George Stacey Staples, Ph.D.
Professor, Department of Mathematics & Statistics
Southern Illinois University Edwardsville
Edwardsville, Illinois 62026-1653
Email:   sstaple at siue.edu


Interests

Clifford algebras, combinatorics, probability on algebraic structures

Books

Peer-Reviewed Publications

  1. G.S. Staples. Zeon matrix inverses and the zeon combinatorial Laplacian
    Adv. Appl. Clifford Algebras 31, 40 (2021).
    DOI: 10.1007/s00006-021-01152-5. Read it online.

  2. A. Davis, G.S. Staples. Zeon and idem-Clifford formulations of Boolean satisfiability
    Adv. Appl. Clifford Algebras 29, 60 (2019).
    DOI:10.1007/s00006-019-0978-8. Read it online.

  3. G.S. Staples. Differential calculus of zeon functions
    Adv. Appl. Clifford Algebras 29, 25 (2019).
    DOI:10.1007/s00006-019-0943-6 . Read it online.

  4. E. Haake, G.S. Staples. Zeros of zeon polynomials and the zeon quadratic formula
    Adv. Appl. Clifford Algebras 29, 21 (2019).
    DOI:10.1007/s00006-019-0938-3. Read it online.

  5. T. Lindell, G.S. Staples. Norm inequalities in zeon algebras
    Adv. Appl. Clifford Algebras 29, 13 (2019).
    DOI:10.1007/s00006-018-0934-z. Read it online.

  6. G.S. Staples, A. Weygandt. Elementary functions and factorizations of zeons
    Adv. Appl. Clifford Algebras 28, 12 (2018).
    DOI: 10.1007/s00006-018-0836-0. Read it online.

  7. G.S. Staples. Hamiltonian cycle enumeration via fermion-zeon convolution
    International Journal of Theoretical Physics, 56 (2017), 3923-3934.
    DOI:10.1007/s10773-017-3381-z. Read it online.

  8. G.S. Staples. Zeons, orthozeons, and processes on colored graphs
    Proceedings of CGI '17, Yokohama, Japan, June 27-30, 2017 ACM, New York, NY, 2017.
    DOI: 10.1145/3095140.3097283

  9. L.M. Dollar, G.S. Staples. Zeon roots
    Adv. Appl. Clifford Algebras, 27 (2017), 1133-1145.
    DOI:10.1007/s00006-016-0732-4. Read it online.

  10. G.S. Staples, T. Stellhorn. Zeons, orthozeons, and graph colorings
    Adv. Appl. Clifford Algebras, 27 (2017), 1825-1845.
    DOI:10.1007/s00006-016-0732-4. Read it online.

  11. R. Schott, G.S. Staples. Generalized zeon algebras: theory and application to multi-constrained path problems
    Adv. Appl. Clifford Algebras, 27 (2017), 45-57
    DOI: 10.1007/s00006-015-0595-0. Read it online.

  12. A. Syarif, A. Abouaissa, L. Idoumghar, P. Lorenz, R. Schott, G.S. Staples. New Path Centrality Based on Operator Calculus Approach for Wireless Sensor Network Deployment
    in IEEE Transactions on Emerging Topics in Computing. (2016).
    DOI: 110.1109/TETC.2016.2585045

  13. G.S. Staples. Kravchuk matrices and induced operators on Clifford algebras
    in Probability on Algebraic and Geometric Structures, Contemporary Mathematics, 668, Amer. Math. Soc., Providence, RI, 2016, pp. 207-221.

  14. G.S. Staples, D. Wylie. Clifford algebra decompositions of conformal orthogonal group elements
    Clifford Analysis, Clifford Algebras and Their Applications, 4 (2015), 223-240. pdf

  15. B. Nefzi, R. Schott, Y.Q. Song, G.S. Staples, E. Tsiontsiou, An operator calculus approach for multi-constrained routing in wireless sensor networks
    Proceedings of the 16th ACM International Symposium on Mobile Ad Hoc Networking and Computing, ACM, New York, 2015, 367-376. DOI: 10.1145/2746285.2746301

  16. C. Cassiday, G.S. Staples On representations of semigroups having hypercube-like Cayley graphs
    Clifford Analysis, Clifford Algebras, and Their Applications, 4 (2015), 111-130. pdf

  17. J. Ben Slimane, R. Schott, Y-Q. Song, G.S. Staples, E. Tsiontsiou, Operator calculus algorithms for multi-constrained paths
    International Journal of Mathematics and Computer Science, 10 (2015), no. 1, 69-104. pdf.

  18. G.S. Staples, Kravchuk polynomials and induced/reduced operators on Clifford algebras
    Complex Analysis and Operator Theory, 9 (2015), 445-478.
    DOI: 10.1007/s11785-014-0377-z. Read it online.

  19. R. Schott, G.S. Staples, Operator calculus and invertible Clifford Appell systems: theory and application to the n-particle fermion algebra
    Infinite Dimensional Analysis, Quantum Probability and Related Topics, 16 (2013), 1350007.
    DOI: 10.1142/S0219025713500070

  20. G. Harris, G.S. Staples, Spinorial formulations of graph problems
    Adv. Appl. Clifford Algebras, 22 (2012), 59-77.
    DOI: 10.1007/s00006-011-0298-0. Read it online.

