arXiv subjects

Francesca Di Patti

Publications and source records attributed to Francesca Di Patti.

At least 19 recordsLinked to original sources

arXiv2026

Noise seeded oscillators: on the role of demographic fluctuations in a multi-populations model

Stochastic oscillations can emerge from a two-population model as triggered by endogenous finite size fluctuations. Here, an extended dynamical scenario is considered in which a third fluctuating species is added to a proto-typical scheme of neuronal interaction. As we shall prove both analytically and numerically, the third added species can enhance or even suppress the emergence of quasi-cycles, namely the coherent oscillations of the two original populations, as instigated by the demographic noise component. In general, investigating the coupled dynamics of noisy oscillators of the type considered could yield an extended framework for synchronization studies, beyond the pioneering setting introduced by Kuramoto.

nlin.AO↗

arXiv2024

Learning in Wilson-Cowan model for metapopulation

The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

q-bio.NC↗

arXiv2024

Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise

The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as a veritable dynamically assisted classifier. To this end the model is supplied with a set of planted attractors which are self-consistently embedded in the inter-nodes coupling matrix, via its spectral decomposition. Learning to classify amounts to sculp the basin of attraction of the imposed equilibria, directing different items towards the corresponding destination target, which reflects the class of respective pertinence. A stochastic variant of the CVFR model is also studied and found to be robust to aversarial random attacks, which corrupt the items to be classified. This remarkable finding is one of the very many surprising effects which arise when noise and dynamical attributes are made to mutually resonate.

cs.LG↗

arXiv2019

MEDEAS-World model calibration for the study of the energy transition

MEDEAS (Modelling the Energy Development under Environmental And Socioeconomic constraint) World is a new global-aggregated energy-economy-environmental model, which runs from 1995 to 2050. In this work, we tested the MEDEAS world model to reproduce the IPCC (International Panel on Climate Change) GHG (Green House Gases) emission pathways consistent with 2 °C Global Warming. We achieved parameter optimizations of the MEDEAS model related to different scenarios until 2050. We chose to provide a sensitivity analysis on the parameters that directly influence the emission curves focusing on the annual growth of the RES (Renewable Energy Sources), GDP (Gross Domestic Product) and annual population growth. From such an analysis, it has been possible to infer the large impact of GDP on the emission scenarios.

physics.soc-ph↗

arXiv2019

Pattern Analysis of World Conflicts over the past 600 years

We analyze the database prepared by Brecke (Brecke 2011) for violent conflict, covering some 600 years of human history. After normalizing the data for the global human population, we find that the number of casualties tends to follow a power law over the whole data series for the period considered, with no evidence of periodicity. We also observe that the number of conflicts, again normalized for the human population, show a decreasing trend as a function of time. Our result agree with previous analyses on this subject and tend to support the idea that war is a statistical phenomenon related to the network structure of the human society.

stat.AP↗

arXiv2017

Hopping in the crowd to unveil network topology

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node that can be chosen randomly. The technique is successfully tested against both synthetic and real data, and shown to estimate with great accuracy also the total number of nodes.

cond-mat.stat-mech↗

arXiv2017

Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs

A normal form approximation for the evolution of a reaction-diffusion system hosted on a directed graph is derived, in the vicinity of a supercritical Hopf bifurcation. Weak diffusive couplings are assumed to hold between adjacent nodes. Under this working assumption, a Complex Ginzburg-Landau equation (CGLE) is obtained, whose coefficients depend on the parameters of the model and the topological characteristics of the underlying network. The CGLE enables one to probe the stability of the synchronous oscillating solution, as displayed by the reaction-diffusion system above Hopf bifurcation. More specifically, conditions can be worked out for the onset of the symmetry breaking instability that eventually destroys the uniform oscillatory state. Numerical tests performed for the Brusselator model confirm the validity of the proposed theoretical scheme. Patterns recorded for the CGLE resemble closely those recovered upon integration of the original Brussellator dynamics.

cond-mat.stat-mech↗

arXiv2016

Global topological control for synchronized dynamics on networks

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point.

