arXiv subjects

Ulisse Ferrari

Publications and source records attributed to Ulisse Ferrari.

25 records · Page 2Linked to original sources

arXiv2016

Learning Maximum Entropy Models from finite size datasets: a fast Data-Driven algorithm allows sampling from the posterior distribution

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case of large but finite datasets. We first show how the steepest descent dynamics is not optimal as it is slowed down by the inhomogeneous curvature of the model parameters space. We then provide a way for rectifying this space which relies only on dataset properties and does not require large computational efforts. We conclude by solving the long-time limit of the parameters dynamics including the randomness generated by the systematic use of Gibbs sampling. In this stochastic framework, rather than converging to a fixed point, the dynamics reaches a stationary distribution, which for the rectified dynamics reproduces the posterior distribution of the parameters. We sum up all these insights in a "rectified" Data-Driven algorithm that is fast and by sampling from the parameters posterior avoids both under- and over-fitting along all the directions of the parameters space. Through the learning of pairwise Ising models from the recording of a large population of retina neurons, we show how our algorithm outperforms the steepest descent method.

cond-mat.dis-nn↗

arXiv2015

Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-$1$ model with $p$-body quenched disordered interaction, with $p>2$, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low density and high density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first- order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a non-zero complexity line. The latter inversion, though, turns out to be preceded by a novel dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode coupling theory equations throughout the space of external thermodynamic parameters and the relationship with the underlying statics is discussed.

cond-mat.dis-nn↗

arXiv2013

Finite size corrections to disordered systems on Erdös-Rényi random graphs

We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the $O(1/N)$ corrections in the replica symmetric phase as a linear combination of the free energies of open and closed chains. We perform a numerical check of the formulae on the Random Field Ising Model at zero temperature, by computing finite size corrections to the ground state energy density.

cond-mat.dis-nn↗

arXiv2012

Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models

An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the β regime. In the original structural glass context this relationship follows from the MCT equations that are obtained making rather uncontrolled approximations and λ has to be treated like a tunable parameter. It is known that a certain class of mean-field spin-glass models is exactly described by MCT equations. In this context, the physical meaning of the so called parameter exponent λ has recently been unveiled, giving a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents in a class of mean-field Ising spin-glass models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model and the Random Orthogonal model.

cond-mat.dis-nn↗

arXiv2012

On the two-steps relaxation of mean-field glasses: p-spin model

Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time correlation function at dynamic criticality. In this work we derive critical slowing down exponents of spin-glass models undergoing discontinuous transitions by computing their Gibbs free energy and connecting the dynamic behavior to static "in-state" properties. Both the spherical and Ising versions are considered and, in the simpler spherical case, a generalization to arbitrary schematic Mode Coupling kernels is presented. Comparison with dynamic results available in literature is performed. Analytical predictions for the Ising case are provided for any $p$.

cond-mat.dis-nn↗

arXiv2012

DnaA and the timing of chromosome replication in Escherichia coli as a function of growth rate

Background: In Escherichia coli, overlapping rounds of DNA replication allow the bacteria to double in faster times than the time required to copy the genome. The precise timing of initiation of DNA replication is determined by a regulatory circuit that depends on the binding of a critical number of ATP-bound DnaA proteins at the origin of replication. The synthesis of DnaA in the cell is controlled by a growth-rate dependent, negatively autoregulated gene found near the origin of replication. Both the regulatory and initiation activity of DnaA depend on its nucleotide bound state and its availability. Results: In order to investigate the contributions of the different regulatory processes to the timing of initiation of DNA replication at varying growth rates, we formulate a minimal quantitative model of the initiator circuit that includes the key ingredients known to regulate the activity of the DnaA protein. This model describes the average-cell oscillations in DnaA-ATP/DNA during the cell cycle, for varying growth rates. We evaluate the conditions under which this ratio attains the same threshold value at the time of initiation, independently of the growth rate. Conclusions: We find that a quantitative description of replication initiation by DnaA must rely on the dependency of the basic parameters on growth rate, in order to account for the timing of initiation of DNA replication at different cell doubling times. We isolate two main possible scenarios for this. One possibility is that the basal rate of regulatory inactivation by ATP hydrolysis must vary with growth rate. Alternatively, some parameters defining promoter activity need to be a function of the growth rate. In either case, the basal rate of gene expression needs to increase with the growth rate, in accordance with the known characteristics of the dnaA promoter.

q-bio.GN↗

arXiv2011

Random, thermodynamic and inverse first order transitions in the Blume-Capel spin-glass

The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of different nature. In given conditions inverse freezing occurs. As $p=2$ the glassy phase is replica symmetric and the transition is always continuous in the phase diagram. For $p>2$ the exact solution for the glassy phase is obtained by the one step replica symmetry breaking Ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include (i) the usual random first order transition (Kauzmann-like) preceded by a dynamic transition, typical of mean-field glasses, (ii) a thermodynamic first order transition with phase coexistence and latent heat and (iii) a regime of inversion of static and dynamic transition lines. In the latter case a thermodynamic stable glassy phase, with zero configurational entropy, is dynamically accessible from the paramagnetic phase. Crossover between different transition regimes are analyzed by means of Replica Symmetry Breaking theory and a detailed study of the complexity and of the stability of the static solution is performed throughout the space of external thermodynamic parameters.

cond-mat.dis-nn↗