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30,400 | Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h: X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\displaystyle Y} to an exampl... | Domain adaptation | 0.804992 |
30,401 | In other words, we have an occurrence if e ( G ) s n s − 1 ≥ O ( n s ) {\displaystyle {\frac {e(G)^{s}}{n^{s-1}}}\geq O(n^{s})} , which simplifies to e ( G ) ≥ O ( n 2 − 1 s ) {\displaystyle e(G)\geq O(n^{2-{\frac {1}{s}}})} , which is the statement of the theorem. In this proof, we are using the supersaturation method... | Forbidden subgraph problem | 0.804991 |
30,402 | We may solve various forbidden subgraph problems by considering supersaturation-type problems. We restate and give a proof sketch of the Kővári–Sós–Turán theorem below: Kővári–Sós–Turán theorem. For every pair of positive integers s , t {\displaystyle s,t} with t ≥ s ≥ 1 {\displaystyle t\geq s\geq 1} , there exists som... | Forbidden subgraph problem | 0.804991 |
30,403 | Equality cases for Turán's theorem come from the Turán graph T ( n , r − 1 ) {\displaystyle T(n,r-1)} . This result can be generalized to arbitrary graphs G {\displaystyle G} by considering the chromatic number χ ( G ) {\displaystyle \chi (G)} of G {\displaystyle G} . Note that T ( n , r ) {\displaystyle T(n,r)} can be... | Forbidden subgraph problem | 0.804991 |
30,404 | Turán's theorem states that for positive integers n , r {\displaystyle n,r} satisfying n ≥ r ≥ 3 {\displaystyle n\geq r\geq 3} , ex ( n , K r ) = ( 1 − 1 r − 1 + o ( 1 ) ) n 2 2 . {\textstyle \operatorname {ex} (n,K_{r})=\left(1-{\frac {1}{r-1}}+o(1)\right){\frac {n^{2}}{2}}.} This solves the forbidden subgraph probl... | Forbidden subgraph problem | 0.804991 |
30,405 | This technique combines the above two ideas. It uses random polynomial type relations when defining the incidences between vertices, which are in some algebraic set. Using this technique to prove the following theorem. Theorem: For every s ≥ 2 {\displaystyle s\geq 2} , there exists some t {\displaystyle t} such that ex... | Forbidden subgraph problem | 0.804991 |
30,406 | The problem may be generalized for a set of forbidden subgraphs S {\displaystyle S}: find the maximal number of edges in an n {\displaystyle n} -vertex graph which does not have a subgraph isomorphic to any graph from S {\displaystyle S} .There are also hypergraph versions of forbidden subgraph problems that are much m... | Forbidden subgraph problem | 0.804991 |
30,407 | In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges ex ( n , G ) {\displaystyle \operatorname {ex} (n,G)} an n {\displaystyle n} -vertex graph can have such that it does not have a subgraph isomorphic to G {\displaysty... | Forbidden subgraph problem | 0.804991 |
30,408 | Theorem (Alon et al., 1999) For t ≥ ( s − 1 ) ! + 1 {\displaystyle t\geq (s-1)!+1} , ex ( n , K s , t ) = Θ ( n 2 − 1 s ) . {\displaystyle \operatorname {ex} (n,K_{s,t})=\Theta (n^{2-{\frac {1}{s}}}).} | Forbidden subgraph problem | 0.804991 |
30,409 | {\displaystyle \operatorname {ex} (n,K_{3,3})\geq \left({\frac {1}{2}}-o(1)\right)n^{5/3}.} Proof outline. Like in the previous theorem, we can take n = p 3 {\displaystyle n=p^{3}} for prime p {\displaystyle p} and let the vertices of our graph be elements of F p 3 {\displaystyle \mathbb {F} _{p}^{3}} . | Forbidden subgraph problem | 0.804991 |
30,410 | The following theorem is a similar result for K 3 , 3 {\displaystyle K_{3,3}} . Theorem (Brown, 1966). ex ( n , K 3 , 3 ) ≥ ( 1 2 − o ( 1 ) ) n 5 / 3 . | Forbidden subgraph problem | 0.804991 |
30,411 | For specific cases, improvements have been made by finding algebraic constructions. A common feature for such constructions is that it involves the use of geometry to construct a graph, with vertices representing geometric objects and edges according to the algebraic relations between the vertices. We end up with no su... | Forbidden subgraph problem | 0.804991 |
30,412 | This lemma allows us to handle bipartite graphs with bounded degree in one part: Theorem (Alon, Krivelevich, and Sudakov, 2003). Let G {\displaystyle G} be a bipartite graph with vertex parts A {\displaystyle A} and B {\displaystyle B} such that every vertex in A {\displaystyle A} has degree at most r {\displaystyle r}... | Forbidden subgraph problem | 0.804991 |
30,413 | This gives the following theorem. Theorem (Bondy and Simonovits, 1974). There exists some constant C {\displaystyle C} such that ex ( n , C 2 k ) ≤ C n 1 + 1 k {\textstyle \operatorname {ex} (n,C_{2k})\leq Cn^{1+{\frac {1}{k}}}} for every positive integer n {\displaystyle n} and positive integer k ≥ 2 {\displaystyle ... | Forbidden subgraph problem | 0.804991 |
