Admissibility (other)

	Admissibility (other) Admissibility may refer to: Law * Admissible evidence, evidence which may be introduced in a court of law * Admissibility (ECHR), whether a case will be considered in the European Convention on Human Rights system Mathematics and logic * Admissible decision rule, in statistical decision theory, a rule which is never dominated * Admissible rule, in logic, a type of rule of inference * Admissible heuristic, in computer science, is a heuristic which is no more than the lowest-cost path to the goal * Admissible prime k-tuple, in number theory regarding possible constellations of prime numbers * Admissible set, in mathematical logic, a transitive set satisfying the axioms of Kripke-Platek set theory * Admissible representation In mathematics, admissible representations are a well-behaved class of representations used in the representation theory of reductive Lie groups and locally compact totally disconnected groups. They were introduced by Harish-Chandra. Real or comp ... , i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissible Evidence Admissible evidence, in a court of law, is any testimonial, documentary, or tangible evidence that may be introduced to a factfinder—usually a judge or jury—to establish or to bolster a point put forth by a party to the proceeding. For evidence to be admissible, it must be relevant and "not excluded by the rules of evidence", which generally means that it must not be unfairly prejudicial, and it must have some indicia of reliability. The general rule in evidence is that all relevant evidence is admissible and all irrelevant evidence is inadmissible, though some countries (such as the United States and, to an extent, Australia) proscribe the prosecution from exploiting evidence obtained in violation of constitutional law, thereby rendering relevant evidence inadmissible. This rule of evidence is called the exclusionary rule. In the United States this was effectuated federally in 1914 under the Supreme Court case '' Weeks v. United States'' and incorporated against th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissibility (ECHR) Under the European Convention on Human Rights, admissibility governs whether an individual or inter-State application will be accepted for consideration on the merits and progress to a full case. Normally, all domestic legal remedies must be exhausted before an application will be considered by the European Court of Human Rights The European Court of Human Rights (ECHR or ECtHR), also known as the Strasbourg Court, is an international court of the Council of Europe which interprets the European Convention on Human Rights. The court hears applications alleging that .... Inter-State cases are subject to more lenient admissibility rules than applications by individuals. References External linksOfficial guide European Convention on Human Rights European Court of Human Rights {{law-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissible Decision Rule In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below. This concept is analogous to Pareto efficiency. Definition Define sets \Theta\,, \mathcal and \mathcal, where \Theta\, are the states of nature, \mathcal the possible observations, and \mathcal the actions that may be taken. An observation x \in \mathcal\,\! is distributed as F(x\mid\theta)\,\! and therefore provides evidence about the state of nature \theta\in\Theta\,\!. A decision rule is a function \delta:\rightarrow , where upon observing x\in \mathcal, we choose to take action \delta(x)\in \mathcal\,\!. Also define a loss function L: \Theta \times \mathcal \rightarrow \mathbb, which specifies the loss we would incur by taking action a \in \mathcal when the true state of nature is \theta \in \Theta. Usually we will take thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissible Rule In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules of the system. In other words, every formula that can be derived using that rule is already derivable without that rule, so, in a sense, it is redundant. The concept of an admissible rule was introduced by Paul Lorenzen (1955). Definitions Admissibility has been systematically studied only in the case of structural (i.e. substitution-closed) rules in propositional non-classical logics, which we will describe next. Let a set of basic propositional connectives be fixed (for instance, \ in the case of superintuitionistic logics, or \ in the case of monomodal logics). Well-formed formulas are built freely using these connectives from a countably infinite set of propositional variables ''p''0, ''p''1, .... A substitution ''σ'' is a function from formulas to formulas that commutes with applications of the connective ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissible Heuristic In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path. It is related to the concept of consistent heuristics. While all consistent heuristics are admissible, not all admissible heuristics are consistent. Search algorithms An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state. The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A* search the evaluation function (where n is the current node) is: f(n) = g(n) + h(n) where :f(n) = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Prime K-tuple In number theory, a prime -tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers. For a -tuple , the positions where the -tuple matches a pattern in the prime numbers are given by the set of integers such that all of the values are prime. Typically the first value in the -tuple is 0 and the rest are distinct positive even numbers. Named patterns Several of the shortest ''k''-tuples are known by other common names: OEIS sequence covers 7-tuples (''prime septuplets'') and contains an overview of related sequences, e.g. the three sequences corresponding to the three admissible 8-tuples (''prime octuplets''), and the union of all 8-tuples. The first term in these sequences corresponds to the first prime in the smallest prime constellation shown below. Admissibility In order for a -tuple to have infinitely many positions at which all of its values are prime, there cannot exist a prime such that the tuple includes every di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Admissible Set In set theory, a discipline within mathematics, an admissible set is a transitive set A\, such that \langle A,\in \rangle is a model of Kripke–Platek set theory (Barwise 1975). The smallest example of an admissible set is the set of hereditarily finite sets. Another example is the set of hereditarily countable sets. See also * Admissible ordinal References * Barwise, Jon (1975). ''Admissible Sets and Structures: An Approach to Definability Theory'', Perspectives in Mathematical Logic, Volume 7, Springer-VerlagElectronic versionon Project Euclid Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent an .... Set theory {{settheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]