Dissimilar bouncy walkers

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants xi_n, where n labels different bouncy walkers, are drawn from a distribution rho(xi_n). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-\alpha) (0<alpha<1) for large xi_n, we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler relaxation, and the the mean square displacement of a tracer particle (MSD) grows as t^delta with time t, where delta=alpha/(1+\alpha). If instead rho is light-tailedsuch that the mean friction constant exist, S(Q,t) decays exponentially and the MSD scales as t^(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.Comment: 11 pages, to appear in Journal of Chemical Physic

Aging dynamics in interacting many-body systems

Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment. Each particle in this single file is trapped for a random waiting time $\tau$ with power law distribution $\psi(\tau)\simeq\tau^{-1- \alpha}$, such that the $\tau$ values are independent, local quantities for all particles. From scaling arguments and simulations, we find that for the scale-free waiting time case $0<\alpha<1$, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) $\langle x^2(t)\rangle\simeq(\log t)^{1/2}$. This extreme slowing down compared to regular single file motion $\langle x^2(t)\rangle\simeq t^{1/2}$ is due to the high likelihood that the labeled particle keeps encountering strongly immobilized neighbors. For the case $1<\alpha<2$ we observe the MSD scaling $\langle x^2(t)\rangle\simeq t^{\gamma}$, where $\gamma2$ we recover Harris law $\simeq t^{1/2}$.Comment: 5 pages, 4 figure

Diabetes Mellitus as a Model of Psychosomatic and Somatopsychic Interrelationships

The article reviews research on the problem of interrelationship between different physical and psychosocial factors in type 1 diabetes mellitus (DM1). The authors consider methodological principles of health-related quality of life (HRQoL) assessment in DM1 patients and stress the need for an integrated biopsychosocial approach to the management of the disease. DM1 is a chronic metabolic disease with an absolute requirement for insulin replacement therapy. The stress inducing nature of DM1 is associated with its unexpected and dramatic manifestation in juvenile years, life-threatening nature of severe hypo-/hyperglycaemias and long-term complications, with the burden of diabetes self-management, threat of work disability, employment and career problems etc. These features of DM1 increase the likelihood of the development of anxiety and depressive disorders, which, in turn, may negatively influence the course of diabetes and in particular, diabetes self-care. This necessitates early diagnosis of emotional and behavioral disturbances in DM1 using self-report instruments as well as clinical assessment. Evidence suggests that active problem-focused coping behavior and adequate social support promote adherence to diabetes regimes and may act as a buffer against negative effects of the disease on HRQoL in DM1 patients. The core element in the HRQoL structure is personal disease picture (as opposed by objective clinical picture) – the cognitive-affectivebehavioral complex reflecting the patient’s personal perception of the disease. Examination of the personal disease picture and attitude towards the ailment in DM1 patients may help to improve understanding of the mechanisms of poor adjustment. Problems in disease adjustment can be detected also by diabetes-specific HRQoL assessment. The measures of HRQoL can be applied as screening instruments useful in increasing the effectiveness of patient-provider interactions and diabetes care.El artículo revisa la investigación del problema de la interrelación entre diferentes factores físicos y psicosociales en la diabetes melitus tipo 1 (DM1). Los autores consideran los principios de la evaluación de la calidad de vida relacionada con la salud (CVRS) en pacientes de DM1 y ponen de manifiesto la necesidad de un abordaje biopsicosocial integrado del manejo de la enfermedad. La DM1 es una enfermedad metabólica crónica con una necesidad absoluta de terapia de reemplazo de insulina. La naturaleza estresante de la DM1 se asocia con su aparición inesperada y dramática durante los años de juventud, la naturaleza peligrosa de las hipo e hiperglucemias y las complicaciones a largo plazo, con la carga del auto-cuidado de la diabetes, la amenaza de discapacidad laboral, problemas de empleo y carrera, etc. Estas características de la DM1 aumentan la probabilidad de desarrollar trastornos de ansiedad y depresivos que, a su vez, pueden afectar negativamente el curso de la diabetes y, en particular, el auto-cuidado de la diabetes. Esto requiere un diagnóstico temprano de los trastornos emocionales y comportamentales en los enfermos de DM1, empleando instrumentos de auto informe además de la evaluación clínica. La evidencia sugiere que el comportamiento de afrontamiento activo centrado en los problemas y el apoyo social adecuado promocionan la adherencia a los regímenes diabéticos y pueden amortiguar los efectos negativos de la enfermedad en la CVRS en los pacientes con DM1. El elemento esencial en la estructura de la CVRS es el cuadro clínico personal (en contraste con el cuadro clínico objetivo)— el complejo cognitivo-afectivo-conductual que refleja la percepción personal que tiene el paciente de su enfermedad. El examen del cuadro de enfermedad personal y la actitud hacia la enfermedad en los pacientes con DM1 puede mejorar la comprensión de los mecanismos de desadaptación. Los problemas en la adaptación a la enfermedad también pueden detectarse por medio de la evaluación de la CVRS específica para la diabetes. Las medidas de CVRS pueden aplicarse como instrumentos de criba útiles para incrementar la efectividad de las interacciones paciente-cuidador y del cuidado de la diabetes

