | 0.811502 |
19,403 | The goal of the optimization then is to minimize where the parameter λ > 0 {\displaystyle \lambda >0} determines the trade-off between increasing the margin size and ensuring that the x i {\displaystyle \mathbf {x} _{i}} lie on the correct side of the margin. By deconstructing the hinge loss, this optimization problem ... | Support vector regression | 0.811501 |
19,404 | Minimizing (2) can be rewritten as a constrained optimization problem with a differentiable objective function in the following way. For each i ∈ { 1 , … , n } {\displaystyle i\in \{1,\,\ldots ,\,n\}} we introduce a variable ζ i = max ( 0 , 1 − y i ( w T x i − b ) ) {\displaystyle \zeta _{i}=\max \left(0,1-y_{i}(\mathb... | Support vector regression | 0.811501 |
19,405 | Ultraviolet spectroscopy has wide applicability in molecular biology, particularly the study of photosynthesis. It has been used to study a wide variety of flowering plants and ferns by researchers in departments of biology, plant physiology and agriculture science as well as molecular genetics.Particularly useful in d... | DU spectrophotometer | 0.8115 |
19,406 | Credited with having "brought about a breakthrough in optical spectroscopy",: 10 the Beckman DU has been identified as "an indispensable tool for chemistry": 207 and "the Model T of laboratory instruments". Approximately 30,000 DU spectrophotometers were manufactured and sold between 1941 and 1976.: 11 The DU enabled r... | DU spectrophotometer | 0.8115 |
19,407 | Wavelengths in the resulting absorption spectrum would differ depending upon the atomic and molecular composition if the material involved.Spectroscopic methods were predominantly used by physicists and astrophysicists. Spectroscopic techniques were rarely taught in chemistry classes and were unfamiliar to most practic... | DU spectrophotometer | 0.8115 |
19,408 | The DU was developed at National Technical Laboratories (later Beckman Instruments) under the direction of Arnold Orville Beckman, an American chemist and inventor. Beginning in 1940, National Technical Laboratories developed three in-house prototype models (A, B, C) and one limited distribution model (D) before moving... | DU spectrophotometer | 0.8115 |
19,409 | One was sold: in February 1941, to the University of California Chemistry department in Los Angeles. : 153 The Model B prototype should be distinguished from a later production model of spectrophotometer that was also referred to as the Model "B". The production Model "B" was introduced in 1949 as a less-expensive, sim... | DU spectrophotometer | 0.8115 |
19,410 | ": 113 Kornberg and Bernard L. Horecker used the Beckman DU spectrophotometer for enzyme assays measuring NADH and NADPH. They determined their extinction coefficients, establishing a basis for quantitative measurements in reactions involving nucleotides. This work became one of the most cited papers in biochemistry. | DU spectrophotometer | 0.8115 |
19,411 | Kornberg used it to purify aconitase, an enzyme in the citric acid cycle. "The enzyme could be assayed in a few minutes by coupling it to isocitrate dehydrogenase and in measuring the NADH formed using the Beckman DU spectrophotometer, an instrument that transformed biochemistry. | DU spectrophotometer | 0.8115 |
19,412 | The Beckman DU spectrophotometer was used in the Cori laboratory to calculate enzyme concentrations, including phosphorylase.Another researcher who spent six months in 1947 at the Cori laboratory, "the most vibrant place in biochemistry" at that time, was Arthur Kornberg. Kornberg was already familiar with the DU spect... | DU spectrophotometer | 0.8115 |
19,413 | (1994). "Systems of Set Constraints with Negative Constraints are NEXPTIME-Complete". Ninth Annual IEEE Symposium on Logic in Computer Science. | Set constraint | 0.811499 |
19,414 | Computer Science Department, Cornell University. 93–1380. Stefansson, K. | Set constraint | 0.811499 |
19,415 | Proceedings of the 34th Symp. on Foundations of Computer Science. pp. | Set constraint | 0.811499 |
19,416 | "Negative Set Constraints with Equality". Ninth Annual IEEE Symposium on Logic in Computer Science. pp. | Set constraint | 0.811499 |
19,417 | Aiken, A., Kozen, D., Wimmers, E.L. (Jun 1993). Decidability of Systems of Set Constraints with Negative Constraints (Technical report). Computer Science Department, Cornell University. | Set constraint | 0.811499 |
19,418 | (1993). "Logical Aspects of Set Constraints" (PDF). Computer Science Logic'93. | Set constraint | 0.811499 |
