Results 201 to 210 of about 796,344 (261)

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.
Akikazu Takeuchi, Shun-ichi Amari
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An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’†

Philosophia Mathematica, 2004
Steve Awodey
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Rethinking equality in mathematics education with category theory

The Mathematics Enthusiast
Kelly Paton
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Category Theory and Structuralism in Mathematics: Syntactical Considerations [PDF]

, 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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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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The role of category theory in contemporary mathematics

, 2009
Jessica M H Grund Carter
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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 the foundations of mathematics: Philosophical excavations

Synthese, 1995
The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the ...
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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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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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