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Neural network software is used to simulate, research, develop, and apply artificial neural networks, software concepts adapted from biological neural networks, and in some cases, a wider array of adaptive systems such as artificial intelligence and machine learning.
## Simulators
Neural network simulators are software... | https://en.wikipedia.org/wiki/Neural_network_software |
Cheney's algorithm, first described in a 1970 ACM paper by C.J. Cheney, is a stop and copy method of tracing garbage collection in computer software systems. In this scheme, the heap is divided into two equal halves, only one of which is in use at any one time. Garbage collection is performed by copying live objects fr... | https://en.wikipedia.org/wiki/Cheney%27s_algorithm |
In computer science, formal specifications are mathematically based techniques whose purpose is to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning ... | https://en.wikipedia.org/wiki/Formal_specification |
In physics, a mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a material medium.
(Vacuum is, from classical perspective, a non-material medium, where electromagnetic waves propagate.)
While waves can move over long distances, the movement of the medium of transmissio... | https://en.wikipedia.org/wiki/Mechanical_wave |
The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch ... | https://en.wikipedia.org/wiki/Doppler_effect |
In computer science, parallel tree contraction is a broadly applicable technique for the parallel solution of a large number of tree problems, and is used as an algorithm design technique for the design of a large number of parallel graph algorithms. Parallel tree contraction was introduced by Gary L. Miller and John ... | https://en.wikipedia.org/wiki/Tree_contraction |
In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and m... | https://en.wikipedia.org/wiki/Particle |
A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or magnetic field. It is an arbitrary closed surface (the boundary of a 3-dimensional region ) used in conjunction with Gauss's law for the correspo... | https://en.wikipedia.org/wiki/Gaussian_surface |
In mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if
$$
T\colon V \to V
$$
is a linear operator on any finite-dimensional vector space, its spectrum is the set of scalars
$$
\lambda
$$
such that
$$
T-\lambda I
$$
is not invertible. The determinant of the matrix equals the pr... | https://en.wikipedia.org/wiki/Spectrum_of_a_matrix |
Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of physics used to describe the spectrum of thermal radiation (frequently called the blackbody function). This law was first derived by Wilhelm Wien in 1896. The equation does accurately describe the short-wavelength (high-f... | https://en.wikipedia.org/wiki/Wien_approximation |
In computer science, a suffix automaton is an efficient data structure for representing the substring index of a given string which allows the storage, processing, and retrieval of compressed information about all its substrings. The suffix automaton of a string
$$
S
$$
is the smallest directed acyclic graph with a d... | https://en.wikipedia.org/wiki/Suffix_automaton |
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scal... | https://en.wikipedia.org/wiki/Experiment |
A think-aloud (or thinking aloud) protocol is a method used to gather data in usability testing in product design and development, in psychology and a range of social sciences (e.g., reading, writing, translation research, decision making, and process tracing).
## Description
Think-aloud protocols involve participants... | https://en.wikipedia.org/wiki/Think_aloud_protocol |
Ponto-geniculo-occipital waves or PGO waves are distinctive wave forms of propagating activity between three key brain regions: the pons, lateral geniculate nucleus, and occipital lobe; specifically, they are phasic field potentials. These waves can be recorded from any of these three structures during and immediately ... | https://en.wikipedia.org/wiki/PGO_waves |
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected... | https://en.wikipedia.org/wiki/Problem_of_points |
In mathematics, the inverse scattering transform is a method that solves the initial value problem for a nonlinear partial differential equation using mathematical methods related to wave scattering. The direct scattering transform describes how a function scatters waves or generates bound-states. The inverse scatter... | https://en.wikipedia.org/wiki/Inverse_scattering_transform |
In computer science, rate-monotonic scheduling (RMS) is a priority assignment algorithm used in real-time operating systems (RTOS) with a static-priority scheduling class. The static priorities are assigned according to the cycle duration of the job, so a shorter cycle duration results in a higher job priority.