  21. R. Schott, G.S. Staples, Connected components and evolution of random graphs: an algebraic approach
    Journal of Algebraic Combinatorics, 35 (2012), 141-156.
    DOI: 10.1007/s10801-011-0297-1. Read it online or click here for the pdf.

  22. H. Cruz-Sanchez, G.S. Staples, R. Schott, Y-Q. Song, Operator calculus approach to minimal paths: Precomputed routing in a store-and-forward satellite constellation
    Proceedings of IEEE Globecom, Anaheim, CA, USA, December 3-7, 2012, pp. 3438-3443.

  23. R. Schott, G.S. Staples, Complexity of counting cycles using zeons
    Computers & Mathematics with Applications, 62 (2011), 1828-1837.
    DOI: 10.1016/j.camwa.2011.06.026

  24. R. Schott, G.S. Staples, Nilpotent adjacency matrices and random graphs
    Ars Combinatoria, 98 (2011), 225-239. (pdf)

  25. R. Schott, G.S. Staples, On the Complexity of Cycle Enumeration for Simple Graphs
    in Guide to Geometric Algebra in Practice, L. Dorst and J. Lasenby (editors), Springer, 2011, pp. 233-249.
    DOI: 10.1007/s00006-008-0143-2

  26. R. Schott, G.S. Staples, Zeons, lattices of partitions, and free probability
    Communications on Stochastic Analysis, 4 (2010), 311-334. (pdf)

  27. R. Schott, G.S. Staples, Operator homology and cohomology in Clifford algebras
    Cubo, A Mathematical Journal, 12 (2010), 299-326.
    DOI: 10.4067/S0719-06462010000200018

  28. R. Schott, G.S. Staples, Dynamic geometric graph processes: adjacency operator approach
    Adv. Appl. Clifford Algebras, 20 (2010), 893-921.
    DOI: 10.1007/s00006-010-0228-6. Read it online.

  29. R. Schott, G.S. Staples, Dynamic random walks in Clifford algebras
    Advances in Pure and Applied Mathematics, 1 (2010), 81-115.
    DOI: 10.1515/APAM.2010.007

  30. R. Schott, G.S. Staples, Reductions in computational complexity using Clifford algebras
    Adv. Appl. Clifford Algebras, 20 (2010), 121-140.
    DOI: 10.1007/s00006-008-0143-2. Read it online.

  31. R. Schott, G.S. Staples, Computational Complexity Reductions Using Clifford Algebras
    in Geometric Algebra Computing for Engineering and Computer Science, E. Bayro-Corrochano and G. Scheuermann (editors), Springer Verlag, 2010, pp. 431-453.

  32. G.S. Staples, A new adjacency matrix for finite graphs
    Adv. Appl. Clifford Algebras, 18 (2008), 979-991.
    DOI: 10.1007/s00006-008-0116-5. Read it online.

  33. R. Schott, G.S. Staples, Nilpotent adjacency matrices, random graphs, and quantum random variables
    Journal of Physics A: Mathematical and Theoretical, 41 (2008), 155205.
    DOI: 10.1088/1751-8113/41/15/155205

  34. R. Schott, G.S. Staples, Random walks in Clifford algebras of arbitrary signature as walks on directed hypercubes, Markov Processes and Related Fields, 14 (2008), 515-542.

  35. G.S. Staples, Norms and generating functions in Clifford algebras
    Adv. Appl. Clifford Algebras, 18 (2008), 75-92.
    DOI: 10.1007/s00006-007-0063-6. Read it online.

  36. R. Schott, G.S. Staples, Partitions and Clifford algebras
    European Journal of Combinatorics, 29 (2008), 1133-1138.
    DOI: 10.1016/j.ejc.2007.07.003

  37. G.S. Staples, Graph-theoretic approach to stochastic integrals with Clifford algebras
    Journal of Theoretical Probability, 20 (2007), 257-274.
    DOI: 10.1007/s10959-007-0064-3. Read it online.

  38. R. Schott, G.S. Staples, Operator calculus and Appell systems on Clifford algebras
    International Journal of Pure and Applied Mathematics, 31 (2006), 427-446.

  39. G.S. Staples, Clifford-algebraic random walks on the hypercube
    Adv. Appl. Clifford Algebras, 15 (2005), 213-232.
    DOI: 10.1007/s00006-005-0014-z. Read it online.

Unreviewed Publications

  • R. Schott, G.S. Staples, Clifford operator calculus: homology, cohomology, and Appell systems, 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics, K. Gürlebeck (ed.), Weimar, Germany, 15--20 July 2011. pdf

  • R. Schott, G.S. Staples, Clifford algebras, random graphs, and quantum random variables, in Quantum Stochastics and Information (Statistics, Filtering and Control), University of Nottingham, UK, 15 - 22 July 2006, V P Belavkin & M Guţă (editors), World Scientific Publishing, 2008.

