Fibromyalgia (FM) is a central disorder characterized by chronic pain, fatigue, insomnia, depression, and other minor symptoms. Knowledge about pathogenesis is lacking, diagnosis difficult, clinical approach puzzling, and patient management disappointing. We conducted a theoretical study based on literature data and computational analysis, aimed at developing a comprehensive model of FM pathogenesis and addressing suitable therapeutic targets. We started from the evidence that FM must involve a dysregulation of central pain processing, is female prevalent, suggesting a role for the hypothalamus-pituitary-gonadal (HPG) axis, and is stress-related, suggesting a role for the HP-adrenocortical (HPA) axis. Central pathogenesis was supposed to involve a pain processing loop system including the thalamic ventroposterolateral nucleus (VPL), the primary somatosensory cortex (SSC), and the thalamic reticular nucleus (TRN). For decreasing GABAergic and/or increasing glutamatergic transmission, the loop system crosses a bifurcation point, switching from monostable to bistable, and converging on a high-firing-rate steady state supposed to be the pathogenic condition. Thereafter, we showed that GABAergic transmission is positively correlated with gonadal-hormone-derived neurosteroids, notably allopregnanolone, whereas glutamatergic transmission is positively correlated with stress-induced glucocorticoids, notably cortisol. Finally, we built a dynamic model describing a multistable, double-inhibitory loop between HPG and HPA axes. This system has a high-HPA/low-HPG steady state, allegedly reached in females under combined premenstrual/postpartum brain allopregnanolone withdrawal and stress condition, driving the thalamocortical loop to the high-firing-rate steady state, and explaining the connection between endocrine and neural mechanisms in FM pathogenesis. Our model accounts for FM female prevalence and stress correlation, suggesting the use of neurosteroid drugs as a possible solution to currently unsolved problems in the clinical treatment of the disease.

In this article, we propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities. We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

Mal de Debarquement Syndrome (MdDS) is a puzzling central vestibular disorder characterized by a long-lasting perception of oscillatory postural instability that may occur after sea travels or flights. We have postulated that MdDS originates from the post-disembarking persistence of an adaptive internal oscillator consisting of a loop system, involving the right and left vestibular nuclei, and the Purkinje cells of the right and left flocculonodular cerebellar cortex, connected by GABAergic and glutamatergic fibers. We have formulated here a mathematical model of the vestibulo-cerebellar loop system and carried out a computational analysis based on a set of differential equations describing the interactions among the loop elements and containing Hill functions that model input-output firing rates relationships among neurons. The analysis indicates that the system acquires a spontaneous and permanent oscillatory behavior for a decrease of threshold and an increase of sensitivity in neuronal input-output responses. These results suggest a role for synaptic plasticity in MdDS pathophysiology, thus reinforcing our previous hypothesis that MdDS may be the result of excessive synaptic plasticity acting on the vestibulo-cerebellar network during its entraining to an oscillatory environment. Hence, our study points to neuroendocrine pathways that lead to increased synaptic response as possible new therapeutic targets for the clinical treatment of the disorder.

We formulate a control problem for positive compartmental systems formed by nodes (buffers) and arcs (flows). Our main result is that, on a finite horizon, we can solve the Pontryagin equations in one shot without resorting to trial and error via shooting. As expected, the solution is bang–bang and the switching times can be easily determined. We are also able to find a cost-to-go-function, in an analytic form, by solving a simple nonlinear differential equation. On an infinite horizon, we consider the Hamilton–Jacobi–Bellman theory and we show that the HJB equation can be solved exactly. Moreover, we show that the optimal solution is constant and the cost-to-go function is linear and copositive. This function is the solution of a nonlinear equation. We propose an iterative scheme for solving this equation, which converges in finite time. We also show that an exact solution can be found if there is a positive external disturbance affecting the process and the problem is formulated in a minsup framework. We finally provide illustrative examples related to flood control and epidemiology.

