Given a model of some atomic positions, these positions and their respective Debye-Waller factors ( or B-factors, accounting for the thermal motion of the atom ) can be refined to fit the observed diffraction data, ideally yielding a better set of phases.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other.

Given the go-ahead, Marston developed Wonder Woman, basing her character on both Elizabeth and Olive Byrne, to be the model of an conventional, liberated, powerful modern woman.

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given the ACE model, researchers can determine what proportion of variance in a trait is heritable, versus the proportions which are due to shared environment or unshared environment.

Given the limited spectrum a wholesale model as noted by the EU Commission reference 2 in such situation is chosen.

Given the shortcomings of the linear regression model for dealing with a dichotomous criterion, it is necessary to use some other analysis.

Given that deviance is a measure of the difference between a given model and the saturated model, smaller values indicate better fit.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.

Given a model of a system, exhaustively and automatically check whether this model meets a given specification.

Given a probability space, consider a single-period binomial model.

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given such a model, the sentence

However, the modelling study also states that " Given the complex, three-dimensional nature of the real Pine Island glacier ... it should be clear that the [...] model is a very crude representation of reality.

:" Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models.

Given the assumptions of the model ( for example, that the profits are reinvested and that capital accumulation does not substitute for skilled labor in production ), the process becomes self-sustaining and leads to modernization and economic development.

Given the model and realizations ( samples ) of the random vector, the task is to estimate both the mixing matrix and the sources.

Given a set of candidate models for the data, the preferred model is the one with the minimum AIC value.

Given a time series of data X < sub > t </ sub >, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series.

Given a good model, it is best to make as many observations as practicable, depending of the expected reliability of prior knowledge, cost of observations, time and resources available, and accuracy required.

Given a model selection problem in which we have to choose between two models, on the basis of observed data D, the plausibility of the two different models M < sub > 1 </ sub > and M < sub > 2 </ sub >, parametrised by model parameter vectors and is assessed by the Bayes factor K given by

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given an evaluation e of variables by elements of M < sub > w </ sub >, we

Given a system of n-dimensional variables ( physical variables ), in k ( physical ) dimensions, write the dimensional matrix M, whose rows are the dimensions and whose columns are the variables: the ( i, j ) th entry is the power of the ith unit in the jth variable.

Given a differentiable manifold M, a vector field on M is an assignment of a tangent vector to each point in M. More precisely, a vector field F is a mapping from M into the tangent bundle TM so that is the identity mapping

Given two complexes M < sub >*</ sub > and N < sub >*</ sub >, a chain map between the two is a series of homomorphisms from M < sub > i </ sub > to N < sub > i </ sub > such that the entire diagram involving the boundary maps of M and N commutes.

Given an SVD of M, as described above, the following two relations hold:

Given a set M of molecules, chemical reactions can be roughly defined as pairs r =( A, B ) of subsets from M.

Given a Hermitian form Ψ on a complex vector space V, the unitary group U ( Ψ ) is the group of transforms that preserve the form: the transform M such that Ψ ( Mv, Mw ) = Ψ ( v, w ) for all v, w ∈ V. In terms of matrices, representing the form by a matrix denoted, this says that.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given an orientable Haken manifold M, by definition it contains an orientable, incompressible surface S. Take the regular neighborhood of S and delete its interior from M. In effect, we've cut M along the surface S. ( This is analogous, in one less dimension, to cutting a surface along a circle or arc.

Given such a G-module M, it is natural to consider the subgroup of G-invariant elements:

Given a smooth curve γ on ( M, g ) and a vector field V along γ its derivative is defined by

Given the above commonalities there appear to be only two string theories: the heterotic string theory ( which is also the type I string theory ) and the type II theory.

Given that assumption, the evidence for the one-seed theory is the fact that a woman can conceive without coming to orgasm ( though this was still a matter of dispute in the ancient world and the Middle Ages ).

Given the medieval medicine's main theory of humorism, spices and herbs were indispensable to balance " humors " in food, a daily basis for good health at a time of recurrent pandemics.

Given gravitation's predominance in shaping cosmological structures, accurate predictions of the universe's past and future require an accurate theory of gravitation.

Given the lack of a significant outer convection zone, theory predicts the absence of a magnetic dynamo in earlier A stars.

The wavelets forming a continuous wavelet transform ( CWT ) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event.

Given the variety of approaches, Economic Geography has taken to many different subject matters, including: the location of industries, economies of agglomeration ( also known as " linkages "), transportation, international trade, economic development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy ( tying into a long history of geographers studying culture-environment interaction ), and globalization.

Given this lack of semantic transparency, researchers, outreach workers, critical theorists and LGBT activists have proposed and use terms such as institutionalized homophobia, state (- sponsored ) homophobia, sexual prejudice, anti-gay bigotry, straight privilege, The Straight Mind ( a collection of essays by French writer Monique Wittig ), heterosexual bias, compulsory heterosexuality or the much lesser known terms heterocentrism, homonegativity, and from gender theory and queer theory, heteronormativity.

; Inverse problem of Galois theory: Given a group G, find an extension of the rational number or other field with G as Galois group.

Given Rico's skill with a firearm, Joe would later posit the theory that Rico was trying to commit suicide by cop out of a deep disgust at what he had become, rather than trying to kill him.

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

Given the shortcomings of the beneficial acclimation hypothesis, researchers are continuing to search for a theory that will be supported by empirical data.

Given that the derivatives as Schwartz distributions are symmetric, this kind of example belongs in the ' fine ' theory of real analysis.

* Bernhard Riemann publishes his paper on number theory, die Anzahl der Primzahlen unter einer gegebenen (" On the Number of Primes Less Than a Given Magnitude ") including the Riemann zeta function and Riemann hypothesis.

Given the possible relationship between awareness and cognition, and consciousness, this theory contributes an interesting perspective in the philosophical and scientific dialogue of awareness and living systems theory.

Given any gene in the body of an organism, we can trace a single chain of ancestor organisms back in time, following the lineage of this one gene, as stated in the coalescent theory.

Given that Fildes is reported to have had a tendency to make " extravagant boasts ", and that the grenade modifications could have been aimed at making it lighter, the validity of the botulinum toxin theory has been questioned.

Given this scaling dimension for, there are certain nonlinear modifications of massless scalar field theory which are also scale-invariant.

Given the suspension of semicha, any beth din existing in medieval or modern times is in theory a court of laymen, acting as arbitrators.

Given the proper conditions, theory Y managers believe that employees will learn to seek out and accept responsibility and to exercise self-control and self-direction in accomplishing objectives to which they are committed.