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The study aimed to determine the status of microbial load of drinking water and seasonal variation of water quality. An institution-based longitudinal study was conducted. 1,141 food establishments were divided into slum and non-slum areas based on their location. Moreover, they were categorized as large and small food establishments. Then, 125 food outlets were selected using a simple random sampling technique. From the selected food outlets, 250 drinking water samples were collected directly from the drinking water storage in the rainy and the dry seasons. Data analysis was conducted using a repeated-measure ANOVA statistical model. The finding indicated that, 26.4% and 10.7% of the food establishments' drinking water was positive for Escherichia coli in the wet and the dry season, respectively. Moreover, 3.2% and 1.6% of the food establishments' drinking water had very high health risk to customers during the wet and the dry season, respectively. The drinking water at the point of use was found to be vulnerable to microbiological contamination and had a serious health risk. Therefore, good sanitation and proper handling of drinking water, and effective drinking water treatment, such as disinfection and filtration, should be practiced in all food establishments.

We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model parameters that ensure that the underlying system is integrable. Three classes of integrable models are thus found. Of these, two classes are well known in literature, but the third has not been studied until recently, and never in the context of the Bethe ansatz. The Bethe equations are derived for the latter model as well as for the associated dynamics encoding the large deviation of the currents., 15 pages, 2 figures. Typo in equation (21) corrected. Extra step detail added in Appendix A, case 1, option \alpha=1; Figure A.1 updated accordingly

We put forward a general field theory for membranes with embedded activators and analyse their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z = 1 and 2 respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, is a suitable candidate for the universal description of the spatiotemporal patterns observed at the leading edge of motile cells. Furthermore, one-loop corrections to the diffusive mean-field exponents reveal universal behaviour distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behaviour., 5 pages, 3 figures

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

Piroplasmosis is caused by tick-borne haemoprotozoa of the generaTheileriaandBabesia. These parasitic infections can cause serious impact on the health of livestock and production. Multiple piroplasm species can infect a single host, but reliable molecular diagnostic tools are needed with which to understand the composition of these complex parasite communities.TheileriaandBabesiavary in their epidemiology, drug sensitivity, pathogenicity and interaction of co-infecting species, but are similar in the animals, become persistent carriers after recovery from primary infection, acting as reservoir hosts. Here, we describe for the first time the use of a deep amplicon sequencing platform to identify proportions of piroplasm species in co-infecting communities and develop the concept of a “haemoprotobiome”. First, four phenotypically-verified species ofTheileriaandBabesiawere used to prepare mock pools with random amounts of the parasites and amplified with four different numbers of PCR cycles to assess sequence representation of each species. Second, we evaluated the detection threshold of the deep amplicon sequencing assay for each of the four species and to assess the accuracy of proportional quantification of all four species. Finally, we applied the assay to the field samples to afford insight of the species composition of piroplasm communities in small and large ruminants in the Punjab province of Pakistan. The “haemoprotobiome” concept has several potential applications in veterinary and human research, including understanding of responses to drug treatment; parasite epidemiology and ecology; species interactions during mixed infections; and parasite control strategies.

We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in the same direction over many lattice sites before reorienting. In the case of two particles, we find the mean first-passage time to a jammed state where the particles occupy adjacent sites and face each other. This is achieved within an approximation that amounts to embedding the one-dimensional system in a higher-dimensional reservoir. Numerical results demonstrate the validity of this approximation, even for small lattices. The results admit a straightforward generalisation to dilute systems comprising more than two particles. A self-consistency condition on the validity of these results suggest that clusters may form at arbitrarily low densities in the ballistic regime, in contrast to what has been found in the diffusive limit., Comment: Version to appear in JSTAT (18 pages; 10 figures)

