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16,400 | Currently there are nearly 1300 different protein folds known, but new folds are still being discovered every year due in significant part to the ongoing structural genomics projects. Many different algorithms have been proposed for finding the correct threading of a sequence onto a structure, though many make use of d... | Threading (protein sequence) | 0.813764 |
16,401 | 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) | 0.813764 |
16,402 | Fold (major structural similarity): Proteins are defined as having a common fold if they have the same major secondary structures in the same arrangement and with the same topological connections. Different proteins with the same fold often have peripheral elements of secondary structure and turn regions that differ in... | Threading (protein sequence) | 0.813764 |
16,403 | Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures... | Parallel tempering | 0.813761 |
16,404 | In type theory, the type of functions accepting values of type A and returning values of type B may be written as A → B or BA. In the Curry–Howard correspondence, function types are related to logical implication; lambda abstraction corresponds to discharging hypothetical assumptions and function application correspond... | First-class functions | 0.813759 |
16,405 | CHIMERE is a chemistry-transport model. It is a computer code that unites a set of equations representing the transport and the chemistry of atmospheric species making it possible to quantify the evolution of air masses and pollution plumes as a function of time on different scales (from urban to continental). Using me... | CHIMERE chemistry-transport model | 0.813758 |
16,406 | Phase 2 - CHIMERE modelAfter reading all the input data, systems of stiff differential equations, including all chemical reactions included in the model (with species having from a few microseconds to several days of lifetime in the atmosphere) are integrated over time and space. At the same time, transport (advection ... | CHIMERE chemistry-transport model | 0.813758 |
16,407 | The CHIMERE model necessitates three main phases: a data preparation phase (pre-processing) essential for a simulation, the model itself for calculating atmospheric concentrations and a results exploitation phase (post-processing). This principle is true for all digital tools of this type (see figure). Phase 1 - pre-pr... | CHIMERE chemistry-transport model | 0.813758 |
16,408 | Current research is revolving around impact of air quality on health, including design of models that can compute the exposure of the population to different pollutants but also to around the consideration of new species to monitor (such as pollen, which are highly allergenic). The latest version of the model includes ... | CHIMERE chemistry-transport model | 0.813758 |
16,409 | Qualitative research, on the other hand, inquires deeply into specific experiences, with the intention of describing and exploring meaning through text, narrative, or visual-based data, by developing themes exclusive to that set of participants.Quantitative research is widely used in psychology, economics, demography, ... | Quantitative approach | 0.813758 |
16,410 | When studying sensitive or controversial topics The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observati... | Quantitative approach | 0.813758 |
16,411 | A labeled vertex is a vertex that is associated with extra information that enables it to be distinguished from other labeled vertices; two graphs can be considered isomorphic only if the correspondence between their vertices pairs up vertices with equal labels. An unlabeled vertex is one that can be substituted for an... | Vertex (graph) | 0.813755 |
16,412 | In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow.Many languages that apply this style attempt to minimize or eliminate side effects by describing what t... | Declarative programming language | 0.813748 |
16,413 | Models, or mathematical representations, of physical systems may be implemented in computer code that is declarative. The code contains a number of equations, not imperative assignments, that describe ("declare") the behavioral relationships. When a model is expressed in this formalism, a computer is able to perform al... | Declarative programming language | 0.813748 |
16,414 | We can also define the functional calculus for not necessarily bounded Borel functions h; the result is an operator which in general fails to be bounded. Using the multiplication by a function f model of a self-adjoint operator given by the spectral theorem, this is multiplication by the composition of h with f. The op... | Completeness condition | 0.813748 |
16,415 | Alternatively, the continuous calculus can be obtained via the Gelfand transform, in the context of commutative Banach algebras. Extending to measurable functions is achieved by applying Riesz-Markov, as above. In this formulation, T can be a normal operator. Given an operator T, the range of the continuous functional ... | Completeness condition | 0.813748 |
16,416 | The existence of a mapping with the properties of a functional calculus requires proof. For the case of a bounded self-adjoint operator T, the existence of a Borel functional calculus can be shown in an elementary way as follows: First pass from polynomial to continuous functional calculus by using the Stone–Weierstras... | Completeness condition | 0.813748 |
16,417 | Formally, the bounded Borel functional calculus of a self adjoint operator T on Hilbert space H is a mapping defined on the space of bounded complex-valued Borel functions f on the real line, such that the following conditions hold πT is an involution-preserving and unit-preserving homomorphism from the ring of complex... | Completeness condition | 0.813748 |
16,418 | Let T be a self-adjoint operator. If E is a Borel subset of R, and 1E is the indicator function of E, then 1E(T) is a self-adjoint projection on H. Then mapping is a projection-valued measure called the resolution of the identity for the self adjoint operator T. The measure of R with respect to Ω is the identity operat... | Completeness condition | 0.813748 |
16,419 | The Oxford Set of Mathematical Instruments is a set of instruments used by generations of school children in the United Kingdom and around the world in mathematics and geometry lessons. The set is marketed in over 100 countries by Helix. It consists of a metal tin embossed on the front with a drawing of Balliol College... | Oxford Set of Mathematical Instruments | 0.813745 |
16,420 | The thesis is an exploration of formal mathematical systems after Gödel's theorem. Gödel showed that for any formal system S powerful enough to represent arithmetic, there is a theorem G which is true but the system is unable to prove. G could be added as an additional axiom to the system in place of a proof. However t... | Systems of Logic Based on Ordinals | 0.813744 |
16,421 | The field is inherently interdisciplinary, and the materials scientists or engineers must be aware and make use of the methods of the physicist, chemist and engineer. Conversely, fields such as life sciences and archaeology can inspire the development of new materials and processes, in bioinspired and paleoinspired app... | Material scientist | 0.813742 |
16,422 | Materials physics is considered a subset of condensed matter physics and applies fundamental condensed matter concepts to complex multiphase media, including materials of technological interest. Current fields that materials physicists work in include electronic, optical, and magnetic materials, novel materials and str... | Material scientist | 0.813742 |
16,423 | As a result, materials science is an increasingly important part of an engineer's education. Materials physics is the use of physics to describe the physical properties of materials. It is a synthesis of physical sciences such as chemistry, solid mechanics, solid state physics, and materials science. | Material scientist | 0.813742 |
16,424 | Materials science evolved, starting from the 1950s because it was recognized that to create, discover and design new materials, one had to approach it in a unified manner. Thus, materials science and engineering emerged in many ways: renaming and/or combining existing metallurgy and ceramics engineering departments; sp... | Material scientist | 0.813742 |
16,425 | OSMI-1 was first identified from high-throughput screening using fluorescence polarization. Further optimization led to the development of OSMI-2, OSMI-3, and OSMI-4, which bind OGT with low-nanomolar affinity. X-ray crystallography showed that the quinolinone-6-sulfonamide scaffold of OSMI compounds act as a uridine m... | Protein O-GlcNAc transferase | 0.813739 |
16,426 | Half-integers occur frequently enough in mathematics and in quantum mechanics that a distinct term is convenient. Note that halving an integer does not always produce a half-integer; this is only true for odd integers. For this reason, half-integers are also sometimes called half-odd-integers. Half-integers are a subse... | Half-integer | 0.813737 |
16,427 | In physics, the Pauli exclusion principle results from definition of fermions as particles which have spins that are half-integers.The energy levels of the quantum harmonic oscillator occur at half-integers and thus its lowest energy is not zero. | Half-integer | 0.813737 |
