We propose a new iterative procedure to find the best time for re-initialization of meta-heuristic algorithms to solve combinatorial optimization problems. The sequence of algorithm executions with different random inizializations evolves at each iteration by either adding new independent executions or extending all existing ones up to the current maximum execution time. This is done on the basis of a criterion that uses a surrogate of the algorithm failure probability, where the optimal solution is replaced by the best so far one. Therefore, the new procedure can be applied in practice. We prove that, with probability one, the maximum time of current executions of the proposed procedure approaches, as the number of iterations diverges, the optimal value minimizing the expected time to find the solution. We apply the new procedure to several Traveling Salesman Problem instances with hundreds or thousands of cities, whose solution is known, and to some instances of a pseudo-Boolean problem. As base algorithm, we use different versions of an Ant Colony Optimization algorithm or a Genetic Algorithm. We compare the results from the proposed procedure with those from the base algorithm. This comparison shows that the failure probability estimated values of the new procedure are several orders of magnitude lower than those of the base algorithm for equal computation cost.

Solvency assessing is a compelling issue for the insurance industry, also in light of the current international risk-based regulations. Internal models have to take into account risk/profit indicators, in order to provide flexible tools aimed at valuing solvency. We focus on a variable annuity with an embedded option involving a participation level which depends on the period financial result. We realize a performance evaluation by means of a suitable indicator, which properly captures both financial and demographic risk drivers. In fact, in the case of life annuity business, assessing solvency has to be framed within a wide time horizon, where specific financial and demographic risks are realized. In this order of ideas, solvency indicators have to capture the amount of capital to cope with the impact of those risk sources over the considered period. The analysis is carried out in accordance with a management perspective, apt to measure the business performance, which requires a correct risk control; in particular we present a study of the dynamics of the profit realized per unit of the total financial value of the contract. On the other hand, the consumer profitability is also measured by means of an utility-equivalent fixed life annuity. Ac-cording to the insureds point of view, we measure their perception of the contract profitability within the expected utility approach.

Diffusion and transport processes constitute a very important field of applied mathematics. They are useful in many different problems ranging from the diffusion of pollutants in the atmosphere and the sea, to the spreading of epidemics. Aside from their practical relevance, such processes have been very important in the history of physics and mathematics. We can recall Einstein's study of Brownian motion which was fundamental to give a definitive experimental evidence of the existence of atoms. Moreover diffusion processes have been the starting point for the building of the mathematical theory of stochastic processes (starting from the work of Langevin). Similarly the study of reaction and diffusion phenomena, starting from the seminal contribution of two 20th-century science giants (Ronald A. Fisher and Andrej N. Kolmogorov) has led to interesting developments both for applications and for the fruitful connections between stochastic processes and partial differential equation. In this article we discuss some general results developed in these areas, including few modern topics, as transport and reaction/diffusion on discrete structures (graphs). Such a theme has a great relevance, e.g. for the dissemination of information through the internet or the spreading of epidemics through the air transport network. I fenomeni di trasporto, e la loro generalizzazione ai casi con reazione, costituiscono un capitolo molto importante della matematica applicata e trovano utilizzo in ambiti molto vari, che vanno dalla diffusione di sostanze inquinanti in atmosfera e in mare, ai processi industriali, alla biomatematica, alla propagazione di epidemie. Oltre alla loro rilevanza pratica, lo studio di tali fenomeni ha portato contributi molto importanti nella storia della fisica e della matematica. Possiamo ricordare lo studio di Einstein sul moto browniano che è stato fondamentale per dare un'evidenza sperimentale definitiva della reale esistenza degli atomi. E, in generale, i processi di diffusione hanno costituito il punto di partenza per la costruzione della teoria matematica dei processi stocastici (a cominciare dal lavoro di Langevin). Analogamente lo studio dei fenomeni con diffusione e reazione, nati dal contributo di due giganti della scienza del 20-mo secolo (Ronald A. Fisher e Andrej N. Kolmogorov) nell'ambito della modellizzazione matematica di problemi biologici, ha poi portato a sviluppi interessanti sia nell'ambito applicativo che per le proficue connessioni tra processi stocastici ed equazioni alle derivate parziali. In questo articolo oltre a presentare alcuni tra i risultati generali sviluppati in questi ambiti, discuteremo anche aspetti più moderni legati al crescente interesse per i fenomeni di trasporto e reazione/diffusione su strutture discrete (grafi), una tematica questa di grande attualità (basti pensare alla diffusione delle informazioni su internet o alla propagazione delle epidemie per mezzo del network dei trasporti aerei) sviluppata attraverso una matematica raffinata.

