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 the conflicting information available, the true identity of his killer may well be lost to history.

" Given a memex, a scholar could create her own knowledge tools as connections within reams of information, share these tools, and use complexes of tools to create yet more sophisticated knowledge that could in turn be deployed toward this work.

Given the discriminator PARTY TYPE ( which could be individual, partnership, C Corporation, Sub Chapter S Association, Association, Governmental Unit, Quasi-governmental agency ) the two subtype entities are PERSON, which contains individual-specific information such as first and last name and date of birth, and ORGANIZATION, which would contain such attributes as the legal name, and organizational hierarchies such as cost centers.

Given that the probability p is known, past outcomes provide no information about future outcomes.

Given testable information, the maximum entropy procedure consists of seeking the probability distribution which maximizes information entropy, subject to the constraints of the information.

Given the chronological information of the Imennik, Tervel would have died in 715.

Given Weyoun's untrustworthy nature, it is unclear which information should be believed.

Given the preceding information, the knowledge gap hypothesis can be expressed using the following set of related propositions:

Given that manufacturers are regarded as authorities and that most sales do not happen on manufacturer Web sites, best-in-class manufacturers take their best content and enable other retailers or dealers to publish the information on their sites.

Given all this information, the probability of the observer having spotted a girl given that the observed student is wearing trousers can be computed by substituting these values in the formula:

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 that the Pauline epistles are generally dated to AD 50 to AD 60, they are the earliest surviving Christian texts that include information about Jesus.

Given only one share, a second share can be crafted to reveal any possible image ; therefore, individual shares reveal no information about the original image.

Given t-1 shares, no information whatsoever can be determined about the secret.

Given a counterfactual conditional, e. g., ' If there had been a circle on the blackboard then there would have been a triangle ', and the subsequent information ' in fact there was no triangle ', participants make the modus tollens inference ' there was no circle ' more often than they do from an indicative conditional ( Byrne and Tasso, 1999 ).

Given the counterfactual conditional and the subsequent information ' in fact there was a circle ', participants make the modus ponens inference as often as they do from an indicative conditional.

Given two random variables X and Y whose joint distribution is known, the marginal distribution of X is simply the probability distribution of X averaging over information about Y.

Given the value of p, and no other information relevant to the question of whether the sun will rise tomorrow, the probability that the sun will rise tomorrow is p. But we are not " given the value of p ".

Given the example above, the two galaxies in question cannot have shared any sort of information ; they are not in " causal contact ".

Given this conflicting information, excluding oats appears to be the only risk-free practice for celiac disease sufferers of all ages.

Given Bernal's Marxist and pro-Soviet sympathies it is perhaps remarkable that there has never been any suggestion that he fed any information in that direction.

Given the predictable timeline of childhood behavior, he proposed " libido development " as a model of normal childhood sexual development, wherein the child progresses through five psychosexual stages — ( i ) the oral, ( ii ) the anal, ( iii ) the phallic, ( iv ) the latent, and ( v ) the genital — in which the source pleasure is in a different erogenous zone.

Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

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

Given a codeword, there are roughly 2 < sup > n H ( p )</ sup > typical output sequences.

The East border is now 24th Avenue E. jogging over at 96th to Swan creek, and south to 104th Street E. The South border is now 104th Street E. jogging over at 14th Avenue E to roughly 109th Street E. and west to Golden Given Road E. The West border is now Golden Given Road E. Golden Given Road E is also the east border of the Jessie Dunlap Donation Land Claim with the north and south borders roughly the same as the combined Meeker claims.

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

Given a more realistic yield of 36 tonnes / hectare ( 3834 US gal / acre ) the area required is about 152, 000 square kilometers, or roughly equal to that of the state of Georgia or of England and Wales.

Given a condition number, the relative error of compensated summation is effectively independent of n. In principle, there is the O ( nε < sup > 2 </ sup >) that grows linearly with n, but in practice this term is effectively zero: since the final result is rounded to a precision ε, the nε < sup > 2 </ sup > term rounds to zero unless n is roughly 1 / ε or larger.

Given that both companies have a work force of approximately 100, 000 employees, and a U. S. employment base of roughly 20, 000 H-1B holders, this indicates that roughly 1 / 5 of the Indian workforce of Infosys & Wipro applied for a visa in 2006.

Given its small staff of only 24 men, the Einsatzgrupppe Ägypten would have needed as much help as possible from the local Arabs and from the Afrika Korps to kill the roughly 50, 000 Jews of Egypt, to say nothing of the half million or so Jews of the Yishuv.