19,419 | A Decision Procedure for a Class of Set Constraints (Technical report). School of Computer Science, Carnegie Mellon University. {{cite tech report}}: CS1 maint: multiple names: authors list (link) Kozen, D. | Set constraint | 0.811499 |
19,420 | "A Decision Procedure for a Class of Set Constraints (Extended Abstract)". Fifth Annual IEEE Symposium on Logic in Computer Science. pp. | Set constraint | 0.811499 |
19,421 | 10th Annual Symposium on Theoretical Aspects of Computer Science. LNCS. Vol. | Set constraint | 0.811499 |
19,422 | "Set Constraints are the Monadic Class". Eight Annual IEEE Symposium on Logic in Computer Science. pp. | Set constraint | 0.811499 |
19,423 | "Solving Systems of Set Constraints (Extended Abstract)". Seventh Annual IEEE Symposium on Logic in Computer Science. pp. | Set constraint | 0.811499 |
19,424 | Computer Science Logic'93. LNCS. Vol. | Set constraint | 0.811499 |
19,425 | The Complexity of Set Constraints (Technical report). Computer Science Department, Cornell University. 93–1352. | Set constraint | 0.811499 |
19,426 | In mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms. Similar to systems of (in)equations between numbers, methods are studied for solving systems of set constraints. Different approaches admit different operators (like "∪", "∩", "\", and function appli... | Set constraint | 0.811499 |
19,427 | Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI, originally High Energy Solar Spectroscopic Imager or HESSI or Explorer 81) was a NASA solar flare observatory. It was the sixth mission in the Small Explorer program (SMEX), selected in October 1997 and launched on 5 February 2002, at 20:58:12 UTC. Its prima... | Reuven Ramaty High Energy Solar Spectroscopic Imager | 0.811496 |
19,428 | HESSI was renamed to RHESSI on 29 March 2002 in honor of Dr. Reuven Ramaty, a pioneer in the area of high energy solar physics. RHESSI was the first space mission named after a NASA scientist. RHESSI was built by Spectrum Astro for Goddard Space Flight Center and was operated by the Space Sciences Laboratory in Berkele... | Reuven Ramaty High Energy Solar Spectroscopic Imager | 0.811496 |
19,429 | Such information will advance understanding of the fundamental high-energy processes at the core of the solar flare phenomena. The primary scientific objective of RHESSI was to understand the following processes that take place in the magnetized plasmas of the solar atmosphere during a flare: Impulsive energy release P... | Reuven Ramaty High Energy Solar Spectroscopic Imager | 0.811496 |
19,430 | The pitch drop experiment at Trinity College Dublin in Ireland was started in October 1944 by an unknown colleague of the Nobel Prize winner Ernest Walton while he was in the physics department of Trinity College. This experiment, like the one at University of Queensland, was set up to demonstrate the high viscosity of... | Pitch drop experiment | 0.811494 |
19,431 | The experiment is monitored by a webcam but technical problems prevented the November 2000 drop from being recorded. The pitch drop experiment is on public display on Level 2 of Parnell building in the School of Mathematics and Physics at the St Lucia campus of the University of Queensland. Hundreds of thousands of Int... | Pitch drop experiment | 0.811494 |
19,432 | In October 2005, John Mainstone and the late Thomas Parnell were awarded the Ig Nobel Prize in physics, a parody of the Nobel Prize, for the pitch drop experiment. Mainstone subsequently commented: I am sure that Thomas Parnell would have been flattered to know that Mark Henderson considers him worthy to become a recip... | Pitch drop experiment | 0.811494 |
19,433 | The modern scientific method which took shape at this time (with Francis Bacon (1561-1626) and Galileo (1564-1642)) contributed to a trend of separating science from theology, with minimal speculation about metaphysics and ethics. (Natural law in the political sense, conceived as universal (i.e., divorced from sectaria... | Laws of physics | 0.811493 |
19,434 | The observation and detection of underlying regularities in nature date from prehistoric times - the recognition of cause-and-effect relationships implicitly recognises the existence of laws of nature. The recognition of such regularities as independent scientific laws per se, though, was limited by their entanglement ... | Laws of physics | 0.811493 |