We consider a class of biological networks where the nodes are associated with first-order linear dynamics and their interactions, which can be either activating or inhibitory, are modelled by nonlinear Michaelis–Menten functions (i.e., Hill functions with unitary Hill coefficient), possibly in the presence of external constant inputs. We show that all the systems belonging to this class admit at most one strictly positive equilibrium, which is stable; this property is structural, i.e., it holds for any possible choice of the parameter values, and topology-independent, i.e., it holds for any possible topology of the interaction network. When the network is strongly connected, the strictly positive equilibrium is the only equilibrium of the system if and only if the network includes either at least one inhibiting function, or a strictly positive external input (otherwise, the zero vector is an equilibrium). The proposed stability results hold also for more general classes of interaction functions, and even in the presence of arbitrary delays in the interactions.

Early detection of the emergence of a new variant of concern (VoC) is essential to develop strategies that contain epidemic outbreaks. For example, knowing in which region a VoC starts spreading enables prompt actions to circumscribe the geographical area where the new variant can spread, by containing it locally. This paper presents ‘funnel plots’ as a statistical process control method that, unlike tools whose purpose is to identify rises of the reproduction number (R_t), detects when a regional R_t departs from the national average and thus represents an anomaly. The name of the method refers to the funnel-like shape of the scatter plot that the data take on. Control limits with prescribed false alarm rate are derived from the observation that regional R_t's are normally distributed with variance inversely proportional to the number of infectious cases. The method is validated on public COVID-19 data demonstrating its efficacy in the early detection of SARS-CoV-2 variants in India, South Africa, England, and Italy, as well as of a malfunctioning episode of the diagnostic infrastructure in England, during which the Immensa lab in Wolverhampton gave 43,000 incorrect negative tests relative to South West and West Midlands territories.

The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of biomolecular condensates, i.e., organelles without a membrane that are associated with cellular metabolism, stress response, and development. RNA, proteins, and small molecules participating in the formation of condensates are also involved in a variety of biochemical reactions: how do the chemical reaction dynamics influence the process of phase separation? Here we are interested in finding chemical reactions that can arrest the growth of condensates, generating stable spatial patterns of finite size (microphase separation), in contrast with the otherwise spontaneous (unstable) growth of condensates. We consider a classical continuum model for phase separation coupled to a chemical reaction network (CRN), and we seek conditions for the emergence of stable oscillations of the solution in space. Given reaction dynamics with uncertain rate constants, but known structure, we derive easily computable conditions to assess whether microphase separation is impossible, possible for some parameter values, or robustly guaranteed for all parameter values within given bounds. Our results establish a framework to evaluate which classes of CRNs favor the emergence of condensates with finite size, a question that is broadly relevant to understanding and engineering life.

Fibromyalgia (FM) is an unsolved central pain processing disturbance. We aim to provide a unifying model for FM pathogenesis based on a loop network involving thalamocortical regions, i.e., the ventroposterior lateral thalamus (VPL), the somatosensory cortex (SC), and the thalamic reticular nucleus (TRN). The dynamics of the loop have been described by three differential equations having neuron mean firing rates as variables and containing Hill functions to model mutual interactions among the loop elements. A computational analysis conducted with MATLAB has shown a transition from monostability to bistability of the loop behavior for a weakening of GABAergic transmission between TRN and VPL. This involves the appearance of a high-firing-rate steady state, which becomes dominant and is assumed to represent pathogenic pain processing giving rise to chronic pain. Our model is consistent with a bulk of literature evidence, such as neuroimaging and pharmacological data collected on FM patients, and with correlations between FM and immunoendocrine conditions, such as stress, perimenopause, chronic inflammation, obesity, and chronic dizziness. The model suggests that critical targets for FM treatment are to be found among immunoendocrine pathways leading to GABA/glutamate imbalance having an impact on the thalamocortical system.

While there is widespread concern regarding the impact of pesticides on honey bees, well-replicated field experiments, to date, have failed to provide clear insights on pesticide effects. Here, we adopt a systems biology approach to gain insights into the web of interactions amongst the factors influencing honey bee health. We put the focus on the properties of the system that depend upon its architecture and not on the strength, often unknown, of each single interaction. Then we test in vivo, on caged honey bees, the predictions derived from this modelling analysis. We show that the impact of toxic compounds on honey bee health can be shaped by the concurrent stressors affecting bees. We demonstrate that the immune-suppressive capacity of the widespread pathogen of bees, deformed wing virus, can introduce a critical positive feed-back loop in the system causing bistability, i.e., two stable equilibria. Therefore, honey bees under similar initial conditions can experience different consequences when exposed to the same stressor, including prolonged survival or premature death. The latter can generate an increased vulnerability of the hive to dwindling and collapse. Our conclusions reconcile contrasting field-testing outcomes and have important implications for the application of field studies to complex systems.

