Search

We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey up to time $t$ decays algebraically as $\sim t^{-\theta(p, \gamma)}$ where the exponent $\theta$ depends continuously on two parameters of the model, with $p$ denoting the probability that a prey survives upon encounter with a predator and $\gamma = D_A/(D_A+D_B)$ where $D_A$ and $D_B$ are the diffusion constants of the prey and the predator respectively. We also compute exactly the probability distribution $P(N|t_c)$ of the total number of encounters till the capture time $t_c$ and show that it exhibits an anomalous large deviation form $P(N|t_c)\sim t_c^{- \Phi\left(\frac{N}{\ln t_c}=z\right)}$ for large $t_c$. The rate function $\Phi(z)$ is computed explicitly. Numerical simulations are in excellent agreement with our analytical results., Comment: 18 pages, 3 figures, accepted for Journal of Physics A Special Issue "Stochastic Resetting: Theory and Applications" 2022

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 consider diffusion under stochastic resetting to the origin in one dimension and compute the mean time to find both of two targets placed either side of the origin. A surprising result is that increasing the distance between two targets can decrease the overall search time. We compute the optimal arrangement of two targets in limiting cases. We generalise to obtain recursive expressions for the mean time to find all of multiple targets. We discuss the relevance to real-world problems of locating multiple targets such as proteins locating clusters of DNA lesions., 9 pages, 3 figures, accepted for European Physical Journal B

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.

In a model of $N$ volume-excluding spheres in a $d$-dimensional tube, we consider how differences between particles in their drift velocities, diffusivities, and sizes influence the steady state distribution and axial particle current. We show that the model is exactly solvable when the geometrical constraints prevent any particle from overtaking every other -- a notion we term quasi-one-dimensionality. Then, due to a ratchet effect, the current is biased towards the velocities of the least diffusive particles. We consider special cases of this model in one dimension, and derive the exact joint gap distribution for driven tracers in a passive bath. We describe the relationship between phase space structure and irreversible drift that makes the quasi-one-dimensional supposition key to the model's solvability., 26 pages, 7 figures

Introduction:Despite advancements in food science and technology, foodborne disease remains one of the major public health problems. Poor sanitation and hygiene conditions of food establishments are the major causes for the occurrence of foodborne disease. Therefore, this study aimed to investigate core determinants of sanitation and hygiene status among food establishments.Methods:Institution-based cross-sectional study design was conducted in Addis Ababa city. A stratified random sampling technique was deployed to select 413 study participants. Data were collected through interview and using observational checklist. Sample size was determined by using a single population proportion formula. To analyze the data, binary logistic regression and multivariable logistic regression analysis was conducted. In all analysis, P-value less than .05 were considered statistically significant.Results:The study revealed that 57.4% of the food establishments were under poor sanitation status. In the multivariable analysis, presence of trained managers on hygiene and sanitation (adjusted odds ratio [AOR] = 6.10 with 95% confidence interval [CI]: 2.41-15.45), presence of renewed licenses (AOR = 3.07 with 95% CI: 1.18-7.99), absence of bureaucratic function to obtain permission to renew the food establishment buildings (AOR = 2.43 with 95% CI: 1.25-4.70), and presence of at least 10-m distance between toilet and kitchen (AOR = 9.19, at 95% CI: 5.63-15.02) were associated significantly with sanitation and hygiene status.Conclusions:Above average of the food establishments were found to be in poor sanitation and hygiene state. Many core determinant factors that influence sanitation and hygienic status of food establishments were identified. The researchers suggest that formal training on sanitation and hygiene for managers of food establishments should be provided to reduce the occurrence of foodborne diseases. Moreover, strong food and water safety policy and strategy should be promulgated to improve sanitation and hygiene status of food establishments.

Recent advances in DNA sequencing and fluorescence imaging have made it possible to monitor the dynamics of ribosomes actively engaged in messenger RNA (mRNA) translation. Here, we model these experiments within the inhomogeneous totally asymmetric simple exclusion process (TASEP) using realistic kinetic parameters. In particular we present analytic expressions to describe the following three cases: (a) translation of a newly transcribed mRNA, (b) translation in the steady state and, specifically the dynamics of individual (tagged) ribosomes and (c) run-off translation after inhibition of translation initiation. In the cases (b) and (c) we develop an effective medium approximation to describe many-ribosome dynamics in terms of a single tagged ribosome in an effective medium. The predictions are in good agreement with stochastic simulations., 12 pages, 9 figures