19,435 | Newton's law of cooling Fourier's law Ideal gas law, combines a number of separately developed gas laws; Boyle's law Charles's law Gay-Lussac's law Avogadro's law, into onenow improved by other equations of stateDalton's law (of partial pressures) Boltzmann equation Carnot's theorem Kopp's law | Laws of physics | 0.811493 |
19,436 | The stationary value for the entire continuum of Lagrangian values corresponding to some path, not just one value of the Lagrangian, is required (in other words it is not as simple as "differentiating a function and setting it to zero, then solving the equations to find the points of maxima and minima etc", rather this... | Laws of physics | 0.811493 |
19,437 | {\displaystyle F={}^{dp}/{}_{dt}.} While these scientific laws explain what our senses perceive, they are still empirical (acquired by observation or scientific experiment) and so are not like mathematical theorems which can be proved purely by mathematics. | Laws of physics | 0.811493 |
19,438 | They also hypothesized the existence of an intermediary between DNA and its protein products, which they called messenger RNA. Between 1961 and 1965, the relationship between the information contained in DNA and the structure of proteins was determined: there is a code, the genetic code, which creates a correspondence ... | History of molecular biology | 0.811492 |
19,439 | In 1940, George Beadle and Edward Tatum demonstrated the existence of a precise relationship between genes and proteins. In the course of their experiments connecting genetics with biochemistry, they switched from the genetics mainstay Drosophila to a more appropriate model organism, the fungus Neurospora; the construc... | History of molecular biology | 0.811492 |
19,440 | In its earliest manifestations, molecular biology—the name was coined by Warren Weaver of the Rockefeller Foundation in 1938—was an idea of physical and chemical explanations of life, rather than a coherent discipline. Following the advent of the Mendelian-chromosome theory of heredity in the 1910s and the maturation o... | History of molecular biology | 0.811492 |
19,441 | If we evaluate the molecular revolution within the context of biological history, it is easy to note that it is the culmination of a long process which began with the first observations through a microscope. The aim of these early researchers was to understand the functioning of living organisms by describing their org... | History of molecular biology | 0.811492 |
19,442 | The development of molecular biology is also the encounter of two disciplines which made considerable progress in the course of the first thirty years of the twentieth century: biochemistry and genetics. The first studies the structure and function of the molecules which make up living things. Between 1900 and 1940, th... | History of molecular biology | 0.811492 |
19,443 | Watson and Crick's model attracted great interest immediately upon its presentation. Arriving at their conclusion on February 21, 1953, Watson and Crick made their first announcement on February 28. In an influential presentation in 1957, Crick laid out the "central dogma of molecular biology", which foretold the relat... | History of molecular biology | 0.811492 |
19,444 | The resurgence of RNA structural biology in the mid-1990s has caused a veritable explosion in the field of nucleic acid structural research. Since the publication of the hammerhead and P4-6 structures, numerous major contributions to the field have been made. Some of the most noteworthy examples include the structures ... | History of molecular biology | 0.811492 |
19,445 | This world is populated by colloids, chemical compounds whose structure and properties were not well defined. The successes of molecular biology derived from the exploration of that unknown world by means of the new technologies developed by chemists and physicists: X-ray diffraction, electron microscopy, ultracentrifu... | History of molecular biology | 0.811492 |
19,446 | But history decided differently: the arrival of the Nazis in 1933 - and, to a less extreme degree, the rigidification of totalitarian measures in fascist Italy - caused the emigration of a large number of Jewish and non-Jewish scientists. The majority of them fled to the US or the UK, providing an extra impulse to the ... | History of molecular biology | 0.811492 |
19,447 | The geographic panorama of the developments of the new biology was conditioned above all by preceding work. The US, where genetics had developed the most rapidly, and the UK, where there was a coexistence of both genetics and biochemical research of highly advanced levels, were in the avant-garde. Germany, the cradle o... | History of molecular biology | 0.811492 |
