arXiv subjects

Giulia Giordano

Publications and source records attributed to Giulia Giordano.

At least 19 recordsLinked to original sources

arXiv2026

Sakawa-Shindo algorithm for optimal control of time-delay systems, with applications to epidemiology

We extend the Sakawa-Shindo algorithm to solve optimal control problems where the system dynamics involve an arbitrary number of discrete state delays. We prove that the algorithm guarantees termination in a finite number of steps, asymptotic first-order optimality of the generated control sequence and convergence of a subsequence to a control satisfying first-order optimality, and we apply it to the optimal design of non-pharmaceutical interventions and vaccination plans for epidemic models with delays associated with incubation period and vaccination.

math.OC↗

arXiv2026

gPC-based robustness analysis of neural systems through probabilistic recurrence metrics

Neuronal systems often preserve their characteristic functions and signalling patterns, also referred to as regimes, despite parametric uncertainties and variations. For neural models having uncertain parameters with a known probability distribution, probabilistic robustness analysis (PRA) allows us to understand and quantify under which uncertainty conditions a regime is preserved in expectation. We introduce a new computational framework for the efficient and systematic PRA of dynamical systems in neuroscience and we show its efficacy in analysing well-known neural models that exhibit multiple dynamical regimes: the Hindmarsh-Rose model for single neurons and the Jansen-Rit model for cortical columns. Given a model subject to parametric uncertainty, we employ generalised polynomial chaos to derive mean neural activity signals, which are then used to assess the amount of parametric uncertainty that the system can withstand while preserving the current regime, thereby quantifying the regime's robustness to such uncertainty. To assess persistence of regimes, we propose new metrics, which we apply to recurrence plots obtained from the mean neural activity signals. The overall result is a novel, general computational methodology that combines recurrence plot analysis and systematic persistence analysis to assess how much the uncertain model parameters can vary, with respect to their nominal value, while preserving the nominal regimes in expectation. We summarise the PRA results through probabilistic regime preservation (PRP) plots, which capture the effect of parametric uncertainties on the robustness of dynamical regimes in the considered models.

q-bio.NC↗

arXiv2025

Separation-free exponential fitting with structured noise, with applications to inverse problems in parabolic PDEs

We investigate the recovery of exponents and amplitudes of an exponential sum, where the exponents $\left\{\lambda_n \right\}_{n=1}^{N_1}$ are the first $N_1$ eigenvalues of a Sturm-Liouville operator, from finitely many measurements subject to measurement noise. This inverse problem is extremely ill-conditioned when the noise is arbitrary and unstructured. Surprisingly, however, the extreme ill-conditioning exhibited by this problem disappears when considering a \emph{structured} noise term, taken as an exponential sum with exponents given by the subsequent eigenvalues $\left\{\lambda_n \right\}_{n=N_1+1}^{N_1+N_2}$ of the Sturm-Liouville operator, multiplied by a noise magnitude parameter $\varepsilon>0$. In this case, we rigorously show that the exponents and amplitudes can be recovered with super-exponential accuracy: we both prove the theoretical result and show that it can be achieved numerically by a specific algorithm. By leveraging recent results on the mathematical theory of super-resolution, we show in this paper that the classical Prony's method attains the analytic optimal error decay also in the ``separation-free'' regime where $\lambda_n \to \infty$ as $n \to \infty$, thereby extending the applicability of Prony's method to new settings. As an application of our theoretical analysis, we show that the approximated eigenvalues obtained by our method can be used to recover an unknown potential in a linear reaction-diffusion equation from discrete solution traces.

math.NA↗

arXiv2025

Robustness and resilience of dynamical networks in biology and epidemiology

Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve many interacting parameters, yet it is crucial for explaining processes from cellular regulation to disease onset and epidemic spreading. Robustness and resilience describe a system's ability to preserve and recover desired behaviours in the presence of intrinsic and extrinsic fluctuations. This survey reviews how different disciplines define these concepts, examines methods for assessing whether key properties of uncertain, networked dynamical systems are structural (parameter-free) or robust (preserved for parameter variations within an uncertainty bounding set), and discusses integrated structural and probabilistic techniques for biological and epidemiological models. The text introduces formal definitions of resilience for families of systems obtained by adding stochastic perturbations to a nominal deterministic model, enabling a probabilistic characterisation of the ability to remain within or return to a prescribed attractor. These definitions generalise probabilistic robustness and shed new light on classical biological examples. In addition, the survey summarises resilience indicators and data-driven tools for detecting resilience loss and regime shifts, drawing on bifurcation analysis to anticipate qualitative changes in system behaviour. Together, these methodologies support the study and control of complex natural systems, guiding the design of biomolecular feedback architectures, the identification of therapeutic targets, the forecasting and management of epidemics, and the detection of tipping points in ecological and biological networks.

