A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems

In this paper we present a dynamical Monte Carlo algorithm which is applicable to systems satisfying a clustering condition: during the dynamical evolution the system is mostly trapped in deep local minima (as happens in glasses, pinning problems etc.). We compare the algorithm to the usual Monte Carlo algorithm, using as an example the Bernasconi model. In this model, a straightforward implementation of the algorithm gives an improvement of several orders of magnitude in computational speed with respect to a recent, already very efficient, implementation of the algorithm of Bortz, Kalos and Lebowitz.Comment: RevTex 7 pages + 4 figures (uuencoded) appended; LPS preprin

Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model

We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N \rightarrow \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We determine a functional Parisi-like order parameter $P_d(q)$ which plays a similar role for the dynamics to that played by the usual function for the statics.Comment: 8 pages, Roma preprin

Time decay of the remanent magnetization in the ±J\pm J spin glass model at T=0

Using the zero-temperature Metropolis dynamics, the time decay of the remanent magnetization in the $\pm J$ Edward-Anderson spin glass model with a uniform random distribution of ferromagnetic and antiferromagnetic interactions has been investigated. Starting from the saturation, the magnetization per spin $m$ reveals a slow decrease with time, which can be approximated by a power law:$m(t)=m_{\infty}+ ({t\over a_{0}})^{a_{1}}$, $a_{1} < 0$. Moreover, its relaxation does not lead it into one of the ground states, and therefore the system is trapped in metastable isoenergetic microstates remaining magnetized. Such behaviour is discussed in terms of a random walk the system performs on its available configuration space.Comment: 9 pages, 3 figure

Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information

We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha<\alpha_c$ the stationary state is shown to be non-unique. For $\alpha\to 0$ we analyse our equations in leading order in $\alpha$, and find asymptotic solutions with diverging volatility \sigma=\order(\alpha^{-{1/2}}) (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility \sigma=\order(\alpha^{{1/2}}). The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.Comment: 15 pages, 6 figures, uses Revtex. Replaced an old version of volatility graph that. Rephrased and updated some reference

Dynamical and Stationary Properties of On-line Learning from Finite Training Sets

The dynamical and stationary properties of on-line learning from finite training sets are analysed using the cavity method. For large input dimensions, we derive equations for the macroscopic parameters, namely, the student-teacher correlation, the student-student autocorrelation and the learning force uctuation. This enables us to provide analytical solutions to Adaline learning as a benchmark. Theoretical predictions of training errors in transient and stationary states are obtained by a Monte Carlo sampling procedure. Generalization and training errors are found to agree with simulations. The physical origin of the critical learning rate is presented. Comparison with batch learning is discussed throughout the paper.Comment: 30 pages, 4 figure

Aging without disorder on long time scales

We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out to be very efficient for the study of glassy systems, which get trapped in local minima on many different time scales. We find strong evidence of aging effects at low temperatures. We relate these effects to the distribution function of the trapping times of single configurations.Comment: 8 pages Revtex, 7 figures uuencoded (Revised version: the figures are now present

Large times off-equilibrium dynamics of a particle in a random potential

We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics with violation of equilibrium theorems. We derive the equations obeyed by the slowly varying part of the two-times correlation and response functions and obtain an analytical solution of these equations. For short-range correlated potentials we find that: {\it i.} the scaling function is non analytic at similar times and this behaviour crosses over to ultrametricity when the correlations become long range, {\it ii.} aging dynamics persists in the limit of zero confining mass with universal features for widely separated times. We compare with the numerical solution to the dynamical equations and generalize the dynamical equations to finite $N$ by extending the variational method to the dynamics.Comment: 70 pages, 7 figures included, uuencoded Z-compressed .tar fil

Real-time non-equilibrium dynamics of quantum glassy systems

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the $p$ spin-glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.Comment: 56 pages, Revtex, 17 figures include

Spatially heterogeneous ages in glassy dynamics

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.Comment: 47 pages, 60 Fig

Why Are Outcomes Different for Registry Patients Enrolled Prospectively and Retrospectively? Insights from the Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF).

Background: Retrospective and prospective observational studies are designed to reflect real-world evidence on clinical practice, but can yield conflicting results. The GARFIELD-AF Registry includes both methods of enrolment and allows analysis of differences in patient characteristics and outcomes that may result. Methods and Results: Patients with atrial fibrillation (AF) and ≥1 risk factor for stroke at diagnosis of AF were recruited either retrospectively (n = 5069) or prospectively (n = 5501) from 19 countries and then followed prospectively. The retrospectively enrolled cohort comprised patients with established AF (for a least 6, and up to 24 months before enrolment), who were identified retrospectively (and baseline and partial follow-up data were collected from the emedical records) and then followed prospectively between 0-18 months (such that the total time of follow-up was 24 months; data collection Dec-2009 and Oct-2010). In the prospectively enrolled cohort, patients with newly diagnosed AF (≤6 weeks after diagnosis) were recruited between Mar-2010 and Oct-2011 and were followed for 24 months after enrolment. Differences between the cohorts were observed in clinical characteristics, including type of AF, stroke prevention strategies, and event rates. More patients in the retrospectively identified cohort received vitamin K antagonists (62.1% vs. 53.2%) and fewer received non-vitamin K oral anticoagulants (1.8% vs . 4.2%). All-cause mortality rates per 100 person-years during the prospective follow-up (starting the first study visit up to 1 year) were significantly lower in the retrospective than prospectively identified cohort (3.04 [95% CI 2.51 to 3.67] vs . 4.05 [95% CI 3.53 to 4.63]; p = 0.016). Conclusions: Interpretations of data from registries that aim to evaluate the characteristics and outcomes of patients with AF must take account of differences in registry design and the impact of recall bias and survivorship bias that is incurred with retrospective enrolment. Clinical Trial Registration: - URL: http://www.clinicaltrials.gov . Unique identifier for GARFIELD-AF (NCT01090362)