On the constrained mock-Chebyshev least-squares

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes whose elements mimic as well as possible the Chebyshev-Lobatto points. In this work we use the simultaneous approximation theory to combine the previous technique with a polynomial regression in order to increase the accuracy of the approximation of a given analytic function. We give indications on how to select the degree of the simultaneous regression in order to obtain polynomial approximant good in the uniform norm and provide a sufficient condition to improve, in that norm, the accuracy of the mock-Chebyshev interpolation with a simultaneous regression. Numerical results are provided.Comment: 17 pages, 9 figure

A Fast Active Set Block Coordinate Descent Algorithm for ℓ1\ell_1-regularized least squares

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the $\ell_1$-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe an active set estimate (i.e. an estimate of the indices of the zero variables in the optimal solution) for the considered problem that tries to quickly identify as many active variables as possible at a given point, while guaranteeing that some approximate optimality conditions are satisfied. A relevant feature of the estimate is that it gives a significant reduction of the objective function when setting to zero all those variables estimated active. This enables to easily embed it into a given globally converging algorithmic framework. In particular, we include our estimate into a block coordinate descent algorithm for $\ell_1$-regularized least squares, analyze the convergence properties of this new active set method, and prove that its basic version converges with linear rate. Finally, we report some numerical results showing the effectiveness of the approach.Comment: 28 pages, 5 figure

Spectral filtering for the resolution of the Gibbs phenomenon in MPI applications

open3Polynomial interpolation on the node points of Lissajous curves using Chebyshev series is an e effective way for a fast image reconstruction in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discontinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the interpolating polynomial. In this work, after a description of the Gibbs phenomenon in two dimensions, we present an adaptive spectral filtering process for the resolution of this phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging.openDe Marchi, Stefano; Erb, Wolfgang; Marchetti, Francesco.DE MARCHI, Stefano; Erb, Wolfgang; Marchetti, Francesc

Spectral filtering for the reduction of the Gibbs phenomenon of polynomial approximation methods on Lissajous curves with applications in MPI

Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an effective way for a fast image reconstruction in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discontinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the approximating polynomial. In this work, after a description of the Gibbs phenomenon and classical filtering techniques in one and several dimensions, we present an adaptive spectral filtering process for the resolution of this phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging

Sull’identificazione di un gruppo fittile arcaico dal santuario di San Biagio della Venella (Metaponto)

Le tre statue fittili oggetto di questo studio provengono dal santuario di San Biagio alla Venella, nel territorio di Metaponto, e precisamente da un unico deposito votivo ubicato al suo interno. Per ragioni di ordine tecnico e iconografico, queste statue appaiono legate da un comune denominatore. Per altro verso, in virtù delle medesime connotazioni, esse si differenziano da tutti gli altri esemplari noti che compongono il corpus della statuaria fittile metapontina e, più in generale, di area ionica. Questa ricerca propone un esame specifico di questi tre manufatti, finalizzato a un migliore inquadramento della loro cronologia e ascendenza stilistica e delle valenze simboliche da esse rivestite. In particolare, un aspetto specifico che sarà approfondito riguarda la possibilità che le statue in questione appartenessero a un sistema semantico unitario, cioè a un gruppo

An Active-Set Algorithmic Framework for Non-Convex Optimization Problems over the Simplex

In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new "nonorthogonality" type of condition. We prove global convergence to stationary points when using an Armijo line search in the given framework. We further describe three different examples of active-set gradient related directions that guarantee linear convergence rate (under suitable assumptions). Finally, we report numerical experiments showing the effectiveness of the approach.Comment: 29 pages, 3 figure

Farm Size Adjustment and Contract Regulation (I. #203/82): Evidence From an Italian Case Study

In Italy, the structure of farm has always shown remarkable elements of weakness. Among these, the small dimension, in terms of arable land, has represented one of the most difficult to resolve. The absence of a legislation that could favour jointness of the property have remarkably reduced the market of the land. In this scenario, a new law n. 203/1982 was lunched. Now farmers are considering rent land a possible strategy to increase hectares. The object of this paper is to analyse the situation of land contract in Campania Region. A better understanding of these topics should improve public policies for a better adjustment process.Adjustment process, contract regulation, farm structure, rented land, Farm Management,

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network

Numerical and experimental characterization of a railroad switch machine

This contribution deals with the numerical and experimental characterization of the structural behavior of a railroad switch machine. Railroad switch machines must meet a number of safety-related conditions such as, for instance, exhibiting the appropriate resistance against any undesired movements of the points due to the extreme forces exerted by a passing train. This occurrence can produce very high stress on the components, which has to be predicted by designers. In order to assist them in the development of new machines and in defining what the critical components are, FEA models have been built and stresses have been calculated on the internal components of the switch machine. The results have been validated by means of an ad-hoc designed experimental apparatus, now installed at the facilities of the Department of Industrial Engineering of the University of Bologna. This apparatus is particularly novel and original, as no Standards are available that provide recommendations for its design, and no previous studies have dealt with the development of similar rigs. Moreover, it has wide potential applications for lab tests aimed at assessing the safety of railroad switch machines and the fulfilment of the specifications by many railway companies