These o... | https://en.wikipedia.org/wiki/Rate-monotonic_scheduling |
A processor register is a quickly accessible location available to a computer's processor. Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms ... | https://en.wikipedia.org/wiki/Processor_register |
In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is:
$$
(U-c) (\varphi - k^2 \varphi) - U \varphi=0,
$$
with
$$
U(z)
$$
the flow velocity of the stead... | https://en.wikipedia.org/wiki/Rayleigh%27s_equation_%28fluid_dynamics%29 |
In probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind) is an absolutely continuous probability distribution. If
$$
p\in[0,1]
$$
has a beta distribution, then the odds
$$
\frac{p}{1-p}
$$
has a beta prime distribution.
## D... | https://en.wikipedia.org/wiki/Beta_prime_distribution |
The hash join is an example of a join algorithm and is used in the implementation of a relational database management system. All variants of hash join algorithms involve building hash tables from the tuples of one or both of the joined relations, and subsequently probing those tables so that only tuples with the same ... | https://en.wikipedia.org/wiki/Hash_join |
Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequencies between 300 MHz and 300 GHz, broadly construed.Pozar, David M. (1993). Microwave Engineering Addison... | https://en.wikipedia.org/wiki/Microwave |
In mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the Galois group. The normal basis theorem states that any finite Galois extension of fields has a normal basis. In algebraic number... | https://en.wikipedia.org/wiki/Normal_basis |
In complex geometry, a Hopf surface is a compact complex surface obtained as a quotient of the complex vector space (with zero deleted)
$$
\Complex^2\setminus \{0\}
$$
by a free action of a discrete group. If this group is the integers the Hopf surface is called primary, otherwise it is called secondary. (Some author... | https://en.wikipedia.org/wiki/Hopf_surface |
Pulmonary embolism (PE) is a blockage of an artery in the lungs by a substance that has moved from elsewhere in the body through the bloodstream (embolism). Symptoms of a PE may include shortness of breath, chest pain particularly upon breathing in, and coughing up blood. Symptoms of a blood clot in the leg may also be... | https://en.wikipedia.org/wiki/Pulmonary_embolism |
Proof of work (also written as proof-of-work, an abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their... | https://en.wikipedia.org/wiki/Proof_of_work |
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the co... | https://en.wikipedia.org/wiki/Electric_current |
In game theory, the battle of the sexes is a two-player coordination game that also involves elements of conflict. The game was introduced in 1957 by R. Duncan Luce and Howard Raiffa in their classic book, Games and Decisions. Some authors prefer to avoid assigning sexes to the players and instead use Players 1 and 2, ... | https://en.wikipedia.org/wiki/Battle_of_the_sexes_%28game_theory%29 |
In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula
$$
\operatorname{\text{Ш}}_{\ T}(t) \ := \sum_{k=-\infty}^{\infty} \delta(t - k T)
$$
for some given period
$$
T
$$
. Here t is a real variable and the sum extends over all integers k.... | https://en.wikipedia.org/wiki/Dirac_comb |
In complex analysis, the open mapping theorem states that if
$$
U
$$
is a domain of the complex plane
$$
\mathbb{C}
$$
and
$$
f: U\to \mathbb{C}
$$
is a non-constant holomorphic function, then
$$
f
$$
is an open map (i.e. it sends open subsets of
$$
U
$$
to open subsets of
$$
\mathbb{C}
$$
, and we have inva... | https://en.wikipedia.org/wiki/Open_mapping_theorem_%28complex_analysis%29 |
In mathematics, a differentiable manifold
$$
M
$$
of dimension n is called parallelizable if there exist smooth vector fields
$$
\{V_1, \ldots,V_n\}
$$
on the manifold, such that at every point
$$
p
$$
of
$$
M
$$
the tangent vectors
$$
\{V_1(p), \ldots, V_n(p)\}
$$
provide a basis of the tangent space at
$$
p
$$... | https://en.wikipedia.org/wiki/Parallelizable_manifold |
In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are not isomorphic to it. Such objects are always algebraic surfaces of general type.
## History
Severi asked if there was a complex surface homeomorphic... | https://en.wikipedia.org/wiki/Fake_projective_plane |
In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space. Exit times and return times are also examples of hitting times.
## Definitions
Let be an ordered index set such as the natural numbers, the non-n... | https://en.wikipedia.org/wiki/Hitting_time |
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.
The five color theorem is implied by the str... | https://en.wikipedia.org/wiki/Five_color_theorem |
In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales, and its opposite, the category Frm of frames. Although these three categorie... | https://en.wikipedia.org/wiki/Complete_Heyting_algebra |
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.
