Computer vision is a field that includes methods for acquiring, processing, analyzing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e. g., in the forms of decisions.

In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument.

These generalizations of the convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Geologists use a number of field, laboratory, and numerical modeling methods to decipher Earth history and understand the processes that occur on and in the Earth.

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems, the variety of which is suggested by the following.

The field of numerical analysis predates the invention of modern computers by many centuries.

But the invention of the computer also influenced the field of numerical analysis, since now longer and more complicated calculations could be done.

Geomorphology seeks to understand landform history and dynamics, and predict future changes through a combination of field observation, physical experiment, and numerical modeling ( Geomorphometry ).

* Numerical relativity, a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativity

Assuming quality ( diffraction limited ) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field.

Abercromby tried to move rapidly against the few French defenders, opting to forgo field cannon and relying instead on the numerical superiority of his 16, 000 troops.

Geomorphologists seek to understand why landscapes look the way they do, to understand landform history and dynamics, and to predict future changes through a combination of field observations, physical experiments, and numerical modeling.

Objective lenses with higher magnifications normally have a higher numerical aperture and a shorter depth of field in the resulting image.

The battle of Champaubert was one of the few times during the War of the Sixth Coalition that France was able to take to the field with a considerable numerical advantage.

In this context, a scalar field should also be independent of the coordinate system used to describe the physical system — that is, any two observers using the same units must agree on the numerical value of a scalar field at any given point of physical space.

The two stars in the black field of the mission patch indicate the flight's numerical designation in the Space Transportation System's mission sequence.

The six white stars in the upper blue field of the mission patch indicate the flight's numerical designation in the Space Transportation System's mission sequence.

The seven white stars in the black field of the mission patch, as well as the arm extending from the shuttle in the shape of a 7, indicate the flight's numerical designation in the Space Transportation System's mission sequence.

When d = 2 these predictions are backed up by arguments from quantum field theory and quantum gravitation, and include predicted numerical values for the exponents.

To lower the computational cost, force fields employ numerical approximations such as shifted cutoff radii, reaction field algorithms, particle mesh Ewald summation, or the newer Particle-Particle Particle Mesh ( P3M ).

The field of linguistic relativity studies remains an active focus of research in psycholinguistics and linguistic anthropology, and continues to generate debate and controversy between proponents of relativism and proponents of universalism.

Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.

* An introduction including more on general relativity and quantum field theory than most.

An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only where the gravitational field is weak.

In addition, relativity theory shows that in moving frames of reference a magnetic field transforms to a field with a nonzero electric component and vice versa ; thus firmly showing that they are two sides of the same coin, and thus the term " electromagnetism ".

This expression is correct in the full theory of general relativity, to lowest order in the gravitational field, and ignoring the variation of the space-space and space-time components of the metric tensor, which only affect fast moving objects.

In 1956, the German-American physicist Friedwardt Winterberg proposed a test of general relativity ( for time slowing in a strong gravitational field ) using accurate atomic clocks placed in orbit inside artificial satellites.

According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure.

The same experimental data shows that time as measured by clocks in a gravitational field — proper time, to give the technical term — does not follow the rules of special relativity.

There are alternatives to general relativity built upon the same premises, which include additional rules and / or constraints, leading to different field equations.

General relativity predicts that the path of light is bent in a gravitational field ; light passing a massive body is deflected towards that body.

String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are believed to be mathematically consistent.

This obviously refutes historical materialism which held that the only things that exist are things composed of the kind of matter with which we are broadly familiar (" traditional matter ")-which was anyway under great strain as noted above from relativity and quantum field theory.

A relativistic formulation in terms of covariant field tensors is used in special relativity, while in quantum mechanics, a version based on the electric and magnetic potentials is preferred.

Although originally expressed in Newton's third law, the conservation of linear momentum also holds in special relativity ( with a modified formula ) and, with appropriate definitions, a ( generalized ) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

‪ File: Wheeler, John-Archibald 1963 Kopenhagen. jpg ‬‬| John Wheeler ( 1911-2008 ): revived interest in general relativity in the United States after World War II, worked with Niels Bohr to explain principles of nuclear fission, tried to achieve Einstein ’ s vision of a unified field theory, coined the terms black hole, quantum foam, wormhole, and the phrase “ it from bit ”.

Presumably, the as yet unknown correct quantum field-theoretic treatment of the gravitational field will become and " look exactly like " Einstein's general theory of relativity in the " low-energy limit ", or, more generally, like the Einstein-Yang-Mills-Dirac System.

Quantum gravity ( QG ) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics ( describing three of the four known fundamental interactions ) with general relativity ( describing the fourth, gravity ).

Quantum field theory depends on particle fields embedded in the flat space-time of special relativity.

General relativity, like electromagnetism, is a classical field theory.

Recent work has shown that by treating general relativity as an effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomena.