As a key effort of the project, we have started developing a unifying framework that integrates both structural and probabilistic, qualitative and quantitative methodologies for the study of systems in the life sciences, and beyond.
We have started developing a framework that integrates the concepts of robustness and resilience, associated with a system’s ability to preserve its functions despite uncertainties, fluctuations and perturbations, both intrinsic and extrinsic. Numerous competing definitions of these concepts coexist and often lack a rigorous control-theoretic formulation, which we have provided in a unified framework for the first time, demonstrating their effectiveness in capturing behaviours of widely used models in biology.
We have obtained rigorous structural results to assess the convergence to periodic orbits that exploit the system structure of strongly 2-cooperative systems, and we have applied our new theory to well-known models in biology, such as the Goodwin oscillator.
We have preliminarily developed novel probabilistic approaches tailored to the sensitivity analysis and the prediction of qualitative behaviours of complex large-scale systems; in particular, the methodologies have been applied to large-scale agent-based opinion formation models.
Moreover, we have started investigating computationally efficient approaches, based on surrogate models obtained through the theory of generalized polynomial chaos, to quantify probabilistic robustness for various types of models in neuroscience. We have also developed a methodology for the efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators, with applications to complex systems also in neuroscience.
We have introduced the concept of qualitative “spiking” behaviour of systems in a structural framework and discussed its relevance in population-infection dynamics.
We have tailored advanced computationally efficient optimal control algorithms, for which we have proven theoretical convergence guarantees, to a general class of epidemiological models. We have investigated the modelling, controllability and optimal control of antimicrobial resistance. The structure of optimization problems in ecology has also been exploited for their efficient solution relying on stability guarantees and nonlinear programming.
We have developed novel approaches to deal with uncertainty and noise in reaction-diffusion dynamics.
As our main interdisciplinary contributions, we have employed structural and/or probabilistic approaches to study physiological systems and explain pathogenesis, to analyse the inherent properties of biomolecular systems and design novel biomolecular circuits with desired behaviours.
We have also developed and analysed new models for epidemics in the host and between hosts, and for the interplay of epidemics and behaviours in populations, as well as for the behaviour of multi-agent systems in nature.
As we had anticipated, structural methodologies can also be profitably applied to uncertain systems in engineering, which we have also considered (in AC circuits and robotics).