We proposed network-decentralized control strategies, in which each actuator can exclusively rely on local information, without knowing the network topology and the external input, ensuring that the flow asymptotically converges to the optimal one with respect to the p -norm. For 1 < p < ∞ , the flow converges to a unique constant optimal up∗. We show that the state converges to the optimal Lagrange multiplier of the optimization problem. Then, we consider networks where the flows are affected by unknown spontaneous dynamics and the buffers need to be driven exactly to a desired set-point. We propose a network-decentralized proportional-integral controller that achieves this goal along with asymptotic flow optimality; now it is the integral variable that converges to the optimal Lagrange multiplier. The extreme cases p=1 and p=∞ are of some interest since the former encourages sparsity of the solution while the latter promotes fairness. Unfortunately, for p=1 or p=∞ these strategies become discontinuous and lead to chattering of the flow, hence no optimality is achieved. We then show how to approximately achieve the goal as the limit for p 1 or p ∞.

Given a class of (bio)Chemical Reaction Networks (CRNs) identified by a stoichiometric matrix S, we define as dual reaction network, CRN∗, the class of (bio)Chemical Reaction Networks identified by the transpose stoichiometric matrix S⊤. We consider both the dynamical systems describing the time evolution of the species concentrations and of the reaction rates. First, based on the analysis of the Jacobian matrix, we show that the structural (i.e., parameter-independent) local stability properties are equivalent for a CRN and its dual CRN ∗. We also assess the structural global stability properties of the two dual networks, analysing both concentration and rate representations. We prove that the existence of a polyhedral (or piecewise-linear) Lyapunov function in concentrations for a CRN is equivalent to the existence of a piecewise-linear in rates Lyapunov function for the dual CRN ∗; in fact, if V is a polyhedral Lyapunov function for a CRN, the dual polyhedral function V∗ is a piecewise-linear in rates Lyapunov function for the dual network. We finally show how duality can be exploited to gain additional insight into biochemical reaction networks.

We consider a class of epidemiological models with an arbitrary number of infected compartments. We show that the logarithmic derivatives of the infected states converge to a consensus; this property rigorously explains the feature empirically observed in real epidemic data: the logarithms of the state variables associated with infected categories tend to behave as "parallel lines". We introduce and characterise the class of contagion functions, i.e., linear co-positive functions of the state variables that decrease (resp. increase) when the reproduction number is smaller (resp. larger) than 1. Finally, we analyse the generalised epidemiological model by considering the susceptible state variable along with a variable that aggregates all the infected compartments: this leads to an auxiliary planar system, governed by two differential inclusions, which has the same structure as the two-dimensional SI model and whose coefficients are functions of the original variables. We prove that well known properties of the classical SI model still hold in this generalised case.

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

Despite their complexity, biological systems are able to endure huge parameter fluctuations and survive in the most diverse environmental conditions. Mathematical tools from graph theory and systems and control theory are naturally well-suited to understand the functioning of biological systems and reveal that their tremendous robustness is often rooted in their peculiar interconnection structure. This survey considers a wide class of ordinary-differential-equation biological models, including chemical reaction networks, and provides an overview of structural approaches proposed in the literature to assess whether a system structure enjoys fundamental qualitative properties, yielding specific types of dynamic or steady-state behaviours, regardless of the precise parameter values.

A well-known property of linear resistive electrical networks is that the current distribution minimizes the total dissipated power. When the circuit includes resistors with nonlinear monotonic characteristic, the current distribution minimizes in general a different functional. We show that, if the nonlinear characteristic is a threshold-like function and the current generator is concentrated in a single point, as in the case of lightning or dielectric discharge, then the current flow is concentrated along a single path, which is a minimum path to the ground with respect to the threshold. We also propose a dynamic model that explains and qualitatively reproduces the lightning transient behavior: initial generation of several plasma branches and subsequent dismissal of all branches but the one reaching the ground first, which is the optimal one.