Research Presentations at Conferences

  • Zeon Matrix Algebra and the Zeon Combinatorial Laplacian
    12th International Conference on Clifford Algebras and Their Applications (ICCA12)
    Hefei, CHINA, August 3-7, 2020. [Online via Zoom]

  • Zeon and Idem-Clifford Formulations of Boolean Satisfiability
    ENGAGE Workshop
    Computer Graphics International 2019 (CGI '19)
    Calgary, CANADA, June 17-20, 2019.

  • Norm Inequalities in Zeon Algebras
    2018 Alterman Conference and School on Geometric Algebra and Kähler Calculus (ACSGAKC 2018)
    Milan, ITALY, July 23-27, 2018.

  • Algebraic Properties of Zeons
    11th International Conference on Clifford Algebras and Their Applications (ICCA11)
    Ghent, BELGIUM, August 7-11, 2017.

  • Zeons, Orthozeons, and Processes on Colored Graphs
    ENGAGE Workshop Keynote Address
    Computer Graphics International 2017 (CGI '17)
    Yokohama, JAPAN, June 27-30, 2017.

  • Traces of Graph-Induced Operators on Fermions and Zeons
    Quantum Structures 2016 (IQSA 2016)
    Leicester, UK, 11-15 July 2016.

  • Graph-Induced Operators on Clifford Algebras
    LLMC 2016 - Langenhop Lecture and SIU Mathematics Conference
    Carbondale, Illinois, USA, 16-17 May 2016.

  • Decomposition Algorithms in Clifford Algebras
    CoCoA 2015 - Combinatorics and Computer Algebra
    Fort Collins, Colorado, USA, 20-24 July 2015.

  • Operator Calculus on Clifford Algebras: Combinatorics to Quantum Probability
    Invited plenary talk, 10th International Conference on Clifford Algebras and Their Applications (ICCA10)
    Tartu, ESTONIA, 4-9 August 2014.

  • Kravchuk Matrices and Induced Operators on Clifford Algebras
    Probability on Algebraic and Geometric Structures
    Southern Illinois University, Carbondale, Illinois, USA, 5-7 June 2014.

  • Combinatorial Semigroups and Induced/Deduced Operators
    The 4th Novi Sad Algebraic Conference & Semigroups and Applications
    Novi Sad, SERBIA, June 2013.

  • Operator calculus approach to minimal paths: Precomputed routing in a store-and-forward satellite constellation (w. H. Cruz-Sanchez, R. Schott, Y-Q. Song), IEEE Globecom 2012, Anaheim, California, USA, December 3-7.

  • Clifford Operator Calculus: Homology, Cohomology, and Appell Systems
    Invited plenary talk, 9th International Conference on Clifford Algebras and Their Applications (ICCA9)
    Weimar, GERMANY, July 2011.

  • On the Complexity of Counting Cycles in Sparse Graphs using Nilpotent Adjacency Matrices
    24th Midwest Conference on Combinatorics, Cryptography, and Computing
    Illinois State University, Normal, Illinois, USA, September 2010.

  • On the Complexity of Cycle Enumeration using Zeons
    Applications of Geometric Algebras in Computer Science and Engineering (AGACSE 2010)
    Amsterdam, The NETHERLANDS, June 2010.

  • Graph-Theoretic Free Cumulants using Zeons
    30th Conference on Quantum Probability and Related Topics
    Santiago, CHILE, November 2009.

  • Reductions in Computational Complexity Using Clifford Algebras
    Applications of Geometric Algebras in Computer Science and Engineering (AGACSE 2008)
    Leipzig, GERMANY, August 2008.

  • Clifford Algebras, Graph Problems, and Computational Complexity
    Invited plenary talk, 8th International Conference on Clifford Algebras and Their Applications
    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 State University, Wichita, Kansas, USA, 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

  • Stochastic Processes on Graphs: Some Theoretical Aspects and Applications
    Probability Seminar, Institut Élie Cartan, Université de Lorraine, Nancy, FRANCE, May 2012.

  • Wireless Networks and Random Graphs: An Operator Calculus Approach
    INRIA, Paris, FRANCE, November 2010.

  • Wireless Networks and Graded Semigroup Algebras
    Southern Illinois University Carbondale, November 2010.

  • Wireless Networks, Random Graphs, and Clifford Algebras
    Institut Élie Cartan, Université Henri Poincaré-Nancy I, Nancy, FRANCE, October 2010.

  • Clifford Algebras, Finite Graphs, and Random Walks
    Southern Illinois University Carbondale, November 2008.

  • Clifford-Algebraic Generating Functions and a Frobenius Norm for Clifford Matrices
    Tennessee Technological University, Cookeville, Tennessee, November 2004.

Software

Below are links to some Mathematica notebooks related to my research. I welcome comments and suggestions for improvements.

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Disclaimer: These software packages are provided "AS IS" without warranty of any kind. Should any program prove defective, the end-user assumes the cost of any necessary service, repair, or correction.
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