# Marco FormentinUniversity of Padova | UNIPD · Department of Mathematics

Marco Formentin

Ph.D. Mathematics

## About

41

Publications

3,966

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290

Citations

Introduction

Welcome to my RG page! I am associate professor at the math department of Padua University. My research topics stand in the line between Statistical Mechanics and Probability Theory with strong interests for applications in complex systems. Recently, I started working on probability models for ecology and interactive human activities.

Additional affiliations

Education

January 2006 - November 2009

## Publications

Publications (41)

We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population interactions are positive; each particle wants to conform to the average position of the particles in its own communi...

Understanding the relation between the structure of brain networks and its functions is a fundamental open question. Simple models of neural activity based on real anatomical networks have proven effective in describing features of whole-brain spontaneous activity when tuned at their critical point. In this work, we show that indeed structural netw...

Understanding the relation between the structure of brain networks and its functions is a fundamental open question. Simple models of neural activity based on real anatomical networks have proven effective in describing features of whole-brain spontaneous activity when tuned at their critical point. In this work, we show that indeed structural netw...

Big data require new techniques to handle the information they come with. Here we consider four datasets (email communication, Twitter posts, Wikipedia articles and Gutenberg books) and propose a novel statistical framework to predict global statistics from random samples. More precisely, we infer the number of senders, hashtags and words of the wh...

We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein–Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectivel...

In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the magnetization has a periodic behavior. Self-organized collective periodicity has been shown for many mean-field model...

We analyze a non-Markovian mean field interacting spin system, related to the Curie–Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal proce...

In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the magnetization has a periodic behavior. Self-organized collective periodicity has been shown for many mean-field model...

In recent years we have witnessed an explosion of data collected for different human dynamics, from email communication to social networks activities. Extract useful information from these huge data sets represents a major challenge. In the last decades, statistical regularities has been widely observed in human activities and various models have b...

We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal proc...

We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein-Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectivel...

Biodiversity provides support for life, vital provisions, regulating services and has positive cultural impacts. It is therefore important to have accurate methods to measure biodiversity, in order to safeguard it when we discover it to be threatened. For practical reasons, biodiversity is usually measured at fine scales whereas diversity issues (e...

We modify the spin-flip dynamics of a Curie-Weiss model with dissipative interaction potential [7] by adding a site-dependent i.i.d. random magnetic field. The purpose is to analyze how the addition of the field affects the time-evolution of the observables in the macroscopic limit. Our main result shows that a Bautin bifurcation point exists and t...

Empirical evidences show that ecosystems with high biodiversity can persist in time even in the presence of few types of resources and are more stable than low biodiverse communities. This evidence is contrasted by the conventional mathematical modeling, which predicts that the presence of many species and/or cooperative interactions are detrimenta...

We modify the spin-flip dynamics of a Curie-Weiss model with dissipative interaction potential (Dai Pra, Fischer and Regoli (2013)) by adding a site-dependent i.i.d. random magnetic field. The purpose is to analyze how disorder affects the time-evolution of the observables in the macroscopic limit. Our main result shows that, whenever the field int...

Biodiversity provides support for life, vital provisions, regulating services and has positive cultural impacts. It is therefore important to have accurate methods to measure biodiversity, in order to safeguard it when we discover it to be threatened. For practical reasons, biodiversity is usually measured at fine scales whereas diversity issues (e...

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equ...

The quantification of tropical tree biodiversity worldwide remains an open and challenging problem.
In fact, more than two-fifths of the number of worldwide trees can be found either in tropical or
sub-tropical forests, but only ≈ 0.000067% of species identities are known. Here, we introduce an
analytical framework that provides robust and accurate...

Empirical observations show that natural communities of species with mutualistic interactions such as plant and pollinators, can have a number of coexisting species of the order of hundreds. However the standard modeling of population dynamics would predict that these systems become less stable than communities with competitive or prey-predator int...

We study a model for email communication due to Gabrielli and Caldarelli, where someone receives and answers emails at the times of independent Poisson processes with intensities $\lambda_{\rm in}>\lambda_{\rm out}$. The receiver assigns i.i.d. priorities to incoming emails according to some atomless law and always answers the email in the mailbox...

Many real systems comprised of a large number of interacting components, as for instance neural networks , may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the prese...

We consider an inviscid stochastically forced dyadic model, where the
additive noise acts only on the first component. We prove that a strong
solution for this problem exists and is unique by means of uniform energy
estimates. Moreover, we exploit these results to establish strong existence and
uniqueness of the stationary distribution.

Investigation of highly structured data sets to unveil statistical regularities is of major importance in complex system research. The first step is to choose the scale at which to observe the process, the most informative scale being the one that includes the important features while disregarding noisy details in the data. In the investigation of...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new pattern for how the reactive dynamics of individuals is distributed across the set of each agent’s contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each diff...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to...

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic noise of...

We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.

Taylor's law (TL) states that the variance V of a non-negative random variable is a power function of its mean M. The ubiquitous empirical verification of TL, typically displaying sample exponents b≃2, suggests a context-independent mechanism. However, theoretical studies of population dynamics predict a broad range of values of b. Here, we explain...

The motility of microorganisms in liquid media is an important issue in
active matter and it is not yet fully understood. Previous theoretical
approaches dealing with the microscopic description of microbial movement have
modeled the propelling force exerted by the organism as a Gaussian white noise
term in the equation of motion. We present experi...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new pattern for how the reactive dynamics of individuals is distributed across the set of each agent’s contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each diff...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to...

Neutral models aspire to explain biodiversity patterns in ecosystems where
species difference can be neglected, as it might occur at a specific trophic
level, and perfect symmetry is assumed between species. Voter-like models
capture the essential ingredients of the neutral hypothesis and represent a
paradigm for other disciplines like social studi...

The temporal statistics exhibited by written correspondence appear to be
media dependent, with features which have so far proven difficult to
characterize. We explain the origin of these difficulties by disentangling the
role of spontaneous activity from decision-based prioritizing processes in
human dynamics, clocking all waiting times through eac...

We extend the construction by Kuelske and Iacobelli of metastates in
finite-state mean-field models in independent disorder to situations where the
local disorder terms are are a sample of an external ergodic Markov chain in
equilibrium. We show that for non-degenerate Markov chains, the structure of
the theorems is analogous to the case of i.i.d....

We present classes of models in which particles are dropped on an arbitrary fixed finite connected graph, obeying adhesion rules with screening. We prove that there is an invariant distribution for the resulting height profile, and Gaussian concentration for functions depending on the paths of the profiles. As a corollary we obtain a law of large n...

We give sharp estimates for time uniform propagation of chaos in some special mean eld spin-flip models exhibiting phase transition.

Abstract: A rigorous approach to Statistical Physics issues often produces interesting
mathematical questions. This Ph.D. thesis is composed of two different parts.
One does not intersect the other, but both research topics lie at the interface between
Probability Theory and StatisticalMechanics.
• In the first part we deal with reconstruction of a...

We give a criterion of the form Q(d)c(M)<1 for the non-reconstructability of tree-indexed q-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix M. Here c(M) is an explicit function, which is convex over the set of M's with a given invariant distribution, that is defined in terms of a (q-1)-dimensional...

We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds of Mossel and Peres. In information theoretic language extremality of the Gibbs measure corresponds to non-re...