arXiv subjects

Fabio Della Rossa

Publications and source records attributed to Fabio Della Rossa.

8 recordsLinked to original sources

arXiv2026

Optimal pinning control of directed hypergraphs

Identifying the nodes that must be directly controlled to steer a network along a desired trajectory remains an open problem for digraphs, and even more so for hypergraphs. In this manuscript, we investigate network systems coupled via directed hypergraphs and consider a broad class of individual dynamics and coupling configurations, extending the definition of type II networks originally formulated for digraphs. For this class of networks with higher-order interactions, we establish necessary and sufficient conditions under which a pinning selection locally ensures successful control. Building on these analytical results, we propose a greedy heuristic for pinning control selection, which demonstrably outperforms existing methods.

math-ph↗

arXiv2023

Emergence and control of synchronization in networks with directed many-body interactions

The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or induced synchronous behavior? Inspired by actuation and measurement constraints typical of physical and engineered systems, we propose a diffusion mechanism over hypergraphs that explains the onset of synchronization through a clarifying analogy with signed graphs. Our findings are mathematically backed by general conditions for convergence to the synchronous state.

nlin.AO↗

arXiv2020

Controlling consensus in networks with symmetries

We study networks with linear dynamics where the presence of symmetries of the pair (A,B) induces a partition of the network nodes in clusters and the matrix A is not restricted to be in Laplacian form. For these networks, an invariant group consensus subspace can be defined, in which the nodes in the same cluster evolve along the same trajectory in time. We prove that the network dynamics is uncontrollable in directions orthogonal to this subspace. Under the assumption that the dynamics parallel to this subspace is controllable, we design optimal controllers that drive the group consensus dynamics towards a desired state. Then, we consider the problem of selecting additional control inputs that stabilize the group consensus subspace and obtain bounds on the minimum number of additional inputs and driver nodes needed to this end. Altogether, our results indicate that it is possible to design independently the control action along and transverse to the group consensus subspace.

math.OC↗

arXiv2020

Analyzing synchronized clusters in neuron networks

The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying assumptions, which often neglect key biological features of neuron networks. Here we propose a general framework to study presence and stability of synchronous clusters in more realistic models of neuron networks, characterized by the presence of delays, different kinds of neurons and synapses. Application of this framework to the directed network of the macaque cerebral cortex provides an interpretation key to explain known functional mechanisms emerging from the combination of anatomy and neuron dynamics. The cluster synchronization analysis is carried out also by changing parameters and studying bifurcations. Despite some simplifications with respect to the real network, the obtained results are in good agreement with previously reported biological data.

math.DS↗

arXiv2020

Intermittent yet coordinated regional strategies can alleviate the COVID-19 epidemic: a network model of the Italian case

The COVID-19 epidemic that emerged in Wuhan China at the end of 2019 hit Italy particularly hard, yielding the implementation of strict national lockdown rules (Phase 1). There is now a hot ongoing debate in Italy and abroad on what the best strategy is to restart a country to exit a national lockdown (Phase 2). Previous studies have focused on modelling possible restarting scenarios at the national level, overlooking the fact that Italy, as other nations around the world, is divided in administrative regions who can independently oversee their own share of the Italian National Health Service. In this study, we show that regionalism, and heterogeneity between regions, is essential to understand the spread of the epidemic and, more importantly, to design effective post Lock-Down strategies to control the disease. To achieve this, we model Italy as a network of regions and parameterize the model of each region on real data spanning almost two months from the initial outbreak. Using the model, we confirm the effectiveness at the regional level of the national lockdown strategy implemented so far by the Italian government to mitigate the spread of the disease and show its efficacy at the regional level. We also propose that differentiated, albeit coordinated, regional interventions can be effective in Phase 2 to restart the country and avoid future recurrence of the epidemic, while avoiding saturation of the regional health systems and mitigating impact on costs. Our study and methodology can be easily extended to other levels of granularity (provinces or counties in the same region or states in other federal countries, etc.) to support policy- and decision-makers.

physics.soc-ph↗

arXiv2019

Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

q-bio.TO↗

arXiv2018

Rethinking network reciprocity over social ties: local interactions make direct reciprocity possible and pave the rational way to cooperation

Since Nowak & May's (1992) influential paper, network reciprocity--the fact that individuals' interactions repeated within a local neighborhood support the evolution of cooperation--has been confirmed in several theoretical models. Essentially, local interactions allow cooperators to stay protected from exploiters by assorting into clusters, and the heterogeneity of the network of contacts--the co-presence of low- and high-connected nodes--has been shown to further favor cooperation. The few available large-scale experiments on humans have however missed these effects. The reason is that, while models assume that individuals update strategy by imitating better performing neighbors, experiments showed that humans are more prone to reciprocate cooperation than to compare payoffs. Inspired by the empirical results, we rethink network reciprocity as a rational form of direct reciprocity on networks--networked rational reciprocity--indeed made possible by the locality of interactions. We show that reciprocal altruism in a networked prisoner's dilemma can invade and fixate in any network of rational agents, profit-maximizing over an horizon of future interactions. We find that networked rational reciprocity works better at low average connectivity and we unveil the role of network heterogeneity. Only if cooperating hubs invest in the initial cost of exploitation, the invasion of cooperation is boosted; it is otherwise hindered. Although humans might not be as rational as here assumed, our results could help the design and interpretation of new experiments in social and economic networks

nlin.AO↗

arXiv2011

Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles

Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems on the interval [0, T ], where T is the period of the critical cycle, as well as multilinear functions from the Taylor expansion of the right-hand sides near the cycle. The formulas allow us to distinguish between various bifurcation scenarios near codim 2 bifurcations. Our formulation makes it possible to use robust numerical boundary-value algorithms based on orthogonal collocation, rather than shooting techniques, which greatly expands its applicability. The actual implementation is described in detail with numerical examples.

math.DS↗