Totally asymmetric tracer particles in an environment of symmetric hard-core particles on a ring are studied. Stationary state properties, including the environment density profile and tracer velocity are derived explicitly for a single tracer. Systems with more than one tracer are shown to factorise into single-tracer subsystems, allowing the single tracer results to be extended to an arbitrary number of tracers. We demonstrate the existence of a cooperative effect, where many tracers move with a higher velocity than a single tracer in an environment of the same size and density. Analytic calculations are verified by simulations. Results are compared to established results in related systems., Added reference. Corrected typo in section 3.1

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate $r$, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate $r$. We then generalise to an arbitrary stochastic process (e.g. L\'evy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field., Comment: 68 pages, Topical Review accepted version to appear in Journal of Physics A: Mathematical and Theoretical 2020

Inspired by recent experimental observations of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particlelike inclusions which stimulate its growth. We find that the coupling between interfacial and inclusions dynamics yields microphase separation and the self-organization of traveling waves. These patterns are strikingly similar to those detected in experiments on biological membranes. Our results further show that the active growth kinetics do not fall into the Kardar-Parisi-Zhang universality class for growing interfaces, displaying instead a novel superposition of scaling and sustained oscillations.

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: whilst the well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the `ahead' arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the `behind' arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct., Comment: 6 pages, 6 figures; revised version contains a small amount of additional discussion and the supplementary figures. To appear in Phys. Rev. Lett

The essential features of many interfaces driven out of equilibrium are described by the same equation---the Kardar-Parisi-Zhang (KPZ) equation. How do living interfaces, such as the cell membrane, fit into this picture? In an endeavour to answer such a question, we proposed in [F. Cagnetta, M. R. Evans, D. Marenduzzo, PRL 120, 258001 (2018)] an idealised model for the membrane of a moving cell. Here we discuss how the addition of simple ingredients inspired by the dynamics of the membrane of moving cells affects common kinetic roughening theories such as the KPZ and Edwards-Wilkinson equations., Comment: 5 pages, 4 figures, FisMat 2019

We present a detailed solution of the active interface equations in the inviscid limit. The active interface equations were previously introduced as a toy model of membrane-protein systems: they describe a stochastic interface where growth is stimulated by inclusions which themselves move on the interface. In the inviscid limit, the equations reduce to a pair of coupled conservation laws. After discussing how the inviscid limit is obtained, we turn to the corresponding Riemann problem: the solution of the set of conservation laws with discontinuous initial condition. In particular, by considering two physically meaningful initial conditions, a giant trough and a giant peak in the interface, we elucidate the generation of shock waves and rarefaction fans in the system. Then, by combining several Riemann problems, we construct an oscillating solution of the active interface with periodic boundaries conditions. The existence of this oscillating state reflects the reciprocal coupling between the two conserved quantities in our system., 22 pages, 11 figures

The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate explicitly an entropy whereby the squares of configuration probabilities are summed, using the matrix product formalism to map the problem to one involving a six direction lattice walk in the upper quarter plane. We derive the generating function across the whole phase diagram, using an obstinate kernel method. This gives the leading behaviour of the Renyi entropy and corrections in all phases of the TASEP. The leading behaviour is given by the result for a Bernoulli measure and we conjecture that this holds for all Renyi entropies. Within the maximal current phase the correction to the leading behaviour is logarithmic in the system size. Finally, we remark upon a special property of equilibrium systems whereby discontinuities in the Renyi entropy arise away from phase transitions, which we refer to as secondary transitions. We find no such secondary transition for this nonequilibrium system, supporting the notion that these are specific to equilibrium cases.

Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in environmental conditions. Here we use a computational model to investigate an alternative possible function of stochastic phenotype switching: as a way to adapt more quickly even in a static environment. We show that when a genetic mutation causes a population to become less fit, switching to an alternative phenotype with higher fitness (growth rate) may give the population enough time to develop compensatory mutations that increase the fitness again. The possibility of switching phenotypes can reduce the time to adaptation by orders of magnitude if the "fitness valley" caused by the deleterious mutation is deep enough. Our work has important implications for the emergence of antibiotic-resistant bacteria. In line with recent experimental findings, we hypothesise that switching to a slower growing - but less sensitive - phenotype helps bacteria to develop resistance by providing alternative, faster evolutionary routes to resistance.