30,414 | For bipartite graphs G {\displaystyle G} , the Erdős–Stone theorem only tells us that ex ( n , G ) = o ( n 2 ) {\displaystyle \operatorname {ex} (n,G)=o(n^{2})} . The forbidden subgraph problem for bipartite graphs is known as the Zarankiewicz problem, and it is unsolved in general. Progress on the Zarankiewicz probl... | Forbidden subgraph problem | 0.804991 |
30,415 | Erdős–Stone theorem states that for all positive integers n {\displaystyle n} and all graphs G {\displaystyle G} , ex ( n , G ) = ( 1 − 1 χ ( G ) − 1 + o ( 1 ) ) ( n 2 ) . {\textstyle \operatorname {ex} (n,G)=\left(1-{\frac {1}{\chi (G)-1}}+o(1)\right){\binom {n}{2}}.} When G {\displaystyle G} is not bipartite, this ... | Forbidden subgraph problem | 0.804991 |
30,416 | Consider an h {\displaystyle h} -uniform hypergraph H {\displaystyle H} with v {\displaystyle v} vertices. The supersaturation theorem states that for every ϵ > 0 {\displaystyle \epsilon >0} , there exists a δ > 0 {\displaystyle \delta >0} such that if G {\displaystyle G} is a graph on n {\displaystyle n} vertices and ... | Forbidden subgraph problem | 0.804991 |
30,417 | The Turán density of a h {\displaystyle h} -uniform graph G {\displaystyle G} is defined to be π ( G ) = lim n → ∞ ex ( n , G ) ( n h ) . {\displaystyle \pi (G)=\lim _{n\to \infty }{\frac {\operatorname {ex} (n,G)}{\binom {n}{h}}}.} It is true that ex ( n , G ) ( n h ) {\displaystyle {\frac {\operatorname {ex} (n,G... | Forbidden subgraph problem | 0.804991 |
30,418 | In the same vein as the above, one can consider the action in one dimension less, i.e. in a contact geometry setting. This gives the Chern–Simons functional. It is written as Chern–Simons theory was deeply explored in physics, as a toy model for a broad range of geometric phenomena that one might expect to find in a gr... | Interaction Lagrangian | 0.804988 |
30,419 | Climate models simulate the CO2-driven warming of the future as well as the past. They operate on principles similar to those underlying models that predict the weather, but they focus on longer-term processes. Climate models typically begin with a starting state and then apply physical laws and knowledge about biology... | Climate sensitivity | 0.804986 |
30,420 | Modelling of the climate system can lead to a wide range of outcomes. Models are often run that use different plausible parameters in their approximation of physical laws and the behaviour of the biosphere, which forms a perturbed physics ensemble, which attempts to model the sensitivity of the climate to different typ... | Climate sensitivity | 0.804986 |
30,421 | "Lichens are fungi that have discovered agriculture" — Trevor GowardA lichen is a combination of fungus and/or algae and/or cyanobacteria that has a very different form (morphology), physiology, and biochemistry than any of the constituent species growing separately. The algae or cyanobacteria benefit their fungal part... | Symbiosis in lichens | 0.804983 |
30,422 | Noncommutative rings are quite different in flavour, since more unusual behavior can arise. While the theory has developed in its own right, a fairly recent trend has sought to parallel the commutative development by building the theory of certain classes of noncommutative rings in a geometric fashion as if they were r... | Ring Theory | 0.804981 |
30,423 | Because these three fields (algebraic geometry, algebraic number theory and commutative algebra) are so intimately connected it is usually difficult and meaningless to decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry, and ... | Ring Theory | 0.804981 |
30,424 | General Isomorphism theorems for rings Nakayama's lemmaStructure theorems The Artin–Wedderburn theorem determines the structure of semisimple rings The Jacobson density theorem determines the structure of primitive rings Goldie's theorem determines the structure of semiprime Goldie rings The Zariski–Samuel theorem dete... | Ring Theory | 0.804981 |
30,425 | Two rings R, S are said to be Morita equivalent if the category of left modules over R is equivalent to the category of left modules over S. In fact, two commutative rings which are Morita equivalent must be isomorphic, so the notion does not add anything new to the category of commutative rings. However, commutative r... | Ring Theory | 0.804981 |