19,448 | Moreover, the developments of the theory of information and cybernetics in the 1940s, in response to military exigencies, brought to the new biology a significant number of fertile ideas and, especially, metaphors. The choice of bacteria and of its virus, the bacteriophage, as models for the study of the fundamental me... | History of molecular biology | 0.811492 |
19,449 | Nevertheless, the chemical nature of genes and their mechanisms of action remained a mystery. Molecular biologists committed themselves to the determination of the structure, and the description of the complex relations between, genes and proteins. The development of molecular biology was not just the fruit of some sor... | History of molecular biology | 0.811492 |
19,450 | Enzymes are proteins, like the antibodies present in blood or the proteins responsible for muscular contraction. As a consequence, the study of proteins, of their structure and synthesis, became one of the principal objectives of biochemists. The second discipline of biology which developed at the beginning of the 20th... | History of molecular biology | 0.811492 |
19,451 | In 1965, Holley et al. purified and sequenced the first tRNA molecule, initially proposing that it adopted a cloverleaf structure, based largely on the ability of certain regions of the molecule to form stem loop structures. The isolation of tRNA proved to be the first major windfall in RNA structural biology. Followin... | History of molecular biology | 0.811492 |
19,452 | Given a set V of variable symbols, the set of lambda terms is defined recursively as follows: every variable symbol x∈V is a lambda term; if x∈V is a variable symbol and t is a lambda term, then λx.t is also a lambda term (abstraction); if t1 and t2 are lambda terms, then ( t1 t2 ) is also a lambda term (application).T... | Finite terms | 0.811491 |
19,453 | In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constru... | Finite terms | 0.811491 |
19,454 | In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. The orig... | Geometrodynamics | 0.811487 |
19,455 | The term geometrodynamics is as a synonym for general relativity. More properly, some authors use the phrase Einstein's geometrodynamics to denote the initial value formulation of general relativity, introduced by Arnowitt, Deser, and Misner (ADM formalism) around 1960. In this reformulation, spacetimes are sliced up i... | Geometrodynamics | 0.811487 |
19,456 | Wheeler was also much intrigued by the fact that the (nonspinning) point-mass solution of general relativity, the Schwarzschild vacuum, has the nature of a wormhole. Similarly, in the case of a charged particle, the geometry of the Reissner–Nordström electrovacuum solution suggests that the symmetry between electric (w... | Geometrodynamics | 0.811487 |
19,457 | Wheeler wanted to reduce physics to geometry in an even more fundamental way than the ADM reformulation of general relativity with a dynamic geometry whose curvature changes with time. It attempts to realize three concepts: mass without mass charge without charge field without fieldHe wanted to lay the foundation for q... | Geometrodynamics | 0.811487 |
19,458 | According to Bernard Derrida and Yves Pomeau , the critical value of the average number of connections is K c = 1 / {\displaystyle K_{c}=1/} . If K {\displaystyle K} is not constant, and there is no correlation between the in-degrees and out-degrees, the conditions of stability is determined by ⟨ K i n ⟩ {\displaystyl... | Random boolean network | 0.811486 |
19,459 | A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determi... | Random boolean network | 0.811486 |
19,460 | The two metrics d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} are said to be topologically equivalent if they generate the same topology on X {\displaystyle X} . The adverb topologically is often dropped. There are multiple ways of expressing this condition: a subset A ⊆ X {\displaystyle A\subseteq X} is d 1 ... | Equivalent metrics | 0.811485 |
19,461 | The continuity of a function is preserved if either the domain or range is remetrized by an equivalent metric, but uniform continuity is preserved only by strongly equivalent metrics. The differentiability of a function f: U → V {\displaystyle f:U\to V} , for V {\displaystyle V} a normed space and U {\displaystyle U} a... | Equivalent metrics | 0.811485 |
