**Dynamical maximum entropy approach to biological networks**

Early Stage Researcher: Marco Faggian

Principle Investigators: Francesco Ginelli (Aberdeen, UABDN – major institution) and Zoran Levnajic (Faculty of Information Studies in Novo Mesto, FIS – partner institution)

In many biological problems, the real underlying network is not sufficiently well known, and it is not possible to formulate *a priori* an accurate mathematical model. One is faced with the “inverse” problem of reconstructing the dynamics and network topology starting from raw data. Maximum entropy methods try to achieve this goal by finding the maximally disordered (in a sense, the most general) probability distribution which is consistent with a carefully chosen set of empirically observed data. From the detailed knowledge of this distribution, much information about the network and its dynamics can be extracted.

Maximum entropy methods have been successful in describing collective and emergent phenomena in biological systems comprising many correlated degrees of freedom. These are typically mapped onto equilibrium systems, so that dynamical properties, often strongly out of equilibrium, are disregarded by these analysis. Newly introduced dynamical maximum entropy methods overcome this limitations by constraining the maximum entropy distribution to empirically observed spatio-temporal correlation functions.

In this project, we aim at extending this approach, originally developed in the context of flocking, to generic, out-of-equilibrium complex oscillatory systems, and biological networks. Comparison with other inverse problem methods will be also carried on. Ideally, inverse methods will be tested both on synthetic and biological datasets.

References:

[1] A. Cavagna et al., Phys. Rev. E **89** 042707 (2014).

[2] E. Schneidman, M. J Berry, R. Segev, and W. Bialek, Nature **440**, 1007 (2006).

[3] Z. Levnajic, Eur. Phys. J. B **7**, 1 (2013)