Posters

Fabian Aguirre Lopez: Imaginary replicas for random loopy graphs

We present a random graph ensemble of sparse simple graphs with a tuneable number of short loops and an arbitrary degree distribution. Interestingly, we observe different topological transitions of the ensemble that depend nontrivially on the system size. In order to predict analytically the behaviour of the ensemble and to calculate the average spectral density with the presence of loops we introduce the method of imaginary replicas. To do so, we first generalise our ensemble to a spectrally constrained graph ensemble, were we have a functional bias at each point of the spectral density. This allows us to calculate leading and subleading contributions to the generating function of the ensemble, given by the solution of a set of functional equations that generalise the typical results for locally tree like graphs.

Paul Baconnier: Selective and Collective Actuation in Active Solids

Active solids consist of out-of-equilibrium units performing mechanical work, that are embedded in an elastic matrix. The concept of active solids is central to autonomous processes in biological systems and the design of new materials. Yet, despite several theoretical proposals, the scarcity of experiments with a good control of the elasto-active coupling limits our understanding of the collective dynamics that have been observed numerically. Here we propose a simple realization of an active elastic solid, in which we characterize the emergence of selective and collective actuation and fully map out the interplay between activity, elasticity and geometry. Polar active agents exert active forces on the nodes of a two dimensional elastic lattice. When the lattice deforms, the displacement field reorient the active agents. For large enough coupling, the lattice nodes perform a collective oscillation around their equilibrium position. Only a few modes are actuated; and, crucially, the selected modes are not necessarily the lowest energy ones. By combining experiments with the numerical and theoretical analysis of an agent based model, we unveil the bifurcation scenario and the selection mechanism by which the collective actuation takes place. Our findings may provide insight into the recently observed oscillatory dynamics in confluent cell monolayers. We envisage that the present selection mechanism may be advantageous to the design of autonomous meta-materials.

Francesco Chippari: Dynamics of thermal first order phase transitions.

We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q>>1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.

Simone Ciarella: Intelligent brute force approach to glasses

In this poster I show three (1-2-3) different situations where machine learning (the "brute force") is combined with statistical physics in order to better understand glasses. In (1) we use supervised learning to predict weather or not a configuration is a two-level-system based on the particles coordinates. In (2) we discuss autoregressive models trained using reinforcement learning in order to generate samples from the Boltzmann distribution. In (3) we construct a multi-layer model, which aims to predict the dynamics of supercooled liquids from static information only.

Hugo Cui: Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime

We consider Kernel Ridge Regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of eigenvalues of the features co-variance. These decays were, however, provided for sizeably different setups, namely in the noiseless case with constant regularization and in the noisy optimally regularized case. Intermediary settings have been left substantially uncharted. We unify and extend this line of work, providing characterization of all regimes and excess error decay rates that can be observed in terms of the interplay of noise and regularization. In particular, we show the existence of a transition in the noisy setting between the noiseless exponents to its noisy values as the sample complexity is increased. Finally, we illustrate how this crossover can also be observed on real data sets.

Ittai Fraenkel: Concatenated Entropy in a Model for the Glass Transition

Compression algorithms, applied to concatenated images of a sample at successive times, provide a first-principle definition of configurational entropy, as well as a practical way of computing it from numerical or even experimental data. This definition relies only on the existence of timescale separation between fast and slow relaxations, and is applicable both in and out of equilibrium.

Jerome Garnier-Brun: A new spin on optimal portfolios

We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed. We compute the average number of solutions and show that its logarithm grows as Nα, where N is the number of assets or species and α≤2/3 depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity m(N) of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem.

Julia Giannini: Bond-space operator disentangles quasi-localized and phononic modes in structural glasses

The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a linear operator defined on the space of particle interactions (bonds) in a disordered material. We find that this bond-force-response operator offers a unique interpretation of QLMs in glasses, and cleanly recovers some of their important statistical and structural features. The analysis presented here reveals the dependence of the number density (per frequency) and spatial extent of QLMs on material preparation protocol.

Bruno Loureiro: Exactly solvable models for high-dimensional machine learning problems

The past decade has witnessed a surge in the development and adoption of machine learning algorithms to solve day-a-day computational tasks. Yet, a solid theoretical understanding of even the most basic tools used in practice is still lacking. Surprisingly, many of the “exotic” behaviours of deep neural networks have shown to hold in models as simple as high-dimensional linear regression. In the poster, I introduce two simple toy models describing learning with correlated features. I motivate how these models encompass many learning problems of interest, e.g. ridge and logistic regression, kernel methods, random features, scattering transforms and transfer learning. Finally, I discuss how these models can be used to approximate real data learning curves in some scenarios.

