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 events, and, Bayes ' rule states that the conditional odds of given are equal to the marginal odds of multiplied by the Bayes factor:

Given our current estimate of the parameters θ < sup >( t )</ sup >, the conditional distribution of the Z < sub > i </ sub > is determined by Bayes theorem to be the proportional height of the normal density weighted by τ:

Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value.

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

* Conditional distribution: Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X ( written " Y | X ") is the probability distribution of Y when X is known to be a particular value.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A

Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G ( x, y ) ( i. e. the sets of morphisms from x to y ).

Given earlier debates by Christian authors about the existence of Jesus, e. g. in Justin Martyr's 2nd century Dialogue with Trypho, it would have been expected that the passage from Josephus would have been used as a component of the arguments.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

* Named entity recognition ( NER ): Given a stream of text, determine which items in the text map to proper names, such as people or places, and what the type of each such name is ( e. g. person, location, organization ).

* Relationship extraction: Given a chunk of text, identify the relationships among named entities ( e. g. who is the wife of whom ).

" Given that science continually seeks to adjust its theories structurally to fit the facts, i. e., adjusts its maps to fit the territory, and thus advances more rapidly than any other field, he believed that the key to understanding sanity would be found in the study of the methods of science ( and the study of structure as revealed by science ).

Given concerns about the previous programs using nuclear-tipped interceptors, in the 1980s the U. S. Army began studies about the feasibility of hit-to-kill vehicles, i. e. interceptor missiles that would destroy incoming ballistic missiles just by colliding with them head-on.

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

* Given a category C with finite coproducts, a cogroup object is an object G of C together with a " comultiplication " m: G → G G, a " coidentity " e: G → 0, and a " coinversion " inv: G → G, which satisfy the dual versions of the axioms for group objects.

Given the simpleness of the design, and high usability with some people ( e. g. those owning an orchard ), some people have started building their own do-it-yourself ( DIY ) fruit press and have uploaded detailed instructions on how to do so.

: Given a command, e. g., "", the shell creates a pipe, then starts both and with stdio for the two commands redirected so that writes its stdout into the input of the pipe while reads stdin from the output of the pipe.

* Given a small, privileged set of inputs ( e. g., reserved words for a compiler ), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.

The isomorphism is not canonical ; it depends on a choice of basis in V. Given a basis ( e < sub > 1 </ sub >, ..., e < sub > n </ sub >) of V and an automorphism T in GL ( V ), we have

Given an isolated physical system, the allowed states of this system ( i. e. the states the system could occupy without violating the laws of physics ) are part of a Hilbert space H. Some properties of such a space are

Given an inelastic reaction with total incoming energy larger than the total detected energy ( i. e. not all outgoing particles are detected in the experiment ), the invariant mass ( also known as the " missing mass ") of the reaction is defined as follows:

Given a closed system in an initial state, if work is done on the system in an adiabatic ( i. e. no heat transfer ) way, and given the final state after a process, the amount of work required to be transferred to the system is the same, irrespective of how this work is performed.

Given the initial positions ( e. g. from theoretical knowledge ) and velocities ( e. g. randomized Gaussian ), we can calculate all future ( or past ) positions and velocities.

Given that, according to the rubrics of both the 1962 and the 1970 Missals, there can be only one celebration of the Good Friday liturgy in each church, the ordinary form of the Roman Rite ( i. e. the post-1970 form, which omits the images of the veil and of blindness ) is the one to be used almost everywhere.

Given that some common statistical packages ( e. g., SAS, SPSS ) do not provide likelihood ratio test statistics, it can be more difficult to assess the contribution of individual predictors in the multiple logistic regression case.

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 " parvorder " arrangement originally advanced is certainly obsolete ( see e. g. Irestedt et al.

Given a theological lead, I asked what he thinks about those who find a religious significance to his plays.

Given a small ball or marbles, he would invent games and play by himself for hours.

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

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

Given that John of Worcester wrote his chronicle after the eruption of the Canterbury – York supremacy struggle, the story of Ealdred renouncing any claims to Worcester needs to be considered suspect.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

Given the ongoing Danish invasion and the youth of his nephews, Alfred's succession probably went uncontested.

) Given the exclusionary and ancestral conception of citizenship held by Greek city-states, a relatively large portion of the population took part in the government of Athens and of other radical democracies like it.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Given the other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.

Given the United States ' large size it has numerous regional variations.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

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 its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

Given BASIC's straightforward nature, it was a simple matter to type in the code from the magazine and execute the program.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.