CliffOC swMATH ID: 4957 Software Authors: Schott, René; Staples, G. Stacey Description: Operator calculus on graphs. Theory and applications in computer science This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations. Homepage: http://www.siue.edu/~sstaple/index_files/research.htm Keywords: Clifford algebras; operator calculus; graph theory; quantum probability; geometric graph processes; time-homogeneous random walks; dynamic walks; iterated stochastic integrals; partition-dependent stochastic measures; Appell systems; operator (co)homology Related Software: CliffMath; CliffSymNil; Mathematica; Omega; Genius; OEIS; mftoolbox; StableBBasisNBM5; RAGlib; CLT; CIRC; Proof General; Haskell; FEPG; Localizer; ISLR; EnvyMyCar; KLAIM; GluCat; Gaigen Cited in: 20 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Operator calculus on graphs. Theory and applications in computer science. Zbl 1264.15025Schott, René; Staples, G. Stacey 2012 all top 5 Cited by 16 Authors 6 Schott, René 6 Staples, George Stacey 4 Neto, Antônio Francisco 1 Ciancia, Vincenzo 1 Davis, Amanda 1 Fonseca, Carolina Rodrigues 1 Gürlebeck, Norman 1 Hansen, Helle Hvid 1 Kupke, Clemens 1 Latella, Diego 1 Loreti, Michele 1 Massink, Mieke 1 Rutten, Jan J. M. M. 1 Stacey Staples, G. 1 Stellhorn, Tiffany 1 Woracek, Harald all top 5 Cited in 11 Serials 6 Advances in Applied Clifford Algebras 2 Logical Methods in Computer Science 1 Mathematics of Operations Research 1 Annals of Operations Research 1 SIAM Review 1 Markov Processes and Related Fields 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Journal of Integer Sequences 1 International Journal of Pure and Applied Mathematics 1 Cubo 1 Complex Analysis and Operator Theory all top 5 Cited in 17 Fields 12 Linear and multilinear algebra; matrix theory (15-XX) 8 Combinatorics (05-XX) 7 Quantum theory (81-XX) 6 Probability theory and stochastic processes (60-XX) 4 Computer science (68-XX) 3 Special functions (33-XX) 2 Operator theory (47-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) Citations by Year