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

## InterestsClifford algebras, combinatorics, probability on algebraic structures## Book- OPERATOR CALCULUS ON GRAPHSTheory and Applications in Computer Science
Imperial College Press, London, 2012. ISBN 978-1-84816-876-3
## Peer-Reviewed Publications- G.S. Staples, A. Weygandt. Elementary functions and factorizations of zeons,
*Advances in Applied Clifford Algebras*(2018) 28:12. 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,
*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.
## SoftwareBelow are links to someMathematica notebooks related to my research. I welcome comments and suggestions for improvements.
- Clifford algebra computations
CliffMath2014a.m
CliffMath2014a.nb
CliffMath2014aExamples.nb
Previous versions: CliffMath2014.m CliffMath2014.nb CliffMath2014Examples.nb CliffMath11.m CliffMath11.nb CliffMath11Examples.nb CliffMath10.m CliffMath10.nb CliffMath10Examples.nb - Zeon, abelian Clifford, and abelian-idempotent Clifford computations
CliffSymNil2014a.m
CliffSymNil2014a.nb
CliffSymNil2014aExamples.nb
Previous versions:
CliffSymNil11.m CliffSymNil11.nb CliffSymNil11Examples.nb CliffSymNil10.m CliffSymNil10.nb CliffSymNil10 Examples.nb - Operator calculus on Clifford algebras
CliffOC11.m - Zeon operator calculus examples
zeonparts.nb - Complexity of cycle enumeration examples
Complexity_of_Cycle_Enumeration.nb - Fermion-zeon convolution examples
FermionZeonConvolution.nb - Clifford algebra decompositions of conformal orthogonal group elements
CO_Decomposition.nb - Zeon Roots
ZeonRoots20160722.nb - Zeon Colorings
ZeonColorings20160721.nb
CliffOC11.nb CliffOC11Examples.nb Previous versions: CliffOC10.m CliffOC10.nb |