Several other promising modeling techniques have been used, including Boolean networks, Petri nets, Bayesian networks, graphical Gaussian models, Stochastic, and Process Calculi.

Gaussian Process Regression ".

The half-intensity diameter of the main lobe of the antenna was about 18'.5, and the brightness temperature was reduced by assuming a Gaussian shape for the antenna beam and a uniformly bright disk for the moon.

The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis ( the symmetrical axis of the system ) are infinitely small, i. e. with infinitesimal objects, images and lenses ; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits.

This ray, named by Abbe a principal ray ( not to be confused with the principal rays of the Gaussian theory ), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction.

For a Gaussian response system ( or a simple RC roll off ), the rise time is approximated by:

This is in P, since an XOR-SAT formula is a system of linear equations mod 2, and can be solved by Gaussian elimination.

The first configuration interaction calculations were carried out in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers.

Among his results, Gauss showed that under a paraxial approximation an optical system can be characterized by its cardinal points and he derived the Gaussian lens formula.

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Dyson recognized the formula as the pair correlation function of the Gaussian unitary ensemble, which has been extensively studied by physicists.

which can be found by setting z = 1 / 2 in the reflection or duplication formulas, by using the relation to the beta function given below with x = y = 1 / 2, or simply by making the substitution u = √ t in the integral definition of the gamma function, resulting in a Gaussian integral.

The notes were widely imitated, which made ( what is now called ) Gaussian elimination a standard lesson in algebra textbooks by the end of the 18th century.

In the absence of rounding errors, direct methods would deliver an exact solution ( like solving a linear system of equations Ax = b by Gaussian elimination ).

Gaussian molecular orbital methods were described in the 1986 book Ab initio molecular orbital theory by Warren Hehre, Leo Radom, Paul v. R.

Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination, which was initially listed as an advancement in geodesy.

Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

Hence, bending a surface will not alter the Gaussian curvature and other surfaces with constant positive Gaussian curvature can be obtained by cutting a small slit in the sphere and bending it.

The unbiased estimator of a weighted population variance ( assuming each is drawn from a Gaussian distribution with variance ) is given by:

The parameter σ decides the spatial spread of the Gaussian along the x-axis, while the Fourier transform shows a spread in wave vector k determined by 1 / σ.

NA is also good at climbing sharp crests by adaptation of the moment matrix, because NA may maximise the disorder ( average information ) of the Gaussian simultaneously keeping the mean fitness constant.

Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first part of the Gaussian elimination method, taking care to preserve the sign of its determinant.

Gaussian laser beams are said to be diffraction limited when their radial beam divergence is close to the minimum possible value, which is given by

Another factor in the growth of CDOs was the 2001 introduction by David X. Li of Gaussian copula models, which allowed for the rapid pricing of CDOs.

The community develops policies by following a formal Policy Development Process as outlined at https :// www. arin. net / policy / pdp. html.

The model is based on the process maturity framework first described in the 1989 book Managing the Software Process by Watts Humphrey.

The DNS Resolution Process reduces the load on individual servers by caching DNS request records for a period of time after a response.

With the advent of a Provisional IRA ceasefire and the beginning of what became known as the Peace Process during the 1990s, the official view of the Rising became more positive and in 1996 an 80th anniversary commemoration at the Garden of Remembrance in Dublin was attended by the Taoiseach and leader of Fine Gael, John Bruton.

The term was earlier used in sociology by Norbert Elias in The Civilizing Process ( 1939 ) and in Marcel Mauss's account of " body techniques " ( techniques du corps ).

These were originated by Professor Colin Ramshaw and led to the concept of Process Intensification: research into these novel technologies is now being pursued by the Process Intensification Group at Newcastle University.

Despite successes such as the revival of economic growth and the beginnings of the Northern Ireland Peace Process, by the mid-1990s the Conservatives were embroiled in ongoing " sleaze " scandals involving various MPs and even Cabinet Ministers.

* The Government of British Trade Unions: A study of Apathy and the Democratic Process in the Transport and General Worker Union by Joseph Goldstein

:* The Papersave process was developed by Battelle Ingenieurtechnik GmbH and is, therefore, sometimes referred to as " the Battelle Process ".

The 1981 book Genes, Mind, and Culture: The Coevolutionary Process by Charles J. Lumsden and E. O. Wilson proposed the theory that genes and culture co-evolve, and that the fundamental biological units of culture must correspond to neuronal networks that function as nodes of semantic memory.

Process art as inspired by Pollock enabled artists to experiment with and make use of a diverse encyclopedia of style, content, material, placement, sense of time, and plastic and real space.

The phrase, " the hammering process " was used by Christian metal band Living Sacrifice for the name of their album The Hammering Process.

Other fundamental rights like the Due Process Clause and the equal protection guarantee of the Fourteenth Amendment was expressly extended to Puerto Rico by the U. S. Supreme court.

Influential to thinkers associated with Postmodernism are Heidegger's critique of the subject-object or sense-knowledge division implicit in Rationalism, Empiricism and Methodological Naturalism, his repudiation of the idea that facts exist outside or separately from the process of thinking and speaking them ( however, Heidegger is not specifically a Nominalist ), his related admission that the possibilities of philosophical and scientific discourse are wrapped up in the practices and expectations of a society and that concepts and fundamental constructs are the expression of a lived, historical exercise rather than simple derivations of external, apriori conditions independent from historical mind and changing experience ( see Johann Gottlieb Fichte, Heinrich von Kleist, Weltanschauung and Social Constructionism ), and his Instrumentalist and Negativist notion that Being ( and, by extension, reality ) is an action, method, tendency, possibility and question rather than a discreet, positive, identifiable state, answer or entity ( see also Process Philosophy, Dynamism, Instrumentalism, Pragmatism and Vitalism ).

Process theology or process thought is a school of thought influenced by the metaphysical process philosophy of Alfred North Whitehead ( 1861 – 1947 ) and further developed by Charles Hartshorne ( 1897 – 2000 ).

Process theology does not deny that God is in some respects eternal, immutable, and impassible, but it contradicts the classical view by insisting that God is in some respects temporal, mutable, and passible.

* The most important work by Paul S. Fiddes is The Creative Suffering of God ( Oxford: Oxford University Press, 1992 ); see also his short overview " Process Theology ," in A. E. McGrath, ed., The Blackwell Encyclopaedia of Modern Christian Thought ( Oxford: Blackwell, 1993 ), 472 – 76.

This resulted in the most famous work of process philosophy, Alfred North Whitehead's Process and Reality, 1929, a work which continues that begun by Hegel but describing a more complex and fluid dynamic ontology.

* Process identifier, a number used by Unix kernels and Windows operating systems to identify a process

*" A Pessimist's View of the Peace Process " by Yigal Carmon.

A comprehensive study to date by Robert Freitas and Ralph Merkle has identified 137 design dimensions grouped into a dozen separate categories, including: ( 1 ) Replication Control, ( 2 ) Replication Information, ( 3 ) Replication Substrate, ( 4 ) Replicator Structure, ( 5 ) Passive Parts, ( 6 ) Active Subunits, ( 7 ) Replicator Energetics, ( 8 ) Replicator Kinematics, ( 9 ) Replication Process, ( 10 ) Replicator Performance, ( 11 ) Product Structure, and ( 12 ) Evolvability.