16,428 | The Long Line is an example of a space which is weakly contractible, but not contractible. This does not contradict Whitehead theorem since the Long Line does not have the homotopy type of a CW-complex. Another prominent example for this phenomenon is the Warsaw circle. | Weakly contractible | 0.813735 |
16,429 | It follows from Whitehead's Theorem that if a CW-complex is weakly contractible then it is contractible. | Weakly contractible | 0.813735 |
16,430 | Pipelined processors commonly use three techniques to work as expected when the programmer assumes that each instruction completes before the next one begins: The pipeline could stall, or cease scheduling new instructions until the required values are available. This results in empty slots in the pipeline, or bubbles, ... | Instruction pipelining | 0.813732 |
16,431 | In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph. | Quartic graph | 0.813732 |
16,432 | Its importance comes from the Banach–Alaoglu theorem. The Banach–Alaoglu theorem can be proved using Tychonoff's theorem about infinite products of compact Hausdorff spaces. When X {\displaystyle X} is separable, the unit ball B ′ {\displaystyle B^{\prime }} of the dual is a metrizable compact in the weak* topology. | Complete norm | 0.813726 |
16,433 | The space X ∗ {\displaystyle X^{*}} of all linear maps from X {\displaystyle X} to the underlying field K {\displaystyle \mathbb {K} } (this space X ∗ {\displaystyle X^{*}} is called the algebraic dual space, to distinguish it from X ′ {\displaystyle X^{\prime }} also induces a topology on X {\displaystyle X} which is ... | Complete norm | 0.813726 |
16,434 | A norm-continuous linear map between two Banach spaces X {\displaystyle X} and Y {\displaystyle Y} is also weakly continuous, that is, continuous from the weak topology of X {\displaystyle X} to that of Y . {\displaystyle Y.} If X {\displaystyle X} is infinite-dimensional, there exist linear maps which are not continuo... | Complete norm | 0.813726 |
16,435 | A Banach algebra is a Banach space A {\displaystyle A} over K = R {\displaystyle \mathbb {K} =\mathbb {R} } or C , {\displaystyle \mathbb {C} ,} together with a structure of algebra over K {\displaystyle \mathbb {K} } , such that the product map A × A ∋ ( a , b ) ↦ a b ∈ A {\displaystyle A\times A\ni (a,b)\mapsto ab\in... | Complete norm | 0.813726 |
16,436 | When working with Banach spaces, it is customary to say that the projective tensor product of two Banach spaces X {\displaystyle X} and Y {\displaystyle Y} is the completion X ⊗ ^ π Y {\displaystyle X{\widehat {\otimes }}_{\pi }Y} of the algebraic tensor product X ⊗ Y {\displaystyle X\otimes Y} equipped with the projec... | Complete norm | 0.813726 |
16,437 | The weak topology on a Banach space X {\displaystyle X} is the coarsest topology on X {\displaystyle X} for which all elements x ′ {\displaystyle x^{\prime }} in the continuous dual space X ′ {\displaystyle X^{\prime }} are continuous. The norm topology is therefore finer than the weak topology. It follows from the Hah... | Complete norm | 0.813726 |
16,438 | In chemistry, ion association is a chemical reaction whereby ions of opposite electric charge come together in solution to form a distinct chemical entity. Ion associates are classified, according to the number of ions that associate with each other, as ion pairs, ion triplets, etc. Ion pairs are also classified accord... | Ion association | 0.813724 |
16,439 | This usage is common in co-ordination chemistry and denotes a complex between a solvated metal cation and an anion. Similarly, a contact ion pair may be termed an inner-sphere complex. The essential difference between the three types is the closeness with which the ions approach each other: fully solvated > solvent-sha... | Ion association | 0.813724 |
16,440 | Triple cations and triple anions have also been characterized in THF solutions.Ion association is an important factor in phase-transfer catalysis, since a species such as R4P+Cl− is formally neutral and so can dissolve easily in a non-polar solvent of low dielectric constant. In this case it also helps that the surface... | Ion association | 0.813724 |
16,441 | The cat NUMTs sequences did not appear to be functional due to the finding of multiple mutations, the differences in mitochondrial and nuclear genetic codes, and the apparent insertion within typically inert centromere regions. The presence of NUMT fragments in the genome is not problematic in all species; for instance... | Nuclear mitochondrial DNA segment | 0.813719 |
16,442 | The New York City Department of Buildings requires a Stationary Engineer's License to practice in the City of New York; to obtain the license one must pass a written and practical exam and have at least five years' experience working directly under a licensed stationary engineer, or one year if in possession of a Bache... | Stationary engineer | 0.813719 |
