An efficient method for computing steady state solutions with Gillespie’s direct method

An efficient method for computing steady state solutions with Gillespie's direct method.

Gillespie's direct method is a stochastic simulation algorithm that may be used to calculate the steady state solution of a chemically reacting system. Recently the all possible states method was introduced as a way of accelerating the convergence of the simulations. We demonstrate that while the all possible states (APS) method does reduce the number of required trajectories, it is actually mu...

A Preconditioned Newton-Krylov Method for Computing Steady-State Pulse Solutions of Mode-Locked Lasers

We solve the periodic boundary value problem for a mode-locked laser cavity using a specially preconditioned matrix-implicit Newton-Krylov solver. Solutions are obtained at least an order of magnitude faster than with dynamic simulation, the standard method. Our method is demonstrated experimentally on a one-dimensional temporal model of an eight femtosecondmode-locked laser operating in the di...

An Efficient Steady-State Analysis Method for Large Boolean Networks with High Maximum Node Connectivity

Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the ...

An Efficient Method for Computing Alignment Diagnoses

Formal, logic-based semantics have long been neglected in ontology matching. As a result, almost all matching systems produce incoherent alignments of ontologies. In this paper we propose a new method for repairing such incoherent alignments that extends previous work on this subject. We describe our approach within the theory of diagnosis and introduce the notion of a local optimal diagnosis. ...

An Elementary Method for Computing the Kostka Coefficients