Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given a left neutral element and for any given then A4 ’ says there exists an such that.

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 both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given the Greek fleet's unpreparedness resulting from the premature outbreak of the war, such an early Ottoman attack might well have been able to achieve a crucial victory.

Given a set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.

Given the toleration of Hinduism, such imperial leeway was not shocking.

Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.

Given the need for such fine regulation of Ca < sup > 2 +</ sup > signaling, it is perhaps unsurprising that dysregulated mitochondrial Ca < sup > 2 +</ sup > has been implicated in several neurodegenerative diseases, while the catalogue of tumor suppressors includes a few that are enriched at the MAM.

Given its continental origin as a fragment of Zealandia, unlike many of the islands of the Pacific such as the Hawaiian chain, New Caledonia is not of geographically recent volcanic provenance.

* 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 ).

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 a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given Poseidon's connection with horses as well as the sea, and the landlocked situation of the likely Indo-European homeland, Nobuo Komita has proposed that Poseidon was originally an aristocratic Indo-European horse-god who was then assimilated to Near Eastern aquatic deities when the basis of the Greek livelihood shifted from the land to the sea, or a god of fresh waters who was assigned a secondary role as god of the sea, where he overwhelmed the original Aegean sea deities such as Proteus and Nereus.

Given a preorder on S one may define an equivalence relation ~ on S such that a ~ b if and only if a b and b a.

Given X such that

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

Given that in such a case pits the freedom of an innocent child against the freedom of the evil-doer, it is not clear why God would not intervene for the sake of the child.

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.

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 a model selection problem in which we have to choose between two models, on the basis of observed data D, the plausibility of the two different models M < sub > 1 </ sub > and M < sub > 2 </ sub >, parametrised by model parameter vectors and is assessed by the Bayes factor K given by