Related papers: Tessellation-valued processes that are generated b…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides…
The adhesion approximation is a simple analytical model suggested for explanation of the major geometrical features of the observed structure in the galaxy distribution on scales from 1 to (a few)x100/h Mpc. It is based on Burgers' equation…
In vitro velocities of several cell types have been measured using computer controlled video microscopy, which allowed to record the cells' trajectories over several days. On the basis of our large data sets we show that the locomotion…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
The Dead Leaves Model (DLM) provides a random tessellation of $d$-space, representing the visible portions of fallen leaves on the ground when $d=2$. For $d=1$, we establish formulae for the intensity, two-point correlations, and asymptotic…
A hallmark of biological tissues, viewed as complex cellular materials, is the active generation of mechanical stresses by cellular processes, such as cell divisions. Each cellular event generates a force dipole that deforms the surrounding…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of minimizers are discussed for different classes of problems,…
Fluctuations of cell state, e.g., abundances of some proteins, have attracted much attention both theoretically and experimentally. The distribution of such state over cells, however, is not only a result of intracellular stochastic…
Stochastic dynamics of several systems can be modeled via piecewise deterministic time evolution of the state, interspersed by random discrete events. Within this general class of systems, we consider time-triggered stochastic hybrid…
The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth,…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…