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Reverse Mathematics and Computability Theory of Domain Theory
2019This paper deals with the foundations of mathematics and computer science, domain theory in particular; the latter studies certain ordered sets, called domains, with close relations to topology. Conceptually speaking, domain theory provides a highly abstract and general formalisation of the intuitive notions ‘approximation’ and ‘convergence’.
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Some Completeness Results in the Mathematical Theory of Computation
Journal of the ACM, 1968A formal theory is described which incorporates the “assignment” function a ( i , k , ξ ) and the “contents” function c ( i , ξ ).
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Computational Methods for A Mathematical Theory of Evidence
2008Many knowledge-based expert systems employ numerical schemes to represent evidence, rate competing hypoth eses, and guide search through the domains problem space. This paper has two objectives: first, to introduce one such scheme developed by Arthur Dempster and Glen Shafer, to a wider audience; second, to present results that can reduce the compu ...
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Two mathematical gestalts for computer theory
Proceedings of the 40th ACM technical symposium on Computer science education, 2009Many Computer Science educators have campaigned to increase mathematical content in the computing curriculum. However, mathematical concepts are often presented in a manner that conflicts with the general mental framework, or gestalt, of CS students. Fortunately, there is more than one gestalt in mathematics.
Kirby McMaster +2 more
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A Mathematical Theory of Energy Efficient Neural Computation and Communication
IEEE Transactions on Information Theory, 2010A neuroscience-based mathematical model of how a neuron stochastically processes data and communicates information is introduced and analyzed. Call the neuron in question 'neuron j", or just "j". The information j transmits approximately describes the time-varying intensity of the excitation j is continuously experiencing from neural spike trains ...
Toby Berger, William B. Levy
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Computational and mathematical organization theory: Perspective and directions
Computational and Mathematical Organization Theory, 1995Computational and mathematical organization theory is an interdisciplinary scientific area whose research members focus on developing and testing organizational theory using formal models. The community shares a theoretical view of organizations as collections of processes and intelligent adaptive agents that are task oriented, socially situated ...
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A basis for a mathematical theory of computation, preliminary report
Papers presented at the May 9-11, 1961, western joint IRE-AIEE-ACM computer conference on - IRE-AIEE-ACM '61 (Western), 1961Programs that learn to modify their own behaviors require a way of representing algorithms so that interesting properties and interesting transformations of algorithms are simply represented. Theories of computability have been based on Turing machines, recursive functions of integers and computer programs.
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Lectures on a Mathematical Theory of Computation
1982These notes were originally written for lectures on the semantics of programming languages delivered at Oxford during Michaelmas Term 1980. The purpose of the course was to provide the foundations needed for the method of denotational semantics; in particular I wanted to make the connections with recursive function theory more definite and to show how ...
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Development of Mathematical Theory in Computer Vision
2014This chapter presents a brief description of chapters devoted to the theoretical development of computer vision. Original investigations in mathematical morphology, estimations of structural changes, the hierarchical adaptive Karhunen-Loeve and projective transforms, among others, provide the great contribution in mathematical foundations of computer ...
Margarita N. Favorskaya, Lakhmi C. Jain
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Logic, Foundations of Mathematics, and Computability Theory
1977I. Formal Development of the Theory of Quantum Logic.- Spectral Theory in Quantum Logics.- Semantics of the Minimal Logic of Quantum Mechanics.- Representations of Groups as Automorphisms on Orthomodular Lattices and Posets.- The Conditional in Abstract and Concrete Quantum Logic.- On the Logical Structure of Quantum Mechanics.- II.
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