16,443 | A conserved quantity is a property or value that remains constant over time in a system even when changes occur in the system. In mathematics, a conserved quantity of a dynamical system is formally defined as a function of the dependent variables, the value of which remains constant along each trajectory of the system.... | Conserved quantity | 0.813717 |
16,444 | Of these, only about 148,000 have been described, with over 8,000 species known to be detrimental to plants and at least 300 that can be pathogenic to humans. Ever since the pioneering 18th and 19th century taxonomical works of Carl Linnaeus, Christiaan Hendrik Persoon, and Elias Magnus Fries, fungi have been classifie... | Fungi | 0.813717 |
16,445 | The discipline of biology devoted to the study of fungi is known as mycology (from the Greek μύκης mykes, mushroom). In the past mycology was regarded as a branch of botany, although it is now known that fungi are genetically more closely related to animals than to plants. Abundant worldwide, most fungi are inconspicuo... | Fungi | 0.813717 |
16,446 | Fungi are the principal decomposers in ecological systems. These and other differences place fungi in a single group of related organisms, named the Eumycota (true fungi or Eumycetes), that share a common ancestor (i.e. they form a monophyletic group), an interpretation that is also strongly supported by molecular phyl... | Fungi | 0.813717 |
16,447 | Later, Elias Magnus Fries (1794–1878) further elaborated the classification of fungi, using spore color and microscopic characteristics, methods still used by taxonomists today. Other notable early contributors to mycology in the 17th–19th and early 20th centuries include Miles Joseph Berkeley, August Carl Joseph Corda... | Fungi | 0.813717 |
16,448 | In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a T... | Recursive language | 0.813713 |
16,449 | Therefore, the modular law can also be stated as Modular law (variant) a ≤ b implies (a ∨ x) ∧ b ≤ a ∨ (x ∧ b).The modular law can be expressed as an equation that is required to hold unconditionally. Since a ≤ b implies a = a ∧ b and since a ∧ b ≤ b, replace a with a ∧ b in the defining equation of the modular law to ... | Modular lattice | 0.813712 |
16,450 | This result is sometimes called the diamond isomorphism theorem for modular lattices. A lattice is modular if and only if the diamond isomorphism theorem holds for every pair of elements. The diamond isomorphism theorem for modular lattices is analogous to the second isomorphism theorem in algebra, and it is a generali... | Modular lattice | 0.813712 |
16,451 | Every distributive lattice is modular.Dilworth (1954) proved that, in every finite modular lattice, the number of join-irreducible elements equals the number of meet-irreducible elements. More generally, for every k, the number of elements of the lattice that cover exactly k other elements equals the number that are co... | Modular lattice | 0.813712 |
16,452 | In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular law a ≤ b implies a ∨ (x ∧ b) = (a ∨ x) ∧ bwhere x, a, b are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the opera... | Modular lattice | 0.813712 |
16,453 | In any lattice, a modular pair is a pair (a, b) of elements such that for all x satisfying a ∧ b ≤ x ≤ b, we have (x ∨ a) ∧ b = x, i.e. if one half of the diamond isomorphism theorem holds for the pair. An element b of a lattice is called a (right) modular element if (a, b) is a modular pair for all elements a. A latti... | Modular lattice | 0.813712 |
16,454 | The definition of modularity is due to Richard Dedekind, who published most of the relevant papers after his retirement. In a paper published in 1894 he studied lattices, which he called dual groups (German: Dualgruppen) as part of his "algebra of modules" and observed that ideals satisfy what we now call the modular l... | Modular lattice | 0.813712 |
16,455 | In these scenarios, modularity is an abstraction of the 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice. In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connect... | Modular lattice | 0.813712 |
16,456 | The ansatz is the special case of electron waves in a periodic crystal lattice using Bloch's theorem as treated generally in the dynamical theory of diffraction. Every crystal is a periodic structure which can be characterized by a Bravais lattice, and for each Bravais lattice we can determine the reciprocal lattice, w... | Band theory | 0.813707 |
