1,720,982 research outputs found
Large Deviations in Renewal Models of Statistical Mechanics
Full text linkIn Ref. [1] the author has recently established sharp large deviation
principles for cumulative rewards associated with a discrete-time renewal
model, supposing that each renewal involves a broad-sense reward taking values
in a separable Banach space. The renewal model has been there identified with
constrained and non-constrained pinning models of polymers, which amount to
Gibbs changes of measure of a classical renewal process. In this paper we show
that the constrained pinning model is the common mathematical structure to the
Poland-Scheraga model of DNA denaturation and to some relevant one-dimensional
lattice models of Statistical Mechanics, such as the Fisher-Felderhof model of
fluids, the Wako-Sait\^o-Mu\~noz-Eaton model of protein folding, and the
Tokar-Dreyss\'e model of strained epitaxy. Then, in the framework of the
constrained pinning model, we develop an analytical characterization of the
large deviation principles for cumulative rewards corresponding to multivariate
deterministic rewards that are uniquely determined by, and at most of the order
of magnitude of, the time elapsed between consecutive renewals. In particular,
we outline the explicit calculation of the rate functions and successively we
identify the conditions that prevent them from being analytic and that underlie
affine stretches in their graphs. Finally, we apply the general theory to the
number of renewals. From the point of view of Equilibrium Statistical Physics
and Statistical Mechanics, cumulative rewards of the above type are the
extensive observables that enter the thermodynamic description of the system.
The number of renewals, which turns out to be the commonly adopted order
parameter for the Poland-Scheraga model and for also the renewal models of
Statistical Mechanics, is one of these observables
Renewal model for dependent binary sequences
Full text linkWe suggest to construct infinite stochastic binary sequences by associating
one of the two symbols of the sequence with the renewal times of an underlying
renewal process. Focusing on stationary binary sequences corresponding to
delayed renewal processes, we investigate correlations and the ability of the
model to implement a prescribed autocovariance structure, showing that a large
variety of subexponential decay of correlations can be accounted for. In
particular, robustness and efficiency of the method are tested by generating
binary sequences with polynomial and stretched-exponential decay of
correlations. Moreover, to justify the maximum entropy principle for model
selection, an asymptotic equipartition property for typical sequences that
naturally leads to the Shannon entropy of the waiting time distribution is
demonstrated. To support the comparison of the theory with data, a law of large
numbers and a central limit theorem are established for the time average of
general observables
Statistical fluctuations under resetting: rigorous results
Full text linkIn this paper we investigate the normal and the large fluctuations of
additive functionals associated with a stochastic process under a general
non-Poissonian resetting mechanism. Cumulative functionals of regenerative
processes are very close to renewal-reward processes and inherit most of the
properties of the latter. Here we review and use the classical law of large
numbers and central limit theorem for renewal-reward processes to obtain same
theorems for additive functionals of a stochastic process under resetting.
Then, we establish large deviation principles for these functionals by
illustrating and applying a large deviation theory for renewal-reward processes
that has been recently developed by the author. We discuss applications of the
general results to the positive occupation time, the area, and the absolute
area of the reset Brownian motion. While introducing advanced tools from
renewal theory, we demonstrate that a rich phenomenology accounting for
dynamical phase transitions emerges when one goes beyond Poissonian resetting.Comment: Submitted to the special issue of Journal of Physics A: Mathematical
and Theoretical on "Stochastic Resetting: Theory and Applications
Large deviation principles for renewal-reward processes
Full text linkWe establish a sharp large deviation principle for renewal–reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle without assuming any exponential moment condition on the law of waiting times and rewards by resorting to a sharp version of Cramér's theory. We also exhibit sufficient conditions for exponential tightness of renewal–reward processes, which leads to a full large deviation principle
Apparent multifractality of self-similar L\'evy processes
Full text linkScaling properties of time series are usually studied in terms of the scaling
laws of empirical moments, which are the time average estimates of moments of
the dynamic variable. Nonlinearities in the scaling function of empirical
moments are generally regarded as a sign of multifractality in the data. We
show that, except for the Brownian motion, this method fails to disclose the
correct monofractal nature of self-similar L\'evy processes. We prove that for