30,426 | Noncommutative rings are an active area of research due to their ubiquity in mathematics. For instance, the ring of n-by-n matrices over a field is noncommutative despite its natural occurrence in geometry, physics and many parts of mathematics. More generally, endomorphism rings of abelian groups are rarely commutativ... | Ring Theory | 0.804981 |
30,427 | In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (g... | Ring Theory | 0.804981 |
30,428 | If X is an affine algebraic variety, then the set of all regular functions on X forms a ring called the coordinate ring of X. For a projective variety, there is an analogous ring called the homogeneous coordinate ring. Those rings are essentially the same things as varieties: they correspond in essentially a unique way... | Ring Theory | 0.804981 |
30,429 | The various hypercomplex numbers were identified with matrix rings by Joseph Wedderburn (1908) and Emil Artin (1928). Wedderburn's structure theorems were formulated for finite-dimensional algebras over a field while Artin generalized them to Artinian rings. In 1920, Emmy Noether, in collaboration with W. Schmeidler, p... | Ring Theory | 0.804981 |
30,430 | More precisely, William Rowan Hamilton put forth the quaternions and biquaternions; James Cockle presented tessarines and coquaternions; and William Kingdon Clifford was an enthusiast of split-biquaternions, which he called algebraic motors. These noncommutative algebras, and the non-associative Lie algebras, were stud... | Ring Theory | 0.804981 |
30,431 | Commutative ring theory originated in algebraic number theory, algebraic geometry, and invariant theory. Central to the development of these subjects were the rings of integers in algebraic number fields and algebraic function fields, and the rings of polynomials in two or more variables. Noncommutative ring theory beg... | Ring Theory | 0.804981 |
30,432 | Algebraic geometry is in many ways the mirror image of commutative algebra. This correspondence started with Hilbert's Nullstellensatz that establishes a one-to-one correspondence between the points of an algebraic variety, and the maximal ideals of its coordinate ring. This correspondence has been enlarged and systema... | Ring Theory | 0.804981 |
30,433 | A ring is called commutative if its multiplication is commutative. Commutative rings resemble familiar number systems, and various definitions for commutative rings are designed to formalize properties of the integers. Commutative rings are also important in algebraic geometry. In commutative ring theory, numbers are o... | Ring Theory | 0.804981 |
30,434 | A basic (and perhaps the most fundamental) question in the classical invariant theory is to find and study polynomials in the polynomial ring k {\displaystyle k} that are invariant under the action of a finite group (or more generally reductive) G on V. The main example is the ring of symmetric polynomials: symmetric ... | Ring Theory | 0.804981 |
30,435 | Representation theory is a branch of mathematics that draws heavily on non-commutative rings. It studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract a... | Ring Theory | 0.804981 |
30,436 | Noncommutative rings resemble rings of matrices in many respects. Following the model of algebraic geometry, attempts have been made recently at defining noncommutative geometry based on noncommutative rings. Noncommutative rings and associative algebras (rings that are also vector spaces) are often studied via their c... | Ring Theory | 0.804981 |
30,437 | In algebraic number theory, R will be taken to be the ring of integers, which is Dedekind and thus regular. It follows that Pic(R) is a finite group (finiteness of class number) that measures the deviation of the ring of integers from being a PID. One can also consider the group completion of P ( R ) {\displaystyle \ma... | Ring Theory | 0.804981 |
30,438 | Closely related concepts are those of depth and global dimension. In general, if R is a noetherian local ring, then the depth of R is less than or equal to the dimension of R. When the equality holds, R is called a Cohen–Macaulay ring. A regular local ring is an example of a Cohen–Macaulay ring. It is a theorem of Serr... | Ring Theory | 0.804981 |
30,439 | Practically all noetherian rings that appear in applications are catenary. Ratliff proved that a noetherian local integral domain R is catenary if and only if for every prime ideal p {\displaystyle {\mathfrak {p}}} , dim R = ht p + dim R / p {\displaystyle \operatorname {dim} R=\operatorname {ht} {\mathfrak {p}}+... | Ring Theory | 0.804981 |
30,440 | In 2022, researchers reported the development of nanoscale brain-inspired artificial synapses, using the ion proton (H+), for 'analog deep learning'. | Physical neural network | 0.804981 |