19,462 | As it is usually stated, the separator theorem states that, in any n {\displaystyle n} -vertex planar graph G = ( V , E ) {\displaystyle G=(V,E)} , there exists a partition of the vertices of G {\displaystyle G} into three sets A {\displaystyle A} , S {\displaystyle S} , and B {\displaystyle B} , such that each of A {\... | Planar Separator Theorem | 0.81148 |
19,463 | Repeated application of the separator theorem produces a separator hierarchy which may take the form of either a tree decomposition or a branch-decomposition of the graph. Separator hierarchies may be used to devise efficient divide and conquer algorithms for planar graphs, and dynamic programming on these hierarchies ... | Planar Separator Theorem | 0.81148 |
19,464 | In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of O ( n ) {\displaystyle O({\sqrt {n}})} vertices from an n-vertex graph (where the... | Planar Separator Theorem | 0.81148 |
19,465 | With some additional work they show by a similar method that there exists a simple cycle separator of size at most 9 n / 2 ≈ 2.12 n {\displaystyle {\sqrt {9n/2}}\approx 2.12{\sqrt {n}}} .Djidjev & Venkatesan (1997) further improved the constant factor in the simple cycle separator theorem to 1.97 n {\displaystyle 1.97{... | Planar Separator Theorem | 0.81148 |
19,466 | Additionally, C {\displaystyle C} must have length exactly 8 n {\displaystyle {\sqrt {8n}}} , as otherwise it could be improved by replacing one of its edges by the other two sides of a triangle. If the vertices in C {\displaystyle C} are numbered (in clockwise order) from 1 {\displaystyle 1} to 8 n {\displaystyle {\sq... | Planar Separator Theorem | 0.81148 |
19,467 | An equivalent formulation is that the edges of any n {\displaystyle n} -vertex planar graph G {\displaystyle G} may be subdivided into two edge-disjoint subgraphs G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} in such a way that both subgraphs have at least n / 3 {\displaystyle n/3} vertices and such that the ... | Planar Separator Theorem | 0.81148 |
19,468 | In a n × n {\displaystyle {\sqrt {n}}\times {\sqrt {n}}} grid graph, a set S {\displaystyle S} of s < n {\displaystyle s<{\sqrt {n}}} points can enclose a subset of at most s ( s − 1 ) / 2 {\displaystyle s(s-1)/2} grid points, where the maximum is achieved by arranging S {\displaystyle S} in a diagonal line near a corn... | Planar Separator Theorem | 0.81148 |
19,469 | Choosing S {\displaystyle S} to be any of these central rows or columns, and removing S {\displaystyle S} from the graph, partitions the graph into two smaller connected subgraphs A {\displaystyle A} and B {\displaystyle B} , each of which has at most n / 2 {\displaystyle n/2} vertices. If r ≤ c {\displaystyle r\leq c}... | Planar Separator Theorem | 0.81148 |
19,470 | By using dynamic programming on a tree decomposition or branch-decomposition of a planar graph, many NP-hard optimization problems may be solved in time exponential in n {\displaystyle {\sqrt {n}}} or n log n {\displaystyle {\sqrt {n}}\log n} . For instance, bounds of this form are known for finding maximum independe... | Planar Separator Theorem | 0.81148 |
19,471 | According to the Koebe–Andreev–Thurston circle-packing theorem, any planar graph may be represented by a packing of circular disks in the plane with disjoint interiors, such that two vertices in the graph are adjacent if and only if the corresponding pair of disks are mutually tangent. As Miller et al. (1997) show, for... | Planar Separator Theorem | 0.81148 |
19,472 | However, every planar graph with maximum degree Δ {\displaystyle \Delta } has an edge separator of size O ( Δ n ) {\displaystyle O({\sqrt {\Delta n}})} .A simple cycle separator in the dual graph of a planar graph forms an edge separator in the original graph. Applying the simple cycle separator theorem of Gazit & Mill... | Planar Separator Theorem | 0.81148 |
19,473 | A variation of the planar separator theorem involves edge separators, small sets of edges forming a cut between two subsets A {\displaystyle A} and B {\displaystyle B} of the vertices of the graph. The two sets A {\displaystyle A} and B {\displaystyle B} must each have size at most a constant fraction of the number n {... | Planar Separator Theorem | 0.81148 |