this class of processes it produces apparent multifractality characterised by a
piecewise-linear scaling function with two different regimes, which match at
the stability index of the considered process. This result is motivated by
previous numerical evidence. It is obtained by introducing an appropriate
stochastic normalisation which is able to cure empirical moments, without
hiding their dependence on time, when moments they aim at estimating do not
exist
Critical Fluctuations in Renewal Models of Statistical Mechanics
Full text linkWe investigate the sharp asymptotic behavior at criticality of the large
fluctuations of extensive observables in renewal models of statistical
mechanics, such as the Poland-Scheraga model of DNA denaturation, the
Fisher-Felderhof model of fluids, the Wako-Sait\^o-Mu\~noz-Eaton model of
protein folding, and the Tokar-Dreyss\'e model of strained epitaxy. These
models amount to Gibbs changes of measure of a classical renewal process and
can be identified with a constrained pinning model of polymers. The extensive
observables that enter the thermodynamic description turn out to be cumulative
rewards corresponding to deterministic rewards that are uniquely determined by
the waiting time and grow no faster than it. The probability decay with the
system size of their fluctuations switches from exponential to subexponential
at criticality, which is a regime corresponding to a discontinuous
pinning-depinning phase transition. We describe such decay by proposing a
precise large deviation principle under the assumption that the subexponential
correction term to the waiting time distribution is regularly varying. This
principle is in particular used to characterize the fluctuations of the number
of renewals, which measures the DNA-bound monomers in the Poland-Scheraga
model, the particles in the Fisher-Felderhof model and the Tokar-Dreyss\'e
model, and the native peptide bonds in the Wako-Sait\^o-Mu\~noz-Eaton model
Equilibrium Properties and Force-Driven Unfolding Pathways of RNA Molecules
No full textThe mechanical unfolding of a simple RNA hairpin and of a 236-base portion of the Tetrahymena thermophila ribozyme is studied by means of an Ising-like model. Phase diagrams and free energy landscapes are computed exactly and suggest a simple two-state behavior for the hairpin and the presence of intermediate states for the ribozyme. Nonequilibrium simulations give the possible unfolding pathways for the ribozyme, and the dominant pathway corresponds to the experimentally observed one
Nearly symmetrical proteins: Folding pathways and transition states
No full textThe folding pathways of the B domain of protein A have been the subject of many experimental and computational studies. Based on a statistical mechanical model, it has been suggested that the native state symmetry leads to multiple pathways, highly dependent on temperature and denaturant concentration. Experiments, however, have not confirmed this scenario. By considering four nearly symmetrical proteins, one of them being the above molecule, here we show that, if contact energies are properly taken into account, a different picture emerges from kinetic simulations of the above-mentioned model. This is characterized by a dominant folding pathway, which is consistent with the most recent experimental results. Given the simplicity of the model, we also report on a direct sampling of the transition state
Fake Truth. The Legal Issue of Archaeological Forgery
No full textArt forgery is a crime against public trust and it is frequently considered to be a violation of truth, intended as the correspondence between language and reality. Starting from the Buonarroti case, the author compares art forgery and fake artwork, which can have an effect of truth, and tries to explain the legal meaning of authentication, which requires a judicial procedure when the controversy of attribution is permanent. Examining the van Meegeren case, the author concludes the analysis with a critique of the correspondence theory of truth and with the proposal of a dialectical model for the authentication of works of art. Finally, considering the F words (forge, false, fake, fictional), it is asserted in the essay that, in today’s culture, fake artwork preserves the profound ambiguity of truth in fiction
On the Mean Residence Time in Stochastic Lattice-Gas Models
No full textA heuristic law widely used in fluid dynamics for steady flows states that the amount of a fluid in a control volume is the product of the fluid influx and the mean time that the particles of the fluid spend in the volume, or mean residence time. We rigorously prove that if the mean residence time is introduced in terms of sample-path averages, then stochastic lattice-gas models with general injection, diffusion, and extraction dynamics verify this law. Only mild assumptions are needed in order to make the particles distinguishable so that their residence time can be unambiguously defined. We use our general result to obtain explicit expressions of the mean residence time for the Ising model on a ring with Glauber + Kawasaki dynamics and for the totally asymmetric simple exclusion process with open boundaries
- …