We review various combinatorial interpretations and mappings of stationary-state probabilities of the totally asymmetric, partially asymmetric and symmetric simple exclusion processes (TASEP, PASEP, SSEP respectively). In these steady states, the statistical weight of a configuration is determined from a matrix product, which can be written explicitly in terms of generalised ladder operators. This lends a natural association to the enumeration of random walks with certain properties. Specifically, there is a one-to-many mapping of steady-state configurations to a larger state space of discrete paths, which themselves map to an even larger state space of number permutations. It is often the case that the configuration weights in the extended space are of a relatively simple form (e.g., a Boltzmann-like distribution). Meanwhile, various physical properties of the nonequilibrium steady state - such as the entropy - can be interpreted in terms of how this larger state space has been partitioned. These mappings sometimes allow physical results to be derived very simply, and conversely the physical approach allows some new combinatorial problems to be solved. This work brings together results and observations scattered in the combinatorics and statistical physics literature, and also presents new results. The review is pitched at statistical physicists who, though not professional combinatorialists, are competent and enthusiastic amateurs., 56 pages, 21 figures

We construct and exactly solve a model of an extended Brownian ratchet. The model comprises an arbitrary number of heterogeneous, growing and shrinking filaments which together move a rigid membrane by a ratchet mechanism. The model draws parallels with the dynamics of actin filament networks at the leading edge of the cell. In the model, the filaments grow and contract stochastically. The model also includes forces which derive from a potential dependent on the separation between the filaments and the membrane. These forces serve to attract the filaments to the membrane or generate a surface tension that prevents the filaments from dispersing. We derive an N -dimensional diffusion equation for the N filament-membrane separations, which allows the steady-state probability distribution function to be calculated exactly under certain conditions. These conditions are fulfilled by the physically relevant cases of linear and quadratic interaction potentials. The exact solution of the diffusion equation furnishes expressions for the average velocity of the membrane and critical system parameters for which the system stalls and has zero net velocity. In the case of a restoring force, the membrane velocity grows as the square root of the force constant, whereas it decreases once a surface tension is introduced.

We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a 1D lattice. We compute rate functions and effective dynamics conditioned on large deviations for these observables. While generally different, for a unique and non-trivial choice of rates (up to a rescaling of time) the velocity rate functions for the two models become identical, whereas the effective processes generating the fluctuations remain distinct. This equivalence coincides with a remarkable parity of the spectra of the processes' generators. For the occupation-time problem, we show that both the passive and active particles undergo a prototypical dynamical phase transition when the average velocity is non-vanishing in the long-time limit., 27 pages, 10 figures

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.

Drug resistant helminths have become a major cause of poor health and production in sheep and goats, and there is a need for diagnostic markers and tools to determine the frequency of resistance alleles in field parasite populations. Gastrointestinal nematode resistance to benzimidazole drugs is caused by a mutation in one of three positions on the isotype 1 β-tubulin locus, and in the absence of markers for resistance to other broad spectrum anthelmintic classes, these provide a relevant study example. Determination of the prevalence of these single nucleotide polymorphisms in field gastrointestinal nematode populations can be impractical using conventional molecular methods, which may be error prone or lack sensitivity at low levels of resistance. Here, we report the development of a novel method based on an Illumina Mi-seq deep amplicon sequencing platform; to sequence the isotype 1 β-tubulin locus of the small ruminant gastrointestinal nematode,Teladorsagia circumcincta, and determine the frequency of the benzimidazole resistance mutations. We validated the method by assessing sequence representation bias in the isotype 1 β-tubulin locus, comparing the results of Illumina Mi-seq and pyrosequencing, and applying the method to populations containing known proportions of resistant and susceptible L3. Finally, we applied the method to field samples collected from ewes and lambs on over a period of one year on three farms, each highlighting different aspects of sheep management and approaches to parasite control. The results show opportunities to build hypotheses with reference to selection pressures leading to differences in resistance allele frequencies between sampling dates, farms and ewes or lambs, and to consider the impact of their genetic fixation or otherwise. This study provides proof of concept of a practical, accurate, sensitive and scalable method to determine frequency of anthelmintic drug resistance mutations in gastrointestinal nematodes in field studies and as a management tool for livestock farmers.

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

Exact solutions of interacting random walk models, such as 1D lattice gases, offer precise insight into the origin of nonequilibrium phenomena. Here, we study a model of run-and-tumble particles on a ring lattice interacting via hardcore exclusion. We present the exact solution for one and two particles using a generating function technique. For two particles, the eigenvectors and eigenvalues are explicitly expressed using two parameters reminiscent of Bethe roots, whose numerical values are determined by polynomial equations which we derive. The spectrum depends in a complicated way on the ratio of direction reversal rate to lattice jump rate, $\omega$. For both one and two particles, the spectrum consists of separate real bands for large $\omega$, which mix and become complex-valued for small $\omega$. At exceptional values of $\omega$, two or more eigenvalues coalesce such that the Markov matrix is non-diagonalizable. A consequence of this intricate parameter dependence is the appearance of dynamical transitions: non-analytic minima in the longest relaxation times as functions of $\omega$ (for a given lattice size). Exceptional points are theoretically and experimentally relevant in, e.g., open quantum systems and multichannel scattering. We propose that the phenomenon should be a ubiquitous feature of classical nonequilibrium models as well, and of relevance to physical observables in this context., Comment: 29 pages, 7 figures, revised submission to J. Stat. Mech

