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 and their generalizations, algebraic combinatorics, symbolic computation

Books

Peer-Reviewed Publications

  • M.M Price, G.S. Staples. Binary Linear Codes via Zeon and Sym-Clifford Algebras.
    In: Silva, D.W., Hitzer, E., Hildenbrand, D. (eds) Advanced Computational Applications of Geometric Algebra. ICACGA 2022. Lecture Notes in Computer Science, vol 13771. Springer, Cham. (2024). DOI: 10.1007/978-3-031-34031-4_18.

  • S. Ewing, G.S. Staples. Zeon and Idem-Clifford formulations of hypergraph problems
    Adv. Appl. Clifford Algebras 32, 61 (2022).
    DOI: 10.1007/s00006-022-01242-y. Read it online.

  • G.S. Staples. Spectrally simple zeros of zeon polynomials
    Adv. Appl. Clifford Algebras 31, 66 (2021).
    DOI: 10.1007/s00006-021-01167-y. Read it online.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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

  • 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

  • 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

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • 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

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

  • 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

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

  • 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

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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

  • 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.

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

  • 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.

Other 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

  • Binary Linear Codes via Zeon and Sym-Clifford Algebras
    International Conference of Advanced Computational Applications of Geometric Algebra (ICACGA)
    Denver, Colorado, USA. October 2-5, 2022. [Online via Zoom]

  • Clifford Algebras and Zeons: Geometry to Combinatorics and Beyond
    International Conference of Advanced Computational Applications of Geometric Algebra (ICACGA)
    Denver, Colorado, USA. October 2-5, 2022. [Online via Zoom]

  • 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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