Minimum entropy production principle from a dynamical fluctuation law

The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical distribution of occupation times for a class of Markov processes, we identify the entropy production as the large deviation rate function, up to leading order when expanding around a detailed balance dynamics. In that way, the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations, and its approximate character gets an explanation. We also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time-reversal.Comment: 17 page

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Quantum state estimation and large deviations

In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one new subsection (4.1) and another (4.2 was 4.1 in the previous version) completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected. References added. Accepted for publication in Rev. Math. Phy

Heat flow in chains driven by thermal noise

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar and in the classical regime by Saito and Dhar and Kundu et al. Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution which turn out to decay exponentially. We, moreover, consider an extension of a single particle model suggested by Derrida and Brunet and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.Comment: Latex: 26 pages and 9 figures, appeared in J. Stat. Mech. P04005 (2012

The target problem with evanescent subdiffusive traps

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time

Regulation of ABCA1 by AMD-Associated Genetic Variants and Hypoxia in iPSC-RPE

Age-related macular degeneration (AMD) is a progressive disease of the macula characterized by atrophy of the retinal pigment epithelium (RPE) and photoreceptor degeneration, leading to severe vision loss at advanced stages in the elderly population. Impaired reverse cholesterol transport (RCT) as well as intracellular lipid accumulation in the RPE are implicated in AMD pathogenesis. Here, we focus on ATP-binding cassette transporter A1 (ABCA1), a major cholesterol transport protein in the RPE, and analyze conditions that lead to ABCA1 dysregulation in induced pluripotent stem cell (iPSC)-derived RPE cells (iRPEs). Our results indicate that the risk-conferring alleles rs1883025 (C) and rs2740488 (A) in ABCA1 are associated with increased ABCA1 mRNA and protein levels and reduced efficiency of cholesterol efflux from the RPE. Hypoxia, an environmental risk factor for AMD, reduced expression of ABCA1 and increased intracellular lipid accumulation. Treatment with a liver X receptor (LXR) agonist led to an increase in ABCA1 expression and reduced lipid accumulation. Our data strengthen the homeostatic role of cholesterol efflux in the RPE and suggest that increasing cellular cholesterol export by stimulating ABCA1 expression might lessen lipid load, improving RPE survival and reducing the risk of developing AMD

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Thymus Extracellular Matrix-Derived Scaffolds Support Graft-Resident Thymopoiesis and Long-Term In Vitro Culture of Adult Thymic Epithelial Cells

The thymus provides the physiological microenvironment critical for the development of T lymphocytes, the cells that orchestrate the adaptive immune system to generate an antigen-specific response. A diverse population of stroma cells provides surface-bound and soluble molecules that orchestrate the intrathymic maturation and selection of developing T cells. Forming an intricate 3D architecture, thymic epithelial cells (TEC) represent the most abundant and important constituent of the thymic stroma. Effective models for in and ex vivo use of adult TEC are still wanting, limiting the engineering of functional thymic organoids and the understanding of the development of a competent immune system. Here a 3D scaffold is developed based on decellularized thymic tissue capable of supporting in vitro and in vivo thymopoiesis by both fetal and adult TEC. For the first time, direct evidences of feasibility for sustained graft-resident T-cell development using adult TEC as input are provided. Moreover, the scaffold supports prolonged in vitro culture of adult TEC, with a retained expression of the master regulator Foxn1. The success of engineering a thymic scaffold that sustains adult TEC function provides unprecedented opportunities to investigate thymus development and physiology and to design and implement novel strategies for thymus replacement therapies

Detection of Variants in 15 Genes in 87 Unrelated Chinese Patients with Leber Congenital Amaurosis

BACKGROUND: Leber congenital amaurosis (LCA) is the earliest onset and most severe form of hereditary retinal dystrophy. So far, full spectrum of variations in the 15 genes known to cause LCA has not been systemically evaluated in East Asians. Therefore, we performed comprehensive detection of variants in these 15 genes in 87 unrelated Han Chinese patients with LCA. METHODOLOGY/PRINCIPAL FINDINGS: The 51 most frequently mutated exons and introns in the 15 genes were selected for an initial scan using cycle sequencing. All the remaining exons in 11 of the 15 genes were subsequently sequenced. Fifty-three different variants were identified in 44 of the 87 patients (50.6%), involving 78 of the 88 alleles (11 homozygous and 56 heterozygous variants). Of the 53 variants, 35 (66%) were novel pathogenic mutations. In these Chinese patients, variants in GUCY2D are the most common cause of LCA (16.1% cases), followed by CRB1 (11.5%), RPGRIP1 (8%), RPE65 (5.7%), SPATA7 (4.6%), CEP290 (4.6%), CRX (3.4%), LCA5 (2.3%), MERTK (2.3%), AIPL1 (1.1%), and RDH12 (1.1%). This differs from the variation spectrum described in other populations. An initial scan of 55 of 215 PCR amplicons, including 214 exons and 1 intron, detected 83.3% (65/78) of the mutant alleles ultimately found in these 87 patients. In addition, sequencing only 9 exons would detect over 50% of the identified variants and require less than 5% of the labor and cost of comprehensive sequencing for all exons. CONCLUSIONS/SIGNIFICANCE: Our results suggest that specific difference in the variation spectrum found in LCA patients from the Han Chinese and other populations are related by ethnicity. Sequencing exons in order of decreasing risk is a cost-effective way to identify causative mutations responsible for LCA, especially in the context of genetic counseling for individual patients in a clinical setting