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

Book

Peer-Reviewed Publications

  • 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, Advances in Applied 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, Advances in Applied 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, Advances in Applied 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, IEEE Transactions on Emerging Topics in Computing. Preprint (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
    Advances in Applied 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
    Advances in Applied 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
    Advances in Applied 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
    Advances in Applied 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
    Advances in Applied 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
    Advances in Applied 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

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

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

  • Nilpotent Adjacency Operators and Minimal Path Problems
    Remote keynote address with Skype Q&A
    Special Section of the 33rd International Geographical Congress:
    W.K. Clifford's Geometric Algebra and Geographical Information Science:
    Development and Applications (GAGIS)

    August 25-26, 2016, Xianlin Campus, Nanjing Normal University, CHINA.

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

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

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

  • 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.
    Conference web page

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

  • Combinatorial Semigroups and Induced/Deduced Operators
    The 4th Novi Sad Algebraic Conference & Semigroups and Applications
    Novi Sad, SERBIA, June 2013.
    Conference web page: NSAC13

  • 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.
    Conference web page: GLOBECOM2012

  • 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.
    Conference web page: ICCA 9

  • 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.
    Conference web page: QP 30

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

  • Clifford Algebras, Graph Problems, and Computational Complexity
    Invited plenary talk, 8th International Conference on Clifford Algebras and Their Applications
    Campinas, BRAZIL, May 2008.
    Conference web page: ICCA 8

  • 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.
    Conference web page: MCCCC 20

  • 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.
    Conference web page: RSA 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.
    Conference web page: ICCA 7

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.