A graph theoretical analysis of the energy landscape of model polymers

In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have non trivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization procedure. This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model. A smaller spectral dimension emerges as a hallmark of stability of the global energy minimum and highlights a non-obvious link between dynamic and thermodynamic properties.Comment: 15 pages, 15 figure

The structure of the hard sphere solid

We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

Optimization by Quantum Annealing: Lessons from Simple Cases

This paper investigates the basic behavior and performance of simulated quantum annealing (QA) in comparison with classical annealing (CA). Three simple one dimensional case study systems are considered, namely a parabolic well, a double well, and a curved washboard. The time dependent Schr\"odinger evolution in either real or imaginary time describing QA is contrasted with the Fokker Planck evolution of CA. The asymptotic decrease of excess energy with annealing time is studied in each case, and the reasons for differences are examined and discussed. The Huse-Fisher classical power law of double well CA is replaced with a different power law in QA. The multi-well washboard problem studied in CA by Shinomoto and Kabashima and leading classically to a logarithmic annealing even in the absence of disorder, turns to a power law behavior when annealed with QA. The crucial role of disorder and localization is briefly discussed.Comment: 16 pages, 9 figure

Weak first order transition in the three-dimensional site-diluted Ising antiferromagnet in a magnetic field

We perform intensive numerical simulations of the three-dimensional site-diluted Ising antiferromagnet in a magnetic field at high values of the external applied field. Even if data for small lattice sizes are compatible with second-order criticality, the critical behavior of the system shows a crossover from second-order to first-order behavior for large system sizes, where signals of latent heat appear. We propose "apparent" critical exponents for the dependence of some observables with the lattice size for a generic (disordered) first-order phase transition.Comment: Final version, accepted for publicatio

Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions

A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in two models where the canonical specific-heat diverges at criticality, thus implying Fisher-renormalization of the critical exponents: the 3D ferromagnetic Ising model and the 2D four-states Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows to simulate systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides extremely accurate determinations of the anomalous dimension and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is impressive, in the Potts case we need to carefully incorporate logarithmic corrections to the microcanonical Ansatz in order to rationalize our data.Comment: 13 pages, 8 figure

Data clustering and noise undressing for correlation matrices

We discuss a new approach to data clustering. We find that maximum likelihood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data. For random, uncorrelated data sets no correlation structure emerges. On the other hand for data sets with a built-in cluster structure, the method is able to detect and recover efficiently that structure. Finally we apply the method to financial time series, where the low temperature behavior reveals a non trivial clustering.Comment: 8 pages, 5 figures, completely rewritten and enlarged version of cond-mat/0003241. Submitted to Phys. Rev.

Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio

A genetic-based algorithm for personalized resistance training

Association studies have identified dozens of genetic variants linked to training responses and sport-related traits. However, no intervention studies utilizing the idea of personalised training based on athlete’s genetic profile have been conducted. Here we propose an algorithm that allows achieving greater results in response to high- or low-intensity resistance training programs by predicting athlete’s potential for the development of power and endurance qualities with the panel of 15 performance-associated gene polymorphisms. To develop and validate such an algorithm we performed two studies in independent cohorts of male athletes (study 1: athletes from different sports (n=28); study 2: soccer players (n=39)). In both studies athletes completed an eight-week high- or low-intensity resistance training program, which either matched or mismatched their individual genotype. Two variables of explosive power and aerobic fitness, as measured by the countermovement jump (CMJ) and aerobic 3-min cycle test (Aero3) were assessed pre and post 8 weeks of resistance training. In study 1, the athletes from the matched groups (i.e. high-intensity trained with power genotype or low-intensity trained with endurance genotype) significantly increased results in CMJ (P=0.0005) and Aero3 (P=0.0004). Whereas, athletes from the mismatched group (i.e. high-intensity trained with endurance genotype or lowintensity trained with power genotype) demonstrated non-significant improvements in CMJ (P=0.175) and less prominent results in Aero3 (P=0.0134). In study 2, soccer players from the matched group also demonstrated significantly greater (P<0.0001) performance changes in both tests compared to the mismatched group. Among non- or low responders of both studies, 82% of athletes (both for CMJ and Aero3) were from the mismatched group (P<0.0001). Our results indicate that matching the individual’s genotype with the appropriate training modality leads to more effective resistance training. The developed algorithm may be used to guide individualised resistance-training interventions

Ising exponents in the two-dimensional site-diluted Ising model

We study the site-diluted Ising model in two dimensions with Monte Carlo simulations. Using finite-size scaling techniques we compute the critical exponents observing deviations from the pure Ising ones. The differences can be explained as the effects of logarithmic corrections, without requiring to change the Universality Class.Comment: 7 pages, 2 postscript figures. Reference correcte