We consider a class of epidemiological models in which a compartmental linear system, including various categories of infected individuals (e.g. asymptomatic, symptomatic, quarantined), is fed back by a positive feedback, representing contagion. The positive feedback gain decreases (in a sort of negative feedback) as the epidemic evolves, due to the decrease in the number of susceptible individuals. We first propose a convergence result based on a special copositive Lyapunov function. Then, we address a major problem for this class of systems: the deep uncertainty affecting parameter values. We face the problem adopting techniques from optimal and robust control theory to assess the sensitivity of the model. For this class of systems, the optimal control solution has a peculiar decoupling property that no shooting procedure is required. Finally, we exploit the obtained bounds to assess the effectiveness of possible epidemic control strategies, including intermittent restrictions adopted during the COVID-19 pandemic.

Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)¹, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model², which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs (R = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs (R = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open–close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses.

In this paper we apply a novel approach to near-infrared subcutaneous palm vascular pattern authentication. The proposed method relies on a recursive algorithm based on a positive linear dynamical system whose evolution depends on the two matrices representing the vein patterns to be compared. The output of the system reaches a high value when a good matching between the two matrices is observed, otherwise it converges rapidly to zero, even in presence of noise. With respect to another algorithm we recently introduced, this approach achieves not only a better authentication performance but also a drastic reduction in terms of computation time. These improvements are demonstrated by means of extensive experiments conducted on challenging datasets.

The negative capacitance operation of a ferroelectric material is not only an intriguing materials science topic, but also a property with important technological applications in nanoscale electronic devices. Despite growing interest for possible applications, the very existence of negative capacitance is still actively debated, even because experimental results for ferroelectric capacitors with or without a metal interlayer led to quite contradicting indications. Here we present a comprehensive analysis of NC operation in ferroelectric capacitors and provide new insights into the discrepancies observed in experiments. Our models duly account for the three-dimensional nature of the problem and show a good agreement with several aspects of recent experiments. Our results also demonstrate that traps at the ferroelectric-dielectric interface play an important role in the feasibility of stable negative capacitance operation in ferroelectric capacitors.

Introduction: Mal de Debarquement Syndrome (MdDS) is a poorly understood neurological disorder affecting mostly perimenopausal women. MdDS has been hypothesized to be a maladaptation of the vestibulo-ocular reflex, a neuroplasticity disorder, and a consequence of neurochemical imbalances and hormonal changes. Our hypothesis considers elements from these theories, but presents a novel approach based on the analysis of functional loops, according to Systems and Control Theory. Hypothesis: MdDS is characterized by a persistent sensation of self-motion, usually occurring after sea travels. We assume the existence of a neuronal mechanism acting as an oscillator, i.e., an adaptive internal model, that may be able to cancel a sinusoidal disturbance of posture experienced aboard, due to wave motion. Thereafter, we identify this mechanism as a multi-loop neural network that spans between vestibular nuclei and the flocculonodular lobe of the cerebellum. We demonstrate that this loop system has a tendency to oscillate, which increases with increasing strength of neuronal connections. Therefore, we hypothesize that synaptic plasticity, specifically long-term potentiation, may play a role in making these oscillations poorly damped. Finally, we assume that the neuromodulator Calcitonin Gene-Related Peptide, which is modulated in perimenopausal women, exacerbates this process thus rendering the transition irreversible and consequently leading to MdDS. Conclusion and Validation: The concept of an oscillator that becomes noxiously permanent can be used as a model for MdDS, given a high correlation between patients with MdDS and sea travels involving undulating passive motion, and an alleviation of symptoms when patients are re-exposed to similar passive motion. The mechanism could be further investigated utilizing posturography tests to evaluate if subjective perception of motion matches with objective postural instability. Neurochemical imbalances that would render individuals more susceptible to developing MdDS could be investigated through hormonal profile screening. Alterations in the connections between vestibular nuclei and cerebellum, notably GABAergic fibers, could be explored by neuroimaging techniques as well as transcranial magnetic stimulation. If our hypothesis were tested and verified, optimal targets for MdDS treatment could be found within both the neural networks and biochemical factors that are deemed to play a fundamental role in loop functioning and synaptic plasticity.