CliffMath swMATH ID: 4955 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: CliffOC; CliffSymNil; Mathematica; Omega; OEIS; Genius; Adinkras; mftoolbox; StableBBasisNBM5; RAGlib; CLT; CIRC; Proof General; Haskell; FEPG; Localizer; ISLR; EnvyMyCar; KLAIM; GluCat Cited in: 23 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Clifford algebras and zeons. Geometry to combinatorics and beyond. Zbl 1431.15001Staples, George Stacey 2020 Operator calculus on graphs. Theory and applications in computer science. Zbl 1264.15025Schott, René; Staples, G. Stacey 2012 all top 5 Cited by 21 Authors 5 Neto, Antônio Francisco 3 Staples, George Stacey 2 Schott, René 1 Ciancia, Vincenzo 1 Davis, Amanda 1 Dollar, Lisa M. 1 Fonseca, Carolina Rodrigues 1 Haake, Erin 1 Hansen, Helle Hvid 1 Kupke, Clemens 1 Latella, Diego 1 Lindell, Theresa 1 Loreti, Michele 1 Mansour, Toufik 1 Massink, Mieke 1 Rutten, Jan J. M. M. 1 Schork, Matthias 1 Stacey Staples, G. 1 Stellhorn, Tiffany 1 Weygandt, Alexander 1 Woracek, Harald all top 5 Cited in 7 Serials 11 Advances in Applied Clifford Algebras 2 Journal of Integer Sequences 2 Logical Methods in Computer Science 1 International Journal of Theoretical Physics 1 Mathematics of Operations Research 1 Annals of Operations Research 1 SIAM Review all top 5 Cited in 17 Fields 15 Combinatorics (05-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 8 Quantum theory (81-XX) 4 Computer science (68-XX) 3 Special functions (33-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) Citations by Year