Paul Chester Kainen | Academic Influence

Paul Chester Kainen's AcademicInfluence.com Rankings

Paul Chester Kainen

Mathematics

#1300

World Rank

#2174

Historical Rank

#540

USA Rank

Measure Theory

#3800

World Rank

#4480

Historical Rank

#1087

USA Rank

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Mathematics

Paul Chester Kainen's Degrees

PhD Mathematics University of Chicago
Bachelors Mathematics University of Chicago

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Why Is Paul Chester Kainen Influential?

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According to Wikipedia, Paul Chester Kainen is an American mathematician, an adjunct associate professor of mathematics and director of the Lab for Visual Mathematics at Georgetown University. Kainen is the author of a popular book on the four color theorem, and is also known for his work on book embeddings of graphs.

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Paul Chester Kainen's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The book thickness of a graph (1979) (371)
Estimates of the Number of Hidden Units and Variation with Respect to Half-Spaces (1997) (110)
Functionally Equivalent Feedforward Neural Networks (1994) (69)
Complexity of Gaussian-radial-basis networks approximating smooth functions (2009) (61)
An Integral Upper Bound for Neural Network Approximation (2009) (49)
Quasiorthogonal dimension of euclidean spaces (1993) (48)
Thickness and coarseness of graphs (1973) (47)
Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks (2012) (47)
Approximation by neural networks is not continuous (1999) (47)
A lower bound for crossing numbers of graphs with applications to Kn, Kp,q, and Q(d) (1972) (46)
Some recent results in topological graph theory (1974) (44)
Utilizing Geometric Anomalies of High Dimension: When Complexity Makes Computation Easier (1997) (37)
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves (2007) (33)
Four Color Problem (2021) (31)
Minimization of Error Functionals over Variable-Basis Functions (2003) (30)
Geometry and Topology of Continuous Best and Near Best Approximations (2000) (29)
Best approximation by Heaviside perceptron networks (2000) (25)
On stable crossing numbers (1978) (24)
Weak adjoint functors (1971) (23)
Best approximation by linear combinations of characteristic functions of half-spaces (2003) (20)
On robust cycle bases (2002) (19)
Continuity of Approximation by Neural Networks in Lp Spaces (2001) (19)
Comparing fixed and variable-width Gaussian networks (2014) (19)
Approximating Multivariable Functions by Feedforward Neural Nets (2013) (17)
Extension of a theorem of Whitney (2007) (16)
Integral combinations of Heavisides (2010) (15)
Universal coefficient theorems for generalized homology and stable cohomotopy. (1971) (14)
On a problem of P. Erdös (1968) (12)
An integral formula for Heaviside neural networks (2004) (12)
On the stable crossing number of cubes (1972) (12)
A generalization of the 5-color theorem (1974) (12)
Quasiorthogonal Dimension (2020) (11)
Estimates of Approximation Rates by Gaussian Radial-Basis Functions (2007) (11)
Uniqueness of network parametrization and faster learning (1994) (9)
Singularities of finite scaling functions (1996) (9)
A Maximal Toroidal Graph which is not a Triangulation. (1973) (8)
Chromatic number and skewness (1975) (8)
Book embeddings of graphs and a theorem of Whitney (2021) (8)
Isolated squares in hypercubes and robustness of commutativity (2002) (8)
Cycle construction and geodesic cycles with application to the hypercube (2014) (8)
Replacing points by compacta in neural network approximation (2004) (7)
On the Ehresmann–Vanbremeersch Theory and Mathematical Biology (2009) (7)
A New View of Hypercube Genus (2021) (6)
Every Commutative Square of Abelian Groups can be Realized by a Homotopy Commutative Square of Moore, or Co-Moore, Spaces (1972) (6)
An octonion model for physics (2004) (6)
On Tractability of Neural-Network Approximation (2009) (5)
On the immersion of digraphs in cubes (1974) (5)
Approximative compactness of linear combinations of characteristic functions (2020) (4)
Graph cycles and diagram commutativity (2012) (4)
CATEGORY THEORY AND LIVING SYSTEMS (4)
Robust cycle bases do not exist for K n , n if n ≥ 8 (2017) (3)
Rates of Minimization of Error Functionals over Boolean Variable-Basis Functions (2005) (3)
Sphere decompositions of hypercubes (2020) (3)
Kernel Networks with Fixed and Variable Widths (2011) (3)
Synergy versus schema (1994) (3)
Quantum interpretations of the four color theorem (2001) (3)
On 2-skeleta of hypercubes (2020) (3)
A geometric method to obtain error-correcting classification by neural networks with fewer hidden units (1996) (3)
Robust cycle bases do not exist for if (2018) (2)
Estimates of Network Complexity and Integral Representations (2008) (2)
Cubic planar bipartite graphs are dispersable (2021) (2)
Recent Results and Mathematical Methods for Functional Approximation by Neural Networks (2007) (2)
Upper bound for linear arboricity (1991) (2)
Relative colorings of graphs (1973) (2)
On Dispersability of Some Circulant Graphs (2021) (2)
Factorization of Platonic Polytopes into canonical spheres (2021) (1)
Predicting in Prague (2001) (1)
A graph-theoretic model for time (2001) (1)
Quadrilateral embedding of G × Q s ∗ (2006) (1)
Lower Bound for Crossing Nw~b~rs with Applications to K, ) K,, ( and (1972) (1)
Graph Bases and Diagram Commutativity (2018) (1)
Canonical Sphere Bases for Simplicial and Cubical Complexes (2023) (0)
Integral Transforms Induced by Heaviside Perceptrons (2020) (0)
Chapter 5 Approximating Multivariable Functions by Feedforward Neural Nets (2013) (0)
Bochner Integrals and Neural Networks (2023) (0)
Construction numbers: How to build a graph? (2023) (0)
Chapter 6 Bochner Integrals and Neural Networks (0)
Relative Colorings sf Gra (1973) (0)
Outerplanar Coarseness of Planar Graphs (2016) (0)
the Czech Republic Minimization of error functionals over variable-basis functions 1 (2017) (0)
Graphs, Groups and Mandalas (1980) (0)
A Sobolev-type upper bound for rates of approximation by linear combinations of plane waves (2005) (0)
Graph embeddings with no Hamiltonian extensions (2023) (0)
ComplexityofGaussian-radial-basisnetworks approximatingsmoothfunctions (2009) (0)
Topological constancy in the visual perception of resonance (2005) (0)
Lunaport: Math, Mechanics & Transport (2021) (0)
Convex geometry and nonlinear approximation (2000) (0)
Graph Bases and Diagram Commutativity (2018) (0)
A ug 2 02 1 FACTORIZATION OF PLATONIC POLYTOPES INTO CANONICAL SPHERES 1 (2021) (0)
On a Problem of Harary (2017) (0)
Long and short walks in trees (1978) (0)
On finite superuniversal graphs (1978) (0)
Fixed and Variable-Width Gaussian Networks (2020) (0)
On dispersability of some products of cycles (2021) (0)
ON THE DICHROMATIC INDEX OF A DIGRAPH (1996) (0)
The role of mathematics in heuristic performance (2000) (0)

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What Schools Are Affiliated With Paul Chester Kainen?

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