3,078 research outputs found
Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems
When simulating molecular systems using deterministic equations of motion
(e.g., Newtonian dynamics), such equations are generally numerically integrated
according to a well-developed set of algorithms that share commonly agreed-upon
desirable properties. However, for stochastic equations of motion (e.g.,
Langevin dynamics), there is still broad disagreement over which integration
algorithms are most appropriate. While multiple desiderata have been proposed
throughout the literature, consensus on which criteria are important is absent,
and no published integration scheme satisfies all desiderata simultaneously.
Additional nontrivial complications stem from simulating systems driven out of
equilibrium using existing stochastic integration schemes in conjunction with
recently-developed nonequilibrium fluctuation theorems. Here, we examine a
family of discrete time integration schemes for Langevin dynamics, assessing
how each member satisfies a variety of desiderata that have been enumerated in
prior efforts to construct suitable Langevin integrators. We show that the
incorporation of a novel time step rescaling in the deterministic updates of
position and velocity can correct a number of dynamical defects in these
integrators. Finally, we identify a particular splitting that has essentially
universally appropriate properties for the simulation of Langevin dynamics for
molecular systems in equilibrium, nonequilibrium, and path sampling contexts.Comment: 15 pages, 2 figures, and 2 table
Formal analysis techniques for gossiping protocols
We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them
Efficiency Analysis of Swarm Intelligence and Randomization Techniques
Swarm intelligence has becoming a powerful technique in solving design and
scheduling tasks. Metaheuristic algorithms are an integrated part of this
paradigm, and particle swarm optimization is often viewed as an important
landmark. The outstanding performance and efficiency of swarm-based algorithms
inspired many new developments, though mathematical understanding of
metaheuristics remains partly a mystery. In contrast to the classic
deterministic algorithms, metaheuristics such as PSO always use some form of
randomness, and such randomization now employs various techniques. This paper
intends to review and analyze some of the convergence and efficiency associated
with metaheuristics such as firefly algorithm, random walks, and L\'evy
flights. We will discuss how these techniques are used and their implications
for further research.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:1212.0220, arXiv:1208.0527, arXiv:1003.146
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