In this work, we consider a scenario in which we have to monitor some locations of interest in a geographical area by means of a wireless sensor network. Our aim is to keep the network operational for as long as possible, while preventing certain sensors from being active simultaneously, since they would interfere with one another causing data loss, need for retransmissions and overall affecting the throughput and efficiency of the network. We propose an exact approach based on column generation, as well as a heuristic algorithm to solve its separation problem. Computational tests prove our approach to be effective, and that the introduction of our heuristic in the Column Generation framework allows significant gains in terms of required computational effort.

According to the European Charter for Researchers «all researchers should ensure [...] that the results of their research are disseminated and exploited, e.g. communicated, transferred into other research settings or, if appropriate, commercialised ...». Therefore, it's part of the researchers' mission to raise the general public awareness with respect to science. This need is further emphasized by a survey of Eurobarometer 2010: society is strongly interested in science but, at the same time, is often scared by the risks connected with new technologies. Moreover, irrational attitudes towards science are prompted by a broad scientific illiteracy. The result is a remarkable distance between the community of scientists and the society at large. Mathematics, in this context, has a peculiarity: on one hand, it is seen as less ``dangerous'' than other sciences, as it is not directly related to current issues perceived as controversial and potentially risky (for example, Ogm or nuclear power). On the other hand, however, too often it is seen as a dry, cold discipline, very far from everyday life, with results determined by who knows millennia ago, and not susceptible of review. One more reason to communicate it. In a time when innovation, technological progress and, ultimately, the well-being of a society depend decisively on the mathematical culture that this society can express, the widespread ignorance of the basics of mathematics is politically, socially and culturally dangerous: raising the percentage of people who dominate at least its basics can be an important engine to accelerate the transition to an authentic ``knowledge society''.

The change in interest from identifying individual molecules to several components in biological samples as well as how they interact is addressed by systems biology. Mathematical, statistical, and computational methods have emerged to deal with the biological complexity exposed in past years by the massive production of high-throughput data through "omics" technologies. This chapter discusses powerful mathematical networks and modeling to identify key components related to rheumatoid arthritis and how to predict the response of different individuals to infections. As the consequence of a better understanding of biological processes, this chapter also presents the creation of new specific devices to diagnosis, treat, and prevent diseases. These nonnatural systems, produced by the insertion of genetic devices into a cell or cell-free systems, or even by editing a genome, are part of the synthetic biology field. The use of synthetic molecules or systems is discussed as attempts to diagnosis and treat cancer, Lyme disease, Ebola, and human immunodeficiency virus, among others. The chapter describes a diversity of ways in which systems and synthetic biology may help understand and control diseases.

In this work, we consider a special choice of sliding vector field on the intersection of two co-dimension 1 manifolds. The proposed vector field, which belongs to the class of Filippov vector fields, will be called moments vector field and we will call moments trajectory the associated solution trajectory. Our main result is to show that the moments vector field is a well defined, and smoothly varying, Filippov sliding vector field on the intersection Σ of two discontinuity manifolds, under general attractivity conditions of Σ. We also examine the behavior of the moments trajectory at first order exit points, and show that it exits smoothly at these points. Numerical experiments illustrate our results and contrast the present choice with other choices of Filippov sliding vector field.

In this paper, we consider selection of a sliding vector field of Filippov type on a discontinuity manifold Σ of co-dimension 3 (intersection of three co-dimension 1 manifolds). We propose an extension of the moments vector field to this case, and—under the assumption that Σ is nodally attractive—we prove that our extension delivers a uniquely defined Filippov vector field. As it turns out, the justification of our proposed extension requires establishing invertibility of certain sign matrices. Finally, we also propose the extension of the moments vector field to discontinuity manifolds of co-dimension 4 and higher.

We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in the Heston model, showing the reliability and the efficiency of the algorithm.

We study a hybrid tree/finite-difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.

Within the theoretical framework of the numerical stability analysis for the Volterra integral equations, we consider a new class of test problems and we study the long-time behavior of the numerical solution obtained by direct quadrature methods as a function of the stepsize. Furthermore, we analyze how the numerical solution responds to certain perturbations in the kernel.

An algorithm for computing the antitriangular factorization of symmetric matrices, relying only on orthogonal transformations, was recently proposed. The computed antitriangular form straightforwardly reveals the inertia of the matrix. A block version of the latter algorithm was described in a different paper, where it was noticed that the algorithm sometimes fails to compute the correct inertia of the matrix.In this paper we analyze a possible cause of the failure of detecting the inertia and propose a procedure to recover it. Furthermore, we propose a different algorithm to compute the antitriangular factorization of a symmetric matrix that handles most of the singularities of the matrix at the very end of the algorithm.Numerical results are also given showing the reliability of the proposed algorithm.

Classical results from spectral theory of stationary linear kinetic equations are applied to efficiently approximate two physically relevant weakly nonlinear kinetic models: a model of chemotaxis involving a biased velocity-redistribution integral term, and a Vlasov-Fokker-Planck (VFP) system. Both are coupled to an attractive elliptic equation producing corresponding mean-field potentials. Spectral decompositions of stationary kinetic distributions are recalled, based on a variation of Case's elementary solutions (for the first model) and on a Sturm-Liouville eigenvalue problem (for the second one). Well-balanced Godunov schemes with strong stability properties are deduced. Moreover, in the stiff hydrodynamical scaling, an hybridized algorithm is set up, for which asymptotic-preserving properties can be established under mild restrictions on the computational grid. Several numerical validations are displayed, including the consistency of the VFP model with Burgers-Hopf dynamics on the velocity field after blowup of the macroscopic density into Dirac masses. (C) 2016 Elsevier Inc. All rights reserved.

