Inverse modeling of time-delayed interactions via the dynamic-entropy formalism.

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counterexamples, as in leukocyte coordination (where signaling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signaling.

Hebbian dreaming for small datasets.

The dreaming Hopfield model constitutes a generalization of the Hebbian paradigm for neural networks, that is able to perform on-line learning when "awake" and also to account for off-line "sleeping" mechanisms. The latter have been shown to enhance storing in such a way that, in the long sleep-time limit, this model can reach the maximal storage capacity achievable by networks equipped with symmetric pairwise interactions. In this paper, we inspect the minimal amount of information that must be supplied to such a network to guarantee a successful generalization, and we test it both on random synthetic and on standard structured datasets (i.

From Pavlov Conditioning to Hebb Learning.

Hebb's learning traces its origin in Pavlov's classical conditioning; however, while the former has been extensively modeled in the past decades (e.g., by the Hopfield model and countless variations on theme), as for the latter, modeling has remained largely unaddressed so far.

Outperforming RBM Feature-Extraction Capabilities by "Dreaming" Mechanism.

Inspired by a formal equivalence between the Hopfield model and restricted Boltzmann machines (RBMs), we design a Boltzmann machine, referred to as the dreaming Boltzmann machine (DBM), which achieves better performances than the standard one. The novelty in our model lies in a precise prescription for intralayer connections among hidden neurons whose strengths depend on features correlations. We analyze learning and retrieving capabilities in DBMs, both theoretically and numerically, and compare them to the RBM reference.

The emergence of a concept in shallow neural networks.

We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable "archetypes" and we show that there exists a critical sample size beyond which the RBM can learn archetypes, namely the machine can successfully play as a generative model or as a classifier, according to the operational routine. In general, assessing a critical sample size (possibly in relation to the quality of the dataset) is still an open problem in machine learning. Here, restricting to the random theory, where shallow networks suffice and the "grandmother-cell" scenario is correct, we leverage the formal equivalence between RBMs and Hopfield networks, to obtain a phase diagram for both the neural architectures which highlights regions, in the space of the control parameters (i.

On the effective initialisation for restricted Boltzmann machines via duality with Hopfield model.

Restricted Boltzmann machines (RBMs) with a binary visible layer of size N and a Gaussian hidden layer of size P have been proved to be equivalent to a Hopfield neural network (HNN) made of N binary neurons and storing P patterns ξ, as long as the weights w in the former are identified with the patterns. Here we aim to leverage this equivalence to find effective initialisations for weights in the RBM when what is available is a set of noisy examples of each pattern, aiming to translate statistical mechanics background available for HNN to the study of RBM's learning and retrieval abilities. In particular, given a set of definite, structureless patterns we build a sample of blurred examples and prove that the initialisation where w corresponds to the empirical average ξ¯ over the sample is a fixed point under stochastic gradient descent.

Boltzmann Machines as Generalized Hopfield Networks: A Review of Recent Results and Outlooks.

The Hopfield model and the Boltzmann machine are among the most popular examples of neural networks. The latter, widely used for classification and feature detection, is able to efficiently learn a generative model from observed data and constitutes the benchmark for statistical learning. The former, designed to mimic the retrieval phase of an artificial associative memory lays in between two paradigmatic statistical mechanics models, namely the Curie-Weiss and the Sherrington-Kirkpatrick, which are recovered as the limiting cases of, respectively, one and many stored memories.

Analysis of temporal correlation in heart rate variability through maximum entropy principle in a minimal pairwise glassy model.

In this work we apply statistical mechanics tools to infer cardiac pathologies over a sample of M patients whose heart rate variability has been recorded via 24 h Holter device and that are divided in different classes according to their clinical status (providing a repository of labelled data). Considering the set of inter-beat interval sequences [Formula: see text], with [Formula: see text], we estimate their probability distribution [Formula: see text] exploiting the maximum entropy principle. By setting constraints on the first and on the second moment we obtain an effective pairwise [Formula: see text] model, whose parameters are shown to depend on the clinical status of the patient.

Detecting cardiac pathologies via machine learning on heart-rate variability time series and related markers.

In this paper we develop statistical algorithms to infer possible cardiac pathologies, based on data collected from 24 h Holter recording over a sample of 2829 labelled patients; labels highlight whether a patient is suffering from cardiac pathologies. In the first part of the work we analyze statistically the heart-beat series associated to each patient and we work them out to get a coarse-grained description of heart variability in terms of 49 markers well established in the reference community. These markers are then used as inputs for a multi-layer feed-forward neural network that we train in order to make it able to classify patients.

Generalized Guerra's interpolation schemes for dense associative neural networks.

In this work we develop analytical techniques to investigate a broad class of associative neural networks set in the high-storage regime. These techniques translate the original statistical-mechanical problem into an analytical-mechanical one which implies solving a set of partial differential equations, rather than tackling the canonical probabilistic route. We test the method on the classical Hopfield model - where the cost function includes only two-body interactions (i.

A statistical inference approach to reconstruct intercellular interactions in cell migration experiments.