Because it is space-filling, its Hausdorff dimension is 2 ... | https://en.wikipedia.org/wiki/Hilbert_curve |
In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, as, for example, mo... | https://en.wikipedia.org/wiki/Log-logistic_distribution |
In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization. Twofish is related to the earlier block cipher Blowfish.
Twofish's distinctive f... | https://en.wikipedia.org/wiki/Twofish |
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, ... | https://en.wikipedia.org/wiki/Cutting-plane_method |
A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increa... | https://en.wikipedia.org/wiki/Hydraulic_jump |
In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product . This is commonly phrased as "a relation on X" or "a (binary) relation over X". An example of a homogeneous relation is the relation of kinship, where the... | https://en.wikipedia.org/wiki/Homogeneous_relation |
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy.
The diffraction pattern resulting from a uniformly ill... | https://en.wikipedia.org/wiki/Airy_disk |
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. However, it turns out that for a large class of semi-elliptic second-order ... | https://en.wikipedia.org/wiki/Stochastic_processes_and_boundary_value_problems |
The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.
This distribution has neither a probability density function nor a probability mass function, since although its cumulative distribution function is a continuous function, the distribution is not absol... | https://en.wikipedia.org/wiki/Cantor_distribution |
In order theory, a branch of mathematics, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another. Like Galois connections, order embeddings constitute a notion which is strictly weaker than the concept of an order isomorphism. Both of these weak... | https://en.wikipedia.org/wiki/Order_embedding |
Banker's algorithm is a resource allocation and deadlock avoidance algorithm developed by Edsger Dijkstra that tests for safety by simulating the allocation of predetermined maximum possible amounts of all resources, and then makes an "s-state" check to test for possible deadlock conditions for all other pending activi... | https://en.wikipedia.org/wiki/Banker%27s_algorithm |
Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of... | https://en.wikipedia.org/wiki/Thermodynamic_equilibrium |
A bookmaker, bookie, or turf accountant is an organization or a person that accepts and pays out bets on sporting and other events at agreed-upon odds.
## History
The first bookmaker, Harry Ogden, stood at Newmarket in 1795, although similar activities had existed in other forms earlier in the eighteenth century.Vample... | https://en.wikipedia.org/wiki/Bookmaker |
Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound (or sound in general) through an ultrasonic grating.
## Introduction
In general, acousto-optic effects are based on the change of the refractive index of a med... | https://en.wikipedia.org/wiki/Acousto-optics |
In game theory, "guess of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to of the average of numbers chosen by all players.
## History
Alain Ledoux is the founding father of the "guess of the ... | https://en.wikipedia.org/wiki/Guess_2%2F3_of_the_average |
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery ... | https://en.wikipedia.org/wiki/Distributive_lattice |
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.
## Example
This is perhaps most readily understood by ... | https://en.wikipedia.org/wiki/Rankit |
The Smith chart (sometimes also called Smith diagram, Mizuhashi chart (), Mizuhashi–Smith chart (), Volpert–Smith chart () or Mizuhashi–Volpert–Smith chart) is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving probl... | https://en.wikipedia.org/wiki/Smith_chart |
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to represen... | https://en.wikipedia.org/wiki/Fixed-point_arithmetic |
In the mathematical subject of geometric group theory, a
### Dehn function
, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms... | https://en.wikipedia.org/wiki/Dehn_function |
In mechanics, strain is defined as relative deformation, compared to a position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual... | https://en.wikipedia.org/wiki/Strain_%28mechanics%29 |
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is similar, but deals with the electronics side of aerospace engineering.
"Aerona... | https://en.wikipedia.org/wiki/Aerospace_engineering |
A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves can all be in the form of Bessel beams. A true Bessel beam is non-diffractive. This means that as it propagates, it does not diffract and spread out; this is in contras... | https://en.wikipedia.org/wiki/Bessel_beam |
In computer science, the segment tree is a data structure used for storing information about intervals or segments. It allows querying which of the stored segments contain a given point. A similar data structure is the interval tree.