30,441 | In 1989 Carver Mead published his book Analog VLSI and Neural Systems, which spun off perhaps the most common variant of analog neural networks. The physical realization is implemented in analog VLSI. This is often implemented as field effect transistors in low inversion. Such devices can be modelled as translinear cir... | Physical neural network | 0.804981 |
30,442 | Another example of a physical neural network is taught by U.S. Patent No. 7,039,619 entitled "Utilized nanotechnology apparatus using a neural network, a solution and a connection gap," which issued to Alex Nugent by the U.S. Patent & Trademark Office on May 2, 2006.A further application of physical neural network is s... | Physical neural network | 0.804981 |
30,443 | Alex Nugent describes a physical neural network as one or more nonlinear neuron-like nodes used to sum signals and nanoconnections formed from nanoparticles, nanowires, or nanotubes which determine the signal strength input to the nodes. Alignment or self-assembly of the nanoconnections is determined by the history of ... | Physical neural network | 0.804981 |
30,444 | A physical neural network is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse or a higher-order (dendritic) neuron model. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as oppose... | Physical neural network | 0.804981 |
30,445 | SLAS Discovery is abstracted and indexed in: Elsevier BIOBASE Biomolecular Interaction Network Database Biotechnology Citation Index Chemical Abstracts Current Contents/Life Sciences EMBASE EMBiology Index Medicus MEDLINE Science Citation Index Expanded ScopusAccording to the Journal Citation Reports, the journal's 201... | SLAS Discovery | 0.80498 |
30,446 | The journal explores how scientists develop and utilize novel technologies and/or approaches to provide and characterize chemical and biological tools to understand and treat human disease. This includes scientific and technical advances in target identification/validation; biomarker discovery; assay development; virtu... | SLAS Discovery | 0.80498 |
30,447 | His dissertation paper was on the numerical study of dendritic solidification. Notable publications include Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems, Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces, Locally-corrected sp... | John Strain (mathematician) | 0.804978 |
30,448 | John Andrew Strain is a Professor of Mathematics at the University of California, Berkeley. His area of interest are Applied Mathematics, Algorithms, Numerical Analysis, and Materials Science. John Strain received his PhD in Mathematics from the University of California, Berkeley in 1988 working with his advisor Alexan... | John Strain (mathematician) | 0.804978 |
30,449 | For this reason, modern universal algebra often treats clones as a representation of algebras which abstracts from their signature. There is only one clone on the one-element set (there are two if nullary operations are considered). The lattice of clones on a two-element set is countable,: 39 and has been completely de... | Clone (algebra) | 0.804973 |
30,450 | Two theories determine isomorphic clones if and only if the corresponding categories of algebras are isomorphic. Conversely every abstract clone determines an algebraic theory with an n-ary operation for each element of Cn. This gives a bijective correspondence between abstract clones and algebraic theories. Every abst... | Clone (algebra) | 0.804973 |
30,451 | Philip Hall introduced the concept of abstract clone. An abstract clone is different from a concrete clone in that the set A is not given. Formally, an abstract clone comprises a set Cn for each natural number n, elements πk,n in Cn for all k ≤ n, and a family of functions ∗:Cm × (Cn)m → Cn for all m and nsuch that c *... | Clone (algebra) | 0.804973 |
30,452 | Typically, publications studying clones as abstract clones, e.g. in the category theoretic setting of Lawvere's algebraic theories, will include nullary operations.Given an algebra in a signature σ, the set of operations on its carrier definable by a σ-term (the term functions) is a clone. Conversely, every clone can b... | Clone (algebra) | 0.804973 |
30,453 | In universal algebra, a clone is a set C of finitary operations on a set A such that C contains all the projections πkn: An → A, defined by πkn(x1, …, xn) = xk, C is closed under (finitary multiple) composition (or "superposition"): if f, g1, …, gm are members of C such that f is m-ary, and gj is n-ary for all j, then ... | Clone (algebra) | 0.804973 |