Migration of cells can be characterized by two prototypical types of motion: individual and collective migration. We propose a statistical inference approach designed to detect the presence of cell-cell interactions that give rise to collective behaviors in cell motility experiments. This inference method has been first successfully tested on synthetic motional data and then applied to two experiments.

Neural Networks with a Redundant Representation: Detecting the Undetectable.

We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4. The latter is known to be able to Hebbian store an amount of patterns scaling as N^{P-1}, where N denotes the number of constituting binary neurons interacting P wisely. We also prove that, by keeping the dense associative network far from the saturation regime (namely, allowing for a number of patterns scaling only linearly with N, while P>2) such a system is able to perform pattern recognition far below the standard signal-to-noise threshold.

First encounters on combs.

We consider two random walkers embedded in a finite, two-dimension comb and we study the mean first-encounter time (MFET) evidencing (mainly numerically) different scalings with the linear size of the underlying network according to the initial position of the walkers. If one of the two players is not allowed to move, then the first-encounter problem can be recast into a first-passage problem (MFPT) for which we also obtain exact results for different initial configurations. By comparing MFET and MFPT, we are able to figure out possible search strategies and, in particular, we show that letting one player be fixed can be convenient to speed up the search as long as we can finely control the initial setting, while, for a random setting, on average, letting one player rest would slow down the search.

Exact results for the first-passage properties in a class of fractal networks.

In this work, we consider a class of recursively grown fractal networks G(t) whose topology is controlled by two integer parameters, t and n. We first analyse the structural properties of G(t) (including fractal dimension, modularity, and clustering coefficient), and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time, and Kemeny's constant), and we highlight that their asymptotic behavior is controlled by the network's size and diameter.

Dreaming neural networks: Forgetting spurious memories and reinforcing pure ones.

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is α∼0.14, far from the theoretical bound for symmetric networks, i.e.

Modeling ozone uptake by urban and peri-urban forest: a case study in the Metropolitan City of Rome.

Urban and peri-urban forests are green infrastructures (GI) that play a substantial role in delivering ecosystem services such as the amelioration of air quality by the removal of air pollutants, among which is ozone (O), which is the most harmful pollutant in Mediterranean metropolitan areas. Models may provide a reliable estimate of gas exchanges between vegetation and atmosphere and are thus a powerful tool to quantify and compare O removal in different contexts. The present study modeled the O stomatal uptake at canopy level of an urban and a peri-urban forest in the Metropolitan City of Rome in two different years.

Organs on chip approach: a tool to evaluate cancer -immune cells interactions.

In this paper we discuss the applicability of numerical descriptors and statistical physics concepts to characterize complex biological systems observed at microscopic level through organ on chip approach. To this end, we employ data collected on a microfluidic platform in which leukocytes can move through suitably built channels toward their target. Leukocyte behavior is recorded by standard time lapse imaging.

Scaling laws for diffusion on (trans)fractal scale-free networks.

Fractal (or transfractal) features are common in real-life networks and are known to influence the dynamic processes taking place in the network itself. Here, we consider a class of scale-free deterministic networks, called (u, v)-flowers, whose topological properties can be controlled by tuning the parameters u and v; in particular, for u > 1, they are fractals endowed with a fractal dimension df, while for u = 1, they are transfractal endowed with a transfractal dimension d̃. In this work, we investigate dynamic processes (i.

The exact Laplacian spectrum for the Dyson hierarchical network.

We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.

Complete integrability of information processing by biochemical reactions.

Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling - based on spin systems - has been proved to be accurate for a wide class of systems matching classical (e.

Two-particle problem in comblike structures.

Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability between two walkers is (qualitatively) independent of whether both walkers are moving or one is kept fixed. On infinite comblike structures this is no longer the case and here we deepen the mechanisms underlying the emergence of a finite probability that two random walkers will never meet, while one single random walker is certain to visit any site.

First-passage phenomena in hierarchical networks.

In this paper we study Markov processes and related first-passage problems on a class of weighted, modular graphs which generalize the Dyson hierarchical model. In these networks, the coupling strength between two nodes depends on their distance and is modulated by a parameter σ. We find that, in the thermodynamic limit, ergodicity is lost and the "distant" nodes cannot be reached.

Emerging Heterogeneities in Italian Customs and Comparison with Nearby Countries.

In this work we apply techniques and modus operandi typical of Statistical Mechanics to a large dataset about key social quantifiers and compare the resulting behaviors of five European nations, namely France, Germany, Italy, Spain and Switzerland. The social quantifiers considered are i. the evolution of the number of autochthonous marriages (i.

Lévy flights with power-law absorption.

We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x(-α) and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is.

Exact calculations of first-passage properties on the pseudofractal scale-free web.

In this paper, we consider discrete time random walks on the pseudofractal scale-free web (PSFW) and we study analytically the related first passage properties. First, we classify the nodes of the PSFW into different levels and propose a method to derive the generation function of the first passage probability from an arbitrary starting node to the absorbing domain, which is located at one or more nodes of low-level (i.e.