Background: In Addis Ababa, the capital of Ethiopia, the urban health extension program was started in 2009. Its approach is based on the assumption that access to and quality of primary health care in urban communities can be improved through transfer of health knowledge and skills to households. The study was conducted to assess the status of urban health extension service utilization and associated factors.Methods: A community based cross–sectional study was conducted to collect data from 628 participants. Sample size was determined by using a single population proportion formula. Binary logistic regression was used for data analysis.Results: The proportion of community utilization of the urban health extension program was found to be 86%. Respondents’ odds of utilizing urban health extension services among those who participated in the planning of urban health extension program activities were 2.8 (AOR=2.8; 95% CI: 1.43-3.70) times the odds of those who did not participate. The household respondents who utilized toilet with hand washing facilities had odds of utilizing urban health extension services that are higher by 2.62 (AOR=2.62 with 95% CI: 1.70-9.77) compared to those not utilizing toilet with hand washing facilities.Conclusions: The study provided important information regarding to the status of community utilization of urban health extension services. Respondents who utilized toilet with hand washing facilities were higher among the respondents who utilized and implemented the urban health extension packages. Respondents who participated in the planning of urban health extension program activities were those who significantly utilized and implemented the urban health extension program.

A simple model for mass transport within a growing fungal filament is reviewed. Inspired by the role of microtubule-transported vesicles, we embody the dynamics of mass along a quasi-one-dimensional hypha with mutually excluding particles hopping on a growing one-dimensional lattice. The model is a generalisation of the totally asymmetric simple exclusion process (TASEP) to a dynamically extending lattice. We discuss mean-field and improved mean-field equations and present a phase diagram of the model's steady-state behaviour which generalises that of the TASEP. In particular we identify a region in which a shock in the density travels forward more slowly than the tip of the lattice and thus moves away from both the boundaries.

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.

We present a pedagogical account of the Lee-Yang theory of equilibrium phase transitions and review recent advances in applying this theory to nonequilibrium systems. Through both general considerations and explicit studies of specific models, we show that the Lee-Yang approach can be used to locate and classify phase transitions in nonequilibrium steady states., Comment: 24 pages, 7 papers, invited paper for special issue of The Brazilian Journal of Physics

We study a zero-range process with two species of interacting particles. We show that the steady state assumes a simple factorised form, provided the dynamics satisfy certain conditions, which we derive. The steady state exhibits a new mechanism of condensation transition wherein one species induces the condensation of the other. We study this mechanism for a specific choice of dynamics., Comment: 8 pages, 3 figures

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds if the steady state satisfies detailed balance. More generally, we consider nonequilibrium steady states where detailed balance does not hold and show how a generalisation of the Einstein relation may be derived in certain cases. In particular, for the asymmetric simple exclusion process and a driven diffusive dimer model, the external perturbation creates and annihilates particles thus breaking the particle conservation of the unperturbed model.

Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to condensation and whose stationary states assume a factorized form: the zero-range process and the misanthrope process, and their various modifications. We also introduce a new model - a misanthrope process with parallel dynamics - that exhibits condensation and has a pair-factorized stationary state., Comment: 15 pages, 2 figures submitted to J. Stat. Mech

We consider networks made of parallel lanes along which particles hop according to driven diffusive dynamics. The particles also hop transversely from lane to lane, hence indirectly coupling their longitudinal dynamics. We present a general method for constructing the phase diagram of these systems which reveals that in many cases their physics reduce to that of single-lane systems. The reduction to an effective single-lane description legitimizes, for instance, the use of a single TASEP to model the hopping of molecular motors along the many tracks of a single microtubule. Then, we show how, in quasi-2D settings, new phenomena emerge due to the presence of non-zero transverse currents, leading, for instance, to strong `shear localisation' along the network.

