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 this information, a timeline of roughly the years 15 – 98 CE can be established for his adult life.

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 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 dangers, the maximum sentence was three months.

Given the maximum observed frequency ( MOF ) for a mode on each day of the month at a given hour, the MUF is the highest frequency for which an ionospheric communications path is predicted on 50 % of the days of the month.

Given that radio communication channels are allocated by agencies such as the Federal Communication Commission giving a prescribed ( maximum ) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK-at the same BER.

Given two points A and B, with A not lower than B, there is just one upside down cycloid that passes through A with infinite slope, passes also through B and does not have maximum points between A and B.

Given the principal stress state, we can use Mohr ’ s circle to solve for the maximum shear stresses our material will experience and conclude that the material will fail if:

Given N independent and identically distributed Rayleigh random variables with parameter, the maximum likelihood estimate of is

# Given a maximum distortion constraint, minimize the bit rate

# Given a maximum bit rate constraint, minimize the distortion

Given the lack of any variable-ratio transmission between the piston engine and the wheels, the designer is forced to compromise between desired torque and desired maximum speed ; the radius of the driving wheels determines this.

Given a source with a fixed voltage and fixed source impedance, the maximum power theorem says this is the only way to extract the maximum power from the source.

Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction.

Given a curve describing the overall drag on the vehicle, it is simple to find the speed at which the total drag forces are the same as the maximum power of the engine.

Given that the crinoline did eventually have a maximum diameter of up to 180 centimetres ( six feet ), it is easy to imagine difficulties in getting through doors, in and out of carriages, and the general problems of moving in such a large structure.

Given a perfect graph G, Lovász forms a graph G * by replacing each vertex v by a clique of t < sub > v </ sub > vertices, where t < sub > v </ sub > is the number of distinct maximum independent sets in G that contain v. It is possible to correspond each of the distinct maximum independent sets in G with one of the maximum independent sets in G *, in such a way that the chosen maximum independent sets in G * are all disjoint and each vertex of G * appears in a single chosen set ; that is, G * has a coloring in which each color class is a maximum independent set.

Given clear that the army under his command was all that Paraguay with maximum effort could have led a successful military campaign against successive Bolivian army, superior in men and materials, making back to the Rio Parapiti.

Given a single distribution, the minimum and the maximum occurring distances become indiscernible as the difference between the minimum and maximum value compared to the minimum value converges to 0:

Given a sample of n independent observations x < sub > 1 </ sub >,..., x < sub > n </ sub > of a p-dimensional zero-mean Gaussian random variable X with covariance R, the maximum likelihood estimator of R is given by

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 discrete random variable with support and with support, the conditional entropy of given is defined as:

Given a bipartite quantum state, the entropy of the entire system is, and the entropies of the subsystems are and.

Given a quantum system with two subsystems A and B, the term joint quantum entropy simply refers to the von Neumann entropy of the combined system.

Given the density matrix ρ, von Neumann defined the entropy as