Large deviation principles for nongradient weakly asymmetric stochastic lattice gases

We consider a lattice gas on the discrete d-dimensional torus $(\mathbb{Z}/N\mathbb{Z})^d$ 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

Bounds on current fluctuations in periodically driven systems

Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol. We obtain a universal bound on current fluctuations for periodically driven systems. This bound is a generalization of the known bound for stationary states. In general, the average rate that bounds fluctuations in periodically driven systems is different from the rate of entropy production. We also obtain a local bound on fluctuations that leads to a trade-off relation between speed and precision in periodically driven systems, which constitutes a generalization to periodically driven systems of the so called thermodynamic uncertainty relation. From a technical perspective, our results are obtained with the use of a recently developed theory for 2.5 large deviations for Markov jump processes with time-periodic transition rates.Comment: 23 pages, 3 figure

A simple method for studying the molecular mechanisms of ultraviolet and violet reception in vertebrates

The Νmaxs and A/B ratios of HBNs of ancestral and present-day pigments. (DOCX 43 kb

Structural differences and differential expression among rhabdomeric opsins reveal functional change after gene duplication in the bay scallop, Argopecten irradians (Pectinidae)

Background Opsins are the only class of proteins used for light perception in image-forming eyes. Gene duplication and subsequent functional divergence of opsins have played an important role in expanding photoreceptive capabilities of organisms by altering what wavelengths of light are absorbed by photoreceptors (spectral tuning). However, new opsin copies may also acquire novel function or subdivide ancestral functions through changes to temporal, spatial or the level of gene expression. Here, we test how opsin gene copies diversify in function and evolutionary fate by characterizing four rhabdomeric (Gq-protein coupled) opsins in the scallop, Argopecten irradians, identified from tissue-specific transcriptomes. Results Under a phylogenetic analysis, we recovered a pattern consistent with two rounds of duplication that generated the genetic diversity of scallop Gq-opsins. We found strong support for differential expression of paralogous Gq-opsins across ocular and extra-ocular photosensitive tissues, suggesting that scallop Gq-opsins are used in different biological contexts due to molecular alternations outside and within the protein-coding regions. Finally, we used available protein models to predict which amino acid residues interact with the light-absorbing chromophore. Variation in these residues suggests that the four Gq-opsin paralogs absorb different wavelengths of light. Conclusions Our results uncover novel genetic and functional diversity in the light-sensing structures of the scallop, demonstrating the complicated nature of Gq-opsin diversification after gene duplication. Our results highlight a change in the nearly ubiquitous shadow response in molluscs to a narrowed functional specificity for visual processes in the eyed scallop. Our findings provide a starting point to study how gene duplication may coincide with eye evolution, and more specifically, different ways neofunctionalization of Gq-opsins may occur

Book Review of: 'Relevance theory : recent developments, current challenges and future directions' by M. Padilla Cruz (ed.)

Gq-opsin sequences included in the phylogenetic analysis. Asterisks represent sequences obtained through Porter et al. [27]. For additional information regarding sequence acquisition not available on Genbank, see supplementary material in Porter et al. [27]. (DOCX 25 kb

A representation formula for large deviations rate functionals of invariant measures on the one dimensional torus

We consider a generic diffusion on the ID torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had been characterized by M. I. Freidlin and A. D. Wentzell as solution of a rather complex optimization problem. We discuss this last problem in full generality and show that it leads to our formula. We express the rate functional by means of a geometric transformation that, with a Maxwell-like construction, creates flat regions. We then consider piecewise deterministic Markov processes on the ID torus and show that the corresponding large deviation rate functional for the stationary distribution is obtained by applying the same transformation. Inspired by this, we prove a universality result showing that the transformation generates viscosity solution of stationary Hamilton-Jacobi equation associated to any Hamiltonian H satisfying suitable weak conditions