Glassy features in constraint satisfaction problems and dynamical scenarios
Ada Altieri
Tue, Feb. 04th 2020, 14:00-15:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers

In this talk, I will discuss relevant underlying connections between the jamming transition in amorphous systems and a continuous constraint satisfaction problem, the non-convex spherical perceptron model [1-2]. A renewed interest in this model, borrowed from neural networks and machine learning domain, has been fostered recently once it has been realized that - reformulated in a continuous version - it actually falls in the same universality class as high dimensional sphere systems.
I will then present my recent results in terms of a Plefka-like expansion, which turns out to be beneficial to define an effective potential (a Thouless-Anderson-Palmer free energy) and to study marginal properties of glassy systems in the low-temperature regime [3-4].
Interestingly, the jamming phenomenology has a broader spectrum of applicability that one might think at first sight and concerns not only structural glasses but also error-correcting codes, traffic flow, transport in crowded biological environments and evolutionary dynamics. Therefore, in the second part of the talk, I will discuss how a mechanism of optimization in the presence of constraints - as for the perceptron model - can provide a suitable theoretical framework to explain critical properties of large ecosystems appearing to be poised at the edge of stability [5]. I will then present my current research activity and future perspectives in this direction, focusing on the MacArthur and the Lotka-Volterra models, respectively.
In the last part, I will also discuss the importance of defining a dynamical mean-field theory formalism for a better investigation of aging dynamics [6] in different universality classes of disordered systems. Such an approach turns out to be of interest in very different contexts ranging from condensed matter, ecology as well as to inference problems.

[1]S. Franz, G. Parisi The simplest model of jamming, J. Phys. A: Math. Theor., 145001 (2016).
[2] S. Franz, G. Parisi, P. Urbani, F. Zamponi, Universal spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution, PNAS 112, 14539 (2015).
[3] A. Altieri, S. Franz, G. Parisi The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential J. Stat. Mech. 093301 (2016).
[4] A. Altieri Higher order corrections to the effective potential close to the jamming transition in the perceptron model Phys. Rev. E 97, 012103 (2018).
[5] A. Altieri, S. Franz, Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems, Rapid Communication in Phys. Rev. E 99, 010401(R) (2019).
[6] A. Altieri, G. Biroli, C. Cammarota, Dynamical Mean-Field Theory Formalism in the aging regime for a class of solvable models, in preparation (2020).

Contact : Marco SCHIRO


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