**Non-Equilibrium Statistical Mechanics for Active Matter**

Emergent properties and pattern formation that appears as collective behavior of systems with large number of constituents is a central aspect in the statistical description of systems far from equilibrium. The extensively correlated dynamics that emerges not due to a change of external parameter but rather as a consequence of “activity” of the constituents (capability of converting ambient free energy into systematic movement) is the unifying characteristic of active matter. Flocking behavior of birds, bacteria and humans are just a few examples of experimentally studied active matter. For living cells such active behavior appears at multicellular (tissue morphogenesis, wound healing), cellular (migration, adhesion, division) and sub-cellular (intracellular transport) length scales. Mechanical and statistical properties of cellular behavior will provide an insight into multi-cellular/cellular/sub-cellular susceptibility to molecular perturbations and enable to obtain a control of such systems.

Understanding cellular behavior on different (length) scales and specifically establishing links between emergent behaviors on larger scales to basic events on smaller scales is the general framework of the research in our lab. The detailed cellular cell state is determined by an enormous number of variables. Such a degree of complexity makes it difficult to build up the global cellular behavior starting from fundamental building blocks. Rather, we use the larger scale behavior, and especially the stochastic properties, to impose general bounds and constraints on the complex interactions of the underlying mechanisms.

**Noisy Data: Modeling and Analysis**

The enormous flow of experimental data enforces us to develop new tools and approaches, in order to properly interpret the information in the data. The presence of “noise” makes it some times extremely difficult to accomplish this task. We exploit various stochastic properties of “noise” to model, test validity and data mining of experimentally obtained results. The main focus in the group is “noisy” single trajectories from systems such as (but not limited to): stock market, colloidal suspensions, sub-cellular transport or life trajectories of a whole cell. For noisy trajectories we: (i) develop novel bounds of possible precision; (ii) elucidate the valuable information located in the data; (iii) model proper stochastic mechanism responsible for the observed behavior.

**Basic Properties of Correlated Random Variables**

The sum of uncorrelated random variables is distributed according to the Normal (or Gaussian) distribution; this important result is the corner stone of Statistical Mechanics. The generalization of the Normal distribution for cases when the variables attain “strange” properties like diverging moments is the mathematical mechanism behind non-equilibrium processes, such as anomalous diffusion. In glassy systems, when the statistical description of thermal equilibrium is not applicable, random microscopic variables of the system are strongly correlated. In our group we develop spatio-temporal stochastic transformations in order to generalize the fundamental result for a sum of random variables. The results are applied to describe transport in random media.