Abstract In this paper, the plasma glucose regulation problem for type 2 diabetic patients is studied. A nonlinear time-delay model of the glucose–insulin regulatory system is exploited to design a quantized sampled-data static output... more
Abstract In this paper, the plasma glucose regulation problem for type 2 diabetic patients is studied. A nonlinear time-delay model of the glucose–insulin regulatory system is exploited to design a quantized sampled-data static output feedback control, using only glucose measurements. It is shown that the proposed control law achieves semiglobal practical stability of the related quantized sampled-data closed-loop glucose–insulin system with arbitrary small steady-state tracking error. The controller involves past values of the glucose, which may not be available in the buffer, for instance because of non-uniform sampling. Such a drawback is overcome by means of spline interpolation. Furthermore, quantization in both input and output channels are taken into account. A pre-clinical validation, concerning the performances of the proposed glucose regulator, is carried out by means of a well-known simulator of diabetic patients, broadly accepted for testing insulin infusion therapies. The simulation results pave the way for further clinical evaluation.
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Over the last decades, the exuberant development of next-generation sequencing has revolutionized gene discovery. These technologies have boosted the mapping of single nucleotide polymorphisms (SNPs) across the human genome, providing a... more
Over the last decades, the exuberant development of next-generation sequencing has revolutionized gene discovery. These technologies have boosted the mapping of single nucleotide polymorphisms (SNPs) across the human genome, providing a complex universe of heterogeneity characterizing individuals worldwide. Fractal dimension (FD) measures the degree of geometric irregularity, quantifying how “complex” a self-similar natural phenomenon is. We compared two FD algorithms, box-counting dimension (BCD) and Higuchi’s fractal dimension (HFD), to characterize genome-wide patterns of SNPs extracted from the HapMap data set, which includes data from 1184 healthy subjects of eleven populations. In addition, we have used cluster and classification analysis to relate the genetic distances within chromosomes based on FD similarities to the geographical distances among the 11 global populations. We found that HFD outperformed BCD at both grand average clusterization analysis by the cophenetic corr...
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In the last few years, mathematical models of lung ventilation have often been used to support the Anesthesiologists and Resuscitators choices in the mechanical ventilator parameters setting. In this context, a real-time control strategy... more
In the last few years, mathematical models of lung ventilation have often been used to support the Anesthesiologists and Resuscitators choices in the mechanical ventilator parameters setting. In this context, a real-time control strategy is doubtless crucial to avoid the occurrence of induced pressure-derived trauma. In the present work, we develop a first version of a simple but realistic physiological lung ventilation mathematical model. The patient-ventilator complex is taken into account by modeling the pressure wave provided by the mechanical lung ventilator as an external (control) input. With the aim of reaching the correct amplitude for the pressure wave at the mouth provided by the mechanical ventilator, hence limiting the risk of Acute Respiratory Distress Syndrome (ARDS), we consider two different scenarios: the patient who needs to be ventilated as a consequence of having an insufficient respiratory drift (assisted ventilation) and the patient without a spontaneous breathing (controlled ventilation). An output-feedback control law is proposed, based on the flow measurements provided by the ventilator, and not exploiting the full knowledge of the model equations and parameters. The considered approach looks promising, since a preliminary in-silico validation of the resulting patient-ventilator system shows that the target value of the tidal volume is readily tracked in both scenarios, without dangerous oscillations and with limited control effort.
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The smoothing problem is here considered for Gauss-Markov random fields defined on a kind of spherical lattice. Various observation models are included in the setting of this paper, such as the case of Gaussian noisy (even correlated)... more
The smoothing problem is here considered for Gauss-Markov random fields defined on a kind of spherical lattice. Various observation models are included in the setting of this paper, such as the case of Gaussian noisy (even correlated) observations available only on a subset of sites, as well as a variable number of process components being measured. An efficient optimal smoothing algorithm is derived, based on the sparse representation of the potential matrix of the random field and on gaussian elimination. In view of applications in weather forecasting, an example using real data is presented, showing the capability of the proposed setting in a task of reconstruction of temperature maps.