In these lectures we give an overview of nonequilibrium stochastic systems. In particular we discuss in detail two models, the asymmetric exclusion process and a ballistic reaction model, that illustrate many general features of nonequilibrium dynamics: for example coarsening dynamics and nonequilibrium phase transitions. As a secondary theme we shall show how a common mathematical structure, the q-deformed harmonic oscillator algebra, serves to furnish exact results for both systems. Thus the lectures also serve as a gentle introduction to things q-deformed., 48 pages LaTeX2e with 9 figures and using elsart.cls (included); Lectures at the International Summer School on Fundamental Problems in Statistical Physics X, August-September 2001, Altenberg, Germany. v2 corrects some errors and includes further discussion/references

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions., Comment: submitted to EPJB, 13 pages

The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which we have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is know exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show how conditions under which it may occur may be related to the existence of an effective long-range energy function. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here., Comment: latex, 28 pages, review article; references updated

The ELVIS HSV Id test kit (an enzyme-linked virus-inducible system) (Diagnostic Hybrids, Inc.) uses genetically engineered BHK cells to produce a detectable enzyme, beta-galactosidase, upon infection with either herpes simplex virus (HSV) type 1 (HSV-1) or HSV-2. Twenty six ELVIS-positive clinical specimens were selected for study by PCR and with monoclonal antibodies because they were originally low-titer HSV-positive specimens by ELVIS but HSV antibody nonreactive upon follow-up staining of the ELVIS monolayer. Twenty-one of 26 specimens were frozen, thawed, and retested with ELVIS without removing the cellular debris from the specimen; 18 were ELVIS positive and 3 were ELVIS negative on retesting. A typing result was provided upon retesting for 14 of 18 ELVIS-positive specimens (11 were HSV-1 and 3 were HSV-2) with HSV-specific monoclonal antibodies; no antibody signal was observed for 4 of 18 ELVIS-positive specimens. Sixteen of 26 specimens were subjected to blinded PCR analysis with two different primer sets, including all those that were repeat tested with ELVIS without success and those that had insufficient quantity for repeat testing. All 16 specimens analyzed were PCR positive with primer set 1; 15 of 16 were also positive with primer set 2, with the HSV type identified for all specimens (7 were HSV-1 and 8 were HSV-2). These results indicate that the original ELVIS result with these low-titer specimens was correct and further confirm the sensitivity and specificity of ELVIS HSV Id as a rapid, cell culture-based kit for the detection of HSV.

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g. cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with {\it simultaneous} updating of all sites. It is equivalent to a special case ($v_{\rm max}=1$) of the Nagel-Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two point functions and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time discrete updating procedures. Through use of this mapping, our results also give new results for these models.

The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time limit behaviour of the generating function of the distance travelled by the defect particle. This allows us to recover steady state properties known from the matrix approach such as the velocity, and obtain new results such as the diffusion constant of the defect particle. In the case where the defect particle is a second class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is Gaussian. Moreover the variance (diffusion constant) grows as L to the power 1/2 where is the system size. This behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system. In the case where the defect particle produces a shock, our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by Ferrari and Fontes., Comment: Latex, 23 pages

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock' contains a finite fraction of the particles, to a homogeneous phase; we study the transition using numerical finite-size scaling. Surprisingly, in the condensed phase the steady state is alternating, with the mean direction of motion of particles reversing stochastically on a timescale proportional to the logarithm of the system size. We present a simple argument to explain this logarithmic dependence. We argue that the reversals are essential to the survival of the condensate. Thus, the discrete directional symmetry is not spontaneously broken., 8 pages LaTeX2e, 5 figures. Uses epsfig and IOP style. Submitted to J. Phys. A (Math. Gen.)

