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Marco Formentin

Publications and source records attributed to Marco Formentin.

18 recordsLinked to original sources
arXiv2026

Pulse desynchronization of neural populations by targeting the centroid of the limit cycle in phase space

The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying oscillating system is not known, as in most practical applications, to determine the specific times and intensities of pulses used for desynchronizaton is a difficult inverse problem. Here we propose a desynchronization scheme for neuronal models of bi-variate neural activity, with possible applications in the medical setting. Our main argument is the existence of a peculiar point in the phase space of the system, the centroid, that is both easy to calculate and robust under changes in the coupling constant. This important target point can be used in a control procedure because it lies in the region of minimal return times of the system.

q-bio.NC↗
arXiv2022

Noise-induced periodicity in a frustrated network of interacting diffusions

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 community. On the other hand, inter-population interactions have different signs: the particles of one population want to conform to the average position of the particles of the other community, while the particles in the latter want to do the opposite. We show that this system features the phenomenon of noise-induced periodicity: in the infinite volume limit, in a certain range of interaction strengths, although the system has no periodic behavior in the zero-noise limit, a moderate amount of noise may generate an attractive periodic law.

math.PR↗
arXiv2021

Effects of local fields in a dissipative Curie-Weiss model: Bautin bifurcation and large self-sustained oscillations

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 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 that, whenever the field intensity is sufficiently strong and the temperature sufficiently low, a periodic orbit emerges through a global bifurcation in the phase space, giving origin to a large-amplitude rhythmic behavior.

math.PR↗
arXiv2020

Rhythmic behavior of an Ising Model with dissipation at low temperature

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 models but, to our knowledge, this is the first example with short-range interaction. This supports the view that self-organized periodicity is not linked with the mean-field assumption but it is a thermodynamic phenomenon compatible with short range interactions.

math.PR↗
arXiv2019

Upscaling human activity data: an ecological perspective

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 been proposed. Here we move from modeling to inference and propose a statistical framework capable to predict global features of human activities from local knowledge. We consider four data sets of human activities: email communication, Twitter posts, Wikipedia articles and Gutenberg books. From the statistics of local activities, such as sent emails per senders, post per hashtags and word occurrences collected in a small sample of the considered dataset, we infer global features, as the number of senders, hashtags and words at the global scale. Our estimates are robust and accurate with a small relative error. Moreover, we predict how abundance of a hashtag or of a word may change through scales. Thus, observing a small portion of tweets and the popularity of a given hashtag among them, we can estimate whether it will remain popular or not in the unseen part of the network. Our approach is grounded on statistical ecology as we discover inference of unseen human activity hallmarks can be mapped into the unseen species problem in biodiversity. Our findings may have applications to different areas, from resource management in emails to collective attention monitoring in Twitter and to language learning process in word databases.

physics.soc-ph↗
arXiv2019

Oscillatory behavior in a model of non-Markovian mean field interacting spins

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 process, an example of two-state semi-Markov process. We associate to the individual dynamics an equivalent Markovian description, which is the subject of our analysis. We study a corresponding interacting particle system, where a mean field interaction is introduced as a time scaling, depending on the overall magnetization of the system, on the waiting times between two successive particle's jumps. Via linearization arguments on the Fokker-Planck mean field limit equation, we give evidence of emerging periodic behavior. Specifically, numerical analysis on the discrete spectrum of the linearized operator, characterized by the zeros of an explicit holomorphic function, suggests the presence of a Hopf bifurcation for a critical value of the temperature, which is in accordance with the one obtained by simulating the N-particle system.

math.PR↗
arXiv2019

A hierarchical mean field model of interacting spins

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, effectively acting as dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics can be thought of as a modification of the Curie--Weiss model. We study the mean field and the two-level hierarchical model, in the latter case restricting to a subcritical regime, corresponding to high temperatures, obtaining macroscopic limits at different spatio-temporal scales and studying the phase transitions in the system. We also formulate a generalization of our results to the $k$-th level hierarchical case, for any $k$ finite, in the subcritical regime. We finally address the supercritical regime, in the zero-temperature limit, for the two-level hierarchical case, proceeding heuristically with the support of numerics.

