Finite-Size Scaling at Phase Coexistence

{}From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better than as an asymptotic expansion, we find that FSS for moments of low order is still complete. We suggest ways of using this theory for the analysis of numerical simulations. We test these methods numerically through the scaling of cumulants and moments of the magnetization in the low-temperature phase of the two-dimensional Ising model. (LaTeX file; ps figures included as shar file)Comment: preprint HLRZ 27/93 and LU TP 93-

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Monte Carlo simulation and global optimization without parameters

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett

Testing Error Correcting Codes by Multicanonical Sampling of Rare Events

The idea of rare event sampling is applied to the estimation of the performance of error-correcting codes. The essence of the idea is importance sampling of the pattern of noises in the channel by Multicanonical Monte Carlo, which enables efficient estimation of tails of the distribution of bit error rate. The idea is successfully tested with a convolutional code

Generalized-ensemble simulations and cluster algorithms

The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the partition function or thermal averages of interest. While this is true in terms of its simplicity and universal applicability, the resulting approach suffers from the presence of temporal correlations of successive samples naturally implied by the Markov chain underlying the importance-sampling simulation. In many situations, these autocorrelations are moderate and can be easily accounted for by an appropriately adapted analysis of simulation data. They turn out to be a major hurdle, however, in the vicinity of phase transitions or for systems with complex free-energy landscapes. The critical slowing down close to continuous transitions is most efficiently reduced by the application of cluster algorithms, where they are available. For first-order transitions and disordered systems, on the other hand, macroscopic energy barriers need to be overcome to prevent dynamic ergodicity breaking. In this situation, generalized-ensemble techniques such as the multicanonical simulation method can effect impressive speedups, allowing to sample the full free-energy landscape. The Potts model features continuous as well as first-order phase transitions and is thus a prototypic example for studying phase transitions and new algorithmic approaches. I discuss the possibilities of bringing together cluster and generalized-ensemble methods to combine the benefits of both techniques. The resulting algorithm allows for the efficient estimation of the random-cluster partition function encoding the information of all Potts models, even with a non-integer number of states, for all temperatures in a single simulation run per system size.Comment: 15 pages, 6 figures, proceedings of the 2009 Workshop of the Center of Simulational Physics, Athens, G

An efficient, multiple range random walk algorithm to calculate the density of states

We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.Comment: 4 pages including 4 ps fig

Influences of state anxiety on gaze behavior and stepping accuracy in older adults during adaptive locomotion

This article is available open access through the publisher’s website at the link below. Copyright © The Authors 2011.OBJECTIVES: Older adults deemed to be at a high risk of falling transfer their gaze from a stepping target earlier than their low-risk counterparts. The extent of premature gaze transfer increases with task complexity and is associated with a decline in stepping accuracy. This study tests the hypothesis that increased anxiety about upcoming obstacles is associated with (a) premature transfers of gaze toward obstacles (i.e., looking away from a target box prior to completing the step on it in order to fixate future constraints in the walkway) and (b) reduced stepping accuracy on the target in older adults. METHODS: High-risk (9) and low-risk (8) older adult participants walked a 10-m pathway containing a stepping target area followed by various arrangements of obstacles, which varied with each trial. Anxiety, eye movements, and movement kinematics were measured. RESULTS: Progressively increasing task complexity resulted in associated statistically significant increases in measures of anxiety, extent of early gaze transfer, and stepping inaccuracies in the high-risk group. DISCUSSION: These results provide evidence that increased anxiety about environmental hazards is related to suboptimal visual sampling behavior which, in turn, negatively influences stepping performance, potentially contributing to increased falls risk in older adults.Biotechnology and Biological Sciences Research Counci

Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases

We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include histograms of subphases. The free energy difference between phases, necessary for attributing the correct statistical weights to the histograms, is determined by a detour in control parameter space via auxiliary systems with short relaxation times. We apply this method to a recently introduced model for structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the authors ([email protected], [email protected]

Successes and Challenges of Optimal Trauma Care for Rural Family Physicians in Kansas

Introduction. Kansas has a regionalized trauma systemwith formal mechanisms for review, however, increasedcommunication with rural providers can uncover opportunitiesfor system process improvement. Therefore, thisqualitative study explored perceptions of family medicinephysicians staffing emergency departments (ED) in rural areas,specifically to determine what is going well and what areasneeded improvement in relation to the trauma system. Methods. A focus group included Kansas rural family physiciansrecruited from a local symposium for family medicinephysicians. Demographic information was collected via surveyprior to the focus group session, which was audiotaped.Research team members read the transcription, identifiedthemes, and grouped the findings into categories for analysis. Results. Seven rural family medicine physicians participated inthe focus group. The majority were male (71%) with the mean age46.71 years. All saw patients in the ED and had treated injuriesdue to agriculture, falls, and motor vehicle collisions. Participantsidentified successes in the adoption and enforcement of standardizedprocesses, specifically through level IV trauma centercertification and staff requirements for Advanced Trauma LifeSupport training. Communication breakdown during patient dischargeand skill maintenance were the most prevalent challenges. Conclusions. Even with an established regionalized traumasystem in the state of Kansas, there continues to be opportunitiesfor improvement. The challenges acknowledged byfocus group participants may not be identified through patientcase reviews (if conducted), therefore tertiary centersshould conduct system reviews with referring hospitals regularlyto improve systemic concerns. KS J Med 2017;10(1):12-16