Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.Comment: 18 pages, 13 figures (in color

Non differentiable large-deviation functionals in boundary-driven diffusive systems

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy in non-equilibrium systems. These singularities are unique to non-equilibrium systems and are a direct consequence of the breaking of time-reversal symmetry. This is demonstrated in an exactly-solvable model and also in numerical simulations on a boundary-driven Ising model. We argue that this singular behavior is expected to occur in models where the compressibility has a deep enough minimum. The mechanism is explained using a simple model.Comment: 5 pages, 3 figure

Atom correlations and spin squeezing near the Heisenberg limit: finite system size effect and decoherence

We analyze a model for spin squeezing based on the so-called counter-twisting Hamiltonian, including the effects of dissipation and finite system size. We discuss the conditions under which the Heisenberg limit, i.e. phase sensitivity $\propto 1/N$, can be achieved. A specific implementation of this model based on atom-atom interactions via quantized photon exchange is presented in detail. The resulting excitation corresponds to the creation of spin-flipped atomic pairs and can be used for fast generation of entangled atomic ensembles, spin squeezing and apllications in quantum information processing. The conditions for achieving strong spin squeezing with this mechanism are also analyzed.Comment: 15 pages, 8 figure

Full counting statistics of information content

We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the R\'enyi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.Comment: 16 pages, 5 figure

Comparing Skill Acquisition Under Varying Onsets of Differential Reinforcement: A Preliminary Analysis

The purpose of the current study was to evaluate the effect of implementing differential reinforcement at different times relative to the onset of teaching new skills to learners with autism spectrum disorder. Specifically, we first determined the most efficient differential reinforcement arrangement for each participant. Using the most efficient arrangement, we evaluated if differential reinforcement from the immediate onset, early onset, or late onset is the most efficient for learners to acquire a new skill. Three children diagnosed with autism spectrum disorder who have a history of receiving intervention based on the principles of applied behavior analysis participated in this study. The immediate onset of differential reinforcement resulted in the most efficient instruction in 6 of 7 comparisons. The results are discussed in light of previous studies and suggestions for future research are provided

Simulating rare events in dynamical processes

Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that are responsible for intermittency in a turbulent liquid, the active regions that allow a supercooled liquid to flow... Simulating them in an efficient, accelerated way, is in fact quite simple. In this paper we review a computational technique to study such rare events in both stochastic and Hamiltonian systems. The method is based on the evolution of a family of copies of the system which are replicated or killed in such a way as to favor the realization of the atypical trajectories. We illustrate this with various examples

The genome of the seagrass Zostera marina reveals angiosperm adaptation to the sea

Seagrasses colonized the sea(1) on at least three independent occasions to form the basis of one of the most productive and widespread coastal ecosystems on the planet(2). Here we report the genome of Zostera marina (L.), the first, to our knowledge, marine angiosperm to be fully sequenced. This reveals unique insights into the genomic losses and gains involved in achieving the structural and physiological adaptations required for its marine lifestyle, arguably the most severe habitat shift ever accomplished by flowering plants. Key angiosperm innovations that were lost include the entire repertoire of stomatal genes(3), genes involved in the synthesis of terpenoids and ethylene signalling, and genes for ultraviolet protection and phytochromes for far-red sensing. Seagrasses have also regained functions enabling them to adjust to full salinity. Their cell walls contain all of the polysaccharides typical of land plants, but also contain polyanionic, low-methylated pectins and sulfated galactans, a feature shared with the cell walls of all macroalgae(4) and that is important for ion homoeostasis, nutrient uptake and O-2/CO2 exchange through leaf epidermal cells. The Z. marina genome resource will markedly advance a wide range of functional ecological studies from adaptation of marine ecosystems under climate warming(5,6), to unravelling the mechanisms of osmoregulation under high salinities that may further inform our understanding of the evolution of salt tolerance in crop plants(7)

Rare coding variants in genes encoding GABA_A receptors in genetic generalised epilepsies: an exome-based case-control study

BACKGROUND: Genetic generalised epilepsy is the most common type of inherited epilepsy. Despite a high concordance rate of 80% in monozygotic twins, the genetic background is still poorly understood. We aimed to investigate the burden of rare genetic variants in genetic generalised epilepsy. METHODS: For this exome-based case-control study, we used three different genetic generalised epilepsy case cohorts and three independent control cohorts, all of European descent. Cases included in the study were clinically evaluated for genetic generalised epilepsy. Whole-exome sequencing was done for the discovery case cohort, a validation case cohort, and two independent control cohorts. The replication case cohort underwent targeted next-generation sequencing of the 19 known genes encoding subunits of GABAA receptors and was compared to the respective GABAA receptor variants of a third independent control cohort. Functional investigations were done with automated two-microelectrode voltage clamping in Xenopus laevis oocytes. FINDINGS: Statistical comparison of 152 familial index cases with genetic generalised epilepsy in the discovery cohort to 549 ethnically matched controls suggested an enrichment of rare missense (Nonsyn) variants in the ensemble of 19 genes encoding GABAA receptors in cases (odds ratio [OR] 2·40 [95% CI 1·41-4·10]; pNonsyn=0·0014, adjusted pNonsyn=0·019). Enrichment for these genes was validated in a whole-exome sequencing cohort of 357 sporadic and familial genetic generalised epilepsy cases and 1485 independent controls (OR 1·46 [95% CI 1·05-2·03]; pNonsyn=0·0081, adjusted pNonsyn=0·016). Comparison of genes encoding GABAA receptors in the independent replication cohort of 583 familial and sporadic genetic generalised epilepsy index cases, based on candidate-gene panel sequencing, with a third independent control cohort of 635 controls confirmed the overall enrichment of rare missense variants for 15 GABAA receptor genes in cases compared with controls (OR 1·46 [95% CI 1·02-2·08]; pNonsyn=0·013, adjusted pNonsyn=0·027). Functional studies for two selected genes (GABRB2 and GABRA5) showed significant loss-of-function effects with reduced current amplitudes in four of seven tested variants compared with wild-type receptors. INTERPRETATION: Functionally relevant variants in genes encoding GABAA receptor subunits constitute a significant risk factor for genetic generalised epilepsy. Examination of the role of specific gene groups and pathways can disentangle the complex genetic architecture of genetic generalised epilepsy. FUNDING: EuroEPINOMICS (European Science Foundation through national funding organisations), Epicure and EpiPGX (Sixth Framework Programme and Seventh Framework Programme of the European Commission), Research Unit FOR2715 (German Research Foundation and Luxembourg National Research Fund)