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- René Schott, G. Stacey Staples
- Eur. J. Comb.
- 2008

- René Schott, G. Stacey Staples
- Ars Comb.
- 2011

While powers of the adjacency matrix of a finite graph reveal information about walks on the graph, they fail to distinguish closed walks from cycles. Using elements of an appropriate commutative, nilpotent-generated algebra, a " new " adjacency matrix can be associated with a random graph on n vertices and |E| edges of nonzero probability. Letting X k… (More)

A number of combinatorial problems are treated using properties of abelian nilpotent-and idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle is known to be NP-complete. By considering entries of Λ k , where Λ is an appropriate nilpotent adjacency matrix, the k-cycles… (More)

- René Schott, G. Stacey Staples
- Computers & Mathematics with Applications
- 2011

- G S Staples
- Journal of neurosurgery
- 1979

- Hugo Cruz-Sanchez, G. Stacey Staples, René Schott, Yeqiong Song
- GLOBECOM
- 2007

—An innovative minimal paths algorithm based on operator calculus in graded semigroup algebras is described. Classical approaches to routing problems invariably require construction of trees and the use of heuristics to prevent com-binatorial explosion. The operator calculus approach presented herein, however, allows such explicit tree constructions to be… (More)

Questions about a graph's connected components are answered by studying appropriate powers of a special " adjacency matrix " constructed with entries in a commutative algebra whose generators are idempotent. The approach is then applied to the Erdös-Rényi model of sequences of random graphs. Developed herein is a method of encoding the relevant information… (More)

- Bilel Nefzi, René Schott, Yeqiong Song, G. Stacey Staples, Evangelia Tsiontsiou
- MobiHoc
- 2015

Wireless sensor networks (WSN) are inherently multi - constrained. They need to preserve energy while offering reliable and timely data reporting for a non-negligible number of scenarios. This is particularly true when a node should decide which forwarder has to be chosen for routing a packet. Nevertheless, solving multi-constrained routing problems is… (More)

A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an… (More)

We present an original algebraic method for cycle enumeration which is well-suited for symbolic computations. Nilpotent adjacency matrix methods are employed to enumerate k-cycles in simple graphs on n vertices for any k ≤ n. Experimental results detailing computation times (in seconds) are compared with algorithms based on the approaches of Bax and Tarjan… (More)