arXiv subjects

Chiara Cammarota

Publications and source records attributed to Chiara Cammarota.

At least 37 records · Page 2Linked to original sources

arXiv2020

Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference

Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin algorithm, in the context of noisy high-dimensional inference. We employ the Langevin algorithm to sample the posterior probability measure for the spiked matrix-tensor model. The typical behaviour of this algorithm is described by a system of integro-differential equations that we call the Langevin state evolution, whose solution is compared with the one of the state evolution of approximate message passing (AMP). Our results show that, remarkably, the algorithmic threshold of the Langevin algorithm is sub-optimal with respect to the one given by AMP. We conjecture this phenomenon to be due to the residual glassiness present in that region of parameters. Finally we show how a landscape-annealing protocol, that uses the Langevin algorithm but violate the Bayes-optimality condition, can approach the performance of AMP.

cs.LG↗

arXiv2019

Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems

Dynamical mean field theory (DMFT) is a tool that allows to analyze the stochastic dynamics of $N$ interacting degrees of freedom in terms of a self-consistent $1$-body problem. In this work, focusing on models of ecosystems, we present the derivation of DMFT through the dynamical cavity method, and we develop a method for solving it numerically. Our numerical procedure can be applied to a large variety of systems for which DMFT holds. We implement and test it for the generalized random Lotka-Volterra model, and show that complex dynamical regimes characterized by chaos and aging can be captured and studied by this framework.

cond-mat.dis-nn↗

arXiv2018

Complexity of energy barriers in mean-field glassy systems

We analyze the energy barriers that allow escapes from a given local minimum in a mean-field model of glasses. We perform this study by using the Kac-Rice method and computing the typical number of critical points of the energy function at a given distance from the minimum. We analyze their Hessian in terms of random matrix theory and show that for a certain regime of energies and distances critical points are index-one saddles and are associated to barriers. We find that the lowest barrier, important for activated dynamics at low temperature, is strictly lower than the "threshold" level above which saddles proliferate. We characterize how the quenched complexity of barriers, important for activated process at finite temperature, depends on the energy of the barrier, the energy of the initial minimum, and the distance between them. The overall picture gained from this study is expected to hold generically for mean-field models of the glass transition.

cond-mat.dis-nn↗

arXiv2018

Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions

We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and on the spiked-tensor model and generalizations. We thoroughly analyze the statistical properties of the corresponding landscapes and characterize the associated geometrical phase transitions. In order to perform our study, we develop a framework based on the Kac-Rice method that allows to compute the complexity of the landscape, i.e. the logarithm of the typical number of stationary points and their Hessian. This approach generalizes the one used to compute rigorously the annealed complexity of mean-field glass models. We discuss its advantages with respect to previous frameworks, in particular the thermodynamical replica method which is shown to lead to partially incorrect predictions.

cond-mat.dis-nn↗

arXiv2018

Experimental Determination of Configurational Entropy in a Two-Dimensional Liquid under Random Pinning

A quasi two-dimensional colloidal suspension is studied under the influence of immobilisation (pinning) of a random fraction of its particles. We introduce a novel experimental method to perform random pinning and, with the support of numerical simulation, we find that increasing the pinning concentration smoothly arrests the system, with a cross-over from a regime of high mobility and high entropy to a regime of low mobility and low entropy. At the local level, we study fluctuations in area fraction and concentration of pins and map them to entropic structural signatures and local mobility, obtaining a measure for the local entropic fluctuations of the experimental system.

cond-mat.soft↗

arXiv2017

Activated Aging Dynamics and Effective Trap Model Description in the Random Energy Model

We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.

cond-mat.dis-nn↗

arXiv2017

Numerical evidences of universal trap-like aging dynamics

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.

cond-mat.dis-nn↗

arXiv2017

Marginally Stable Equilibria in Critical Ecosystems

In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by our numerical studies, shows that for strong and heterogeneous interactions the system displays multiple equilibria which are all marginally stable. This property allows us to obtain general identities between diversity and single species responses, which generalize and saturate May's bound. By connecting the model to systems studied in condensed matter physics, we show that the multiple equilibria regime is analogous to a critical spin-glass phase. This relation provides a new perspective as to why many systems in several different fields appear to be poised at the edge of stability and also suggests new experimental ways to probe marginal stability.

cond-mat.stat-mech↗

arXiv2015

First Principle Computation of Random Pinning Glass Transition, Glass Cooperative Length-Scales and Numerical Comparisons

