George Stacey Staples, Ph.D.

Department of Mathematics & Statistics

Southern Illinois University Edwardsville

Edwardsville, Illinois 62026-1653

(618) 650-2364

 

Email: sstaple at siue.edu

Interests

 

Probability on algebraic structures, Clifford algebras, graph theory and combinatorics

 

Papers Published or Accepted for Publication

 

Dynamic geometric graph processes: adjacency operator approach (w. René Schott)

                Advances in Applied Clifford Algebras,
                Accepted for publication. 

 

Dynamic random walks in Clifford algebras (w. René Schott)

                Advances in Pure and Applied Mathematics,
                Accepted for publication.
                http://www.heldermann.de/APA/apacover.htm

Reductions in computational complexity using Clifford algebras (w. René Schott)

                Advances in Applied Clifford Algebras,
                Accepted for publication. 

A new adjacency matrix for finite graphs  

                Advances in Applied Clifford Algebras, 18 (2008), 979-991 .

                http://dx.doi.org/10.1007/s00006-008-0116-5

Nilpotent adjacency matrices, random graphs, and quantum random variables

(w. René Schott)

                 Journal of Physics A: Mathematical and Theoretical, 41 (2008) 155205.

Random walks in Clifford algebras of arbitrary signature as walks on directed hypercubes  

(w.  René Schott)

                 Markov Processes and Related Fields, 14 (2008), 515-542.

Norms and generating functions in Clifford algebras 

                 Advances in Applied Clifford Algebras, 18 (2008), 75-92.

                 Online at  http://www.springerlink.com/content/1661-4909/

Nilpotent adjacency matrices and random graphs (w.  René Schott) [pdf]

                 Ars Combinatoria

                 Accepted for publication.

Partitions and Clifford algebras (w. René Schott)

                 European Journal of Combinatorics, 29 (2008), 1133-1138.

Graph-theoretic approach to  stochastic integrals with Clifford algebras

                 Journal of Theoretical Probability, 20 (2007), 257-274.

                 http://www.springerlink.com/content/1572-9230/

Operator calculus and Appell systems on Clifford algebras    (w. René Schott)

                 International Journal of Pure and Applied Mathematics, 31 (2006), 

                 427-446.

 

Clifford-algebraic random walks on the hypercube

                 Advances in Applied Clifford Algebras 15 (2005), 213-232.

                 Online at  www.clifford-algebras.org/v15/v152/cont152.html

 

 

Book Chapter 

 

Computational complexity reductions using Clifford algebras (w. René Schott)
    Geometric Algebra Computing for Engineering and Computer Science,
    Springer Verlag 2009, E. Bayro-Corrochano and G. Scheuermann (editors).
    In press.
 

Conference Proceedings

   
Clifford algebras, random graphs, and quantum random variables  (w. René Schott)
    QUANTUM STOCHASTICS AND INFORMATION
    Statistics, Filtering and Control
    University of Nottingham, UK 15 - 22 July 2006
    edited by V P Belavkin & M Guţă (University of Nottingham, UK)
    Published by World Scientific Publishing
    Pub. date: Sept 2008
    ISBN 978-981-283-295-5
   
    http://www.worldscibooks.com/physics/6942.html

 

 

Research Presentations at Conferences

 

“Reductions in Computational Complexity Using Clifford Algebras”

             3rd International Conference on Applications of Geometric Algebras

             in Computer Science and Engineering,

             Leipzig, Germany, August 2008.

 
“Clifford Algebras, Graph Problems, and Computational Complexity”

             Invited plenary talk,  8th International Conference on Clifford Algebras

             and Their Applications in Mathematical Physics,

             Campinas, Brazil, May 2008.

"Three Algebras Related to Random Graphs and Quantum Probability”

             4th International Conference of Applied Mathematics and Computing,

             Plovdiv, Bulgaria, August 2007.

“How Can NP Graph Problems Be Moved Into P?”

             20th Midwest Conference on Combinatorics, Cryptography, and

             Computing, Wichita, Kansas, October 2006.

“Clifford Algebras, Random Graphs, and Quantum Probability”

             27th International Conference on Quantum Probability and Infinite

             Dimensional Analysis, Nottingham, England, July 2006.

           

“Clifford Algebras and Random Graphs”

             12th International Conference on Random Structures

             and Algorithms, Poznan, Poland, August 2005.

“Clifford-Algebraic Generating Functions  and a Frobenius Norm for Clifford Matrices”

             7th International Conference on Clifford Algebras and

             Their Applications, Toulouse, France, May 2005.

 

Invited Seminars & Colloquia

 

 

“Clifford Algebras, Finite Graphs, and Random Walks"
             Invited colloquium presentation,
            Southern Illinois University Carbondale, November 2008.

 

“Clifford-Algebraic Generating Functions and a Frobenius Norm for Clifford Matrices”

             Invited seminar talk,  Tennessee Technological University,

             Cookeville, Tennessee, November 2004.

 

 

Prepublications

 

Zeons, lattices of partitions, and free probability (w. René Schott)

  

Cycles and components in geometric graphs: adjacency operator approach (w. René Schott)

Operator homology and cohomology in Clifford algebras (w. René Schott)   [pdf]

Connected components and evolution of random graphs: an algebraic approach (w. René Schott), [pdf]

Professional Affiliations

 

American Mathematical Society (AMS)

Association for Quantum Probability and Infinite Dimensional Analysis (AQPIDA)

Clifford Algebras International Research Open Studies Center (CAIROS)

 

Software

 

Below are links to some Mathematica notebooks I’ve been working on.  It’s all open source, and I welcome comments and suggestions for improvements.

 

 

Clifford algebra computations

 

CliffMath08.nb                           Source

CliffMath08.m                            Package

CliffMath08 Examples.nb      Simple Examples

 

 

 

Cl_n^nil , Cl_n^sym, and Cl_n^id computations

 

CliffSymNil08.nb                         Source

CliffSymNil08.m                          Package

CliffSymNil08 Examples.nb    Simple Examples