NP-hardness of the cluster minimization problem revisited

The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analog of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge

Home accidents amongst elderly people: A locality study in Scotland

Aim The aim of this locality study was to collect information on reported and unreported accidents amongst elderly people living in one locality in Scotland. Method Postal Survey- A postal questionnaire was sent to 3,757 men and women aged 65+ years living in one locality. The questionnaire asked respondents to indicate how many accidents they had experienced in the past twelve months, plus to indicate type and location. Information was gathered on living arrangements, ethnicity, gender, age and deprivation. Respondents were asked if they would be willing to take part in an interview study. Interview Study - One hundred elders who had had at least one accident in the previous twelve months were interviewed. Results Postal Survey - Over a third of the respondents in the postal survey reported having had an accident in the previous twelve months. Bumps and drops and falls were the most common type of accident. Most accidents happened in the kitchen. Women reported more falls than men and those living alone reported more accidents than those living with others. Age was associated with the prevalence of accidents, but the association was somewhat curvilinear, with accidents decreasing with age and then increasing again. Interview Study – Interviewees found it hard to differentiate one accident from another. Considerable reluctance to visit the GP after an accident was noted, with many not attending even for serious accidents. Almost forty percent were ‘very’ distressed after their accident, and a quarter reported a loss of confidence. However, most did not worry about accidents. Few thought that their age, health or medications were a cause of their accidents

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see http://www.smallsystems.d

Energy landscape and phase transitions in the self-gravitating ring model

We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the self-gravitating ring model. We show analytically that the criterion correctly singles out the phase transition between a homogeneous and a clustered phase and also suggests the presence of another phase transition, not previously known. On the basis of the properties of the energy landscape we conjecture on the nature of the latter transition

Energy Landscape and Global Optimization for a Frustrated Model Protein

The three-color (BLN) 69-residue model protein was designed to exhibit frustrated folding. We investigate the energy landscape of this protein using disconnectivity graphs and compare it to a Go model, which is designed to reduce the frustration by removing all non-native attractive interactions. Finding the global minimum on a frustrated energy landscape is a good test of global optimization techniques, and we present calculations evaluating the performance of basin-hopping and genetic algorithms for this system.Comparisons are made with the widely studied 46-residue BLN protein.We show that the energy landscape of the 69-residue BLN protein contains several deep funnels, each of which corresponds to a different β-barrel structure

Deceptive signals of phase transitions in small magnetic clusters

We present an analysis of the thermodynamic properties of small transition metal clusters and show how the commonly used indicators of phase transitions like peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see http://www.smallsystems.d

The statistics of critical points of Gaussian fields on large-dimensional spaces

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of relevance to glassy and disordered systems, and to landscape scenarios coming from the anthropic approach to string theory.Comment: 5 page

Real world and tropical cyclone world. Part I: high-resolution climate model verification

Recent global climate models with sufficient resolution and physics offer a promising approach for simulating real-world tropical cyclone (TC) statistics and their changing relationship with climate. In the first part of this study, we examine the performance of a high-resolution (;40-km horizontal grid) global climate model, the atmospheric component of the Australian Community Climate and Earth System Simulator (ACCESS) based on the Met Office Unified Model (UM8.5) Global Atmosphere (GA6.0). The atmospheric model is forced with observed sea surface temperature, and 20 years of integrations (1990–2009) are analyzed for evaluating the simulated TC statistics compared with observations. The model reproduces the observed climatology, geographical distribution, and interhemispheric asymmetry of global TC formation rates reasonably well. The annual cycle of regional TC formation rates over most basins is also well captured. However, there are some regional biases in the geographical distribution of TC formation rates. To identify the sources of these biases, a suite of model-simulated large-scale climate conditions that critically modulate TC formation rates are further evaluated, including the assessment of a multivariate genesis potential index. Results indicate that the model TC genesis biases correspond well to the inherent biases in the simulated large-scale climatic states, although the relative effects on TC genesis of some variables differs between basins. This highlights the model’s mean-state dependency in simulating accurate TC formation rates

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

How glassy are orientational dynamics of rodlike molecules near the isotropic-nematic transition?

In an attempt to quantitatively characterize the recently observed slow dynamics in the isotropic and nematic phase of liquid crystals, we investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dynamics in line with the estbalished methods in supercooled liquids, we construct a relaxation time versus scaled inverse temperature plot, and demonstrate that one can indeed define a 'fragility index' for thermotropic liquid crystals, that depends on density and aspect ratio. The values of the fragility parameter are surprisingly in the range one observed for glass forming liquids. A plausible correlation between the energy landscape features and the observed fragility is discussed.Comment: 7 figures and 8 page