16,457 | In statistical genetics, Felsenstein's tree-pruning algorithm (or Felsenstein's tree-peeling algorithm), attributed to Joseph Felsenstein, is an algorithm for computing the likelihood of an evolutionary tree from nucleic acid sequence data. The algorithm is often used as a subroutine in a search for a maximum likelihoo... | Felsenstein's tree-pruning algorithm | 0.813706 |
16,458 | Another advancement of the method was achieved by introduction of degenerate bases instead of universal inosine and the use of optimized DNA polymerases, further increasing the ratio of introduced transversions. This modified SeSaM-TV+ method in addition allows for and favors the introduction of two consecutive nucleot... | Sequence Saturation Mutagenesis | 0.813706 |
16,459 | The Viterbi algorithm is named after Andrew Viterbi, who proposed it in 1967 as a decoding algorithm for convolutional codes over noisy digital communication links. It has, however, a history of multiple invention, with at least seven independent discoveries, including those by Viterbi, Needleman and Wunsch, and Wagner... | Viterbi Algorithm | 0.813706 |
16,460 | The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models (HMM).... | Viterbi Algorithm | 0.813706 |
16,461 | {\displaystyle I(V)=\left\{f\in K\mid f(x)=0{\text{ for all }}x\in V\right\}.} For any affine algebraic set V, the coordinate ring or structure ring of V is the quotient of the polynomial ring by this ideal. : 4 | Algebraic set | 0.813701 |
16,462 | Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets. This topology is called the Zariski topology. : 2 Given a subset V of An, we define I(V) to be the ideal of all polynomial functions vanishing on V: I ( V ) = { f ∈ K ∣ f ( x ) = 0 for all x ∈ V } . | Algebraic set | 0.813701 |
16,463 | A subset V of An is called an affine algebraic set if V = Z(S) for some S.: 2 A nonempty affine algebraic set V is called irreducible if it cannot be written as the union of two proper algebraic subsets. : 3 An irreducible affine algebraic set is also called an affine variety. : 3 (Some authors use the phrase affine va... | Algebraic set | 0.813701 |
16,464 | For an algebraically closed field K and a natural number n, let An be an affine n-space over K, identified to K n {\displaystyle K^{n}} through the choice of an affine coordinate system. The polynomials f in the ring K can be viewed as K-valued functions on An by evaluating f at the points in An, i.e. by choosing value... | Algebraic set | 0.813701 |
16,465 | Let A be a not-necessarily-commutative algebra over a field k. Even if A is not commutative, it can still happen that A has a Z {\displaystyle \mathbb {Z} } -filtration so that the associated ring gr A = ⨁ i = − ∞ ∞ A i / A i − 1 {\displaystyle \operatorname {gr} A=\bigoplus _{i=-\infty }^{\infty }A_{i}/{A_{i-1}}} is... | Algebraic set | 0.813701 |
16,466 | Let C be a smooth complete curve and Pic ( C ) {\displaystyle \operatorname {Pic} (C)} the Picard group of it; i.e., the group of isomorphism classes of line bundles on C. Since C is smooth, Pic ( C ) {\displaystyle \operatorname {Pic} (C)} can be identified as the divisor class group of C and thus there is the deg... | Algebraic set | 0.813701 |
16,467 | It attempts to decompose the world in terms of interfaces that vary on a single type. To deal with the real problems you need multisorted algebras — families of interfaces that span multiple types. I find OOP philosophically unsound. | Object Oriented Programming | 0.813699 |
16,468 | The large amount of data about biological systems that is accumulating in the literature makes it necessary to collect and digest information using the tools of bioinformatics. The UCSC Genome Browser presents a diverse collection of annotation datasets (known as "tracks" and presented graphically), including mRNA alig... | UCSC Genome Browser | 0.813698 |
16,469 | Initially built and still managed by Jim Kent, then a graduate student, and David Haussler, professor of Computer Science (now Biomolecular Engineering) at the University of California, Santa Cruz in 2000, the UCSC Genome Browser began as a resource for the distribution of the initial fruits of the Human Genome Project... | UCSC Genome Browser | 0.813698 |
16,470 | The UCSC Genome Browser is an online and downloadable genome browser hosted by the University of California, Santa Cruz (UCSC). It is an interactive website offering access to genome sequence data from a variety of vertebrate and invertebrate species and major model organisms, integrated with a large collection of alig... | UCSC Genome Browser | 0.813697 |
16,471 | A holonomic function, also called a D-finite function, is a function that is a solution of a homogeneous linear differential equation with polynomial coefficients. Most functions that are commonly considered in mathematics are holonomic or quotients of holonomic functions. In fact, holonomic functions include polynomia... | Linear ODE | 0.813696 |