math-ph↗

arXiv2025

Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems

We introduce a new class of functions, called Attractivity Guarantee (AG)-functions, to certify the attractivity of sets for uncertain nonlinear switched systems in discrete time. The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function, and hence the robust local attractivity of the set itself. We illustrate the proposed framework through examples that elucidate the theoretical concepts, and through the case study of a nonlinear switched system modelling antimicrobial resistance, which highlights the practical relevance of the approach to the analysis of biological systems.

eess.SY↗

arXiv2025

Observer-Based Sampled-Data Stabilisation of Switched Systems with Lipschitz Nonlinearities and Dwell-Time

We investigate the stabilisation of nominally linear-affine switched systems with uncertain Lipschitz nonlinearities under dwell-time constraints, using a sampled-data switching law based on a state observer. We design the switching law based on Lyapunov-Metzler inequalities, accounting for the sampled-data output measurements, and we derive time-dependent LMI conditions for global asymptotic stability (or, in the presence of switching affine terms, ultimate boundedness) of the resulting closed-loop system. We obtain an estimate of the average quadratic cost and a bound on its maximum deviation from the actual cost. Moreover, we discuss the feasibility of the derived LMIs. Specifically, we show how the observer gains can be incorporated into the matrix inequalities, provide equivalent reduced-order LMI conditions, and prove that the time dependence of the LMIs can be removed by discretising on a finite grid. Numerical examples, including practical applications to real-world engineering scenarios in power systems, illustrate our theoretical results and compare them with an existing approach for output-feedback stabilisation of switched systems, subject to sampled-data measurements

math.OC↗

arXiv2025

Threshold sensing yields optimal path formation in Physarum polycephalum

The model organism Physarum polycephalum is known to perform decentralised problem solving despite absence of nervous system. Experimental evidence and modelling studies have linked these abilities, and in particular maze-solving, to some sort of memory and adaptation. However, despite compelling hypotheses, it is still not clear whether the tasks are solved optimally, and which key dynamical mechanisms enable Physarum's impressive abilities. Here, we employ a circuital network model for the foraging behaviour of Physarum polycephalum to prove that threshold sensing yields the emergence of unique and optimal paths that connect food sources and solve mazes. We also prove which conditions lead to alternative paths, thus elucidating how the organism achieves flexibility and adaptation in a self-organised manner. These findings are aligned with experimental evidences and provide insight into the evolution of primitive intelligence. Our results can also inspire the development of threshold-based algorithms for computing applications.

physics.bio-ph↗

arXiv2025

Efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators

Reconstructing the attractors of complex nonlinear dynamical systems from available measurements is key to analyse and predict their time evolution. Existing attractor reconstruction methods typically rely on topological embedding and may produce poor reconstructions, which differ significantly from the actual attractor, because measurements are corrupted by noise and often available only for some of the state variables and/or their combinations, and the time series are often relatively short. Here, we propose the use of Homogeneous Differentiators (HD) to effectively de-noise measurements and more faithfully reconstruct attractors of nonlinear systems. Homogeneous Differentiators are supported by rigorous theoretical guarantees about their de-noising capabilities, and their results can be fruitfully combined with time-delay embedding, differential embedding and functional observability. We apply our proposed HD-based methodology to simulated dynamical models of increasing complexity, from the Lorenz system to the Hindmarsh-Rose model and the Epileptor model for neural dynamics, as well as to empirical data of EEG recordings. In the presence of corrupting noise of various types, we obtain drastically improved quality and resolution of the reconstructed attractors, as well as significantly reduced computational time, which can be orders of magnitude lower than that of alternative methods. Our tests show the flexibility and effectiveness of Homogeneous Differentiators and suggest that they can become the tool of choice for preprocessing noisy signals and reconstructing attractors of highly nonlinear dynamical systems from both theoretical models and real data.

