Reduction, reduced, or reduce may refer to:
Science
Chemistry
Computing and algorithms
- Reduction (complexity) In computability theory and computational complexity theory, a reduction is a transformation of one problem into another problem. Depending on the transformation used this can be used to define complexity classes on a set of problems – a transformation of one problem into another problem.
- Graph reduction – an efficient version of non-strict evaluation
- Strength reduction Operator strength reduction involves using mathematical identities to replace slow math operations with faster operations. The cost and benefits will depend highly on the target CPU and sometimes on the surrounding code . Examples of this include – a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
- Reduction (recursion theory) – given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A?
- L-reduction In computer science, in particular in the study of approximation algorithms, an L-reduction is a transformation of optimization problems which linearly preserves approximability features. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies of computational – a transformation of optimization problems which keeps the approximability features
- Variance reduction In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations. Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In – a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations
- Partial order reduction In computer science, partial order reduction is a technique for reducing the size of the state-space to be searched by a model checking algorithm. It exploits the commutativity of concurrently executed transitions, which result in the same state when executed in different orders. Thus, this reduction technique is best suited for asynchronous – a technique for reducing the size of the state-space to be searched by a model checking algorithm
- Bit Rate Reduction – an audio compression method
- Reduce (computer algebra system) The development of the REDUCE computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many[citation needed] scientists from all over the world have contributed to its development under his direction – a general-purpose computer algebra system geared towards applications in physics
- Reduce (higher-order function) In functional programming, fold, also known variously as reduce, accumulate, compress or inject, is a family of higher-order functions that process a data structure in some order and build up a return value. Typically, a fold deals with two things: a combining function, and a data structure, typically a list of elements. The fold then proceeds to – in functional programming, a family of higher-order functions that process a data structure in some order and build up a return value
- Reduced instruction set computer The acronym RISC , for reduced instruction set computer, represents a CPU design strategy emphasizing the insight that simplified instructions that "do less" may still provide for higher performance if this simplicity can be utilized to make instructions execute very quickly. Many proposals for a "precise" definition have been – a CPU design philosophy that favors an instruction set reduced both in size and complexity of addressing modes, in order to enable easier implementation, greater instruction level parallelism, and more efficient compilers
Pure mathematics and statistics
- Reduction (mathematics) In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the – the rewriting of an expression into a simpler form
- Beta reduction In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. It was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s as part of an investigation into the foundations of mathematics, but has emerged as a useful tool in the – the rewriting of an expression from lambda calculus into a simpler form
- Dimension reduction In statistics, dimension reduction is the process of reducing the number of random variables under consideration, and can be divided into feature selection and feature extraction. In physics, dimension reduction is a widely discussed phenomenon, whereby a physical system exists in three dimensions, but its properties behave like those of a lower- – the process of reducing the number of random variables under consideration
- Lattice reduction In mathematics, the goal of lattice basis reduction is given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice – given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors
- Reduction of order Reduction of order is a technique in mathematics for solving second-order ordinary differential equations. It is employed when one solution y1 is known and a second linearly independent solution y2(x) is desired – a technique for solving second-order ordinary differential equations
- Relation reduction In logic and mathematics, relation reduction and relational reducibility have to do with the extent to which a given relation is determined by an indexed family or a sequence of other relations, called the relation dataset. The relation under examination is called the reductandum. The relation dataset typically consists of a specified relation – the extent to which a given relation is determined by an indexed family or a sequence of other relations, called the relation dataset
- Reduction of the structure group In mathematics, in particular the theory of principal bundles, one can ask if a G-bundle "comes from" a subgroup H < G. This is called reduction of the structure group , and makes sense for any map , which need not be an inclusion (despite the terminology) – for a G-bundle B and a map an H-bundle BH such that the pushout is isomorphic to B
- Reduction system Examples of reduction systems include string rewriting systems, term rewriting systems, lambda calculus under lambda conversion, and combinatory reduction systems, reduction strategy In code optimization during the translation of computer programs into an executable form, and in mathematical reduction generally, a reduction strategy for a term rewriting system determines which reducible subterms should be reduced (contracted) within a term; it may be the case that a term may contain multiple redexes which are disjoint from one, the application of rewriting systems to eliminate reducible expressions.