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A metabolic pathway made of a cascade of biochemical reactions is considered, with a substrate which is eventually transformed into the final product by means of a sequence of reactions, each catalyzed by the same enzyme. The amount of... more
A metabolic pathway made of a cascade of biochemical reactions is considered, with a substrate which is eventually transformed into the final product by means of a sequence of reactions, each catalyzed by the same enzyme. The amount of the enzyme varies according to discrete noisy processes of production and elimination. A feedback acts on the final product clearance rate, exerted by the final product accumulation itself: higher final product levels lead to a faster dynamics. The aim of this note is to investigate how the noise scales with the length of the cascade and how the feedback impacts on the noise propagation. To this end, a Stochastic Hybrid System (SHS) formulation is exploited, with the enzyme production/clearance processes constituting the noise source. The noise propagation is measured in terms of the square of the coefficient of variation of the final product, and computations are carried out by means of the equations of moments, which are estimated in closed form aft...
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In recent years, there has been a rise in Major Incidents with big impact on the citizens health and the society. Without the possibility of conducting live experiments when it comes to physical trauma, only an accurate in-silico... more
In recent years, there has been a rise in Major Incidents with big impact on the citizens health and the society. Without the possibility of conducting live experiments when it comes to physical trauma, only an accurate in-silico reconstruction allows us to identify organizational solutions with the best possible chance of success, in correlation with the limitations on available resources (e.g. medical team, first responders, treatments, transports, and hospitals availability) and with the variability of the characteristic of event (e.g. type of incident, severity of the event and type of lesions). Utilizing modelling and simulation techniques, a simplified mathematical model of physiological evolution for patients involved in physical trauma incident scenarios has been developed and implemented. The model formalizes the dynamics, operating standards and practices of medical response and the main emergency service in the chain of emergency management during a Major Incident.
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Most of the existing results available in the literature concerning symbolic control design of purely continuous or hybrid systems assume full information of the state which in concrete applications may be not available. This partial... more
Most of the existing results available in the literature concerning symbolic control design of purely continuous or hybrid systems assume full information of the state which in concrete applications may be not available. This partial information to the controller translates into the necessity to revisit existing methods on symbolic control design. This paper aims at addressing this issue and deals with symbolic control design of discrete-time nonlinear control systems affected by disturbances with specifications expressed as regular languages and where controllers can access state information only through quantized measurements.
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Metabolic networks are known to deal with the chemical reactions responsible to fuel cellular activities with energy and carbon source and, as a matter of fact, to set the growth rate of the cell. To this end, feedback and regulatory... more
Metabolic networks are known to deal with the chemical reactions responsible to fuel cellular activities with energy and carbon source and, as a matter of fact, to set the growth rate of the cell. To this end, feedback and regulatory networks play a crucial role to handle adaptation to external perturbations and internal noise. In this work, a cellular resource is assumed to be activated at the end of a metabolic pathway, by means of a cascade of transformations. Such a cascade is triggered by the catalytic action of an enzyme that promotes the first transformation. The final product is responsible for the cellular growth rate modulation. This mechanism acts in feedback at the enzymatic level, since the enzyme (as well as all species) is subject to dilution, with the dilution rate set by growth. Enzymatic production is modeled by the occurrence of noisy bursts: a Stochastic Hybrid System is exploited to model the network and to investigate how such noise propagates on growth fluctua...
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Modeling and control of ground vehicles have become a major research field in the last few years, due to the increasing diffusion of driver assistance technologies and the persistent need for guaranteeing safety and comfort of driver and... more
Modeling and control of ground vehicles have become a major research field in the last few years, due to the increasing diffusion of driver assistance technologies and the persistent need for guaranteeing safety and comfort of driver and passengers. Although vehicle control systems require a large set of measurements to perform accurate computations, due to the possible unavailability and the non-negligible cost of sensors, it is not always possible to assume the direct knowledge of some important dynamic quantities involved, among which a major role is taken by its lateral velocity. In this letter, we address the design and implementation of an asymptotic sampled-data state observer for the vehicle single-track model. The observer only exploits the knowledge of sparse yaw-rate samples, which are obtained by relatively cheap digital gyroscopic devices, to reconstruct the continuous behavior of lateral velocity and yaw rate. However, due to the inherent properties of the vehicle single-track model, the observer is theoretically guaranteed to work only in the presence of sufficiently bounded driver maneuvers. Consequently and in view of a practical exploitation in a realistic setting, we preliminarily validate the approach by means of simulations of the observer applied to a more general vehicle model, including parameter variations, unmodeled dynamics, and quantization. The results seem to confirm the potential of the approach.
