We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
We introduce the concept of effective fraction, defined as the expected probability that a configuration from the lowest index replica successfully reaches the highest index replica during a replica exchange Monte Carlo simulation. We then argue that the effective fraction represents an adequate measure of the quality of the sampling technique, as far as swapping is concerned. Under the hypothesis that the correlation between successive exchanges is negligible, we propose a technique for the computation of the effective fraction, a technique that relies solely on the values of the acceptance probabilities obtained at the end of the simulation. The effective fraction is then utilized for the study of the efficiency of a popular swapping scheme in the context of parallel tempering in the canonical ensemble. For large dimensional oscillators, we show that the swapping probability that minimizes the computational effort is 38.74%. By studying the parallel tempering swapping efficiency for a 13-atom Lennard-Jones cluster, we argue that the value of 38.74% remains roughly the optimal probability for most systems with continuous distributions that are likely to be encountered in practice.
Non-linear difference equation models are employed in biology to describe the dynamics of certain populations and their interaction with the environment. In this paper we analyze a non-linear system describing community intervention in mosquito control through management of their habitats. The system takes the general form:where the function h ∈ C 1 ([0, ∞) → [0, 1]) satisfying certain properties, will denote either h(t) = h 1 (t) = e −t and/or h(t) = h 2 (t) = 1/(1 + t). We give conditions in terms of parameters for boundedness and stability. This enables us to explore the dynamics of prevalence/community-activity systems as affected by the range of parameters.
In this work, we analyze a system of nonlinear difference equations describing community intervention in mosquito control. More specifically, we extend the model given in [M. Predescu, R. Levins, T. Awerbuch, Analysis of a nonlinear system for community intervention in mosquito control, Discrete Contin. Dyn. Syst. Ser. B 6 (3) (2006) 605-622] to allow for consciousness to be created in an ongoing way by educational efforts that are independent of the presence of mosquito breeding sites. In order to quantify the effect of random external events, such as weather or public concerns, we consider a stochastic version of the model. Numerical simulations show that the stochastic model is consistent with the deterministic one.
In this paper, we formulate a nonlinear system of difference equations that models the three-stage life cycle of the deer tick over four seasons. We study the effect of seasonality on the stability and oscillatory behavior of the tick population by comparing analytically the seasonal model with a non-seasonal one. The analysis of the models reveals the existence of two equilibrium points. We discuss the necessary and sufficient conditions for local asymptotic stability of the equilibria and analyze the boundedness and oscillatory behavior of the solutions. A main result of the mathematical analysis is that seasonality in the life cycle of the deer tick can have a positive effect, in the sense that it increases the stability of the system. It is also shown that for some combination of parameters within the stability region, perturbations will result in a return to the equilibrium through transient oscillations. The models are used to explore the biological consequences of parameter variations reflecting expected environmental changes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.