We focus on the extension of the MLD2P4 package of parallel Algebraic MultiGrid (AMG) preconditioners, with the objective of improving its robustness and efficiency when dealing with sparse linear systems arising from anisotropic PDE problems on general meshes. We present a parallel implemen- tation of a new coarsening algorithm for symmetric positive definite matrices, which is based on a weighted matching approach. We discuss preliminary re- sults obtained by combining this coarsening strategy with the AMG components available in MLD2P4, on linear systems arising from applications considered in the Horizon 2020 Project "Energy oriented Centre of Excellence for computing applications" (EoCoE).

Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction-diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well-posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species.

Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. In the present work, in the context of general finite frames, we derive an oracle expression for the mean quadratic risk of a linear diagonal de-noising procedure which immediately yields the optimal linear diagonal estimator. Moreover, we obtain an expression for an unbiased estimator of the risk of any smooth shrinkage rule. This last result motivates a set of practical estimation procedures for general finite frames that can be viewed as the generalization of the classical procedures for orthonormal bases. A simulation study verifies the effectiveness of the proposed procedures with respect to the classical ones and confirms that the correlations induced by frame structure should be explicitly treated to yield an improvement in estimation precision.

Macrophages derived from monocyte precursors undergo specific polarization processes which are influenced by the local tissue environment: classically-activated (M1) macrophages, with a pro-inflammatory activity and a role of effector cells in Th1 cellular immune responses, and alternatively-activated (M2) macrophages, with anti-inflammatory functions and involved in immunosuppression and tissue repair. At least three different subsets of M2 macrophages, namely M2a, M2b and M2c, are characterized in the literature based on their eliciting signals. The activation and polarization of macrophages is achieved through many, often intertwined, signaling pathways. To describe the logical relationships among the genes involved in macrophage polarization, we used a computational modeling methodology, namely, logical (Boolean) modeling of gene regulation. We integrated experimental data and knowledge available in the literature to construct a logical network model for the gene regulation driving macrophage polarization to the M1, M2a, M2b and M2c phenotypes. Using the software GINsim and BoolNet we analysed the network dynamics under different conditions and perturbations to understand how they affect cell polarization. Dynamic simulations of the network model, enacting the most relevant biological conditions, showed coherence with the observed behaviour of in vivo macrophages. The model could correctly reproduce the polarization toward the four main phenotypes as well as to several hybrid phenotypes, which are known to be experimentally associated to physiological and pathological conditions. We surmise that shifts among different phenotypes in the model mimic the hypothetical continuum of macrophage polarization, with M1 and M2 being the extremes of an uninterrupted sequence of states. Furthermore, model simulations suggest that anti-inflammatory macrophages are resilient to shift back to the pro-inflammatory phenotype.

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and axisymmetric (3D) configurations show how an injection of matrix-degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix-degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport. Both effects are consistent with previous biological observations.

We tackle the issue of measuring and understanding the visitors' dynamics in a crowded museum in order to create and calibrate a predictive mathematical model. The model is then used as a tool to manage, control and optimize the fruition of the museum. Our contribution comes with one successful use case, the Galleria Borghese in Rome, Italy.