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Chemical Master Equations (CMEs) provide a comprehensive way to model the probabilistic behavior in biochemical networks. Despite their widespread diffusion in systems biology, the explicit computation of their solution is often avoided... more
Chemical Master Equations (CMEs) provide a comprehensive way to model the probabilistic behavior in biochemical networks. Despite their widespread diffusion in systems biology, the explicit computation of their solution is often avoided in favor of purely statistic Monte Carlo methods, due to the dramatically high dimension of the CME system.In this work, we investigate some structural properties of CMEs and their solutions, focusing on the efficient computation of the stationary distribution. We introduce a generalized notion of one-step process, which results in a sparse dynamic matrix describing the collection of the scalar CMEs, showing a recursive block-tridiagonal structure as well. Further properties are inferred by means of a graph-theoretical interpretation of the reaction network. We exploit this structure by proposing different methods, including a dedicated LU decomposition, to compute the explicit solution.Examples are included to illustrate the introduced concepts and to show the effectiveness of the proposed approach.
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Abstract This paper addresses the problem of vehicle attitude control by means of active front steering and rear torque vectoring in the presence of saturating actuators. A novel approach of actuation balancing is proven to be the optimal... more
Abstract This paper addresses the problem of vehicle attitude control by means of active front steering and rear torque vectoring in the presence of saturating actuators. A novel approach of actuation balancing is proven to be the optimal way to keep the vehicle off saturation or, at least, to postpone the saturation occurrences as much as possible. To this end, a control law is proposed, achieving the tracking goal while keeping the balancing among the actuators. Exponential tracking is shown in nominal (non-saturated) conditions, where the optimality guarantees that the actuators remain as far as possible from their bounds. However, in hard conditions, saturations may still occur and tracking may be lost. Hence, it is shown how to modify dynamically the reference signals in order to compensate the lack of control action of actuators entering a possible saturation condition. As a consequence, less strict references are obtained and the tracking goal is recovered, while keeping the actuators within their saturation bounds. On top of the formal results, the method is validated by means of simulations performed in a non-ideal setting, including parameter uncertainties and unmodeled actuation delays.
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Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population... more
Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population model, based on a linear partial differential equation with variable coefficients. The model is characterized by three rate functions: a new-adult population glycemic profile, a glycemia-dependent mortality rate and a glycemia-dependent average worsening rate. First, we formally analyze some properties of the solution, the transient behavior and the equilibrium distribution. Then, we identify the key parameters and functions of the model from real-life data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steady-state behavior. The interest of the model is that, while it summarizes the evolution of diabetes in the population in a completely different way with respect to previously published Monte Carlo aggregations of individual-based models, it does appear to offer a good approximation of observed reality and of the features expected in the clinical setting. The model can offer insights in pharmaceutical research and be used to assess possible public health intervention strategies.
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This paper addresses the problem of vehicle attitude control in the presence of saturating actuators. A novel approach of actuation balancing is proven to be the best way to keep the vehicle off saturation or, at least, to postpone the... more
This paper addresses the problem of vehicle attitude control in the presence of saturating actuators. A novel approach of actuation balancing is proven to be the best way to keep the vehicle off saturation or, at least, to postpone the saturation occurrences as late as possible. In hard conditions, this may be not sufficient to guarantee tracking; hence the joint design of a load–balancing control law and an adapted reference generator is addressed, in order to cope with the lack in the control action and prevent unstable behaviors. On top of the formal results, the method is validated by means of simulations.
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The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions... more
The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to v...