2,448 research outputs found
Large deviation principles for nongradient weakly asymmetric stochastic lattice gases
We consider a lattice gas on the discrete d-dimensional torus
with a generic translation invariant, finite range
interaction satisfying a uniform strong mixing condition. The lattice gas
performs a Kawasaki dynamics in the presence of a weak external field E/N. We
show that, under diffusive rescaling, the hydrodynamic behavior of the lattice
gas is described by a nonlinear driven diffusion equation. We then prove the
associated dynamical large deviation principle. Under suitable assumptions on
the external field (e.g., E constant), we finally analyze the variational
problem defining the quasi-potential and characterize the optimal exit
trajectory. From these results we deduce the asymptotic behavior of the
stationary measures of the stochastic lattice gas, which are not explicitly
known. In particular, when the external field E is constant, we prove a
stationary large deviation principle for the empirical density and show that
the rate function does not depend on E.Comment: Published in at http://dx.doi.org/10.1214/11-AAP805 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Large deviations of the empirical flow for continuous time Markov chains
We consider a continuous time Markov chain on a countable state space and
prove a joint large deviation principle for the empirical measure and the
empirical flow, which accounts for the total number of jumps between pairs of
states. We give a direct proof using tilting and an indirect one by contraction
from the empirical process.Comment: Minor revision, to appear on Annales de l'Institut Henri Poincare (B)
Probability and Statistic
Large deviations for a stochastic model of heat flow
We investigate a one dimensional chain of harmonic oscillators in which
neighboring sites have their energies redistributed randomly. The sites
and are in contact with thermal reservoirs at different temperature
and . Kipnis, Marchioro, and Presutti \cite{KMP} proved that
this model satisfies {}Fourier's law and that in the hydrodynamical scaling
limit, when , the stationary state has a linear energy density
profile , . We derive the large deviation
function for the probability of finding, in the stationary
state, a profile different from . The function
has striking similarities to, but also large differences from, the
corresponding one of the symmetric exclusion process. Like the latter it is
nonlocal and satisfies a variational equation. Unlike the latter it is not
convex and the Gaussian normal fluctuations are enhanced rather than suppressed
compared to the local equilibrium state. We also briefly discuss more general
model and find the features common in these two and other models whose
is known.Comment: 28 pages, 0 figure
An analytical framework to nowcast well-being using mobile phone data
An intriguing open question is whether measurements made on Big Data
recording human activities can yield us high-fidelity proxies of socio-economic
development and well-being. Can we monitor and predict the socio-economic
development of a territory just by observing the behavior of its inhabitants
through the lens of Big Data? In this paper, we design a data-driven analytical
framework that uses mobility measures and social measures extracted from mobile
phone data to estimate indicators for socio-economic development and
well-being. We discover that the diversity of mobility, defined in terms of
entropy of the individual users' trajectories, exhibits (i) significant
correlation with two different socio-economic indicators and (ii) the highest
importance in predictive models built to predict the socio-economic indicators.
Our analytical framework opens an interesting perspective to study human
behavior through the lens of Big Data by means of new statistical indicators
that quantify and possibly "nowcast" the well-being and the socio-economic
development of a territory
Large deviations for diffusions: Donsker-Varadhan meet Freidlin-Wentzell
We consider a diffusion process on and prove a large deviation
principle for the empirical process in the joint limit in which the time window
diverges and the noise vanishes. The corresponding rate function is given by
the expectation of the Freidlin-Wentzell functional per unit of time. As an
application of this result, we obtain a variational representation of the rate
function for the Gallavotti-Cohen observable in the small noise and large time
limits
Congenital Chagas disease in a Bolivian newborn in Bergamo (Italy)
Chagas disease (CD) is an uncommon disease in Europe. Its epidemiology has changed because of mass migration from Latin America to Europe. Herein we describe a congenital case of CD in a Bolivian newborn in Bergamo, the main city of residence for the Bolivian community in Italy. At delivery, serological analyses evidenced IgG antibodies against Trypanosoma cruzi both in the child and mother, as expected. Hemoscopic analyses on peripheral blood were repeatedly negative during the first months of life. Eventually, thanks to T. cruzi Real Time polymerase chain reaction (RT-PCR) positivity on peripheral blood and development of progressive anemia in the following weeks, congenital Chagas disease was diagnosed and benznidazole-based therapy started. A progressive antibodies' index decrease was observed till negativity (306 days apart). RT-PCR was negative at the end of treatment. Our case is instructive and management of congenital CD is discussed from the perspective of a non-endemic country
Fronteras en movimiento. Migraciones hacia la Unión Europea en el contexto mediterráneo
Ricard Zapata-Barrero y Xavier Ferrer-Gallardo (eds.). Barcelona: Edicions Bellaterra, 2012, 345 pp
Flows, currents, and cycles for Markov chains: Large deviation asymptotics
We consider a continuous time Markov chain on a countable state space. We prove a joint large deviation principle (LDP) of the empirical measure and current in the limit of large time interval. The proof is based on results on the joint large deviations of the empirical measure and flow obtained in Bertini et al. (in press). By improving such results we also show, under additional assumptions, that the LDP holds with the strong L1
topology on the space of currents. We deduce a general version of the Gallavotti–Cohen (GC) symmetry for the current field and show that it implies the so-called fluctuation theorem for the GC functional. We also analyze the large deviation properties of generalized empirical currents associated to a fundamental basis in the cycle space, which, as we show, are given by the first class homological coefficients in the graph underlying the Markov chain. Finally, we discuss in detail some examples
Geography of science: competitiveness and inequality
We characterize the temporal dynamics of Scientific Fitness, as defined by the Economic Fitness and Complexity (EFC) framework, and R&D expenditures at the geographic scale of nations. Our analysis highlights common patterns across similar research systems, and shows how develop-ing nations (China in particular) are quickly catching up with the developed world. This paints the picture of a general growth of scientific and technical capabilities of nations induced by the spreading of information typical of the scientific environment. Shifting the focus of the analysis to the regional level, we find that even developed nations display a considerable level of inequal-ity in the Scientific Fitness of their internal regions. Further, we assess comparatively how the competitiveness of each geographic region is distributed over the spectrum of research sectors. Overall, the Scientific Fitness represents the first high quality estimation of the scientific strength of nations and regions, opening new policy-making applications for better allocating resources, filling inequality gaps and ultimately promoting innovation
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