16,472 | Moreover, these closure properties are effective, in the sense that there are algorithms for computing the differential equation of the result of any of these operations, knowing the differential equations of the input.Usefulness of the concept of holonomic functions results of Zeilberger's theorem, which follows.A hol... | Linear ODE | 0.813696 |
16,473 | These findings represent the birth of molecular biology. In 1986 DNA analysis was first used for criminal investigative purposes when police in the UK requested Dr. Alec Jeffreys of the University of Leicester to verify or disprove a suspect's rape-murder "confession." In this particular case, the suspect had confessed... | DNA molecule | 0.813695 |
16,474 | A debate continues about who should receive credit for the discovery.In an influential presentation in 1957, Crick laid out the central dogma of molecular biology, which foretold the relationship between DNA, RNA, and proteins, and articulated the "adaptor hypothesis". Final confirmation of the replication mechanism th... | DNA molecule | 0.813695 |
16,475 | Methods have been developed to purify DNA from organisms, such as phenol-chloroform extraction, and to manipulate it in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistry make intensive use of these techniques in recombinant DNA technology. Recombinant DNA is ... | DNA molecule | 0.813695 |
16,476 | CDC Scientific Data, Surveillance, Health Statistics, and Laboratory Information. Behavioral Risk Factor Surveillance System (BRFSS), the world's largest, ongoing telephone health-survey system. Mortality Medical Data System. Abortion statistics in the United States CDC WONDER (Wide-ranging ONline Data for Epidemiologi... | Centers for Disease Control and Prevention | 0.813695 |
16,477 | The CDC is organized into "Centers, Institutes, and Offices" (CIOs), with each organizational unit implementing the agency's activities in a particular area of expertise while also providing intra-agency support and resource-sharing for cross-cutting issues and specific health threats.As of the most recent reorganizati... | Centers for Disease Control and Prevention | 0.813695 |
16,478 | Most CDC centers are located in Atlanta. Building 18, which opened in 2005 at the CDC's main Roybal campus (named in honor of the late Representative Edward R. Roybal), contains the premier BSL4 laboratory in the United States.A few of the centers are based in or operate other domestic locations: The National Center fo... | Centers for Disease Control and Prevention | 0.813695 |
16,479 | They included one of only two official repositories of smallpox in the world, with the other one located at the State Research Center of Virology and Biotechnology VECTOR in the Russian Federation. In 2014, the CDC revealed they had discovered several misplaced smallpox samples while their lab workers were "potentially... | Centers for Disease Control and Prevention | 0.813695 |
16,480 | It was renamed to the plural Centers for Disease Control effective October 14, 1980, as the modern organization of having multiple constituent centers was established. By 1990, it had four centers formed in the 1980s: the Center for Infectious Diseases, Center for Chronic Disease Prevention and Health Promotion, the Ce... | Centers for Disease Control and Prevention | 0.813695 |
16,481 | In Native Science, Cajete describes how Indigenous peoples of the Americas have "a lived and creative relationship with the natural world" and a heightened "awareness of the subtle qualities of a place." The book notes how the scientific community has benefited from the traditional ecological knowledge of Indigenous pe... | Native Science | 0.813694 |
16,482 | The book is used Leech Lake Tribal College's class Anishinaabe Understanding of Ecology. == References == | Native Science | 0.813694 |
16,483 | A point p where the above Jacobian matrix has rank two is called regular, or, more properly, the parametrization is called regular at p. The tangent plane at a regular point p is the unique plane passing through p and having a direction parallel to the two row vectors of the Jacobian matrix. The tangent plane is an aff... | Surface (geometry) | 0.813692 |
16,484 | A point of the surface where at least one partial derivative of f is nonzero is called regular. At such a point ( x 0 , y 0 , z 0 ) {\displaystyle (x_{0},y_{0},z_{0})} , the tangent plane and the direction of the normal are well defined, and may be deduced, with the implicit function theorem from the definition given a... | Surface (geometry) | 0.813692 |