- Reduced form In statistics, and particularly in econometrics, the reduced form of a system of equations is the result of solving the system for the endogenous variables. This gives the latter as a function of the exogenous variables, if any – in statistics, an equation which relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest (W) and the instruments (Z)
- Reduced ring In ring theory, a commutative ring R is called a reduced ring if it has no non-zero nilpotent elements. A commutative algebra over a commutative ring is called a reduced algebra if its underlying ring is reduced – a ring with no non-zero nilpotent elements
- Reduced residue system A reduced residue system modulo n is a set of φ integers such that each integer is relatively prime to n and no two are congruent modulo n. Here φ denotes Euler's totient function – a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n
- Reduced product – a construction that generalizes both direct product and ultraproduct
- Reduced word In group theory, a word is any written product of group elements and their inverses. For example, if x, y, and z are elements of a group G, then xy, z-1xzz, and y-1zxx-1yz-1 are words in the set {x, y, z}. Words play an important role in the theory of free groups and presentations, and are central objects of study in combinatorial group theory – in a free group, a word with no adjacent generator-inverse pairs
- Reduced homology In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero. This change is required to make statements without some number of exceptional cases – a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero
- Reduced row echelon form Every non-zero matrix can be reduced to an infinite number of echelon forms via elementary matrix transformations. However, all matrices and their row echelon forms correspond to exactly one matrix in reduced row echelon form – a certain reduced row echelon form of a matrix which completely and uniquely determines its row space
Physics
Technology
Philosophy
- Reduction (philosophy) Reduction is the process by which one object, property, concept, theory, etc., is shown to be explicable in terms of another, lower level, concept, object, property, etc. For example, we say that chemical properties such as the boiling point of a substance are reducible to that substance’s atomic properties, because we are able to explain why a – the process by which one object, property, concept, theory, etc., is shown to be entirely dispensable in favor of another
- Intertheoretic reduction – in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory
- Eidetic reduction Eidetic reduction is a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena. Eidetic reduction requires that a phenomenologist examine the essence of a mental object, be it a simple mental act, or the unity of consciousnes itself, with the intention of drawing out the absolutely necessary – a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena
Medicine
- Weight loss Weight loss, in the context of medicine, health or physical fitness, is a reduction of the total body weight, due to a mean loss of fluid, body fat or adipose tissue and/or lean mass, namely bone mineral deposits, muscle, tendon and other connective tissue. It can occur unintentionally due to an underlying disease or can arise from a conscious
- Selective reduction Selective reduction is the practice of reducing the number of fetuses in a multifetal pregnancy (those involving more than one fetus). With selective reduction, one or more fetuses are "selected" for termination. This procedure is often performed after a congenital defect has been identified. Prenatal diagnostic testing may be used to – (or fetal reduction), the practice of reducing the number of fetuses in a multifetal pregnancy
- Reduction (orthopedic surgery) – a medical procedure to restore a fracture or dislocation to the correct alignment.
- Ventricular reduction Ventricular reduction is a type of operation in cardiac surgery to reduce enlargement of the heart from cardiomyopathy or ischemic aneurysm formation – a type of operation in cardiac surgery
- Urea reduction ratio The urea reduction ratio , is a dimensionless number used to quantify hemodialysis treatment adequacy – (URR), a dimensionless number used to quantify hemodialysis treatment adequacy
Cosmetic surgery
Epidemiology
Linguistics
- Accent reduction Accent reduction, also known as accent modification, is a systematic approach used to learn or adopt a new accent. It is the process of learning the sound system of a language or dialect. The methodology involves several steps, which include identifying deviations in the person's current speech from the desired accent (such as pronunciation, – modifying one's foreign accent towards that of a native speaker
- Vowel reduction Vowel reduction is the term in phonetics that refers to various changes in the acoustic quality of vowels , which are related to changes in stress, sonority, duration, loudness, articulation, or position in the word , and which are perceived as "weakening". It most often makes the vowels shorter as well – any change in vowel quality perceived as "weakening"
- Relaxed pronunciation Relaxed pronunciation is a phenomenon that happens when the syllables of common words are slurred together. It is almost always present in normal speech, in all natural languages (not in some constructed languages such as Loglan or Lojban, which are designed so that all words are parsable) – slurring of syllables of common words
- Definite article reduction – use of vowel-less forms of the English definite article in Northern England
Politics and social policy
History
Other
- Reduction (cooking) – the process of thickening or intensifying the flavor of a liquid mixture such as a soup, sauce, wine, or juice by evaporation
- Reduction to practice – in United States patent law, the embodiment of the concept of an invention
- Reduction in rank – military law
- Piano reduction – sheet music for the piano that was once music for other instruments that was reduced to its most basic components within a two line staff for piano
- Ego reduction – predicated on the use of Sigmund Freud's concept of the ego
See also
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