math.PR↗
arXiv2018

Reconciling cooperation, biodiversity and stability in complex ecological communities

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 equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

q-bio.PE↗
arXiv2018

Reconciling cooperation, biodiversity and stability in complex ecological communities

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 equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

q-bio.PE↗
arXiv2016

Rhythmic behavior in a two-population mean field Ising model

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 present paper we study some dynamical features of a two-population generalization of the mean field Ising model with the scope of investigating simple mechanisms capable to generate rhythm in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intra-population interactions of different strengths suffices for the emergence of a robust periodic behavior.

cond-mat.stat-mech↗
arXiv2016

Application of optimal data-based binning method to spatial analysis of ecological datasets

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 spatial patterns, the optimal scale defines the optimal bin size of the histogram in which to visualize the empirical density of the pattern. In this paper we investigate a method proposed recently by K.~H.~Knuth to find the optimal bin size of an histogram as a tool for statistical analysis of spatial point processes. We test it through numerical simulations on various spatial processes which are of interest in ecology. We show that Knuth optimal bin size rule reducing noisy fluctuations performs better than standard kernel methods to infer the intensity of the underlying process. Moreover it can be used to highlight relevant spatial characteristics of the underlying distribution such as space anisotropy and clusterization. We apply these findings to analyse cluster-like structures in plants' arrangement of Barro Colorado Island rainforest.

stat.AP↗
arXiv2015

New activity pattern in human interactive dynamics

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 each different correspondent of a given writer, generate a family of heavy-tailed distributions, which have largely the same features for all agents, and whose characteristic times grow exponentially with the rank of each correspondent. We furthermore show that this universal behavioral pattern emerges robustly by considering weighted moving averages of the priority-conditioned response-time probabilities generated by a basic prioritization model. Our findings clarify how the range of priorities in the inputs from one's environment underpin and shape the dynamics of agents embedded in a net of reactive relations. These newly revealed activity patterns might be present in other general interactive environments, and constrain future models of communication and interaction networks, affecting their architecture and evolution.

physics.soc-ph↗
arXiv2015

Neutral dynamics with environmental noise: age-size statistics and species lifetimes

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 [${\cal{O}} ({\sqrt N})$] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems - age size relationships and species extinction time - in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics and discuss their relevance to realistic models of community dynamics.

q-bio.PE↗
arXiv2015

Collective periodicity in mean-field models of cooperative behavior

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.

math.PR↗
arXiv2014

Sample and population exponents of generalized Taylor's law

Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests a context-independent mechanism. However, theoretical studies of population dynamics predict a broad range of values of $b$. Here, we explain this apparent contradiction by using large deviations theory to derive a generalized TL in terms of sample and populations exponents $b_{jk}$ for the scaling of the $k$-th vs the $j$-th cumulant (conventional TL is recovered for $b=b_{12}$), with the sample exponent found to depend predictably on the number of observed samples. Thus, for finite numbers of observations one observes sample exponents $b_{jk}\simeq k/j$ (thus $b\simeq2$) independently of population exponents. Empirical analyses on two datasets support our theoretical results.

q-bio.PE↗
arXiv2014

Phenomenological modeling of the motility of self-propelled microorganisms

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 experimental results for ciliates of the genus Colpidium, which do not agree with the Gaussian white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion, such as velocity distribution and velocity autocorrelation.

physics.bio-ph↗
arXiv2013

Time to absorption for a heterogeneous neutral competition model

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 studies and chemical reactions. In a system where each individual can interact with all the other members of the community, the typical time to reach an absorbing state with a single species scales linearly with the community size. Here we show, by using a rigorous approach within a large deviation principle and confirming previous approximate and numerical results, that in a heterogeneous voter model the typical time to reach an absorbing state scales exponentially with the system size, suggestive of an asymptotic active phase.

math.PR↗