Rituparno Mandal: Rheology and Shear Ordering of Active Glass

Dense active matter systems are ubiquitous in nature, with examples ranging from the cytoplasm, tissues of motile cells to traffic jams. Though many recent studies have explored the dynamical and transport aspects of such active glasses, an understanding of the rheological behaviour of these fascinating out-of-equilibrium systems remains elusive. Using extensive molecular dynamics simulation of a model active glass forming system under steady shear, we establish the existence of different dynamical states: disordered, propulsion-induced ordered and shear-induced ordered (SIO). Combining simulation results with an analytical theory we rationalise the qualitative features of the SIO phase, which is facilitated by the applied shear and appears without any alignment interactions or particle shape anisotropies.

David Martin: Fluctuation-induced first order transition in models of collective motion

We study the role of noise on the nature of the transition to collective motion. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turns changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including topological models in which alignment between particles occurs through "metric-free" rules, which were believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

Flavio Nicoletti: Localisation Properties in the m-component full range Spin Glass at T=0

The full range m-component vectorial Spin Glass at T=0 under an external field is a valid tool to modelise low-energy excitations of real glasses. In particular, the Spin-Glass transition in the field is a delocalisation transition for the soft modes: in the paramagnetic phase, the system exhibits localisation in the low-energy modes, and delocalises when entering the Spin-Glass Phase. While an analytical solution for the thermodynamic system is available, strong finite size effects are observed close to the critical point, which make the finite size system quite different from the asymptotic one.

Jacopo Niedda: The mode-locked p-spin model: a spin glass model for random lasers

The mode-locked p-spin model is a spin glass model that can be used to describe the interaction of light modes in multimodal lasers from a statistical mechanics point of view. This model is particularly useful in describing random lasers [1], where the amplification of light takes place in a disordered medium due to multiple scattering. In random lasers many light modes compete for amplification and spikes in the emission spectrum occur at different wavelengths from shot-to-shot. While there is still a lack of a complete first principles theory of random lasers, the mode-locked p-spin model faces the essential issue in describing the random lasing phenomenon: the complex interplay between the disorder of the medium and the non-linearity of the interactions. The model has been solved with the replica method only under some very particular conditions leading to a fully connected graph of interactions, where standard mean-field methods can be used [2-3]. As a result, a random first order phase transition has been characterized, corresponding to the mode-locking transition from a continuous wave phase to an ultra-short pulses phase. We are now focusing on the study of the general model, considering a selection rule for the modes participating to the non-linear interactions, which leads to a one order dilution with respect to the fully connected model. We will present some results obtained with numerical simulations of the model, that we are performing in order to better characterize the random first order transition and to validate the presence of a power condensation transition [4-5].

Mauro Pastore: Critical properties of the SAT/UNSAT transitions in the classication problem of structured data

In this contribution, I present the critical properties of two constraint satisfaction problems (CSPs) arising in the context of the supervised learning task of classification of structured data. Indeed, when the objects to classify are not isolated points, two interesting questions can be formulated: (i) how many classifications, for a typical instance of a dataset of object-label pairs, are there; (ii) how many of them, for a typical instance of the objects alone, are there when the labels can be chosen at will. In the case of binary linear classification of simplexes of points, these problems can be studied with the replica method: while the first problem present a SAT/UNSAT transition which is marginal from the point of view of stability of the replica symmetric solution, the second one present an additional full replica symmetry breaking transition. Conclusions can be drawn about the nature of the space of solutions.

Gianmarco Perrupato: The zero temperature Bethe lattice spin glass in a random field

We investigate at zero temperature the replica symmetry broken (RSB) phase of the Bethe lattice spin-glass (SG) in a random field. From the properties of the k-RSB cavity solution we deduce an equation for the distribution of the extremal values taken by the cavity fields. This distribution turns out not to depend on the parameters defining the RSB, and predicts the existence of a cluster of spins having the same effective local field on all local ground states. One of the main consequences of this picture is the possibility to formulate a Ginzburg criterion leading to an upper critical dimension Dᵤ=8, at variance with the classic results Dᵤ=6 yielded by the finite-temperature replica field theory.

