Motion of particles adhering to the leading lamella of crawling cells.

ABSTRACT Time-lapse films of particle motion on the leading lamella of chick heart fibroblasts and mouse peritoneal macrophages were analyzed. The particles were composed of powdered glass or powdered aminated polystyrene and were 0.5-1.0 /um in radius. Particle motions were described by steps in position from one frame of the time-lapse movies to the next. The statistics of the step-size distribution of the particles were consistent with a particle in Brownian motion subject to a constant force. From the Brownian movement, we have calculated the two-dimensional diffusion coefficient of different particles. These vary by more than an order of magnitude (10-11-10-1 ° cm'/s) even for particles composed of the same material and located very close to each other on the surface of the cell. This variation was not correlated with particle size but is interpretable as a result of different numbers of adhesive bonds holding the particles to the cells. The constant component of particle movement can be interpreted as a result of a constant force acting on each particle (0.1-1.0 X 10-e dyn). Variations in the fractional coefficient for particles close to each other on the cell surface do not yield corresponding differences in velocity, suggesting that the frictional coefficient and the driving force vary together. This is consistent with the hypothesis that the particles are carried by flo

Motion of particles adhering to the leading lamella of crawling cells

Time-lapsed films of particle motion on the leading lamella of chick heart fibroblasts and mouse peritoneal macrophages were analyzed. The particles were composed of powdered glass or powdered aminated polystyrene and were 0.5-1.0 micrometer in radius. Particle motions were described by steps in position from one frame to the time-lapse movies to the next. The statistics of the step-size distribution of the particles were consistent with a particle in Brownian motion subject to a constant force. From the Brownian movement, we have calculated the two-dimensional diffusion coefficient of different particles. These vary by more than an order of magnitude (10(-11)-10(-10) cm2/s) even for particles composed of the same material and located very close to each other on the surface of the cell. This variation was not correlated with particle size but is interpretable as a result of different numbers of adhesive bonds holding the particles to the cells. The constant component of particle movement can be interpreted as a result of a constant force acting on each particle (0.1-1.0 x 10(-8) dyn). Variations in the fractional coefficient for particles close to each other on the cell surface do not yield corresponding differences in velocity, suggesting that the frictional coefficient and the driving force vary together. This is consistent with the hypothesis that the particles are carried by flow of the membrane as a whole or by flow of some submembrane material. The utility of our methods for monitoring cell motile behavior in biologically interesting situations, such as a chemotactic gradient, is discussed

Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.Comment: 6 pages, 4 figures

Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games

We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From this it is proved that the Skeptic's Bayesian strategy weakly forces the strong law of large numbers (SLLN) with the convergence rate of O(\sqrt{\log n/n})$ and if Reality violates SLLN then the exponential growth rate of the capital process is very accurately described in terms of the Kullback divergence between the average of Reality's moves when she violates SLLN and the average when she observes SLLN. We also investigate optimality properties associated with Bayesian strategy

On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015

Condensation of Silica Nanoparticles on a Phospholipid Membrane

The structure of the transient layer at the interface between air and the aqueous solution of silica nanoparticles with the size distribution of particles that has been determined from small-angle scattering has been studied by the X-ray reflectometry method. The reconstructed depth profile of the polarizability of the substance indicates the presence of a structure consisting of several layers of nanoparticles with the thickness that is more than twice as large as the thickness of the previously described structure. The adsorption of 1,2-distearoyl-sn-glycero-3-phosphocholine molecules at the hydrosol/air interface is accompanied by the condensation of anion silica nanoparticles at the interface. This phenomenon can be qualitatively explained by the formation of the positive surface potential due to the penetration and accumulation of Na+ cations in the phospholipid membrane.Comment: 7 pages, 5 figure

A simple mean field model for social interactions: dynamics, fluctuations, criticality

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analize long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.Comment: 37 pages, 2 figure