cond-mat.stat-mech↗

arXiv2016

Benjamin-Feir instabilities on directed networks

The Complex Ginzburg-Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of topological instability, reminiscent of the Benjamin-Feir type. The analysis is initially carried out for a specific class of networks, characterized by a circulant adjacency matrix. This allows us to delineate analytically the domain in the parameter space for which the generalized instability occurs. We then move forward to considering the family of non linear oscillators coupled via a generic direct, though balanced, graph. The characteristics of the emerging patterns are discussed within a self-consistent theoretical framework.

cond-mat.stat-mech↗

arXiv2016

Drift-induced Benjamin-Feir instabilities

A modified version of the Ginzburg-Landau equation is introduced which accounts for asymmetric couplings between neighbors sites on a one-dimensional lattice, with periodic boundary conditions. The drift term which reflects the imposed microscopic asymmetry seeds a generalized class of instabilities, reminiscent of the Benjamin-Feir type. The uniformly synchronized solution is spontaneously destabilized outside the region of parameters classically associated to the Benjamin-Feir instability, upon injection of a non homogeneous perturbation. The ensuing patterns can be of the traveling wave type or display a patchy, colorful mosaic for the modulus of the complex oscillators amplitude.

cond-mat.stat-mech↗

arXiv2016

Noise Processing by MicroRNA-Mediated Circuits: the Incoherent Feed-Forward Loop, Revisited

The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro} and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using stochastic simulations validated by analytical calculations based on van Kampen's expansion, we revisit the noise-buffering capacity of the miRNA-mediated Incoherent Feed Forward Loop (IFFL), a small module that is widespread in the gene regulatory networks of higher eukaryotes, in order to account for the effects of intermittency in the transcriptional activity of the modulator gene. We show that bursting considerably alters the circuit's ability to control static protein noise. By comparing with other regulatory architectures, we find that direct transcriptional regulation significantly outperforms the IFFL in a broad range of kinetic parameters. This suggests that, under pulsatile inputs, static noise reduction may be less important than dynamical aspects of noise and information processing in characterising the performance of regulatory elements.

q-bio.MN↗

arXiv2015

The second will be first: competition on directed networks

Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data.

physics.soc-ph↗

arXiv2015

Multiple scale theory of topology driven pattern on directed networks

Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from neuroscience, to computer networks and traffic systems. Due to the peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points can turn unstable, on a directed support, because of the topology of the network, a phenomenon which cannot be induced on undirected graphs. A linear analysis can be performed to single out the conditions that underly the instability. The complete characterization of the patterns, which are eventually attained beyond the linear regime of exponential growth, calls instead for a full non linear treatment. By performing a multiple time scale perturbative calculation, we here derive an effective equation for the non linear evolution of the amplitude of the most unstable mode, close to the threshold of criticality. This is a Stuart-Landau equation whose complex coefficients appear to depend on the topological features of the embedding directed graph. The theory proves adequate versus simulations, as confirmed by operating with a paradigmatic reaction-diffusion model.

cond-mat.stat-mech↗

arXiv2014

Optimal search strategies on complex networks

Complex networks are ubiquitous in nature and play a role of paramount importance in many contexts. Internet and the cyberworld, which permeate our everyday life, are self-organized hierarchical graphs. Urban traffic flows on intricate road networks, which impact both transportation design and epidemic control. In the brain, neurons are cabled through heterogeneous connections, which support the propagation of electric signals. In all these cases, the true challenge is to unveil the mechanisms through which specific dynamical features are modulated by the underlying topology of the network. Here, we consider agents randomly hopping along the links of a graph, with the additional possibility of performing long-range hops to randomly chosen disconnected nodes with a given probability. We show that an optimal combination of the two jump rules exists that maximises the efficiency of target search, the optimum reflecting the topology of the network.

physics.soc-ph↗

arXiv2012

Multispecies reaction diffusion models and the Turing instability revisited

The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.

physics.bio-ph↗

arXiv2012

Stochastic Turing Patterns on a Network

The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically, and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium.

cond-mat.stat-mech↗

arXiv2011

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.

cond-mat.stat-mech↗

arXiv2011

Non-Gaussian fluctuations in stochastic models with absorbing barriers

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.

cond-mat.stat-mech↗