q-bio.NC↗

arXiv2025

Recent trends in socio-epidemic modelling: behaviours and their determinants

The spreading dynamics of infectious diseases is influenced by individual behaviours, which are in turn affected by the level of awareness about the epidemic. Modelling the co-evolution of disease transmission and behavioural changes within a population enables better understanding, prediction and control of epidemics. Here, our primary goal is to provide an overview of the most popular modelling approaches, ranging from compartmental mean-field to agent-based models, with a particular focus on how behavioural factors are incorporated into epidemic dynamics. We classify modelling approaches based on the fundamental conceptual distinction between models of behaviours and models of behavioural determinants (such as awareness, beliefs, opinions, or trust); in particular, we observe that most studies model and interpret the variables related to individual responses either as behaviours or as determinants, with the implicit assumption that they correlate linearly. Based on preliminary empirical observations, we then challenge this assumption by analysing a recent dataset about time series of social indicators, collected during the COVID-19 pandemic. We examine the case study of Italian regions and we discover that behavioural responses are poorly explained by awareness, beliefs or trust, thereby calling for a careful interpretation of the modelling assumptions and for the development of further models, which fully account for the inherent complexity of individual responses and human behaviours.

physics.soc-ph↗

arXiv2025

Failure and Success in Single-Drug Control of Antimicrobial Resistance

We propose a mathematical model of Antimicrobial Resistance in the host to predict the failure of two antagonists of bacterial growth: the immune response and a single-antibiotic therapy. After characterising the initial bacterial load that cannot be cleared by the immune system alone, we define the success set of initial conditions for which an infection-free equilibrium can be reached by a viable single-antibiotic therapy, and we provide a rigorously defined inner approximation of the set. For initial conditions within the success set, we propose an optimal control framework to design single-drug therapies.

q-bio.PE↗

arXiv2025

Resilience of the positive gene autoregulation loop

Gene expression in response to stimuli is regulated by transcription factors (TFs) through feedback loop motifs, aimed at maintaining the desired TF concentration despite uncertainties and perturbations. In this work, we consider a stochastic model of the positive gene autoregulating feedback loop and we probabilistically quantify its resilience, \textit{i.e.}, its ability to preserve the equilibrium associated with a prescribed concentration of TFs, and the corresponding basin of attraction, in the presence of noise. We show that the formation of larger oligomers, corresponding to larger Hill coefficients of the regulation function, and thus to sharper non-linearities, improves the system resilience, even close to critical concentrations of TFs. We also explore a complementary definition of resilience that can be assessed within a stochastic formulation relying on the Fokker-Planck equation. Our formal results are accompanied by numerical simulations.

nlin.AO↗

arXiv2025

Instability of equilibrium and convergence to periodic orbits in strongly 2-cooperative systems

We consider time-invariant nonlinear $n$-dimensional strongly $2$-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly $2$-cooperative systems enjoy a strong Poincare-Bendixson property: bounded solutions that maintain a positive distance from the set of equilibria converge to a periodic solution. For strongly $2$-cooperative systems whose trajectories evolve in a bounded and invariant set that contains a single unstable equilibrium, we provide a simple criterion for the existence of periodic trajectories. Moreover, we explicitly characterize a positive-measure set of initial conditions which yield solutions that asymptotically converge to a periodic trajectory. We demonstrate our theoretical results using two models from systems biology, the $n$-dimensional Goodwin oscillator and a $4$-dimensional biomolecular oscillator with RNA-mediated regulation, and provide numerical simulations that verify the theoretical results.

math.DS↗

arXiv2024

Bottom-up robust modeling for the foraging behavior of Physarum polycephalum

The true slime mold \textit{Physarum polycephalum} has the remarkable capability to perform self-organized activities such as network formation among food sources. Despite well reproducing the emergence of slime networks, existing models are limited in the investigation of the minimal mechanisms, at the microscopic scale, that ensure robust problem-solving capabilities at the macroscopic scale. To this end, we develop three progressively more complex multi-agent models to provide a flexible framework to understand the self-organized foraging and network formation behaviors of \textit{Physarum}. The hierarchy of models allows for a stepwise investigation of the minimal set of rules that allow bio-inspired computing agents to achieve the desired behaviors on nutrient-poor substrates. By introducing a quantitative measure of connectedness among food sources, we assess the sensitivity of the model to user-defined and bio-inspired parameters, as well as the robustness of the model to parameter heterogeneity across agents. We ultimately observe the robust emergence of pattern formation, in line with experimental evidence. Overall, our study sheds light onto the basic mechanisms of self-organization and paves the way towards the development of decentralized strategies for network formation in engineered systems, focusing on trade-offs between biological fidelity and computational efficiency.