Linda Ravazzano: Unjamming of active rotators

From a statistical physics point of view, one of the most interesting features of active particles assemblies, is the richness of dynamical phases they can undergo varying internal parameters such as density, adhesion strength or self-propulsion.

Most theoretical studies of active matter consider self-propelled particles driven by active forces. The observation of the motion of Chlamydomonas reinhardtii algae, in which the active particles have not only the ability of self-propel, but also to self-rotate, suggests, however, that active torques may also play an important and yet unexplored role.

Inspired by that, we simulate the dynamics of a system of interacting active 2D disks endowed with active torques and self-propulsive forces.

We studied this model system of active rotators in different conditions: at low packing fractions, where adhesion causes the formation of small rotating clusters, at higher densities, where our simulations show a jamming to unjamming transition promoted by active torques and hindered by adhesion, and in presence of both self-propulsion and self-rotation, studying the interplay between those quantities and deriving a phase diagram. Our results yield a comprehensive picture of the dynamics of active rotators, highlighting the importance of the internal degrees of freedom of the active particles in determining the collective behavior of the system and providing useful guidance to interpret experimental results in cellular systems where rotations might play a role.

Saverio Rossi: The Elasto-Plastic Model near the yielding transition: An analogy with the Random Field Ising Model

The yielding transition is the passage from an essentially elastic to a plastic regime in materials deformation. We investigate how it varies from ductile to brittle with the initial preparation of the sample, and we compare these results with a version of the Random Field Ising Model.

Vittoria Sposini: Brownian yet non-Gaussian dynamics and heterogeneous systems

A considerable number of systems have been reported in which Brownian yet non-Gaussian dynamics is observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This behaviour has been interpreted as resulting from diffusion in heterogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. In this poster I am going to present my work on the statistical analysis of random diffusivity models. Moreover, few insights on future studies related to glass-forming systems are also provided.

Diego Tapias: Localization in the Sparse Barrat-Mézard trap model

I will introduce the Barrat-Mézard trap model on a sparse network as a model aimed at understanding glassy properties in physical systems. My focus will be on the methods employed to obtain the spectral density of relaxation rates and the localization properties of the eigenvectors of the Master Operator.

Stephen Thornton: Jamming and Rigidity Percolation in the CPA

The coherent potential approximation (CPA) is a powerful effective medium theory that can be used to study disordered systems. Applied to lattices with randomly percolated bonds, the zero-frequency predictions of the theory reproduce a line of continuous classical phase transitions across which lattices lose bulk and shear rigidity simultaneously, known as rigidity percolation. By stacking multiple coupled sublattices, one can also reproduce a transition akin to jamming, where the bulk modulus jumps discontinuously and the shear modulus grows continuously.

By extending the analysis of the CPA to the frequency-dependent case, we can explore a phase diagram that includes both jamming and rigidity percolation. These two transitions turn out to have different critical exponents, and so there is a novel crossover scaling that can be recovered from the CPA analysis. We are also able to investigate the behavior of susceptibilities, such as the density-density response, as we approach these transitions.

Ruben Zakine: Predicting phase transitions in nonequilibrium systems

Predicting phase transitions in thermal systems is one of the major achievements of equilibrium statistical mechanics. In contrast, in nonequilibrium systems where energy or momentum are continuously injected, there is no unifying theory of phase changes as yet. In particular we can explain why water freezes at 273K and boils at 373K, but we do not fully understand what drives a bacterial population to condense or spread. Here, I will show how large deviation theory allows us to infer the phase diagrams of some nonequilibrium systems through an optimization problem that can be solved by efficient numerical methods. As illustrations of the approach, I will calculate the phase diagram of two models: a generic non-equilibrium system that has drawn the attention of physicists in recent years, and a system of interacting particles that can move, reproduce, and die.

Yiwei Zhang: Collective behaviours of pulsating soft particles

Cells in densed tissues have periodically and collectively fluctuating sizes, giving rise to density wave propagation without particle migration. Here we propose a 2D model filled by actively pulsating soft spheres as a minimal model to mimic this process. The wave pattern independent of particle migration has been reproduced along with other dynamical phases. A phase diagram has been measured for this novel active matter model and the key phase transitions involved are investigated, at both particle-based level and hydrodynamic level.