Selected Publications by Paul C. Kainen

Neural networks and nonlinear approximation

Geometry and topology of best and near-best approximation, Journal of Approximation Theory, 105 (2000) 252-262 (co-authors: Vera Kurkova and Andrew Vogt).

Approximation by neural networks is not continuous, Neurocomputing 29 (1999) 45-56 (co-authors: Vera Kurkova and Andrew Vogt).

An integral formula for Heaviside neural networks, Neural Network World 10 (3) (2000) 313-319 (co-authors: Vera Kurkova and Andrew Vogt).

Continuity of approximation by neural networks in L^p spaces, Annals of Operations Research, to appear (co-authors: Vera Kurkova and Andrew Vogt).

Best approximation by Heaviside perceptron networks, Neural Networks 13(7) (2000) 695-697. (co-authors: Vera Kurkova and Andrew Vogt). postscript or LaTeX .

Convexity and nonlinear approximation


Graph theory

The cube of a path is maximal planar Bull. of the Inst. of Combinatorics and its Applications 7 (1993) 55-56 (co-author: Frank Harary).

Every graph of cyclic bandwidth 3 is toroidal, Bull. of the Inst. of Combinatorics and its Applications 27 (1999) 81-84 (co-authors: Frank Harary and Adrian Riskin).

On finite superuniversal graphs, Discrete Math 24 (1978) No. 3, 235-249 (co-authors: Paul Erdos and Steve Hechler).

The Four-Color Problem: Assaults and Conquest, McGraw-Hill, New York, 1977; reprinted by Dover Publications, New York, 1986 (co-author: Thomas Saaty).

Quantum interpretations of the four color theorem, a technical report as of about May, 1999 draft only . This paper is a longer version of a talk given at the Institute for Theoretical Studies in Prague in Jan. 1999.

On robust cycle bases (for proceedings of the 9th Quadrennial International Conference in Graph Theory, Combinatorics, Algorithms, and Applications, Western Michigan University, Kalamazoo, MI, June, 2000; Y. Alavi, D. M. Jones, D. R. Lick and J. Liu, Eds.); this paper has been slightly updated as of Feb. 13, 2001.

A graph-theoretic model for time (for proceedings of CASYS2000, Liege, Belgium) (this won a ``best paper'' award for its symposium)

Geometry

A uniform bound for rearranged vector sums, Geombinatorics 3 (1993) 10-12.

On quasiorthogonal dimension of euclidean space, Applied Math. Lett. 6 (1993) 7-10 (co-author: Vera Kurkova).

An octonion model for physics (for proceedings of ECHO IV Conference, 2000, Odense, Denmark)

Heuristics, category theory and cognition

On parallel heuristics, Neural Network World 5 (1991) 281-286.

Graph heuristics for biomolecules, Nanobiology 1 (1992) 469-476.

Abstract computation in biology, Proc. of ECHO I (Amiens, 1996),

Mathematical cognition, J. of Evolution and Cognition 4 (1998) 81-89.

Isolated squares in hypercubes and robustness of commutativity, Cahiers Topologie Geom. Differentielle Categ., to appear. postscript ; this is related to the paper on robust cycle bases mentioned above.

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