arXiv subjects
Publications and source records attributed to Oliver Mason.
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm which computes the Markov chain tree vector of a stochastic matrix.
The physiology of voltage gated ion channels is complex and insights into their gating mechanism is incomplete. Their function is best represented by Markov models with relatively large number of distinct states that are connected by thermodynamically feasible transitions. On the other hand, popular models such as the one of Hodgkin and Huxley have empirical assumptions that are generally unrealistic. Experimental protocols often dictate the number of states in proposed Markov models, thus creating disagreements between various observations on the same channel. Here we aim to propose a limit to the minimum number of states required to model ion channels by employing a paradigm to define stationary conductance in a class of ion-channels. A simple expression is generated using concepts in elementary thermodynamics applied to protein conformational transitions. Further, it matches well many published channel current-voltage characteristics and parameters of the model are found to be identifiable and easily determined from usual experimental protocols.
We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions recently described in \cite{SunWang} for the existence of L-K functionals. We also provide related conditions for positive coupled differential-difference positive systems and for systems of neutral type that are not necessarily positive. Finally, corresponding results for discrete-time systems are described.
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to absolute norms. The semigroups under consideration may be generated by discrete-time systems, continuous-time systems or continuous-time systems with jumps. The existence of extremal norms is used to extend results on the Lipschitz continuity of the joint spectral radius beyond the known case of semigroups that are irreducible in the representation theory interpretation of the word.
The Markov Chain Tree Theorem is extended to the max algebra and possible applications to ranking problems are discussed.
The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by considering multi-objective generalisations of the single objective optimisation problem solved in these earlier papers. We relate the existence of globally optimal solutions to the commutativity properties of the associated matrices; we relate min-max optimal solutions to the generalised spectral radius; and we prove that Pareto optimal solutions are guaranteed to exist.
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.