q-bio.PE↗

arXiv2024

Data informed epidemiological-behavioural modelling

Augmenting classical epidemiological models with information from the social sciences helps unveil the interplay between contagion dynamics and social responses. However, multidisciplinary integration of social analysis and epidemiological modelling is often challenging, due to scarcity of vast and reliable data sources and because ad hoc modelling assumptions may not reproduce empirically observed patters. Here, we test the hypothesis that awareness and information spreading straightforwardly translates into behavioural responses, analysing empirical data to generate insights about their dynamics and relationships. We employ such results to build a data-informed behavioural-epidemiological model that elucidates the impact of compliant behaviours and the role of centralised regulations in mitigating epidemics. We investigate model properties and its benefits in integrating theoretical modelling and data.

physics.soc-ph↗

arXiv2024

Convergence to periodic orbits in 3-dimensional strongly 2-cooperative systems

The flow of a $k$-cooperative system maps the set of vectors with up to~$(k-1)$ sign variations to itself. Strongly $2$-cooperative systems satisfy a strong \Poincare-Bendixson property: any bounded solution that evolves in a compact set containing no equilibria converges to a periodic orbit. For $3$-dimensional strongly $2$-cooperative nonlinear systems, we provide a simple sufficient condition that guarantees the existence, in the state space, of an invariant compact set that includes no equilibrium points. Thus, any solution emanating from this set converges to a periodic orbit. We characterize explicitly the set of initial conditions from which the trajectory converges to a periodic solution. We demonstrate our theoretical results on two well-known models in biochemistry: a 3D Goodwin oscillator model and the 3D Field-Noyes ordinary-differential-equation (ODE) model for the Belousov-Zhabotinskii reaction.

math.OC↗

arXiv2024

Efficient gPC-based quantification of probabilistic robustness for systems in neuroscience

Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable when addressing complex models in neuroscience, we propose an alternative to computationally expensive Monte Carlo (MC) methods by introducing and analysing the generalised polynomial chaos (gPC) framework for uncertainty quantification. We consider both intrusive and non-intrusive gPC approaches, which turn out to be scalable and allow for a fast comprehensive exploration of parameter spaces. Focusing on widely used models of neural dynamics as case studies, we explore the trade-off between efficiency and accuracy of gPC methods, and we adopt the proposed methodology to investigate parametric uncertainties in models that feature multiple dynamic regimes.

q-bio.QM↗

arXiv2024

Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting

Given a reaction-diffusion equation with unknown right-hand side, we consider a nonlinear inverse problem of estimating the associated leading eigenvalues and initial condition modes from a finite number of non-local noisy measurements. We define a reconstruction criterion and, for a small enough noise, we prove the existence and uniqueness of the desired approximation and derive closed-form expressions for the first-order condition numbers, as well as bounds for their asymptotic behavior in a regime when the number of measured samples is fixed and the inter-sampling interval length tends to infinity. When computing the sought estimates numerically, our simulations show that the exponential fitting algorithm ESPRIT is first-order optimal, as its first-order condition numbers have the same asymptotic behavior as the analytic condition numbers in the considered regime.

math.OC↗

arXiv2023

Controlling identical linear multi-agent systems over directed graphs

We consider the problem of synchronizing a multi-agent system (MAS) composed of several identical linear systems connected through a directed graph.To design a suitable controller, we construct conditions based on Bilinear Matrix Inequalities (BMIs) that ensure state synchronization.Since these conditions are non-convex, we propose an iterative algorithm based on a suitable relaxation that allows us to formulate Linear Matrix Inequality (LMI) conditions.As a result, the algorithm yields a common static state-feedback matrix for the controller that satisfies general linear performance constraints.Our results are achieved under the mild assumption that the graph is time-invariant and connected.

cs.MA↗