arXiv subjects

Anna Poggialini

Publications and source records attributed to Anna Poggialini.

7 recordsLinked to original sources

arXiv2026

Synchronization, Kinematic Waves and Spike-Phase-Separation in Feedback Ising Neural Networks on Heterogeneous Graphs

Structural heterogeneity constrains collective dynamics in complex systems. However, its analytical tractability out of equilibrium remains limited. In this work, we study a class of kinetic Ising neural networks driven out of equilibrium by a homeostatic feedback loop between the neuronal excitability and the population firing rate. Using a Curie-Weiss heterogeneous mean-field approximation validated by Monte Carlo simulations, we provide an analytical characterization of how a macroscopic synchronized limit cycle emerges via an Andronov-Hopf bifurcation on heterogeneous networks. We derive closed-form phase boundaries and show that the onset of oscillations is explicitly controlled by network heterogeneity through the degree moment ratio. Degree heterogeneity decouples the spiking rate per neuron m from the spiking rate per synapse u, generating physical phenomena absent in homogeneous systems. These include (i) kinematic waves of sequential, degree-ordered activations propagating from the network periphery to the hubs, and (ii) a low-temperature phase-separated state emerging via a pitchfork bifurcation. We prove that for highly heterogeneous topologies, this phase-separated fixed point stabilizes and dynamically destroys the synchronized limit cycle. These results provide a mathematical framework for understanding how heterogeneity regulates macroscopic oscillations and out-of-equilibrium transitions in neural networks

cond-mat.stat-mech↗

arXiv2026

Scaling and tuning to criticality in resting-state human magnetoencephalography

From 1/f noise to neuronal avalanches, evidence of scaling in brain activity has been increasingly linked to tuning to or near criticality. The concept of scaling is intimately related to the renormalization group (RG), in essence providing coarse-grained, simplified descriptions that generalize to classes of diverse physical systems. Following the RG idea, scaling laws have been reported in populations of spiking neurons at microscopic scales. Whether similar scaling principles govern large-scale neural activity in the human brain and how they relate to underlying neural physiology remains unresolved. Here, we analyze large-scale electrophysiological recordings (MEG) of human resting-state brain activity and apply a RG-inspired coarse-graining approach to track collective neural dynamics across spatial scales. We find that multiple observables exhibit robust scale-invariant behavior under coarse-graining: activity variance and correlations grow according to power laws, covariance eigenspectra follow a characteristic scaling relation, and neuronal avalanche statistics remain invariant. Using an analytically tractable neural network model, we show that the observed scaling signatures arise when the system operates slightly below criticality, and that the scaling exponents depend on the excitation-inhibition balance. These findings demonstrate that RG-inspired scaling analysis can uncover signatures of critical dynamics in non-invasive human electrophysiology and suggest a principled route toward estimating excitation-inhibition balance from large-scale brain recordings.

q-bio.NC↗

arXiv2026

Shortest-path percolation on scale-free networks

The shortest-path percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially selected, and if the length of the shortest path connecting the node pairs is smaller than a tunable budget parameter, then all edges along such a path are removed from the network. As edges are progressively removed, the network eventually breaks into multiple microscopic components, undergoing a percolation-like transition. It is known that SPP transition on Erdős-Rényi networks (ERNs) belongs to same universality class as of the ordinary bond percolation if the budget parameter is finite; for unbounded budget, instead, the SPP transition becomes more abrupt than the ordinary percolation transition. By means of large-scale numerical simulations and finite-size scaling analysis, here we study the SPP transition on random scale-free networks (SFNs) characterized by power-law degree distributions. We find, in contrast with ordinary percolation, that the transition is identical to the one observed on ERNs, denoting independence from the degree exponent. Still, we distinguish finite- and infinite-budget SPP universality classes. Our findings follow from the fact that the SPP process drastically homogenizes the heterogeneous structure of SFNs before the SPP transition takes place.

physics.soc-ph↗

arXiv2025

Non-normal Dynamics on Non-reciprocal Networks: Reactivity and Effective Dimensionality in Neural Circuits

Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple levels: locally, in the dynamics of individual units, and globally, in the topology of their interactions. In this work, we investigate how these two forms of non-reciprocity interact in networks of neuronal populations. At the local level, each population is modeled by a non-reciprocally coupled set of excitatory and inhibitory neural populations exhibiting transient amplification and reactivity. At the network level, these populations are coupled via directed, asymmetric connections that introduce structural non-normality. Since non-reciprocal interactions generically lead to non-normal linear operators, we frame both local and global asymmetries in terms of non-normal dynamics. Using a modified Wilson-Cowan framework, we analyze how the interplay between these two types of non-normality shapes the system's behavior. We show that their combination leads to emergent collective dynamics, including fluctuation-driven transitions, dimensionality reduction, and novel nonequilibrium steady states. Our results provide a minimal yet flexible framework to understand how multi-scale non-reciprocities govern complex dynamics in neural and other interconnected systems.

physics.bio-ph↗

arXiv2024

Multi-scale Laplacian community detection in heterogeneous networks

Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem of complex network theory. By taking advantage of the recent Laplacian Renormalization Group, we scrutinize information diffusion pathways throughout networks to shed further light on this issue. Based on inter-node communicability, our definition provides a clear-cut framework for resolving the multi-scale mesh of structures in complex networks, disentangling their intrinsic arboreal architecture. As it does not consider any topological null-model assumption, the LRG naturally permits the introduction of scale-dependent optimal partitions. Moreover, we demonstrate the existence of a particular class of nodes, called 'metastable' nodes, that switching regions to which they belong at different scales, likely playing a pivotal role in cross-regional communication and, therefore, in managing macroscopic effects of the whole network.

physics.soc-ph↗

arXiv2024

Networks with many structural scales: a Renormalization Group perspective

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a constant entropy-loss rate across scales in a renormalization-group coarse-graining setting. This framework enables us to differentiate between scale-free and scale-invariant networks, revealing distinct characteristics within each class. Furthermore, we offer a comprehensive inventory of genuinely scale-invariant networks, both natural and artificially constructed, demonstrating, e.g., that the human connectome exhibits notable features of scale invariance. Our findings open new avenues for exploring the scale-invariant structural properties crucial in biological and socio-technological systems.

cond-mat.stat-mech↗

arXiv2023

Emergence of collective self-oscillations in minimal lattice models with feedback

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions. Here we consider classical lattice models, namely the Ising, the Blume-Capel and the Potts models, with a feedback among the order and control parameters. With linear response theory we derive low-dimensional dynamical systems for mean field cases that quantitatively reproduce many-body stochastic simulations. In general, we find that the usual equilibrium phase transitions are taken over by complex bifurcations where self-oscillations emerge, a behavior that we illustrate by the feedback Landau theory. For the case of the Ising model, we obtain that the bifurcation that takes over the critical point is non-trivial in finite dimensions. We provide numerical evidence that in 2D the most probable value of the amplitude follows the Onsager law. We illustrate multi-stability for the case of discontinuously emerging oscillations in the Blume-Capel model, whose tricritical point is substituted by the Bautin bifurcation. For the Potts model with q = 3 colors we highlight the appearance of two mirror stable limit cycles at a bifurcation line and characterize the onset of chaotic oscillations that emerge at low temperature through either the Feigenbaum cascade of period doubling or the Aifraimovich-Shilnikov scenario of a torus destruction. We show that entropy production singularities as a function of the temperature correspond to change in the spectrum of Lyapunov exponents. Our results show that mean-field behaviour can be described by the bifurcation theory of low-dimensional dynamical systems, which paves the way for the definition of universality classes of collective oscillations.

cond-mat.stat-mech↗