30,454 | In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is i... | Helstrom metric | 0.804971 |
30,455 | This result is related to the equipartition theorem. Thus the kinetic energy per Kelvin of one mole of (monatomic ideal gas) is 3 = 3R/2. | Kinetic-molecular theory | 0.80497 |
30,456 | The force of this particle's collision with the wall is The total force on the wall due to collisions by molecules impacting the walls with a range of possible values of v x {\displaystyle v_{x}} is where the bar denotes an average over the possible velocities of the N particles. Since the motion of the particles is ra... | Kinetic-molecular theory | 0.80497 |
30,457 | In molecular biology, the GA module, or protein G-related albumin-binding module, is a protein domain which occurs on the surface of numerous Gram-positive bacterial pathogens. Protein G of group C and G Streptococci interacts with the constant region of IgG and with human serum albumin. The GA module is composed of a ... | GA module | 0.804969 |
30,458 | Research on Language and Computation was a quarterly peer-reviewed academic journal covering research in computational linguistics and natural language processing. It was established in 2003 and ceased publication in December 2010. The journal was published by Springer Science+Business Media. | Research on Language and Computation | 0.804968 |
30,459 | For primary impacts, based on geometry, the most probable impact angle is 45° between two objects, and the distribution falls off rapidly outside of the range 30° – 60°. It is observed that impact angle has little effect on the shape of primary craters, except in the case of low angle impacts, where the resulting crate... | Secondary impact | 0.804963 |
30,460 | Secondary craters are impact craters formed by the ejecta that was thrown out of a larger crater. They sometimes form radial crater chains. In addition, secondary craters are often seen as clusters or rays surrounding primary craters. The study of secondary craters exploded around the mid-twentieth century when researc... | Secondary impact | 0.804963 |
30,461 | A hypermultiplet is a type of representation of an extended supersymmetry algebra, in particular the matter multiplet of N = 2 {\displaystyle {\mathcal {N}}=2} supersymmetry in 4 dimensions, containing two complex scalars Ai, a Dirac spinor ψ, and two further auxiliary complex scalars Fi. The name "hypermultiplet" come... | Vector supermultiplet | 0.804962 |
30,462 | This enolate then acts as a nucleophile and can attack an electrophilic aldehyde. The Aldol product is then deprotonated forming another enolate followed by the elimination of water in an E1cB dehydration reaction. Aldol reactions are a key reaction in organic chemistry because they provide a means of forming carbon-ca... | E1cB elimination reaction | 0.80496 |
30,463 | The E1cB-elimination reaction is an important reaction in biology. For example, the penultimate step of glycolysis involves an E1cB mechanism. This step involves the conversion of 2-phosphoglycerate to phosphoenolpyruvate, facilitated by the enzyme enolase. | E1cB elimination reaction | 0.80496 |
30,464 | In plane geometry, a Hofstadter point is a special point associated with every plane triangle. In fact there are several Hofstadter points associated with a triangle. All of them are triangle centers. Two of them, the Hofstadter zero-point and Hofstadter one-point, are particularly interesting. | Hofstadter points | 0.804959 |
30,465 | In vector calculus, the surface gradient is a vector differential operator that is similar to the conventional gradient. The distinction is that the surface gradient takes effect along a surface. For a surface S {\displaystyle S} in a scalar field u {\displaystyle u} , the surface gradient is defined and notated as ∇ S... | Surface gradient | 0.804957 |
30,466 | Let F {\displaystyle \mathbb {F} } be a real closed field. (For example F {\displaystyle \mathbb {F} } could be the field of real numbers R {\displaystyle \mathbb {R} } .) A subset S {\displaystyle S} of F n {\displaystyle \mathbb {F} ^{n}} is a semialgebraic set if it is a finite union of sets defined by polynomial eq... | Semialgebraic set | 0.804955 |
30,467 | Igor Walukiewicz, "Completeness of Kozen's Axiomatisation of the Propositional Mu-Calculus" | Symposium on Logic in Computer Science | 0.804954 |
30,468 | Eugenio Moggi, "Computational lambda-calculus and monads" | Symposium on Logic in Computer Science | 0.804954 |
