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Edwin J Beggs

Publications and source records attributed to Edwin J Beggs.

2 recordsLinked to original sources

On human-centred security: A new systems model based on modes and mode transitions

We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.

cs.CR↗

Noncommutative geodesics and the KSGNS construction

We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2(C) and C(Z_n), though restricting to classical real time. On the way we have to consider the reality of a noncommutative vector field, and for this we propose a definition depending on a state on the algebra.

math.QA↗