**Phase transitions in computer simulations : the Tethered Monte Carlo method**

### Beatriz Seoane Bartolomé (LPT-ENS, Paris)

In this talk, I will present a powerful Monte Carlo method that I developed during my PhD [1,2] and extended recently [3], designed to efficiently study phase transitions at equilibrium. The principle is very simple, by means of external constraints to the system, we are able to avoid the traditional critical (exponential) slowing down associated to the second (first) order transition, and thus reach much larger system sizes than with traditional methods. Furthermore, the reconstruction of the constrained free energy is much simpler than in other similar methods, such as the famous Umbrella Sampling, allowing us to both fix multiple constraints at the same time, and to extract magnitudes such as the inter-facial free energy with an unusual high precision. In particular, I will discuss the Tethered Monte Carlo strategy in the context of a toy model for crystalline porous media [3].

[1] J. Stat. Phys. 144, 554 (2011).

[2] Phys. Rev. Lett. 108, 165701 (2012).

[3] The Journal of Chemical Physics 147 , 084704 (2017).

## Statistical Physics-inspired models of biological network: collective behavior in neuronal ensembles

### Ulisse Ferrari (Institut de la Vision, Inserm & UPMC)

In both cortices and sensory systems, information is represented and transmitted through the correlated activity of large neuronal networks. Neurons, in fact, do not work independently: each of them drives the activity of the others, thus working as a collective ensemble. Methods borrowed from Statistical Physics and Machine Learning are powerful tools for characterizing the collective behavior of large systems and hence offer promising approaches to understand the activity of neuronal populations. In this talk I will show how the Maximum Entropy principle, applied to cortical in-vivo recording, allows for characterizing and comparing the population behavior during wakefulness and deep sleep. Then, I will use hidden-layer models, point processes and “experimental” linear response theory to account for non-linear stimulus processing in sensory networks, such as the retina. These approaches allow for constructing high performing models of the retinal population response to visual stimuli and thus for characterizing how a network of neurons can encode and transmit visual information.