Paul C. Kainen

发表

Approximating Multivariable Functions by Feedforward Neural Nets

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2013, Handbook on Neural Information Processing.

Convex geometry and nonlinear approximation

Paul C. Kainen, 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

Complexity of Gaussian-radial-basis networks approximating smooth functions

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2009, J. Complex..

Estimates of Approximation Rates by Gaussian Radial-Basis Functions

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2007, ICANNGA.

Extension of a theorem of Whitney

Paul C. Kainen, Shannon Overbay, P. C. Kainen, 2007, Appl. Math. Lett..

The Four Color Problem: Assaults and Conquests

Paul C. Kainen, Thomas L. Saaty, Robin Wilson, 1979 .

Bochner Integrals and Neural Networks

Paul C. Kainen, Andrew Vogt, P. C. Kainen, 2023, Handbook on Neural Information Processing.

Graph Bases and Diagram Commutativity

Richard H. Hammack, Paul C. Kainen, P. C. Kainen, 2018, Graphs Comb..

Robust cycle bases do not exist for if

Richard H. Hammack, Paul C. Kainen, P. C. Kainen, 2018, Discret. Appl. Math..

Continuity of Approximation by Neural Networks in Lp Spaces

Paul C. Kainen, Vera Kurková, Andrew Vogt, 2001, Ann. Oper. Res..

Cycle construction and geodesic cycles with application to the hypercube

Paul C. Kainen, P. C. Kainen, 2014, Ars Math. Contemp..

Minimization of Error Functionals over Variable-Basis Functions

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2003, SIAM J. Optim..

Approximation by neural networks is not continuous

Paul C. Kainen, Vera Kurková, Andrew Vogt, 1999, Neurocomputing.

An Integral Upper Bound for Neural Network Approximation

Paul C. Kainen, Vera Kurková, 2009, Neural Computation.

Replacing points by compacta in neural network approximation

Paul C. Kainen, 2004, J. Frankl. Inst..

Uniqueness of network parametrization and faster learning

Vladik Kreinovich, Paul C. Kainen, Vera Kurková, 1994, Neural Parallel Sci. Comput..

Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2012, IEEE Transactions on Information Theory.

Kernel Networks with Fixed and Variable Widths

Paul C. Kainen, Vera Kurková, 2011, ICANNGA.

Approximative compactness of linear combinations of characteristic functions

Paul C. Kainen, Věra Kůrková, Andrew Vogt, 2020, J. Approx. Theory.

Best approximation by linear combinations of characteristic functions of half-spaces

Paul C. Kainen, Vera Kurková, Andrew Vogt, 2003, J. Approx. Theory.

The book thickness of a graph

Paul C. Kainen, Frank R. Bernhart, Frank Bernhart, 1979, J. Comb. Theory, Ser. B.

On Tractability of Neural-Network Approximation

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2009, ICANNGA.

Estimates of Network Complexity and Integral Representations

Paul C. Kainen, Vera Kurková, P. C. Kainen, 2008, ICANN.

Rates of Minimization of Error Functionals over Boolean Variable-Basis Functions

Marcello Sanguineti, Paul C. Kainen, Vera Kurková, 2005, J. Math. Model. Algorithms.

Estimates of the Number of Hidden Units and Variation with Respect to Half-Spaces

Vladik Kreinovich, Paul C. Kainen, Vera Kurková, 1997, Neural Networks.

Functionally Equivalent Feedforward Neural Networks

Paul C. Kainen, Vera Kurková, P. C. Kainen, 1994, Neural Computation.

Comparing fixed and variable-width Gaussian networks

Paul C. Kainen, Vera Kurková, P. C. Kainen, 2014, Neural Networks.

A geometric method to obtain error-correcting classification by neural networks with fewer hidden units

Paul C. Kainen, Vera Kurková, 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

Best approximation by Heaviside perceptron networks

Paul C. Kainen, Vera Kurková, Andrew Vogt, 2000, Neural Networks.

On robust cycle bases

Paul C. Kainen, 2002, Electron. Notes Discret. Math..

On finite superuniversal graphs

Paul Erdös, Paul C. Kainen, Stephen H. Hechler, 1978, Discret. Math..

The Four-Color Problem

Paul C. Kainen, Thomas L. Saaty, 1977 .

A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves

Paul C. Kainen, Vera Kurková, Andrew Vogt, 2007, J. Approx. Theory.

On stable crossing numbers

Paul C. Kainen, Arthur T. White, 1978, J. Graph Theory.

On dispersability of some products of cycles

Paul C. Kainen, Shannon Overbay, Samuel S. Joslin, 2021 .

Cubic planar bipartite graphs are dispersable

Paul C. Kainen, Shannon Overbay, 2021 .

Lunaport: Math, Mechanics & Transport pdf

Paul C. Kainen, P. C. Kainen, 2021, ArXiv.

On dispersability of some circulant graphs

Paul C. Kainen, Shannon Overbay, Samuel S. Joslin, 2021 .

A New View of Hypercube Genus

Richard H. Hammack, Paul C. Kainen, 2021, Am. Math. Mon..

Recent Results and Mathematical Methods for Functional Approximation by Neural Networks

Paul C. Kainen, 2007 .

On the stable crossing number of cubes

Paul C. Kainen, P. C. Kainen, 1972 .

Lower Bound for Crossing Nw~b~rs with Applications to K, ) K,, ( and

Paul C. Kainen, 1972 .

Some recent results in topological graph theory

Paul C. Kainen, P. C. Kainen, 1974 .

Thickness and coarseness of graphs

Paul C. Kainen, P. C. Kainen, 1973 .

Graph cycles and diagram commutativity

Paul C. Kainen, 2012 .

A generalization of the 5-color theorem

Paul C. Kainen, P. C. Kainen, 1974 .

Integral combinations of Heavisides

Paul C. Kainen, Věra Kůrková, Andrew Vogt, 2010 .

A lower bound for crossing numbers of graphs with applications to Kn, Kp,q, and Q(d)

Paul C. Kainen, P. C. Kainen, 1972 .

Chromatic number and skewness

Paul C. Kainen, 1975 .

Geometry and Topology of Continuous Best and Near Best Approximations

Paul C. Kainen, Andrew Vogt, Vra Krková, 2000 .

Quasiorthogonal dimension of euclidean spaces

Paul C. Kainen, P. C. Kainen, V. Kůrková, 1993 .

On a problem of P. Erdös

Paul C. Kainen, P. C. Kainen, 1968 .

Robust cycle bases do not exist for K n , n if n ≥ 8

Richard H. Hammack, Paul C. Kainen, P. C. Kainen, 2017 .

An integral formula for Heaviside neural networks

Paul C. Kainen, P. C. Kainen, 2004 .

Utilizing Geometric Anomalies of High Dimension: When Complexity Makes Computation Easier

Paul C. Kainen, P. C. Kainen, 1997 .

Book embeddings of graphs and a theorem of Whitney

Paul C. Kainen, Shannon Overbay, P. C. Kainen, 2021, 2110.00820.

Weak adjoint functors

Paul C. Kainen, P. C. Kainen, 1971 .