Showing papers by "David A. Kessler published in 2018"

First Detected Arrival of a Quantum Walker on an Infinite Line.

Abstract: The first detection of a quantum particle on a graph is shown to depend sensitively on the distance $\ensuremath{\xi}$ between the detector and initial location of the particle, and on the sampling time $\ensuremath{\tau}$. Here, we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an infinite line, using a tight-binding lattice Hamiltonian with nearest-neighbor hops. Universal features of the first detection probability are uncovered and simple limiting cases are analyzed. These include the large $\ensuremath{\xi}$ limit, the small $\ensuremath{\tau}$ limit, and the power law decay with the attempt number of the detection probability over which quantum oscillations are superimposed. For large $\ensuremath{\xi}$ the first detection probability assumes a scaling form and when the sampling time is equal to the inverse of the energy band width nonanalytical behaviors arise, accompanied by a transition in the statistics. The maximum total detection probability is found to occur for $\ensuremath{\tau}$ close to this transition point. When the initial location of the particle is far from the detection node we find that the total detection probability attains a finite value that is distance independent.

Confluent and nonconfluent phases in a model of cell tissue

Abstract: The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and size, and the interaction between adjacent cells is a byproduct of this additive energy. We generalize this model so as to allow zero or partial contact between cells. We identify several phases, two of which (solid confluent and liquid confluent) were found in previous studies that imposed confluency but others that are novel. Transitions in this model may be relevant for understanding both normal development as well as cancer metastasis.

Darwinian selection of host and bacteria supports emergence of Lamarckian-like adaptation of the system as a whole

Abstract: The relatively fast selection of symbiotic bacteria within hosts and the potential transmission of these bacteria across generations of hosts raise the question of whether interactions between host and bacteria support emergent adaptive capabilities beyond those of germ-free hosts. To investigate possibilities for emergent adaptations that may distinguish composite host-microbiome systems from germ-free hosts, we introduce a population genetics model of a host-microbiome system with vertical transmission of bacteria. The host and its bacteria are jointly exposed to a toxic agent, creating a toxic stress that can be alleviated by selection of resistant individuals and by secretion of a detoxification agent (“detox”). We show that toxic exposure in one generation of hosts leads to selection of resistant bacteria, which in turn, increases the toxic tolerance of the host’s offspring. Prolonged exposure to toxin over many host generations promotes anadditional form of emergent adaptation due to selection of hosts based on detox produced by their bacterial community as a whole (as opposed to properties of individual bacteria). These findings show that interactions between pure Darwinian selections of host and its bacteria can give rise to emergent adaptive capabilities, including Lamarckian-like adaptation of the host-microbiome system. This article was reviewed by Eugene Koonin, Yuri Wolf and Philippe Huneman.

Spectral dimension controlling the decay of the quantum first-detection probability

Abstract: We consider a quantum system that is initially localized at ${\mathbit{x}}_{\text{in}}$ and that is repeatedly projectively probed with a fixed period $\ensuremath{\tau}$ at position ${\mathbit{x}}_{\mathrm{d}}$. We ask for the probability ${F}_{n}$ that the system is detected at ${\mathbit{x}}_{\mathrm{d}}$ for the very first time, where $n$ is the number of detection attempts. We relate the asymptotic decay and oscillations of ${F}_{n}$ with the system's energy spectrum, which is assumed to be absolutely continuous. In particular, ${F}_{n}$ is determined by the Hamiltonian's measurement spectral density of states (MSDOS) $f(E)$ that is closely related to the density of energy states (DOS). We find that ${F}_{n}$ decays like a power law whose exponent is determined by the power-law exponent ${d}_{S}$ of $f(E)$ around its singularities ${E}^{*}$. Our findings are analogous to the classical first passage theory of random walks. In contrast to the classical case, the decay of ${F}_{n}$ is accompanied by oscillations with frequencies that are determined by the singularities ${E}^{*}$. This gives rise to critical detection periods ${\ensuremath{\tau}}_{c}$ at which the oscillations disappear. In the ordinary case ${d}_{S}$ can be identified with the spectral dimension associated with the DOS. Furthermore, the singularities ${E}^{*}$ are the van Hove singularities of the DOS in this case. We find that the asymptotic statistics of ${F}_{n}$ depend crucially on the initial and detection state and can be wildly different for out-of-the-ordinary states, which is in sharp contrast to the classical theory. The properties of the first-detection probabilities can alternatively be derived from the transition amplitudes. All our results are confirmed by numerical simulations of the tight-binding model, and of a free particle in continuous space both with a normal and with an anomalous dispersion relation. We provide explicit asymptotic formulas for the first-detection probability in these models.

Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs

Abstract: We examine the bi-scaling behavior of Levy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ ~ τ β . An example of such a process is regular Levy walks, where β = 1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β = 3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles’ position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models.

Simulation of spatial systems with demographic noise.

Abstract: The demographic (shot) noise in population dynamics scales with the square root of the population size. This process is very important, as it yields an absorbing state at zero field, but simulating it, especially on spatial domains, is a nontrivial task. Here, we analyze two similar methods that were suggested for simulating the corresponding Langevin equation, one by Pechenik and Levine and the other by Dornic, Chate, and Munoz (DCM). These methods are based on operator-splitting techniques and the essential difference between them lies in which terms are bundled together in the splitting process. Both these methods are first order in the time step so one may expect that their performance will be similar. We find, surprisingly, that when simulating the stochastic Ginzburg-Landau equation with two deterministic metastable states, the DCM method exhibits two anomalous behaviors. First, the stochastic stall point moves away from its deterministic counterpart, the Maxwell point, when decreasing the noise. Second, the errors induced by the finite time step are larger by a significant factor (i.e., >10×) in the DCM method. We show that both these behaviors are the result of a finite-time-step induced shift in the deterministic Maxwell point in the DCM method, due to the particular operator splitting employed. In light of these results, care must be exercised when computing quantities like phase-transition boundaries (as opposed to universal quantities such as critical exponents) in such stochastic spatial systems.

Environmental Stochasticity and the Speed of Evolution

Abstract: Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

Front propagation and clustering in the stochastic nonlocal Fisher equation

Abstract: In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.

Darwinian selection of host and bacteria supports emergence of Lamarckian-like adaptation of the system as a whole

Abstract: The relatively fast selection of symbiotic bacteria within hosts and the potential transmission of these bacteria across generations of hosts raise the question of whether interactions between host and bacteria support emergent adaptive capabilities beyond those of germ-free hosts. To investigate possibilities for emergent adaptations that may distinguish composite host-microbiome systems from germ-free hosts, we introduce a population genetics model of a host-microbiome system with vertical transmission of bacteria. The host and its bacteria are jointly exposed to a toxic agent, creating a toxic stress that can be alleviated by selection of resistant individuals and by secretion of a detoxification agent (“detox”). We show that toxic exposure in one generation of hosts leads to selection of resistant bacteria, which in turn, increases the toxic tolerance of the host’s offspring. Prolonged exposure to toxin over many host generations promotes anadditional form of emergent adaptation due to selection of hosts based on detox produced by their bacterial community as a whole (as opposed to properties of individual bacteria). These findings show that interactions between pure Darwinian selections of host and its bacteria can give rise to emergent adaptive capabilities, including Lamarckian-like adaptation of the host-microbiome system. This article was reviewed by Eugene Koonin, Yuri Wolf and Philippe Huneman.

Darwinian selection of host and bacteria supports emergence of Lamarckian-like adaptation of the system as a whole

Abstract: Background: The relatively fast selection of symbiotic bacteria within hosts and the potential transmission of these bacteria across generations of hosts raise the question of whether interactions between host and bacteria support emergent adaptive capabilities beyond those of germ-free hosts. Results: To investigate possibilities for emergent adaptations that may distinguish composite host-microbiome systems from germ-free hosts, we introduce a population genetics model of a host-microbiome system with vertical transmission of bacteria. The host and its bacteria are jointly exposed to a toxic agent, creating a toxic stress that can be alleviated by selection of resistant individuals and by secretion of a detoxification agent (″detox″). We show that toxic exposure in one generation of hosts leads to selection of resistant bacteria, which in turn, increases the toxic tolerance of the host′s offspring. Prolonged exposure to toxin over many host generations promotes additional form of emergent adaptation due to selection of hosts based on detox capabilities of their bacterial community as a whole (as opposed to properties of individual bacteria). Conclusions: These findings show that interactions between pure Darwinian selections of host and its bacteria can give rise to emergent adaptive capabilities, including Lamarckian-like adaptation of the host-microbiome system.