The Alaska Time Zone applies to the territory of the state of Alaska east of 169 ° 30 ′ W. Given that the UTC − 9 time corresponds to the solar time at 9 × 15 ° = 135 ° W ( roughly, Juneau ), the westernmost locales of the Alaska Time Zone are off by up to 169 ° 30 ′ − 135 ° = 34 ° 30 ′ from local solar time.

Given a mean AGB lifetime of one Myr and an outer velocity of, its maximum radius can be estimated to be roughly ( 30 light years ).

Given the structure of the Canadian infantry platoon, the MCpl is roughly equivalent to the British rank of corporal, second in command of an infantry section.

Given the distance to the epicenter of the Loma Prieta ( roughly 70 miles or 113 kilometers south of San Francisco ), there was great surprise at the localized destruction around the Bay Area.

Given an n × n matrix A and an eigenvalue λ < sub > i </ sub > of this matrix, there are two numbers measuring, roughly speaking, the number of eigenvectors belonging to λ < sub > i </ sub >.

" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.

Given more time to prepare for trial, Kidd likely would have been able to find the deposition Palmer gave when he was captured in Rhode Island two years earlier.

Given the rigorous admission process it is not surprising that CUNY BA boasts a 70 % graduation rate within an average of 2. 2 years and that 60 % graduate with academic honors.

Given these origins, there have been various suggestions over the years to rename the town ( for example, to " Invernevis ").

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

" Given that there's a gulf of 100, 000, 000 light years, he checks his diary to find out what he had been doing that day, and finds out that it was something he wished to hide.

Given the preponderance of men among the colonists in the early years, generally European men married American Indian women.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given proper nutrition, exercise, and veterinary care, most whippets live for 12 to 15 years.

Given that propensity to noble rot was a factor in Hungarian vineyard demarcations some 50 years before a messenger was supposedly mugged on his way to Schloss Johannisberg in Germany, the Hungarians probably have a better case.

" Given the situation in Spain for several years regarding terrorist attacks, these ties can be considered objectively as a threat to democracy ," the court said, also adding that these parties " contradicted the concept of a ' democratic society ' and presented a major danger to Spain's democracy ".

Given the variety of laws passed by Congress to disenfranchise US Citizens in Washington, DC or on US Bases, it is nearly impossible to thoroughly summarize two hundred years of history of disenfranchisement and alienation of in alienable rights, for Local, State and Federal Rights levels in these places.

" Given that declaration, along with seven years of bombings and the wording of their communiques throughout that time that strove to present an image of a powerful organization spread secretly throughout all sectors of society, the authorities took significant action.

Given the traditional account of the Kali Yuga lasting 432, 000 years and having started in 3102 BCE, which makes these claims problematic.

Given that the Liber historiae Francorum admits four years for Chlothar's reign, it remains possible that Chlothar began to exert some real authority when his mentors deemed him an adult, 669.

Given that under the External Relations Act the role of representing Ireland in the accreditation of ambassadors belonged to the King of Ireland on the advice of the Irish government, between those years the Irish head of state was unambiguously the King of Ireland.

Given that even players with poor chess knowledge can use the strongest computer programs to analyse their games, the gap between the beginner and master player has narrowed in recent years.

Given the team's poor results in the last few years, which she attributes to Coach D ' Amato's " old-school methods ", she attempts to take a more hands-on approach to the team, including bringing in an innovative Offensive Coordinator Nick Crozier.

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 the value of the vehicle many " extra " cars have appeared over the years, even some sharing the same chassis number.

Given Dirichlet's young age ( he was 23 years old at the time ), Humboldt was only able to get him a trial position at the Prussian Military Academy in Berlin while remaining nominally employed by the University of Breslau.

Given the older ages of these stars, and the short lifetimes of micrometer-sized dust grains around stars due to Poynting Robertson drag, collisions, and radiation pressure ( typically hundreds to thousands of years ), it is thought that this dust is from the collisions of planetesimals ( e. g. asteroids, comets ).

Given that the Ashuruballit I synchronism with Akhenaten has become the crucial link between Egyptian and Mesopotamian history in recent years, this issue is a key area of focus and dispute.

Given a Vulcan's life expectancy of approximately 250 years, it is possible that she is still alive at the time of Star Trek: The Original Series and subsequent movies.