Reduction, reduced, or reduce may refer to:

Science and technology

Chemistry

* Reduction (chemistry), part of a reduction-oxidation (redox) reaction in which atoms have their oxidation state changed. **

Organic redox reaction Organic reductions or organic oxidations or organic redox reactions are redox reactions that take place with organic compounds. In organic chemistry oxidations and reductions are different from ordinary redox reactions, because many reactions carr ...

, a redox reaction that takes place with organic compounds ** Ore reduction: see

smelting Smelting is a process of applying heat to ore, to extract a base metal. It is a form of extractive metallurgy. It is used to extract many metals from their ores, including silver, iron, copper, and other base metals. Smelting uses heat and a ch ...

Computing and algorithms

* Reduction (complexity), a transformation of one problem into another problem *

Reduction (recursion theory) In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated by the question: given sets A and B of natural numbers, is it possible to effectively conver ...

, 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? *

Bit Rate Reduction Bit Rate Reduction, or BRR, also called Bit Rate Reduced, is a name given to an audio data compression, audio compression method used on the SPC700 sound coprocessor used in the Super Nintendo Entertainment System, SNES, as well as the audio proces ...

, an audio compression method *

Data reduction Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimental data, experimentally into a corrected, ordered, and simplified form. The purpose of data reduction can be two-fold: reduce the ...

, simplifying data in order to facilitate analysis *

Graph reduction In computer science, graph reduction implements an efficient version of non-strict evaluation, an evaluation strategy where the arguments to a function are not immediately evaluated. This form of non-strict evaluation is also known as lazy evaluati ...

, an efficient version of non-strict evaluation *

L-reduction In computer science, particularly the study of approximation algorithms, an L-reduction ("''linear reduction''") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserv ...

, a transformation of optimization problems which keeps the approximability features *

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 or automated planning and scheduling algorithm. It exploits the commutativity of concurrently executed transitio ...

, a technique for reducing the size of the state-space to be searched by a model checking algorithm * Strength reduction, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function * Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations *

Reduce (computer algebra system) Reduce is a general-purpose computer algebra system geared towards applications in physics. The development of the Reduce computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world ha ...

, a general-purpose computer algebra system geared towards applications in physics *

Reduce (higher-order function) In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the resu ...

, 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 computing, a CPU design philosophy favoring an instruction set reduced in size and complexity of addressing, to simplify implementation, instruction level parallelism, and compiling

Pure mathematics and statistics

* Reducible as the opposite of irreducible (mathematics) * Reduction (mathematics), the rewriting of an expression into a simpler form * Beta reduction, the rewriting of an expression from lambda calculus into a simpler form * Dimension reduction, the process of reducing the number of random variables under consideration * Lattice reduction, given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors *

Subject reduction In type theory, a type system has the property of subject reduction (also subject evaluation, type preservation or simply preservation) if evaluation of expressions does not cause their type to change. Formally, if Γ ⊢ ''e''1 : ''τ'' and ''e''1 ...

or preservation, a rewrite of an expression that does not change its type * Reduction of order, a technique for solving second-order ordinary differential equations * Reduction of the structure group, for a

G

-bundle

B

and a map

H \to G

H

-bundle

B_H

such that the pushout

B_H \times_H G

is isomorphic to

B

* Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions * Reduced form, 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 homology, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero * Reduced product, a construction that generalizes both direct product and ultraproduct * Reduced residue system, a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n * Reduced ring, a ring with no non-zero nilpotent elements *

Reduced row echelon form In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination. A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and column echelon form means that Gaussian el ...

, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space * Reduced word, in a free group, a word with no adjacent generator-inverse pairs

Medicine

Medical procedures

* Lung volume reduction surgery, a treatment for chronic obstructive pulmonary disease *

Selective reduction Selective reduction is the practice of reducing the number of fetuses in a multiple pregnancy, such as quadruplets, to a twin or singleton pregnancy. The procedure is also called multifetal pregnancy reduction. The procedure is most commonly don ...

(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 Ventriculectomy, or ventricular reduction, is a type of operation in cardiac surgery to reduce enlargement of the heart from cardiomyopathy or ischemic aneurysm formation. In these procedures, part of the ventricular wall is resected.A Batista proc ...

, a type of operation in cardiac surgery * Cosmetic surgery: ** Breast reduction ** Jaw reduction

Other uses in medicine

Weight loss Weight loss, in the context of medicine, health, or physical fitness, refers to a reduction of the total body mass, by a mean loss of fluid, body fat (adipose tissue), or lean mass (namely bone mineral deposits, muscle, tendon, and other conn ...