19,474 | A universal graph for a family F {\displaystyle {\mathcal {F}}} of graphs is a graph that contains every member of F {\displaystyle {\mathcal {F}}} as a subgraphs. Separators can be used to show that the n {\displaystyle n} -vertex planar graphs have universal graphs with n {\displaystyle n} vertices and O ( n 3 / 2 ) ... | Planar Separator Theorem | 0.81148 |
19,475 | Spectral clustering methods, in which the vertices of a graph are grouped by the coordinates of the eigenvectors of matrices derived from the graph, have long been used as a heuristic for graph partitioning problems for nonplanar graphs. As Spielman & Teng (2007) show, spectral clustering can also be used to derive an ... | Planar Separator Theorem | 0.81148 |
19,476 | The sphere separators constructed in this way partition the input graph into subgraphs of at most n ( d + 1 ) / ( d + 2 ) {\displaystyle n(d+1)/(d+2)} vertices. The size of the separators for k {\displaystyle k} -ply ball intersection graphs and for k {\displaystyle k} -nearest-neighbor graphs is O ( k 1 / d n 1 − 1 / ... | Planar Separator Theorem | 0.81148 |
19,477 | Graphs of genus g {\displaystyle g} also have edge separators of size O ( g Δ n ) {\displaystyle O({\sqrt {g\Delta n}})} .Graphs of bounded genus form an example of a family of graphs closed under the operation of taking minors, and separator theorems also apply to arbitrary minor-closed graph families. In particular, ... | Planar Separator Theorem | 0.81148 |
19,478 | Some sparse graphs do not have separators of sublinear size: in an expander graph, deleting up to a constant fraction of the vertices still leaves only one connected component.Possibly the earliest known separator theorem is a result of Jordan (1869) that any tree can be partitioned into subtrees of at most n / 2 {\dis... | Planar Separator Theorem | 0.81148 |
19,479 | Frederickson showed that an r {\displaystyle r} -division can be found in O ( n log n ) {\displaystyle O(n\log n)} time by recursive application of separator theorem. The sketch of his algorithm to solve the problem is as follows. Preprocessing Phase: Partition the graph into carefully selected subsets of vertices an... | Planar Separator Theorem | 0.81148 |
19,480 | For weighted but undirected planar graphs, the shortest cycle is equivalent to the minimum cut in the dual graph and can be found in O ( n log log n ) {\displaystyle O(n\log \log n)} time, and the shortest cycle in an unweighted undirected planar graph (its girth) may be found in time O ( n ) {\displaystyle O(n)} .... | Planar Separator Theorem | 0.81148 |
19,481 | Separator decompositions can be of use in designing efficient divide and conquer algorithms for solving problems on planar graphs. As an example, one problem that can be solved in this way is to find the shortest cycle in a weighted planar digraph. This may be solved by the following steps: Partition the given graph G ... | Planar Separator Theorem | 0.81148 |
19,482 | Lipton & Tarjan (1980) observed that the separator theorem may be used to obtain polynomial time approximation schemes for NP-hard optimization problems on planar graphs such as finding the maximum independent set. Specifically, by truncating a separator hierarchy at an appropriate level, one may find a separator of si... | Planar Separator Theorem | 0.81148 |
19,483 | The size of the separator S {\displaystyle S} constructed in this way is at most 8 n ≈ 2.83 n {\displaystyle {\sqrt {8n}}\approx 2.83{\sqrt {n}}} . The vertices of the separator and the two disjoint subgraphs can be found in linear time.This proof of the separator theorem applies as well to weighted planar graphs, in w... | Planar Separator Theorem | 0.81148 |
19,484 | Submillimetre astronomy or submillimeter astronomy (see spelling differences) is the branch of observational astronomy that is conducted at submillimetre wavelengths (i.e., terahertz radiation) of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands... | Submillimeter astronomy | 0.811479 |
19,485 | If one starts by concluding that the levels of nurture received by the child are insufficient, one then needs to consider the developmental levels achieved by the child. Further challenges arise, however, as even when one has established developmental delay and exposure to low levels of nurture, one needs to rule out t... | Child development | 0.811473 |
19,486 | In many cases a model can be converted to a function of the form: m(f,p,q)where the vector function m gives the errors between the data p, and the model predictions. The vector q gives some variable parameters that are the model's unknown parts. The parameters q vary with the operating conditions c in a manner to be de... | Grey box completion and validation | 0.811472 |
