Results 191 to 200 of about 429,595 (233)

Mathematical theory on formation of category detecting nerve cells

Biological Cybernetics, 1978
The nerve cells are believed to have such ability of self-organization that, given a number of input patterns, each cell tunes itself to become responsive to only one of the patterns, or to one subset of patterns having some features in common. The detectors of patterns or pattern subsets are formed in this manner.
Amari, Shun-ichi, Takeuchi, Akikazu
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Category Theory: The Language of Mathematics

Philosophy of Science, 1999
In this paper I argue that category theory ought to be seen as providing thelanguagefor mathematical discourse. Against foundational approaches, I argue that there is no need toreduceeither the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories.
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Does Category Theory Provide a Framework for Mathematical Structuralism?†

Philosophia Mathematica, 2003
Category theory and topos theory were suggested as a structuralist framework for mathematics autonomous w.r.t. set theory. The paper criticises this approach. It is argued that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves.
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Mathematical Applications of Category Theory

1984
The interaction between category theory and set theory by A. Blass Synthetic calculus of variations by M. Bunge and M. Heggie The representation of limits, lax limits and homotopy limits as sections by J. W. Gray Open locales and exponentiation by P. T. Johnstone Eilenberg-Mac Lane toposes and cohomology by A. Joyal and G. Wraith A combinatorial theory
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Mathematical modelling by help of category theory

Die Lösung eines jeden ingenieurtechnischen Problems beginnt mit einem Modellierungsprozess, der ein Modell bereitstellt, das ein zu betrachtendes System darstellt. Die entscheidende Frage für die praktische Verwendung von Modellen besteht darin, zu beurteilen, ob das Modell und die Ergebnisse seiner Verwendung vertrauenswürdig sind.
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Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering

Applied Mathematics & Information Sciences, 2017
In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category. The objects of the category represent all the elements and components of the system and the arrows represent the relations ...
Mabrok, Mohamed, Ryan, Michael J.
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Semantic Category theory and Semantic Intertwine: the anathema of mathematics

Kybernetes, 2014
Purpose – The recent scientific observation that human information processing involves four independent data types, has pinpointed a source of fallacious arguments within many domains of human thought. The species-unique ability to assign observable characteristics to purely conceptual entities has created beautiful ...
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Category theory, applications to the foundations of mathematics

2018
Since the 1960s Lawvere has distinguished two senses of the foundations of mathematics. Logical foundations use formal axioms to organize the subject. The other sense aims to survey ‘what is universal in mathematics’. The ontology of mathematics is a third, related issue.
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On graph theoretical SAR and the mathematical theory of categories

Journal of Molecular Structure: THEOCHEM, 1991
Abstract Chemical graph theory provides a special framework for solving many structure-activity relationship (SAR) problems such as boiling points, resonance energies, and pharmacological properties. The theorems by Muirhead (1901) and Karamata (1932), whereby certain sequences of numbers may be compared, have been used to establish SARs.
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Category Theory and Structuralism in Mathematics: Syntactical Considerations

1997
Thus, to be is to be related and the “essence” of an “entity” is given by its relations to its “environment”. This claim is striking: it seems to describe perfectly well the way objects of a category are characterized and studied. Consider, for instance, the fundamental notion of product in a category C: a product for two objects A and B of C is an ...
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