A segment tree for a set of n intervals uses O(n log n) storage and can be built in O... | https://en.wikipedia.org/wiki/Segment_tree |
In telecommunications, a carrier wave, carrier signal, or just carrier, is a periodic waveform (usually sinusoidal) that conveys information through a process called modulation. One or more of the wave's properties, such as amplitude or frequency, are modified by an information bearing signal, called the message signal... | https://en.wikipedia.org/wiki/Carrier_wave |
The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita connection or Riemannian connection of the given metric. Because it is canonically defined by such ... | https://en.wikipedia.org/wiki/Fundamental_theorem_of_Riemannian_geometry |
A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people... | https://en.wikipedia.org/wiki/Machine |
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivi... | https://en.wikipedia.org/wiki/Permittivity |
The Tower of Hanoi (also called The problem of Benares Temple, Tower of Brahma or Lucas' Tower, and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the dis... | https://en.wikipedia.org/wiki/Tower_of_Hanoi |
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form
$$
x^2\equiv n \pmod{p},
$$
where
$$
x,n \in \mathbf{F}_{p}
$$
, so n is the square of x, and where
$$
p
$$
is an odd prime. Here
$$
\mathbf{F}_p
$$
denotes the finite field with
$$
p
$$
elements;
$$
\{0,1,\d... | https://en.wikipedia.org/wiki/Cipolla%27s_algorithm |
In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used ... | https://en.wikipedia.org/wiki/Transfinite_number |
In mathematics, Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940.
Two matrices A and B with complex number entries are said to be unitarily equivalent if there exists a unitary matrix U such ... | https://en.wikipedia.org/wiki/Specht%27s_theorem |
In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The theorem was developed by topologists Samuel Eilenberg and Saunders MacLane. They discovered that, when topologists were writing proofs to establish equivalence of variou... | https://en.wikipedia.org/wiki/Acyclic_model |
In mathematics, the composition operator
$$
\circ
$$
takes two functions,
$$
f
$$
and
$$
g
$$
, and returns a new function
$$
h(x) := (g \circ f) (x) = g(f(x))
$$
. Thus, the function is applied after applying to .
$$
(g \circ f)
$$
is pronounced "the composition of and ".
Reverse composition, sometimes deno... | https://en.wikipedia.org/wiki/Function_composition |
(Main list of acronyms)
__NOTOC__
- W
- (s) Tungsten (from German Wolfram)
- (i) Watt
- (i) Wednesday
- (i) West
- (i) Games Won in sporting competitions
## W0–9
- W3C – (i) World Wide Web Consortium
- w/ – (p) With: Software w/Documentation. Typically used in advertising or to abbreviate headings. Never use... | https://en.wikipedia.org/wiki/List_of_acronyms%3A_W |
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e. a semi-ellipse, centered at (0, 0):
$$
f(x)={2 \over \pi R^2}\sqrt{R^2-x^2\,}\,
$$
for −R ≤ x ≤ R, and f(x) = 0 if ... | https://en.wikipedia.org/wiki/Wigner_semicircle_distribution |
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P waves may be transmitted through gas... | https://en.wikipedia.org/wiki/P_wave |
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.
The goal is to compute
$$
\gamma
$$
such that
$$
\alpha ^ \gamma = \beta
$$
, where
$$
\beta
$$
belongs... | https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm_for_logarithms |
The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973,Richard Guy, John Horto... | https://en.wikipedia.org/wiki/Doomsday_rule |
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula or a mathematical expression. More formally, a mathematical symbol is an... | https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols |
Business cycles are intervals of general expansion followed by recession in economic performance. The changes in economic activity that characterize business cycles have important implications for the welfare of the general population, government institutions, and private sector firms.
There are many definitions of a ... | https://en.wikipedia.org/wiki/Business_cycle |
A branch, jump or transfer is an instruction in a computer program that can cause a computer to begin executing a different instruction sequence and thus deviate from its default behavior of executing instructions in order. Branch (or branching, branched) may also refer to the act of switching execution to a different... | https://en.wikipedia.org/wiki/Branch_%28computer_science%29 |
In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a go... | https://en.wikipedia.org/wiki/Tomita%E2%80%93Takesaki_theory |
Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Re... | https://en.wikipedia.org/wiki/Princeton_University |
In game theory, the traveler's dilemma (sometimes abbreviated TD) is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surpri... | https://en.wikipedia.org/wiki/Traveler%27s_dilemma |
, or , is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. One example of a polarized transverse wave is vibrations traveling along a taut string, for example,... | https://en.wikipedia.org/wiki/Polarization_%28waves%29 |
Adaptive Huffman coding (also called Dynamic Huffman coding) is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.