In this paper, a general approach to de la Vallée Poussin means is given and the resulting near best polynomial approximation is stated by developing simple sufficient conditions to guarantee that the Lebesgue constants are uniformly bounded. Not only the continuous case but also the discrete approximation is investigated and a pointwise estimate of the generalized de Vallée Poussin kernel has been stated to this purpose. The theory is illustrated by several numerical experiments.

Mortality models play a basic role in the evaluation of longevity risk by demographers and actuaries. Their performance strongly depends on the different patterns shown by mortality data in different countries. A comprehensive quantitative comparison of the most used methods for forecasting mortality is presented, aimed at evaluating both the goodness of fit and the forecasting performance of these mortality models on Italian demographic data. First, the classical Lee-Carter model is compared to some generalizations that change the order of Singular Value Decomposition approximation and include cohort effects. Then one-way and two-way functional data approaches are considered. Such an analysis extends the current literature on Italian mortality data, on both the number of considered models and their rigorous assessment. Results indicate that generally functional models outperform the classical ones; unfortunately, even if the cohort effect is quite substantial, a suitable procedure for its robust and efficient evaluation is yet to be proposed. To this end, a viable correction for cohort effects is suggested and its performance tested on some of the presented models.

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier- Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filter- ing, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

The largest part of the Earth's atmosphere ozone is located in the stratosphere, forming the so-called ozone layer. This layer played a key role in the development of life on Earth and still protects the planet from the most Dangerous ultraviolet radiation. After the discovery of the high ozone depletion potential of some anthropogenic origin substances (e.g. chlorofluorocarbons), some limitations in the production of the major ozone-depleting substances (ODS) have been applied with the Montreal Protocol in 1987. The reduction of the ODS concentrations in the stratosphere started in the mid-1990s and, thereafter, the stratospheric ozone layer should have started its recovery. In the attempt to detect this recovery we use the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) measurements to estimate the stratospheric ozone trend in the mission period (July 2002 - April 2012). In particular, we use MIPAS products generated with Version 7 of the Level 2 (L2v7) algorithm operated by the European Space Agency. The L2v7 data are based on the MIPAS Level 1b radiances Version 7. These radiances are calculated with an improved radiometric calibration that exploits a time-dependent non-linearity correction scheme. After this correction the residual drift of the calibration error is smaller than 1% across the entire mission, thus allowing to determine accurate trend estimates.

In this paper we revisit the problem of finding an orthogonal similarity transformation that puts an $n\times n$ matrix $A$ in a block upper-triangular form that reveals its Jordan structure at a particular eigenvalue $\lambda_0$. The obtained form in fact reveals the dimensions of the null spaces of $(A-\lambda_0 I)^i$ at that eigenvalue via the sizes of the leading diagonal blocks, and from this the Jordan structure at $\lambda_0$ is then easily recovered. The method starts from a Hessenberg form that already reveals several properties of the Jordan structure of $A$. It then updates the Hessenberg form in an efficient way to transform it to a block-triangular form in ${\cal O}(mn^2)$ floating point operations, where $m$ is the total multiplicity of the eigenvalue. The method only uses orthogonal transformations and is backward stable. We illustrate the method with a number of numerical examples.

The paper proposes a new methodological approach for the product performance analysis into the actuarial context. Two indexes are proposed as restyled versions of the corresponding most popular ones: They have been adapted into the actuarial assessment preserving the plainness in the interpretation of the numerical results. The paper offers a practical implementation of the new approach in the case of a specific contract, containing itself innovative profiles: It concerns a life annuity in which the installments are scaled by a demographic index and contains an embedded option linked to the financial profit participating quota. It is a new life product linked at the same time to the financial and demographic volatility. The product project is studied in its profitability performance assuming stochastic hypotheses for the financial and demographic systematic risks. The indexes are implemented in a conditional quantile simulated framework and tables and graphs illustrate their trends as function of time. The results give an example of the usefulness of the proposed indexes in the phase of decisions about the product design feasibility. Moreover some suggestions concerning the consumer's perception of the contract profitability are obtained by means of a utility-equivalent fixed annuity.

Within the framework of general relativity, we investigate the tidal acceleration of astrophysical jets relative to the central collapsed configuration ("Kerr source"). To simplify matters, we neglect electromagnetic forces throughout; however, these must be included in a complete analysis. The rest frame of the Kerr source is locally defined via the set of hypothetical static observers in the spacetime exterior to the source. Relative to such a fiducial observer fixed on the rotation axis of the Kerr source, jet particles are tidally accelerated to almost the speed of light if their outflow speed is above a certain threshold, given roughly by one-half of the Newtonian escape velocity at the location of the reference observer; otherwise, the particles reach a certain height, reverse direction and fall back toward the gravitational source.

In this paper we are concerned with the simulation of crowds in built environments, where obstacles play a role in the dynamics and in the interactions among pedestrians. First of all, we review the state-of-the-art of the techniques for handling obstacles in numerical simulations. Then, we introduce a new modeling technique which guarantees both impermeability and opacity of the obstacles, and does not require ad hoc runtime interventions to avoid collisions. Most important, we solve a complex optimization problem by means of the Particle Swarm Optimization method in order to exploit the so-called Braess's paradox. More precisely, we reduce the evacuation time from a room by adding in the walking area multiple obstacles optimally placed and shaped.

A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces

We derive a rule for the reconstruction of the internal heat transfer coefficient hint of a pipe, from temperature maps collected on the external face. The pipe is subjected to internal heating by connecting two electrodes to the external surface. To estimate hint we apply the perturbation theory to a thin plate approximation of a boundary value problem for the stationary heat equation.[object Object]