Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given a set of integers, does some nonempty subset of them sum to 0?

Given is each element's name, atomic number, year of first report, name of the discoverer, and some notes related to the discovery.

Given the magnitude of the disaster, reconstruction and economic recovery will remain the primary focus of the Salvadoran Government for some time to come.

Given its roughly constant size, the encyclopaedia has needed to reduce or eliminate some topics to accommodate others, resulting in controversial decisions.

Given good circumstances one might be able to discern the result of some human activity such as the changing of the Netherlands ' coast or the partial drying out of the Aral Sea, but even that would not be easy.

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

Given steady funding throughout, the R-7 developed with some speed.

Given the widespread expansion in the tenth revision, it is not possible to convert ICD-9 data sets directly into ICD-10 data sets, although some tools are available to help guide users.

He also made some good long-term signings like Gary Speed and Shay Given.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

Given that in biology many phyla, families and genera have some species that live in the sea and others that live on land, marine biology classifies species based on the environment rather than on taxonomy.

Given a specific task to solve, and a class of functions, learning means using a set of observations to find which solves the task in some optimal sense.

Given a base for the topology, in order to prove convergence of a net it is necessary and sufficient to prove that there exists some point x, such that ( x < sub > α </ sub >) is eventually in all members of the base containing this putative limit.

Given this and other evidence, many scholars agree that Peter was martyred in Rome under Nero, although some scholars argue that he may have been martyred in Palestine.

Given that the validity of conclusions drawn from a statistical analysis depend on the validity of any assumptions made, it is clearly important that these assumptions should be reviewed at some stage.

Given its stability, similarity and relative proximity to the Sun, Tau Ceti is consistently listed as a target for the Search for Extra-Terrestrial Intelligence ( SETI ), and it appears in some science fiction literature.

noted, " Given that the bandwidth for conducting crawls is neither infinite nor free, it is becoming essential to crawl the Web in not only a scalable, but efficient way, if some reasonable measure of quality or freshness is to be maintained.

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 the difference between their roles and emphases, some scholars have speculated that the interactions between the Æsir and the Vanir reflect the types of interaction that were occurring between social classes ( or clans ) within Norse society at the time.

Given the lack of evidence of many Freudian hypotheses, some scientific researchers proposed the existence of unconscious mechanisms that are very different from the Freudian ones.

* Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely occurs as a substring at some position.

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Given where and, determine the value of and using the chain rule.

The question concerned the educational value of pre-Christian classical thought: " Given that the body of knowledge of the pre-Christian Romans was heathen in origin, was it safe to teach it to Christian children?

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

* Given a binary operation, an idempotent element ( or simply an idempotent ) for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result.

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.

In the account books of Johanna, Duchess of Brabant and Wenceslaus I, Duke of Luxemburg, an entry dated May 14, 1379 reads: " Given to Monsieur and Madame four peters, two forms, value eight and a half moutons, wherewith to buy a pack of cards ".

Given the current value of the port of Toledo to Ohio, it can be reasonably suggested that both sides benefitted from the conflict.

Given a function f: X → Y, the set X is the domain of f ; the set Y is the codomain of f. In the expression f ( x ), x is the argument and f ( x ) is the value.

Given the ( period, cash flow ) pairs (, ) where is the total number of periods, the net present value is given by:

Given a collection of pairs ( time, cash flow ) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.

Given the ( period, cash flow ) pairs (, ) where is a positive integer, the total number of periods, and the net present value, the internal rate of return is given by in:

Given that the absolute vorticity is positive ( negative ) in the Northern ( Southern ) hemisphere, the threshold value should be taken as positive ( negative ) north ( south ) of the equator.

Given the price of 1 / 32 Mark for six small fruit pies ( as seen in Dragonsinger ), it places the value at around $ 20 to the Mark.

Given such a field, an absolute value can be defined on it.

Given a locally compact topological field K, an absolute value can be defined as follows.

Given such an absolute value on K, a new induced topology can be defined on K. This topology is the same as the original topology.

Given the parallels between visual and musical arts, it is possible that general acceptance of the value of digital art will progress in much the same way as the increased acceptance of electronically produced music over the last three decades.

Given its strategic value, Winston Churchill would later quote a telegram he sent to the Chief of the Imperial General Staff on 4 June 1940: " To lose Crete because we had not sufficient bulk of forces there would be a crime.

Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.

Given the high value of these areas for wildlife species, close to 70 % of this big-tree old growth forest is protected in reserves, and will never be eligible for harvest.

Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, ( written X → Y ) if, and only if, each X value is associated with precisely one Y value.