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Thompson made further contributions to Galois theory, representation theory, coding theory, and, working on the proof of the nonexistence of a plane of order 10, the theory of finite projective planes.
Section 2 discusses two types of arguments for expected utility theory: representation theorems, and long-run statistical arguments.
According to an isomorphism theory, representation is a matter of mirroring the relations among the elements in the represented domain in the relations among elements in the representing domain.
This chapter outlines three levels at which information processing tasks—including cognitive and perceptual ones must be understood: computational theory, representation and algorithm, and hardware implementation.
The approximation of functions by integral operators with positive definite kernels is widely used in many branches of mathematics, such as approximation theory, representation theory, theory of differential equations, Fourier analysis, and singular integral theory.
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Cortical network architecture has predominantly been investigated visually using graph theory representations.
Segal notes this advantage in response to a result obtained by (Haag 1955), that field theory representations of free fields are unitarily inequivalent to representations of interacting fields.
In general, the abstractions offered by graph theory representations (i) facilitate the analysis of network performance, (ii) provide a unifying framework for comparisons of features across different systems and (iii) assist the mathematical characterisation of system properties and dynamics.
We show that under various initial conditions and known facts about agent beliefs and abilities, the meta-theory representation yields good results.
Andrew Rehfeld (2006) has offered a general theory of representation which simply identifies representation by reference to a relevant audience accepting a person as its representative.
As a result, the biosemantic theory of representation is only halfway there: any complete theory of representation must account for the aboutness of those many representations that are misrepresentations.
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