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The effects of alcohol have been widely studied during the past century, corroborating the idea that this tiny chemical compound acts throughout most of our neurotransmitter systems since it is capable of inducing addictive behaviour. Two of the most serious problems of alcohol addiction are craving and relapse; several studies have demonstrated that relapse is related to the anxious state which occurs during withdrawal, and it has been proved that this behavioural modifications results from an alteration of the dopaminergic and serotonergic systems. An important role in the neurobiology of alcohol addiction is played by acetaldehyde (ACD), ethanol first metabolite. Our recent studies indeed, have demonstrated that ACD itself is able to induce CRH release from hypothalamic explants, underlying the central role played by ACD in alcohol-induced modifications of the HPA axis. Moreover, for the first time, this group has shown that ACD is able to induce and maintain an operant drinking behaviour after repeated abstinence periods, and in the presence of a conflict situation in rats, mimicking the same characteristics as alcohol. ACD is produced either peripherally or within the brain by alcohol dehydrogenase and catalase, respectively. Studies assert that the highest concentrations of catalase in the brain are mainly located in aminergic neurons suggesting that ACD could take part in alcohol action in those circuitries. Further investigations are then necessary to fully understand the molecular mechanisms underlying the neurochemical and behavioural modifications induced by ACD, as a mediator of alcohol activity in the brain., peer-reviewed

Numerical solution of optimal control problems via the Dynamic Programming (DP) approach is mainly motivated by the search for feedback controls for generic nonlinear Lipchitz continuous vectorfields and costs.

This paper proposes an online evolutive procedure to optimize the Material Removal Rate in a turning process considering a stochastic constraint. The usual industrial approach in finishing operations is to change the tool insert at the end of each machining feature to avoid defective parts. Consequently, all parts are produced at highly conservative conditions (low levels of feed and speed), and therefore, at low productivity. In this work, a framework to estimate the stochastic constraint of tool wear during the production of a batch is proposed. A simulation campaign was carried out to evaluate the performances of the proposed procedure. The results showed that it was possible to improve the Material Removal Rate during the production of the batch and keeping the probability of defective parts under a desired level.

We investigate optimal reachability and grasping problems for a planar soft manipulator, from both a theoretical and numerical point of view. The underlying control model describes the evolution of the symmetry axis of the device, which is subject to inextensibility and curvature constraints, a bending moment and a curvature control. Optimal control strategies are characterized with tools coming from the optimal control theory of PDEs. We run some numerical tests in order to validate the model and to synthetize optimal control strategies.

Using characteristics to treat advection terms in time-dependent PDEs leads to a class of schemes, e.g., semi-Lagrangian and Lagrange-Galerkin schemes, which preserve stability under large Courant numbers, and may therefore be appealing in many practical situations. Unfortunately, the need of locating the feet of characteristics may cause a serious drop of efficiency in the case of unstructured space grids, and thus prevent the use of large time-step schemes on complex geometries. In this paper, we perform an in-depth analysis of the main recipes available for characteristic location, and propose a technique to improve the efficiency of this phase, using additional information related to the advecting vector field. This results in a clear improvement of execution times in the unstructured case, thus extending the range of applicability of large time-step schemes.

We discuss the general framework of a stochastic two-player, hybrid differential game, and we apply it to the modelling of a “match race” between two sailing boats, namely a competition in which the goal of both players is to proceed in the windward direction, while trying to slow down the other player. We provide a convergent approximation scheme for the computation of the value function of the game, and we validate the approach on some typical racing scenarios.

We address an optimal reachability problem in constrained environments for hyper-redundant and soft planar manipulators. Both the discrete and continuous devices are inextensible and they are characterized by a bending moment, representing a natural resistance to leave the position at rest, an inequality constraint forcing the bending below a fixed threshold, and a control term prescribing local bending. After introducing the model and characterizing the associated equilibria, we set the problem in the framework of optimal control theory and we present some simulations related to its numerical solution.

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-tained by deriving first-order optimality conditions for the control problem, and we providesome numerical experiments in the case of smart traffic lights for a 2-1 junction., Comment: 20 pages, 6 figures

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an agent of one of the populations represented by the components of the mixture model, and we introduce a corresponding optimal control problem. In this way, we obtain a multi-population Mean Field Games system which characterizes the parameters of the finite mixture model. Our method can be interpreted as a continuous version of the classical Expectation–Maximization algorithm.

We propose an “optimize-then-discretize” approach for the numerical solution of optimal control problems for systems with delays in both state and control. We first derive the optimality conditions and an explicit representation of the gradient of the cost functional. Then, we use explicit discretizations of the state/costate equations and employ general-purpose Non-Linear Programming (NLP) solvers, in particular Conjugate Gradient or Quasi-Newton schemes, to easily implement a descent method. Finally, we prove convergence of the algorithm to stationary points of the cost, and present some numerical simulations on model problems, including performance evaluation.

We consider a system of differential equations of Monge-Kantorovich type which describes the equilibrium configurations of granular material poured by a constant source on a network. Relying on the definition of viscosity solution for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions and P. E. Souganidis, we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out.

We discuss convergence results for a class of finite difference schemes approximating Mean Field Games systems either on the torus or a network. We also propose a quasi-Newton method for the computation of discrete solutions, based on a least squares formulation of the problem. Several numerical experiments are carried out including the case with two or more competing populations.

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out.

3D printers based on the additive manufacturing technology create objects layer-by-layer dropping fused material. As a consequence, strong overhangs cannot be printed because the new-come material does not find a suitable support over the last deposed layer. In these cases, one can add support structures (scaffolds) which make the object printable, to be removed at the end. In this paper, we propose a level set based method to create object-dependent support structures, specifically conceived to reduce both the amount of additional material and the printing time. We also review some open problems about 3D printing which can be of interests for the mathematical community.

We propose a new approach to the numerical solution of cell problems arising in the homogenization of Hamilton--Jacobi equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming from the discretization of the corresponding cell problems. We show that our method is able to solve efficiently cell problems in very general contexts, e.g., for first and second order scalar convex and nonconvex Hamiltonians, weakly coupled systems, dislocation dynamics, and mean field games, also in the case of more competing populations. A large collection of numerical tests in dimensions one and two shows the performance of the proposed method, both in terms of accuracy and computational time.