30,469 | The ACM–IEEE Symposium on Logic in Computer Science (LICS) is an annual academic conference on the theory and practice of computer science in relation to mathematical logic. Extended versions of selected papers of each year's conference appear in renowned international journals such as Logical Methods in Computer Scien... | Symposium on Logic in Computer Science | 0.804954 |
30,470 | Patrice Godefroid, Pierre Wolper, "A partial approach to model checking" Joshua Hodas, Dale A. Miller, "Logic programming in a fragment of intuitionistic linear logic" Dexter Kozen, "A completeness theorem for Kleene algebras and the algebra of regular events" | Symposium on Logic in Computer Science | 0.804954 |
30,471 | Parosh A. Abdulla, Karlis Cerans, Bengt Jonsson, Yih-Kuen Tsay, "General decidability theorems for infinite-state systems" Iliano Cervesato, Frank Pfenning, "A Linear Logical Framework" | Symposium on Logic in Computer Science | 0.804954 |
30,472 | Leo Bachmair, Nachum Dershowitz, Jieh Hsiang, "Orderings for Equational Proofs" E. Allen Emerson, Chin-Laung Lei, "Efficient Model Checking in Fragments of the Propositional Mu-Calculus (Extended Abstract)" Moshe Y. Vardi, Pierre Wolper, "An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Rep... | Symposium on Logic in Computer Science | 0.804954 |
30,473 | Model organisms have been used in the study of PRKCZ function. A conditional knockout mouse line, called Prkcztm1a(EUCOMM)Wtsi was generated as part of the International Knockout Mouse Consortium program – a high-throughput mutagenesis project to generate and distribute animal models of disease to interested scientists... | Protein kinase C zeta type | 0.804951 |
30,474 | Symmetric spaces are classified as follows. First, the universal cover of a symmetric space is still symmetric, so we can reduce to the case of simply connected symmetric spaces. (For example, the universal cover of a real projective plane is a sphere.) Second, the product of symmetric spaces is symmetric, so we may as... | Simple Lie group | 0.80495 |
30,475 | The compressive strength and hardness of diamond and various other materials, such as boron nitride, (which has the closely related zincblende structure) is attributed to the diamond cubic structure. Similarly, truss systems that follow the diamond cubic geometry have a high capacity to withstand compression, by minimi... | Diamond structure | 0.80495 |
30,476 | The four nearest neighbors of each point may be obtained, in this coordinate system, by adding one to each of the four coordinates, or by subtracting one from each of the four coordinates, accordingly as the coordinate sum is zero or one. These four-dimensional coordinates may be transformed into three-dimensional coor... | Diamond structure | 0.804949 |
30,477 | In mathematics, Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/π. They devised several other algorithms. They published the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity. | Borwein's algorithm | 0.804946 |
30,478 | Applying magnetic theory to the study of biology is a biophysical technique that started to appear in Germany in the early 1920s. Possibly the first demonstration was published by Alfred Heilbronn in 1922; his work looked at viscosity of protoplasts. The following year, Freundlich and Seifriz explored rheology in echin... | Magnetic tweezers | 0.804945 |
30,479 | {\displaystyle {\begin{aligned}f(t)=&{\frac {1}{2\pi }}\int F(\omega )\mathrm {e} ^{i\omega t}\mathrm {d} t\\x(t)=&{\frac {1}{2\pi }}\int X(\omega )\mathrm {e} ^{i\omega t}\mathrm {d} t.\end{aligned}}} This leads to: X ( ω ) = F ( ω ) 6 π i R η ω + F l {\displaystyle X(\omega )={\frac {F(\omega )}{6\pi iR\eta \omega +{... | Magnetic tweezers | 0.804945 |
30,480 | The equipartition theorem states that the mean energy that is stored in this "spring" is equal to 1 2 k B T {\displaystyle {\frac {1}{2}}k_{B}T} per degree of freedom. Since only one direction is considered here, the potential energy of the system reads: ⟨ E p ⟩ = 1 2 F l ⟨ δ x 2 ⟩ = 1 2 k B T {\displaystyle \langle E_... | Magnetic tweezers | 0.804945 |
30,481 | genetics botany zoology biological systematics evolution biochemistry molecular biology cell biology, including all aspects of normal cell functioning, from embryonic to differentiated tissues and in different pathological states physiology neurobiology radiobiology immunology, including human immunology human biology,... | Archives of Biological Sciences | 0.804944 |