A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place in these models are related to contact processes or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments and numerical simulations. In the smooth phase the symmetry of the underlying dynamics is spontaneously broken. A family of order parameters which are not conserved by the dynamics is defined as well as conjugate fields which couple to these order parameters. The corresponding critical behavior is studied and novel exponents identified and measured. We also show how continuous symmetries can be broken in one dimension. A field theory appropriate for studying the roughening transition is introduced and discussed., RevTeX, 18 pages, 15 postscript figures

We study the phenomenon of jamming in driven diffusive systems. We introduce a simple microscopic model in which jamming of a conserved driven species is mediated by the presence of a non-conserved quantity, causing an effective long range interaction of the driven species. We study the model analytically and numerically, providing strong evidence that jamming occurs; however, this proceeds via a strict phase transition (with spontaneous symmetry breaking) only in a prescribed limit. Outside this limit, the nearby transition (characterised by an essential singularity) induces sharp crossovers and transient coarsening phenomena. We discuss the relevance of the model to two physical situations: the clustering of buses, and the clogging of a suspension forced along a pipe., Comment: 8 pages, 4 figures, uses epsfig. Submitted to Europhysics Letters

We present a numerical simulation study of the dynamics of filopodial growth in the presence of active transport by myosin X motors. We employ both a microscopic agent-based model, which captures the stochasticity of the growth process, and a continuum mean-field theory which neglects fluctuations. We show that in the absence of motors, filopodia growth is overestimated by the continuum mean-field theory. Thus fluctuations slow down the growth, especially when the protrusions are driven by a small number (10 or less) of F-actin fibres, and when the force opposing growth (coming from membrane elasticity) is large enough. We also show that, with typical parameter values for eukaryotic cells, motors are unlikely to provide an actin transport mechanism which enhances filopodial size significantly, unless the G-actin concentration within the filopodium greatly exceeds that of the cytosol bulk. We explain these observations in terms of order-of-magnitude estimates of diffusion-induced and advection-induced growth of a bundle of Brownian ratchets., Comment: 20 pages, 8 figures, accepted by Physical Biology

Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in traffic and gelation in networks. We show here that the same condensation scenario, which normally happens only if the underlying probability distribution has tails heavier than exponential, can occur for light-tailed distributions in the presence of additional constraints. We demonstrate this phenomenon on the sample variance, whose probability distribution conditioned on the particular value of the sample mean undergoes a phase transition. The transition is manifested by a change in behavior of the large deviation rate function., 5 pages, 3 figures

We investigate the conditions under which a moving condensate may exist in a driven mass transport system. Our paradigm is a minimal mass transport model in which $n-1$ particles move simultaneously from a site containing $n>1$ particles to the neighbouring site in a preferred direction. In the spirit of a Zero-Range process the rate $u(n)$ of this move depends only on the occupation of the departure site. We study a hopping rate $u(n) = 1 + b/n^\alpha$ numerically and find a moving strong condensate phase for $b > b_c(\alpha)$ for all $\alpha >0$. This phase is characterised by a condensate that moves through the system and comprises a fraction of the system's mass that tends to unity. The mass lost by the condensate as it moves is constantly replenished from the trailing tail of low occupancy sites that collectively comprise a vanishing fraction of the mass. We formulate an approximate analytical treatment of the model that allows a reasonable estimate of $b_c(\alpha)$ to be obtained. We show numerically (for $\alpha=1$) that the transition is of mixed order, exhibiting exhibiting a discontinuity in the order parameter as well as a diverging length scale as $b\searrow b_c$., Comment: 15 figs, 20 pages

We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the steady-state distributions and study the late time relaxation behavior to the stationary state., Comment: 13 pages, 4 figures

It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain., 42 pages

We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area $a$ and returning to the origin for the first time after time $\tau$. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory., Comment: 28 pages, 6 figures, invited paper for Special Issue of J. Phys. A "Emerging talents"

A simple two-species asymmetric exclusion model is introduced. It consists of two types of oppositely charged particles driven by an electric field and hopping on an open chain. The phase diagram of the model is calculated in the meanfield approximation and by Monte Carlo simulations. Exact solutions are given for special values of the parameters defining its dynamics. The model is found to exhibit two phases in which spontaneous symmetry breaking takes place, where the two currents of the two species are not equal.

