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 model M of a Skolem theory T, the smallest substructure containing a certain set A is called the Skolem hull of A.

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 proper combustion chamber design, pre-ignition can generally be eliminated by proper spark plug selection, proper fuel / air mixture adjustment, and periodic cleaning of the combustion chambers.

Given his military service, the selection of Arthur proved to be prudent, as he acted as the King's, and thus the Canadian Commander-in-Chief's, representative through the first years of World War I.

Given his small number of games for Queensland, Healy ’ s selection for the Australian team to tour Pakistan in late 1988 was a major surprise.

He is perhaps better known today through his keyboard harmony exercises, Basses et Chantes Données which was a favorite teaching tool of his pupil, the legendary pedagogue Nadia Boulanger, and subsequently many of her students including Narcis Bonet who has republished a selection of these exercises under the title Paul Vidal, Nadia Boulanger: A Collection of Given Basses and Melodies ".

Given enough choice, a large population of customers, and negligible stocking and distribution costs, the selection and buying pattern of the population results in the demand across products having a power law distribution or Pareto distribution.

Given Nobunaga's reputation at the time as the unruly " Fool of Owari " ( Owari no Utsuke 尾張の虚け ), it was also not impossible for Dōsan to want Nōhime to assassinate him as she was skilled in both the sword and a selection of martial arts.

Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

* Given a recursively enumerable set A of positive integers that has insoluble membership problem, ⟨ a, b, c, d | a < sup > n </ sup > ba < sup > n </ sup > = c < sup > n </ sup > dc < sup > n </ sup >: n ∈ A ⟩ is a finitely generated group with a recursively enumerable presentation whose word problem is insoluble

# Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone.

Informally it solves the following problem: Given an integer N, find its prime factors.

Given a set of integers, FIND-SUBSET-SUM is the problem of finding some nonempty subset of the integers that adds up to zero ( or returning the empty set if there is no such subset ).

Given a set of integers, SUBSET-SUM is the problem of finding whether there exists a subset summing to zero.

Given the distance from the main body, our problem is to determine the form of the surface that satisfies the equipotential condition.

The law states that " given enough eyeballs, all bugs are shallow "; or more formally: " Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix will be obvious to someone.

Given two bodies, one with mass m < sub > 1 </ sub > and the other with mass m < sub > 2 </ sub >, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass

With regard to African Americans, Gilman wrote in the American Journal of Sociology: “ The problem, is this: Given: in the same country, Race A, progressed in social evolution, say, to Status 10 ; and Race B, progressed in social evolution, say, to Status 4..

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

# Retrieve: Given a target problem, retrieve from memory cases relevant to solving it.

* Rural postman problem: Given is also a subset of the edges.

Given the global nature of gonococcal and meningococcal diseases, the worldwide distribution of antibiotics, differing social practices in controlling and monitoring antibiotic availability, and geographical differences in treatment regimens, it is likely that the global problem of antibiotic resistance will continue in the foreseeable future.

The Mastermind satisfiability problem is a decision problem that asks, " Given a set of guesses and the number of colored and white pegs scored for each guess, is there at least one secret pattern that generates those exact scores?

Given the problem of defining death ( absence of EEG, heart beat, ...) it is hard to imagine a set of quantum parameters that could be used in constructing such superposition.

Given the informal setting, this might be unimportant ; however, teachers see this as a problem, fearing and claiming that contemporary young people are inappropriately and incorrectly extending the practice to academic homework and essays.

Given that the problem of high textbook prices is linked to the " broken " economics of the market, requiring publishers to disclose textbook prices to faculty is a solution pursued by a number of legislatures.

De Rationis Sectione sought to resolve a simple problem: Given two straight lines and a point in each, draw through a third given point a straight line cutting the two fixed lines such that the parts intercepted between the given points in them and the points of intersection with this third line may have a given ratio.

De Tactionibus embraced the following general problem: Given three things ( points, straight lines, or circles ) in position, describe a circle passing through the given points and touching the given straight lines or circles.