* In epidemiology: **

Relative risk reduction In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an unexposed group. It is computed as (I_u - I_e) / I_u, where I_e is the incidence in the expo ...

, the absolute risk reduction by the control event rate **

Absolute risk reduction The risk difference (RD), excess risk, or attributable risk is the difference between the risk of an outcome in the exposed group and the unexposed group. It is computed as I_e - I_u, where I_eis the incidence in the exposed group, and I_u is the ...

, the decrease in risk of a given activity or treatment in relation to a control activity or treatment * Urea reduction ratio (URR), a dimensionless number used to quantify hemodialysis treatment adequacy

Physics

Dimensional reduction Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in ''D'' spacetime dimensions can be redefined in a lower number of dimensions ''d'', by taking all the fields ...

, the limit of a compactified theory where the size of the compact dimension goes to zero *

Reduction criterion In quantum information theory, the reduction criterion is a necessary condition a mixed state must satisfy in order for it to be separable. In other words, the reduction criterion is a ''separability criterion''. It was first proved and independe ...

, in quantum information theory, a necessary condition a mixed state must satisfy in order for it to be separable * Reduced mass, the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics *

Reduced properties In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility facto ...

(pressure, temperature, or volume) of a fluid, defined based on the fluid's critical point

Other uses in science and technology

* Lithic reduction, in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone *

Noise reduction Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an und ...

, in acoustic or signal processing * Reduction drive, a mechanical device to shift rotational speed

Arts and media

* ''Reducing'' (film), a 1931 American film *

Reduction (music) In music, a reduction is an arrangement or transcription of an existing score or composition in which complexity is lessened to make analysis, performance, or practice easier or clearer; the number of parts may be reduced or rhythm may be s ...

, music arranged for smaller resources (piano) for easier analysis or performance

Linguistics

Accent reduction Accent reduction, also known as accent modification or accent neutralization, is a systematic approach for learning or adopting a new speech Accent (dialect), accent. It is the process of learning the sound system (or phonology) and melodic inton ...

, modifying one's foreign accent towards that of a native speaker *

Vowel reduction In phonetics, vowel reduction is any of various changes in the acoustic ''quality'' of vowels as a result of changes in stress, sonority, duration, loudness, articulation, or position in the word (e.g. for the Creek language The Muscogee lang ...

, any change in vowel quality perceived as "weakening" **

Vowel reduction in English Stress is a prominent feature of the English language, both at the level of the word ''(lexical stress)'' and at the level of the phrase or sentence ''(prosodic stress)''. Absence of stress on a syllable, or on a word in some cases, is frequently ...

* Relaxed pronunciation, slurring of syllables of common words *

Definite article reduction Definite article reduction (DAR) is the term used in recent linguistic work to refer to the use of vowel-less forms of the definite article ''the'' in Northern dialects of English English, for example in the Yorkshire dialect. DAR is often represen ...

, use of vowel-less forms of the English definite article in Northern England

Philosophy

Reductionism Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical pos ...

, a range of philosophical systems * Reductio ad absurdum, a form of argument in which a proposition is disproven by following its implications to an absurd consequence *

Eidetic reduction Eidetic reduction is a technique in the study of essences in Edmund Husserl's 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 technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena *

Intertheoretic reduction In philosophy of science, intertheoretic reduction occurs when a reducing theory makes predictions that perfectly or almost perfectly match the predictions of a reduced theory, while the reducing theory explains or predicts a wider range of phenom ...

, in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory

Settlements

Reductions Reductions ( es, reducciones, also called ; , pl. ) were settlements created by Spanish rulers and Roman Catholic missionaries in Spanish America and the Spanish East Indies (the Philippines). In Portuguese-speaking Latin America, such redu ...

, settlements in Spanish America intended to control and Christianize Indians * Indian reductions in the Andes, settlements in the Andes to control and Christianize Indians

Other uses

* 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 (military) A reduction, in military tactics, is accomplished when an encircling force conducts successful offensive operations over an invested force. The "reduction" refers to the shrinking in size of the pocket of territory occupied by the invested force, ...

, the siege and capture of a fortified place * Reduction (Sweden), a return to the Crown of fiefs that had been granted to the Swedish nobility * Reduce (waste), practices of minimizing waste * Reduction, Pennsylvania, unincorporated community, United States * Reduction in rank, in military law * Reduction to practice, in United States patent law, the embodiment of the concept of an invention *

Ego reduction The concept of ego reduction is predicated on the use of Sigmund Freud's concept of the ego to describe the conscious adult self; and broadly describes the deflating of an over-inflated or egotistical sense of oneself - a curtailment of what Iris M ...

, predicated on the use of Sigmund Freud's concept of the ego