We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1d lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially spontaneously form in the system, begin to move at increasing speed as they gain particles. Ultimately, they produce a moving condensate which comprises a finite fraction of the mass in the system. We show that, in contrast with previously studied models of condensation, the relaxation time to steady state decreases as an inverse power of ln L with system size L and that condensation is instantenous for L-->infinity., 5 pages, 5 figures, minor changes, references added

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r^*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers., Comment: 4 pages revtex, 1 .eps figure included

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.

The asymmetric exclusion model describes a system of particles hopping in a preferred direction with hard core repulsion. These particles can be thought of as charged particles in a field, as steps of an interface, as cars in a queue. Several exact results concerning the steady state of this system have been obtained recently. The solution consists of representing the weights of the configurations in the steady state as products of non-commuting matrices.

The distribution of local minima in the energy landscape of the infinite-ranged Ising spin glass is studied by calculation of the average number of pairs of metastable states with fixed overlap and energies. The average number forms an upper bound on the typical number. It is known that below a critical energy metastable states are globally (strongly) correlated. Above the critical energy the upper bound on pairs of metastable states suggests that although metastable states are only locally (weakly) correlated, an interesting local structure of the energy landscape may be present

International audience; Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be solved exactly in the case of open boundaries. Here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices. With this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules. They obtain several explicit forms for these non-commuting matrices which are, in the general case, infinite-dimensional. Their approach allows exact expressions to be derived for the current and density profiles. Finally they discuss briefly two possible generalizations of their results: the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles.

Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way migration. Our model applies to asexual, rapidly evolving organisms such as microbes. Our key finding is a dynamical phase transition at a critical value of the migration rate. The time to reach steady state diverges at this critical migration rate. Above the transition, the population is dominated by immigrants from the primary habitat. Below the transition, the genetic composition of the population is highly non-trivial, with multiple coexisting quasispecies which are not native to either habitat. Using results from localization theory, we show that the critical migration rate may be very small --- demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration., Comment: 4+ pages, 4 figures

Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden "catastrophes", the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the "no switching" strategy, the population maximises its instantaneous growth rate, regardless of catastrophes. In the "switching" strategy, the microbial switching rate is tuned to minimise the environmental response. Which of these strategies is most favourable depends on the parameters of the model. Previous studies have shown that microbial switching can be favourable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximise their growth in catastrophic responsive environments., Comment: 9 pages, 10 figures; replaced with revised version

The authors consider a neural network proposed by Coolen and Kuijk (1989) that has interactions composed of two competing elements. The first is the Hopfield interaction for recall of a set of stored patterns. The second is interactions between pairs of sites arranged so that the configuration undergoes a symmetry transformation at each parallel update. First they consider the effect of the symmetry-transform interactions alone. They show that for sequential updating the symmetry transformation is no longer carried out faithfully, but rather the spin configuration tends to a symmetry invariant. In order to understand how the retrieval phase of the Hopfield model is disrupted by the symmetry-transform interactions they perform a replica symmetric analysis. They demonstrate that the symmetry-transform interactions generate a noise very similar to that of random external fields on the memory states. The phase diagram suggests the possibility of symmetry-invariant recognition for an extensive number of patterns and an optimal value for the symmetry-transform interaction strength. They present numerical simulations of the model under parallel dynamics to confirm these predictions.

A total of 471 positive blood cultures obtained over a 3-month period were identified and evaluated for day of positivity by the BACTEC NR660. Of all positive blood cultures, 73% (344) were detected within the first 2 days, and 94% (441) were detected through day 4. The proportion of positive cultures detected at day 5 was significantly lower than that at day 4 (p less than 0.01). Patient chart review revealed that two of 30 isolates (0.4% of all positive isolates) identified on days 5-7 were considered clinically significant and would have been missed if cultures would not have been evaluated for seven days. Therefore, very limited additional patient benefit is derived after greater than 4 days of growth and detection by the BACTEC NR660.