Reduction

Reduction is generally the process of reducing something, i.e. making it smaller or lesser in some way.

Reduction, reduced, reduce, or similar 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, a redox reaction that takes place with organic compounds
- Ore reduction: see smelting

Computing and mathematics

Reducible as the opposite of irreducible (mathematics)
Reduction (mathematics), the rewriting of an expression into a simpler form
Reduction (complexity), a transformation of one problem into another problem

Data science and array processing

Data reduction, simplifying data in order to facilitate analysis
Reduce (higher-order function), in functional programming, a family of higher-order functions that process a data structure in some order and build up a return value
Reduction operator, a type of operator that is commonly used in parallel programming to reduce the elements of an array into a single result.
Dimension reduction, the process of reducing the number of random variables under consideration
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 row echelon form, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space
Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations

Model theory, abstract algebra, and geometry

Partial order reduction, a technique for reducing the size of the state-space to be searched by a model checking algorithm
Lattice reduction, given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors
Reduction of the structure group, for a $G$ -bundle $B$ and a map $H\to G$ an $H$ -bundle $B_{H}$ such that the pushout $B_{H}\times _{H}G$ is isomorphic to $B$
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 ring, a ring with no non-zero nilpotent elements
Reduced word, in a free group, a word with no adjacent generator-inverse pairs

Other uses in computer science theory

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?
Graph reduction, an efficient version of non-strict evaluation
L-reduction, a transformation of optimization problems which keeps the approximability features
Strength reduction, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
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
Beta reduction, the rewriting of an expression from lambda calculus into a simpler form
Subject reduction or preservation, a rewrite of an expression that does not change its type
Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions

Other uses in computing and mathematics

Bit Rate Reduction, an audio compression method
Reduce (computer algebra system), a general-purpose computer algebra system geared towards applications in physics
Reduction of order, a technique for solving second-order ordinary differential equations
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

Medicine

Medical procedures

Lung volume reduction surgery, a treatment for chronic obstructive pulmonary disease
Selective reduction (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, a type of operation in cardiac surgery
Cosmetic surgery:
- Breast reduction
- Jaw reduction

Other uses in medicine

Weight loss
In epidemiology:
- Relative risk reduction, the absolute risk reduction by the control event rate
- Absolute risk reduction, 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, the limit of a compactified theory where the size of the compact dimension goes to zero
Reduction criterion, 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 (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, 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), music arranged for smaller resources (piano) for easier analysis or performance

Linguistics

Accent reduction, modifying one's foreign accent towards that of a native speaker
Vowel reduction, any change in vowel quality perceived as "weakening"
- Vowel reduction in English
Definite article reduction, use of vowel-less forms of the English definite article in Northern England

Philosophy

Reductionism, 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, a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena
Bracketing (phenomenology), also known as phenomenological reduction or transcendental reduction
Intertheoretic reduction, in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory

Military and politics

Reduction in rank, in military law
Reduction (military), the siege and capture of a fortified place
Reductions, resettlements of indigenous peoples in Spanish-colonized America intended to control and Christianize Indians
- Indian reductions in the Andes, settlements in the Andes to control and Christianize Indians
Reduction (Sweden), a return to the Crown of fiefs that had been granted to the Swedish nobility

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
Reduce (waste), practices of minimizing waste
Reduction, Pennsylvania, unincorporated community, United States
Reduction to practice, in United States patent law, the embodiment of the concept of an invention
Ego reduction, predicated on the use of Sigmund Freud's concept of the ego

Reduction

Science and technology

Chemistry

Computing and mathematics

Data science and array processing

Model theory, abstract algebra, and geometry

Other uses in computer science theory

Other uses in computing and mathematics

Medicine

Medical procedures

Other uses in medicine

Physics

Other uses in science and technology

Arts and media

Linguistics

Philosophy

Military and politics

Other uses

See also