19,487 | Once a selection of non-zero values is made, the remaining coefficients in A can be determined by minimizing m(f,p,Ac) over the data with respect to the nonzero values in A, typically by non-linear least squares. Selection of the nonzero terms can be done by optimization methods such as simulated annealing and evolutio... | Grey box completion and validation | 0.811472 |
19,488 | The Lorentz transformations reduce to the Galilean transformations for low velocities much less than the speed of light c. The magnitudes of 4-vectors are invariants - not "conserved", but the same for all inertial frames (i.e. every observer in an inertial frame will agree on the same value), in particular if A is the... | Physical laws | 0.81147 |
19,489 | Special relativityThe two postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms of relative motion. They can be stated as "the laws of physics are the same in all inertial frames" and "the speed of light is constant and has the same value in all inertial frames". The sa... | Physical laws | 0.81147 |
19,490 | Residual strength is the load or force (usually mechanical) that a damaged object or material can still carry without failing. Material toughness, fracture size and geometry as well as its orientation all contribute to residual strength. == References == | Residual strength | 0.811469 |
19,491 | The Journal of Mathematical Physics, Analysis, Geometry is a quarterly peer-reviewed scientific journal covering mathematics as applied to physics. It is published by the Verkin Institute for Low Temperature Physics and Engineering and was established in 1994 as Mathematical Physics, Analysis, Geometry. Papers are publ... | Journal of Mathematical Physics, Analysis, Geometry | 0.811468 |
19,492 | A neurochemical is a small organic molecule or peptide that participates in neural activity. The science of neurochemistry studies the functions of neurochemicals. | Neurochemical | 0.811467 |
19,493 | Random access (more precisely and more generally called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of addressable elements roughly as easily and efficiently as any other, no matter how many elements may be in the set. In computer science it is... | Random access | 0.811467 |
19,494 | Climate is governed by physical principles which can be expressed as differential equations. These equations are coupled and nonlinear, so that approximate solutions are obtained by using numerical methods to create global climate models. Climate is sometimes modeled as a stochastic process but this is generally accept... | Climatology | 0.811465 |
19,495 | This descriptive climatology was mainly an applied science, giving farmers and other interested people statistics about what the normal weather was and how great chances were of extreme events. To do this, climatologists had to define a climate normal, or an average of weather and weather extremes over a period of typi... | Climatology | 0.811465 |
19,496 | This includes an emerging class of mechanically superior biomaterials based on microstructural features and designs found in nature. Thus, self-assembly is also emerging as a new strategy in chemical synthesis and nanotechnology. Molecular crystals, liquid crystals, colloids, micelles, emulsions, phase-separated polyme... | Biocompatible material | 0.811465 |
19,497 | Biomaterials science encompasses elements of medicine, biology, chemistry, tissue engineering and materials science. Note that a biomaterial is different from a biological material, such as bone, that is produced by a biological system. Additionally, care should be exercised in defining a biomaterial as biocompatible, ... | Biocompatible material | 0.811465 |
19,498 | A biomaterial is a substance that has been engineered to interact with biological systems for a medical purpose, either a therapeutic (treat, augment, repair, or replace a tissue function of the body) or a diagnostic one. The corresponding field of study, called biomaterials science or biomaterials engineering, is abou... | Biocompatible material | 0.811465 |
19,499 | In logic, a logical framework provides a means to define (or present) a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to a type inhabitation problem in the framework type theory. This approach has been used successfully for (interactive) aut... | Edinburgh Logical Framework | 0.811464 |
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