Single-file dynamics with different diffusion constants

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.Comment: 9 pages, 5 figures. Journal of Chemical Physics (in press

Single-file diffusion with non-thermal initial conditions

Single-file diffusion is a theoretically challenging many-body problem where the calculation of even the simplest observables, e.g. mean square displacement, for a tracer particle requires a heavy mathematical machinery. There is therefore a need for simple approaches which predict qualitatively correct behaviours. Here we put forward one such method which we use to investigate the influence of non-thermal initial conditions on the dynamics of a tracer particle. With our new approach we reproduce, up to scaling, several known asymptotic results for the tracer particle mean square displacement.Comment: 4 pages, 1 figur

A Drift-Diffusion Model of Interval Timing in the Peak Procedure

Drift-diffusion models (DDMs) are a popular framework for explaining response times in decision-making tasks. Recently, the DDM architecture has been used to model interval timing. The Time-adaptive DDM (TDDM) is a physiologically plausible mechanism that adapts in real-time to different time intervals while preserving timescale invariance. One key open question is how the TDDM could deal with situations where reward is omitted, as in the peak procedure—a benchmark in the timing literature. When reward is omitted, there is a consistent pattern of correlations between the times at which animals start and stop responding. Here we develop a formulation of the TDDM’s stationary properties that allows for the derivation of such correlations analytically. Using this simplified formulation we show that a TDDM with two thresholds–one to mark the start of responding and another the stop–can reproduce the same pattern of correlations observed in the data, as long as the start threshold is allowed to be noisy. We confirm this by running simulations with the standard TDDM formulation and show that the simplified formulation approximates well the full model under steady-state conditions. Moreover, we show that this simplified version of the TDDM is formally equivalent to Scalar Expectancy Theory (SET) under stationary behaviours, the most prominent theory of interval timing. This equivalence establishes the TDDM as a more complete drift-diffusion based theory with SET as a special case under steady-state conditions

Cyclical population dynamics of automatic versus controlled processing : an evolutionary pendulum

Psychologists, neuroscientists, and economists often conceptualize decisions as arising from processes that lie along a continuum from automatic (i.e., “hardwired” or over-learned, but relatively inflexible) to controlled (less efficient and effortful, but more flexible). Control is central to human cognition, and plays a key role in our ability to modify the world to suit our needs. Given its advantages, reliance on controlled processing may seem predestined to increase within the population over time. Here, we examine whether this is so by introducing an evolutionary game theoretic model of agents that vary in their use of automatic versus controlled processes, and in which cognitive processing modifies the environment in which the agents interact. We find that, under a wide range of parameters and model assumptions, cycles emerge in which the prevalence of each type of processing in the population oscillates between two extremes. Rather than inexorably increasing, the emergence of control often creates conditions that lead to its own demise by allowing automaticity to also flourish, thereby undermining the progress made by the initial emergence of controlled processing. We speculate that this observation may have relevance for understanding similar cycles across human history, and may lend insight into some of the circumstances and challenges currently faced by our species