16,485 | The combinatorial study of such arrangements of triangles (or, more generally, of higher-dimensional simplexes) is the starting object of algebraic topology. This allows the characterization of the properties of surfaces in terms of purely algebraic invariants, such as the genus and homology groups. The homeomorphism c... | Surface (geometry) | 0.813692 |
16,486 | In topology, a surface is generally defined as a manifold of dimension two. This means that a topological surface is a topological space such that every point has a neighborhood that is homeomorphic to an open subset of a Euclidean plane. Every topological surface is homeomorphic to a polyhedral surface such that all f... | Surface (geometry) | 0.813692 |
16,487 | This is made more exact by the implicit function theorem: if f(x0, y0, z0) = 0, and the partial derivative in z of f is not zero at (x0, y0, z0), then there exists a differentiable function φ(x, y) such that f ( x , y , φ ( x , y ) ) = 0 {\displaystyle f(x,y,\varphi (x,y))=0} in a neighbourhood of (x0, y0, z0). In othe... | Surface (geometry) | 0.813692 |
16,488 | A rational surface is a surface that may be parametrized by rational functions of two variables. That is, if fi(t, u) are, for i = 0, 1, 2, 3, polynomials in two indeterminates, then the parametric surface, defined by x = f 1 ( t , u ) f 0 ( t , u ) y = f 2 ( t , u ) f 0 ( t , u ) z = f 3 ( t , u ) f 0 ( t , u ) , {\di... | Surface (geometry) | 0.813692 |
16,489 | A projective surface in a projective space of dimension three is the set of points whose homogeneous coordinates are zeros of a single homogeneous polynomial in four variables. More generally, a projective surface is a subset of a projective space, which is a projective variety of dimension two. Projective surfaces are... | Surface (geometry) | 0.813692 |
16,490 | Polynomials with coefficients in any field are accepted for defining an algebraic surface. However, the field of coefficients of a polynomial is not well defined, as, for example, a polynomial with rational coefficients may also be considered as a polynomial with real or complex coefficients. Therefore, the concept of ... | Surface (geometry) | 0.813692 |
16,491 | The exact definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface may move ... | Surface (geometry) | 0.813692 |
16,492 | Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, supercon... | Reverse polarity | 0.813691 |
16,493 | Jürgen Tautz, Helga R. Heilmann: The Buzz about Bees – Biology of a Superorganism, Springer-Verlag 2008. ISBN 978-3-540-78727-3 Bert Hölldobler, E. O. Wilson: "The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies", W.W. Norton, 2008. ISBN 978-0-393-06704-0 Selin Kesebir (2012). | Superorganism | 0.81368 |
16,494 | Spencer used the organistic idea to engage in extended analysis of social structure, conceding that it was primarily an analogy. So, for Spencer, the idea of the super-organic best designated a distinct level of social reality above that of biology and psychology, and not a one-to-one identity with an organism. Neverth... | Superorganism | 0.81368 |
16,495 | This process called syntrophy ("eating together") might be linked to the evolution of eukaryote cells and involved in the emergence or maintenance of life forms in challenging environments on Earth and possibly other planets. Superorganisms tend to exhibit homeostasis, power law scaling, persistent disequilibrium and e... | Superorganism | 0.81368 |
16,496 | The classical equipartition theorem predicts that the heat capacity ratio (γ) for an ideal gas can be related to the thermally accessible degrees of freedom (f) of a molecule by γ = 1 + 2 f , or f = 2 γ − 1 . {\displaystyle \gamma =1+{\frac {2}{f}},\quad {\text{or}}\quad f={\frac {2}{\gamma -1}}.} Thus we observe that ... | Heat capacity ratio | 0.813678 |
16,497 | Again, not every set of Likert scaled items can be used for Rasch measurement. The data has to be thoroughly checked to fulfill the strict formal axioms of the model. However, the raw scores are the sufficient statistics for the Rasch measures, a deliberate choice by Georg Rasch, so, if you are prepared to accept the r... | Likert scaling | 0.813676 |
16,498 | Peter Stanley Dixon (1929–1993). Professor Emeritus of Biology at University of California. William Dwyn Isaac (1905–1995). | History of phycology | 0.813671 |
16,499 | The mycelium and organic substrate needed to incubate properly and this time is crucial as it is the period that these particles interact together and bind into one to form a dense network and hence form a composite. During this incubation period, mycelium uses the essential nutrients such as carbon, minerals, and wate... | Living building material | 0.813668 |
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