Interview to the MIT professor of Mathematics Gigliola Staffilani

Storia sulla rivista Topolino sul primo calcolatore del CNR nel 1955

Volume di Comics&Science dedicato alle donne in matematica

Albo di Comics&Science dedicato alla fisica delle particelle in collaborazione con ISM e una storia di Zerocalcare

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps, which are not known in advance. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the stability and convergence properties of the numerical dynamic. The basic idea is to investigate how the error propagates in successive impacts by decomposing the numerical integration process of the overall system into a sequence of discretized perturbed problems.

We present an extension of recent relativistic Lattice Boltzmann methods based on Gaussian quadratures for the study of fluids in (2+1) dimensions. The new method is applied to the analysis of electron flow in graphene samples subject to electrostatic drive; we show that the flow displays hydro-electronic whirlpools in accordance with recent analytical calculations as well as experimental results.

We address the problem of forecasting sales for fresh and highly perishable products, in the general context of supply chain management. The forecasting activity refers to the single item in a given store and started from a pre-processing phase for data analysis and normalization. Then data was used as input for a forecasting algorithm designed to be user interactive. We implemented three forecasting methods: ARIMA, ARIMAX and transfer function models. The exogenous components of the forecasting models took the impact of prices into account. The best configuration of these models is dynamically chosen via two alternative methods: (i) a two-step procedure, based on properly selected statistical indicators, (ii) a Sequential Parameter Optimization approach for automatic parameter tuning. The user or the decision maker at the store level should not be exposed to the complexity of the forecasting system which - for this reason - is designed to adaptively select the best model configuration at every forecast session, to be used for each item/store combination. A set of real data based on 19 small and medium sized stores and 156 fresh products was employed to evaluate both quality of forecasting results and their effects on the order planning activity, where sales forecasting is considered as a proxy of the expected demand. Some examples are reported and discussed. Our results confirm that there is no 'one-size-fits-all' forecasting model, whose performance strictly depends on the specific characteristics of the underlying data. This supports the adoption of a data-driven tool to automate the dynamic selection of the most appropriate forecasting model. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Il contributo della modellistica matematica/computazionale alla bioinformatica

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The angle of directional change of tracer trajectories in rotating Rayleigh-Benard convection is studied as a function of the time increment tau between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change theta(t, tau) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Theta(tau) = <vertical bar theta(t, tau)vertical bar > with tau shows a transition from the ballistic regime Theta(tau) similar to tau(c) with c = 1] for tau less than or similar to tau(n), with tau(n) the Kolmogorov timescale, to a scaling with smaller exponent c for tau(n) less than or similar to tau less than or similar to T-L, with T-L the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro greater than or similar to 2.5) and is decreasing for increasing rotation rates when Ro less than or similar to 2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro greater than or similar to 2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro less than or similar to 2.5. In the viscous BLs, the PDFs of theta(t, tau) and scaling properties of Theta (tau) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro greater than or similar to 2.5) or of Ekman type (Ro less than or similar to 2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.

Particle-laden turbulent flows occur in a variety of industrial applications as well as in naturally occurring flows. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we employ a fully-resolved numerical simulation based on a lattice Boltzmann scheme, to investigate turbulent flow with large neutrally buoyant particles in a pipe flow at low Reynolds number and in dilute regimes. The energy input is kept fixed resulting in a Reynolds number based on the friction velocity around 250. Two different particle radii were used giving a particle-pipe diameter ratio of 0.05 and 0.075. The number of particles is kept constant resulting in a volume fraction of 0.54% and 1.83%, respectively. We investigated Eulerian and Lagrangian statistics along with the stresslet exerted by the fluid on the spherical particles. It was observed that the high particle-to-fluid slip velocity close to the wall corresponds locally to events of high energy dissipation, which are not present in the single-phase flow. The migration of particles from the inner to the outer region of the pipe, the dependence of the stresslet on the particle radial positions and a proxy for the fragmentation rate of the particles computed using the stresslet have been investigated.