By Rene Schott, G. Stacey Staples

ISBN-10: 1848168764

ISBN-13: 9781848168763

This pioneering booklet offers a learn of the interrelationships between operator calculus, graph idea, and quantum likelihood in a unified demeanour, with major emphasis on symbolic computations and an eye fixed towards functions in machine technological know-how.

provided during this booklet are new tools, equipped at the algebraic framework of Clifford algebras, for tackling vital genuine international difficulties similar, yet now not constrained to, instant communications, neural networks, electric circuits, transportation, and the area broad net. Examples are recommend in Mathematica in the course of the booklet, including applications for acting symbolic computations.

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**Extra info for Operator Calculus On Graphs: Theory and Applications in Computer Science**

**Example text**

1} ... ......................................................................................................... • e • • e • • The three-dimensional hypercube as the Cayley graph of B3,0 / eα . Fixing the set B = {e1 , . . , en }, the power set of B is in one-to-one correspondence with the vertices of Qn via the binary subset representation (a1 a2 · · · an ) ↔ eI ⇔ ai = 1 i ∈ I, 0 otherwise.

F− (xn ) denotes the ideal of R[x1 , . . , xn ] generated by the polynomials {f+ (x1 ), . . , f− (xn )}. Moreover, the abelian null blade algebra has the following polynomial interpretation: B p,q sym B ∧n sym ∼ = R[x1 , . . , xn ]/ x1 2 , . . , xn 2 . 79) Similar polynomial interpretations can be formulated for the nonabelian algebras by considering the ring of polynomials with anticommuting indeterminates {ξ1 , . . , ξn }. In particular, B p,q ∼ = R[ξ1 , . . , ξn ]/ f+ (ξ1 ), . . 80) B ∧n ∼ = R[ξ1 , .

101 • • Fig. 1 001 e{2} • e • e • e∅ • e{1,2,3} • • . ........ .. .. . ... .... . ..... . .... ..... . . . . ... . {1,2} ...... ..... ......................................................................................................... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... {3} ... {1,3} ... . . . . . . . . . . . .

### Operator Calculus On Graphs: Theory and Applications in Computer Science by Rene Schott, G. Stacey Staples

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