The be... | https://en.wikipedia.org/wiki/Adaptive_Huffman_coding |
In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables.
## Definition
The probability density function for the random matrix X (n × p) that follows the matrix normal d... | https://en.wikipedia.org/wiki/Matrix_normal_distribution |
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.
The size of the largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (t... | https://en.wikipedia.org/wiki/Antichain |
In the studies of Fourier optics, sound synthesis, stellar interferometry, optical tweezers, and diffractive optical elements (DOEs) it is often important to know the spatial frequency phase of an observed wave source. In order to reconstruct this phase the Adaptive-Additive
### Algorithm
(or AA algorithm), which der... | https://en.wikipedia.org/wiki/Adaptive-additive_algorithm |
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs. Magnitude as a ... | https://en.wikipedia.org/wiki/Magnitude_%28mathematics%29 |
In engineering, a factor of safety (FoS) or safety factor (SF) expresses how much stronger a system is than it needs to be for its specified maximum load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the str... | https://en.wikipedia.org/wiki/Factor_of_safety |
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of ... | https://en.wikipedia.org/wiki/Strength_of_materials |
In physics, Landau damping, named after its discoverer, Soviet physicist Lev Davidovich Landau (1908–68), is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a re... | https://en.wikipedia.org/wiki/Landau_damping |
In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel's lemma holds. They were introduced by , who named them after Kurt Hensel. Azumaya originally allowed Henselian rings to be non-commutative, but most authors now restrict them to be commutative.
Some standard references for Hensel rings ... | https://en.wikipedia.org/wiki/Henselian_ring |
In computer science, Ukkonen's algorithm is a linear-time, online algorithm for constructing suffix trees, proposed by Esko Ukkonen in 1995. The algorithm begins with an implicit suffix tree containing the first character of the string. Then it steps through the string, adding successive characters until the tree is co... | https://en.wikipedia.org/wiki/Ukkonen%27s_algorithm |
Parimutuel betting, or pool betting, is a betting system in which all bets of a particular type are placed together in a pool; taxes and the house-take, or vigorish, are deducted, and payoff odds are calculated by sharing the pool among all winning bets. In some countries it is known as the tote after the totalisator, ... | https://en.wikipedia.org/wiki/Parimutuel_betting |
In mathematics, the base change theorems relate the direct image and the inverse image of sheaves. More precisely, they are about the base change map, given by the following natural transformation of sheaves:
$$
g^*(R^r f_* \mathcal{F}) \to R^r f'_*(g'^*\mathcal{F})
$$
where
$$
\begin{array}{rcl} X' & \stackrel{g'}\to ... | https://en.wikipedia.org/wiki/Base_change_theorems |
Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two al... | https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem |
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at a point in space represents a probability density at that point.
Probability amplitudes provide a relationship between the quantum state vector of a system and th... | https://en.wikipedia.org/wiki/Probability_amplitude |
In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the systems initial state, slowing a systems time evolution.
Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuri... | https://en.wikipedia.org/wiki/Quantum_Zeno_effect |
A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The ... | https://en.wikipedia.org/wiki/Phase-type_distribution |
In computer science, a perfect hash function for a set is a hash function that maps distinct elements in to a set of integers, with no collisions. In mathematical terms, it is an injective function.
Perfect hash functions may be used to implement a lookup table with constant worst-case access time. A perfect hash f... | https://en.wikipedia.org/wiki/Perfect_hash_function |
A scalar is an element of a field which is used to define a vector space.
In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multipl... | https://en.wikipedia.org/wiki/Scalar_%28mathematics%29 |
An absorption wavemeter is a simple electronic instrument used to measure the frequency of radio waves. It is an older method of measuring frequency, widely used from the birth of radio in the early 20th century until the 1970s, when the development of inexpensive frequency counters, which have far greater accuracy, m... | https://en.wikipedia.org/wiki/Absorption_wavemeter |
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