66 research outputs found
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 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 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 spin glass model at T=0
Using the zero-temperature Metropolis dynamics, the time decay of the
remanent magnetization in the 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
reveals a slow decrease with time, which can be approximated by a power
law:, . 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 of the
number of possible values for the external information over the number
of trading agents. In the limit we calculate the location
of the phase transition (signaling the onset of anomalous response),
and solve the statics for exactly. The temporal correlations
in global market fluctuations turn out not to decay to zero for infinitely
widely separated times. For the stationary state is shown to
be non-unique. For we analyse our equations in leading order in
, 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
-dimensional random potential when . 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 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 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)
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