30,482 | The Archives of Biological Sciences is a multidisciplinary journal that covers original research in a wide range of subjects in life science, including biology, ecology, human biology and biomedical research. The journal features articles in genetics, botany and zoology (including higher and lower terrestrial and aquat... | Archives of Biological Sciences | 0.804944 |
30,483 | The Archives of Biological Sciences is a multidisciplinary journal that covers original research in a wide range of subjects in life science, including biology, ecology, human biology and biomedical research. | Archives of Biological Sciences | 0.804944 |
30,484 | Serbian Biological Society Institute for Biological Research "Siniša Stanković", University of Belgrade Faculty of Biology, University of Belgrade Department of Biology and Ecology, Faculty of Sciences, University of Novi Sad Institute for the Application of Nuclear Energy (INEP) Faculty of Sciences, University of Banj... | Archives of Biological Sciences | 0.804944 |
30,485 | In random graphs, the algebraic connectivity decreases with the number of vertices, and increases with the average degree.The exact definition of the algebraic connectivity depends on the type of Laplacian used. Fan Chung has developed an extensive theory using a rescaled version of the Laplacian, eliminating the depen... | Algebraic connectivity | 0.804943 |
30,486 | If the number of vertices of an undirected connected graph with nonnegative edge weights is n and the diameter is D, the algebraic connectivity is also known to be bounded below by algebraic connectivity ≥ 1 n D {\displaystyle {\text{algebraic connectivity}}\geq {\frac {1}{nD}}} , and in fact (in a result due to Brenda... | Algebraic connectivity | 0.804943 |
30,487 | The algebraic connectivity of undirected graphs with nonnegative weights, a ( G ) ≥ 0 {\displaystyle a(G)\geq 0} with the inequality being strict if and only if G is connected. However, the algebraic connectivity can be negative for general directed graphs, even if G is a connected graph. Furthermore, the value of the ... | Algebraic connectivity | 0.804943 |
30,488 | Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable... | Digital image analysis | 0.804942 |
30,489 | automatic number plate recognition; optical character recognition, such as automatic license plate detection. remote sensing, such as detecting intruders in a house, and producing land cover/land use maps. robotics, such as to avoid steering into an obstacle. security, such as detecting a person's eye color or hair col... | Digital image analysis | 0.804942 |
30,490 | The applications of digital image analysis are continuously expanding through all areas of science and industry, including: assay micro plate reading, such as detecting where a chemical was manufactured. astronomy, such as calculating the size of a planet. automated species identification (e.g. plant and animal species... | Digital image analysis | 0.804942 |
30,491 | Particle Physics: A comprehensive introduction. Addison Wesley. ISBN 978-0-8053-8736-0. | Elementary particle | 0.804942 |
30,492 | ISBN 978-981-238-149-1. Close, Frank (2004). Particle Physics: A very short introduction. | Elementary particle | 0.804942 |
30,493 | String theory is a model of physics whereby all "particles" that make up matter are composed of strings (measuring at the Planck length) that exist in an 11-dimensional (according to M-theory, the leading version) or 12-dimensional (according to F-theory) universe. These strings vibrate at different frequencies that de... | Elementary particle | 0.804942 |
30,494 | Landau theory in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. It can also be adapted to systems under externally-applied fields, and used as a quantitative model for discontinuous (i.e., first-order) transitions. Althoug... | Landau theory | 0.804942 |
30,495 | Veltman, Martinus (2003). Facts and Mysteries in Elementary Particle Physics. World Scientific. | Elementary particle | 0.804942 |
30,496 | (2004) Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. ISBN 0-8018-7971-X. | Elementary particle | 0.804942 |
30,497 | Oerter, Robert (2006) The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume. Schumm, Bruce A. | Elementary particle | 0.804942 |
30,498 | John Gribbin (2000) Q is for Quantum – An Encyclopedia of Particle Physics. Simon & Schuster. ISBN 0-684-85578-X. | Elementary particle | 0.804942 |
30,499 | Feynman, R.P. & Weinberg, S. (1987) Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures. Cambridge Univ. | Elementary particle | 0.804942 |
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