Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm. The algorithm is proved to be convergent and an error estimate is also given. Numerical tests on a bidimensional problem show that our algorithm outperforms Tikhonov regularization when the measurements are distorted by high noise.

The purpose of neuroimaging is to investigate the brain functionality through the localization of the regions where bioelectric current flows, starting from the measurements of the magnetic field produced in the outer space. Assuming that each component of the current density vector possesses the same sparse representation with respect to a pre-assigned multiscale basis, regularization techniques to the magnetic inverse problem are applied. The linear inverse problem arising can be approximated by iterative algorithms based on gradient steps intertwined with thresholding operations with joint-sparsity constraints. We propose some numerical tests in order to show the features of the numerical algorithm, also regarding the performance in terms of CPU occupancy.

In this paper we introduce a simulation algorithm based on fluid dynamic models to reproduce the behavior of traffic in a portion of the urban network in Rome. Numerical results, obtained comparing experimental data with numerical solutions, show the effectiveness of our approximation. (c) 2009 Elsevier Inc. All rights reserved.

Neural current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured in the outer space, gives rise to a highly ill-posed and ill-conditioned inverse problem. We use a joint sparsity constraint as a regularization term and we propose an efficient iterative thresholding algorithm to recover the current distribution. Some numerical tests are also displayed.

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured by sophisticated superconducting devices in a noninvasive way, gives rise to a highly ill-posed and ill-conditioned inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. In particular, we use a joint sparsity constraint as a regulariza- tion term and we propose an efficient iterative thresholding algorithm to reconstruct the current distribution. Some bidimensional experiments are presented in order to show the algorithm properties.

Many problems in applied sciences require to spatially resolve an unknown electrical current distribution from its external magnetic field. Electric currents emit magnetic fields which can be measured by sophisticated superconducting devices in a noninvasive way. Applications of this technique arise in several fields, such as medical imaging and non-destructive testing, and they involve the solution of an inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. The solution of linear inverse problems with sparsity constraints can be efficiently obtained by iterative algorithms based on gradient steps intertwined with thresholding operations. We test this algorithms to numerically solve the magnetic inverse problem with a joint sparsity constraint.

We introduce some numerical approximations to a quasilinear problem proposed by G. I. Barenblatt to describe non-equilibrium two-phase fluid flows in permeable porous media, which apply to secondary oil recovery from natural reservoirs. Taking into account the theoretical results of global existence and uniqueness, we approximate the solutions by three numerical schemes, namely, the Diagonal First Order schemes (DFO and DFO2) and the Diagonal Second Order scheme (DSO). For DFO schemes convergence is proved. The schemes' behaviour is analysed and discussed through some numerical experiments.

In this paper we introduce a computation algorithm to trace car paths on road networks, whose load evolution is modeled by conservation laws. This algorithm is composed of two parts: computation of solutions to conservation equations on each road and localization of car position resulting by interactions with waves produced on roads. Some applications and examples to describe the behavior of a driver traveling in a road network are shown. Moreover, a convergence result for wave front tracking approximate solutions, with BV initial data on a single road, is established.

We introduce a simulation algorithm based on a fluid-dynamic model for traffic flows on road networks, which are considered as graphs composed by arcs that meet at some junctions. The approximation of scalar conservation laws along arcs is made by three velocities Kinetic schemes with suitable boundary conditions at junctions. Here we describe the algorithm and we give an example. © 2006 Elsevier B.V. All rights reserved.

This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [ ], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solvers are defined. We study the equilibria of the resulting dynamics, moreover some numerical experiments on sample supply chains are reported. We provide also a comparison, both of equilibria and experiments, with the model of [ ].

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

We introduce new Laguerre-type population dynamics models. These models arise quite naturally by substituting in classical models the ordinary derivatives with the Laguerre derivatives and therefore by using the so called Laguerre-type exponentials instead of the ordinary exponential. The L-exponentials e(n)(t) are increasing convex functions for t >= 0, but increasing slower with respect to exp t. For this reason these functions are useful in order to approximate different behaviors of population growth. We consider mainly the Laguerre-type derivative D(t)tD(t), connected with the L-exponential el(t), and investigate the corresponding modified logistic, Bernoulli and Gompertz models. Invariance of the Volterra-Lotka model is mentioned. (C) 2006 Elsevier Inc. All rights reserved.

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occurr and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which proceeds processing each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

New computation algorithms for a fluid-dynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more efficient method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new method, namely the Fast Shock Fitting method (FSF), based on good theorical properties of the solution of the problem is introduced. Numerical results and efficience tests are presented in order to show the behaviour of FSF in comparison with G, FG and a conservative scheme of second order.

General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.