As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction $c$ of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase diagram as a function of $c$ and of the packing fraction $ϕ$, showing a line of RPGT ending in a critical point. We also obtain first microscopic results on cooperative length-scales characterizing medium-range amorphous order in Hard Spere glasses and indirect quantitative information on a key thermodynamic quantity defined in proximity of ideal glass transitions, the amorphous surface tension. Finally, we present numerical results of pair correlation functions able to differentiate the liquid and the glass phases, as predicted by the analytic computations.

cond-mat.dis-nn↗

arXiv2014

Fluctuations and Shape of Cooperative Rearranging Regions in Glass-Forming Liquids

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that super-cooled liquids are characterized by two different static lengths: the point-to-set $ξ_{PS}$ which is a measure of the spatial extent of cooperative rearranging regions and the wandering length $ξ_\perp$ which is related to the fluctuations of their shape. We find that $ξ_\perp$ grows when approaching the glass transition but slower than $ξ_{PS}$. The wandering length increases as $s_c^{-1/2}$, where $s_c$ is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids.

cond-mat.dis-nn↗

arXiv2014

Spontaneous energy-barrier formation in an entropy-driven glassy dynamics

The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyse it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regime of realistic models of glass-formers. In this case, we found that typical dynamical paths episodically reach an high fixed threshold energy unexpectedly giving rise to a simple thermally activated aging phenomenology. In order to unveil this peculiar aging behavior we introduce a novel description of the dynamics in terms of spontaneously emerging dynamical basins.

cond-mat.dis-nn↗

arXiv2013

Random-field-like criticality in glass-forming liquids

We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration. We discuss to what extent this field-theoretical description and the mapping to the random field Ising model hold in the whole supercooled liquid regime, in particular near the glass transition.

cond-mat.dis-nn↗

arXiv2012

A general approach to systems with randomly pinned particles: unfolding and clarifying the Random Pinning Glass Transition

Pinning a fraction of particles from an equilibrium configuration in supercooled liquids has been recently proposed as a way to induce a new kind of glass transition, the Random Pinning Glass Transition (RPGT). The RPGT has been predicted to share some features of standard thermodynamic glass transitions and usual first order ones. Thanks to its special nature, the approach and the study of the RPGT appears to be a fairly reachable task compared to the daunting problem of inspecting standard glass transitions. In this Letter we generalize the pinning particle procedure. We study a mean-field system where the pinned configuration is extracted from the equilibrium distribution at temperature $T'$ and the thermodynamics of the non pinned particles is observed at a lower temperature $T$. A more complicated physics emerges from this generalization eventually clarifying the origin and the peculiar characteristics of the RPGT.

cond-mat.dis-nn↗

arXiv2012

Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis

We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.

cond-mat.dis-nn↗

arXiv2012

Patch-repetition correlation length in glassy systems

We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A l^{d-1} down to length-scales of the order of one, where A is a positive constant, s_c is the configurational entropy density and d the spatial dimension. In consequence, the only meaningful length that can be defined from patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical length-scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, on the possible real space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size.

cond-mat.stat-mech↗

arXiv2011

Aging and relaxation near Random Pinning Glass Transitions

Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual Mode Coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c - T phase diagram delimited by those two lines leads to aging. By extending our results to finite dimensional systems we predict non-interrupted aging only for quenches on the ideal glass transition line and two very different types of equilibrium relaxations for quenches below and above it.

cond-mat.dis-nn↗

arXiv2011

Ideal Glass Transitions by Random Pinning

We study the effect of freezing the positions of a fraction $c$ of particles from an equilibrium configuration of a supercooled liquid at a temperature $T$. We show that within the Random First-Order Transition theory pinning particles leads to an ideal glass transition for a critical fraction $c=c_{K}(T)$ even for moderate super-cooling, e.g. close to the Mode-Coupling transition temperature. We first derive the phase diagram in the $T-c$ plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for $|c-c_{K}(T)|\rightarrow 0$, in particular the divergence of length and time scales. These are dominated by two zero-temperature fixed points. We also show that for $c=c_{K}(T)$ the typical distance between frozen particles is related to the static point-to-set lengthscale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.

cond-mat.dis-nn↗

arXiv2010

Renormalization group analysis of the random first order transition

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.

cond-mat.dis-nn↗