We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the stationary position distribution and analyse the emergence of a delta peak at the resetting position. In the case of a power-law distribution for the refractory period we find slow relaxation. We generalise our results to the case when the resetting period and the refractory period are correlated, by computing the Laplace transform of the survival probability of the process and the mean first passage time, i.e., the mean time to completion of a task. We also compute exactly the joint distribution of the active and absorption time to a fixed target., Major revision including amended title. 15 pages 1 figure. Accepted for Journal of Physics A Mathematical and Theoretical Letters

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

We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability by stochastically alternating its direction. Until now, this behaviour has been seen in models based on continuum field equations only by appealing to long-range interactions that are not present in the simulation model. Here, we derive a set of stochastic field equations with local interactions that reproduces both qualitatively and quantitatively the behaviour of the agent-based model, including the alternating flock phase. A crucial component is a multiplicative noise term of the voter model type in the dynamics of the local polarization whose magnitude is inversely proportional to the local density. We show that there is an important subtlety in determining the physically appropriate noise, in that it depends on a careful choice of the field variables used to characterise the system. We further use the resulting equations to show that a nonlinear alignment interaction of at least cubic order is needed for flocking to arise.

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random envinronment which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponens to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2 whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy., 13 pages, 19 figures

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting., Comment: 16 pages, 1 figure, version accepted in Journal of Physics A

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

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, Poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces., Comment: 27 pages, 4 figures, Mathematica notebook as supplementary material

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.

We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory kernel, we show analytically how different asymptotic behaviours of the variance of the particle position emerge at long times. These range from standard diffusive ($\sigma^2 \sim t$) all the way to anomalous ultraslow growth $\sigma^2 \sim \ln \ln t$., Comment: 13 pages, 1 figure, submitted to J. Stat. Mech: Theory. Exp

We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed. It leads to the phase diagram of the models. Depending on the values of the boundary rates, we obtain for each species shock waves, maximal current, or low/high densities phases., 23 pages

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.

We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid for all values of the asymmetry parameter q. Due to the relationship between the matrix algebra and the q-deformed quantum harmonic oscillator algebra we find that q-Hermite polynomials, along with their orthogonality properties and generating functions, are of great utility. We employ two distinct sets of q-Hermite polynomials, one for q1. It turns out that these correspond to two distinct regimes: the previously studied case of forward bias (q1) where the boundaries support a current opposite in direction to the bulk bias. For the forward bias case we confirm the previously proposed phase diagram whereas the case of reverse bias produces a new phase in which the current decreases exponentially with system size., 27 pages LaTeX2e, 3 figures, includes new references and further comparison with related work. To appear in J. Phys. A

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.

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 exploring a larger set of beneficial mutations while avoiding deleterious ones., 9 pages, 5 figures (main text) + 3 pages, 5 figures (supplementary information)

We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state. This stationary distribution has a rich structure comprising three components: a jammed component, where the particles are adjacent and block each other; an attractive component, where the probability distribution for the distance between particles decays exponentially; and an extended component in which the distance between particles is uniformly distributed. The attraction between the particles is sufficiently strong that even in the limit where continuous space is recovered for a finite system, the two walkers spend a finite fraction of time in a jammed configuration. Our results potentially provide a route to understanding the motility-induced phase separation characteristic of active matter from a microscopic perspective., 8 pages, 3 figures

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.

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. Finally we consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time. We study optimal properties of the mean first passage time and show that a threshold function is at least locally optimal for the problem of minimizing the mean first passage time., 15 pages, 4 figures

We study stochastic processes in which the trajectories are constrained so that the process realises a large deviation of the unconstrained process. In particular we consider stochastic bridges and the question of inequivalence of path ensembles between the microcanonical ensemble, in which the end points of the trajectory are constrained, and the canonical or s ensemble in which a bias or tilt is introduced into the process. We show how ensemble inequivalence can be manifested by the phenomenon of temporal condensation in which the large deviation is realised in a vanishing fraction of the duration (for long durations). For diffusion processes we find that condensation happens whenever the process is subject to a confining potential, such as for the Ornstein-Uhlenbeck process, but not in the borderline case of dry friction in which there is partial ensemble equivalence. We also discuss continuous-space, discrete-time random walks for which in the case of a heavy tailed step-size distribution it is known that the large deviation may be achieved in a single step of the walk. Finally we consider possible effects of several constraints on the process and in particular give an alternative explanation of the interaction-driven condensation in terms of constrained Brownian excursions., 22 pages, 7 figures, minor revision

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.