We present a set of difference equations which represents the discrete counterpart of a large class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of the discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.

We apply the techniques of monotone and relative rearrangements to the non rearrangement invariant spaces Lp(·) (? ) with variable exponent. In particular, we show that the maps u ? L p( ·) (? ) -> k(t )u* ? L p * (·)(0, meas? ) and u ? L p( ·) (? ) -> u* ? Lp* (·) (0, meas? ) are locally ?-Ho?lderian (u * (resp. p* ) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents.

Stationary thermography can be used for investigating the functional form of a nonlinear cooling lawthat describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergence and sensitivity analysis of a finite difference method for the numerical solution of the Cauchy problem for Laplace's equation, based on the Störmer-Verlet scheme.

We present a numerical investigation of a degenerate nonlinear parabolic-elliptic system, which describes the chemical aggression of limestones under the attack of SO_2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as well as some examples of the numerical behavior of the solutions.

The interaction of a Reissner-Nordstro ̈m black hole and a charged massive particle is studied in the framework of perturbation theory. The particle backreaction is taken into account, studying the effect of general static perturbations of the hole following the approach of Zerilli. The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields to first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. The existence of a singularity-free solution of the Einstein-Maxwell system requires that the charge-to-mass ratios of the black hole and of the particle satisfy an equilibrium condition which is in general dependent on the separation between the two bodies. If the black hole is undercritically charged (i.e. its charge-to-mass ratio is less than one), the particle must be overcritically charged, in the sense that the particle must have a charge-to-mass ratio greater than one. If the charge-to-mass ratios of the black hole and of the particle are both equal to one (so that they are both critically charged, or ‘‘extreme’’), the equilibrium can exist for any separation distance, and the solution we find coincides with the linearization in the present context of the well-known Majumdar-Papapetrou solution for two extreme Reissner- Nordstro ̈m black holes. In addition to these singularity-free solutions, we also analyze the corresponding solution for the problem of a massive particle at rest near a Schwarzschild black hole, exhibiting a strut singularity on the axis between the two bodies. The relations between our perturbative solutions and the corresponding exact two-body solutions belonging to the Weyl class are also discussed.

The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains L-y and of the maximum of excess viscosity (Delta eta)(M) is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of gamma(c)similar to 1/t(D) where t(D) is the diffusive time. L-y and (Delta eta)(M) behave as L-y similar to gamma(-alpha) and (Delta eta)(M)similar to gamma(nu) with alpha=alpha(s)=0.18 +/- 0.02, nu=nu(s)=-2.00 +/- 0.01 and alpha=alpha(w)=0.25 +/- 0.01, nu=nu(w)=-0.68 +/- 0.04 in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.

Vehicle routing and scheduling are two main issues in the hazardous material (hazmat) transportation problem. In this paper, we study the problem of managing a set of hazmat transportation requests in terms of hazmat shipment route selection and actual departure time definition. For each hazmat shipment, a set of minimum and equitable risk alternative routes from origin to destination points and a preferred departure time are given. The aim is to assign a route to each hazmat shipment and schedule these shipments on the assigned routes in order to minimize the total shipment delay, while equitably spreading the risk spatially and preventing the risk induced by vehicles traveling too close to each other. We model this hazmat shipment scheduling problem as a job-shop scheduling problem with alternative routes. No-wait constraints arise in the scheduling model as well, since, supposing that no safe area is available, when a hazmat vehicle starts traveling from the given origin it cannot stop until it arrives at the given destination. A tabu search algorithm is proposed for the problem, which is experimentally evaluated on a set of realistic test problems over a regional area, evaluating the provided solutions also with respect to the total route risk and length.

This paper deals with the generation of minimal risk paths for the road transportation of hazardous materials between an origin–destination pair of a given regional area. The main considered issue is the selection of paths that minimize the total risk of hazmat shipments while spreading the risk induced on the population in an equitable way. The problem is mathematically formulated, and two heuristic algorithms are proposed for its solution. Substantially, these procedures are modified versions of Yen's algorithm for the k-shortest path problem, which take into due consideration the risk propagation resulting from close paths and spread the risk equitably among zones of the geographical region in which the transportation network is embedded. Furthermore, a lower bound based on a Lagrangean relaxation of the given mathematical formulation is also provided. Finally, a series of computational tests, referring to a regional area is reported.

A filter based on the Hankel-Lanczos singular value decomposition (HLSVD) technique is presented and applied for the first time to X-ray diffraction (XRD) data. Synthetic and real powder XRD intensity profiles of nanocrystals are used to study the filter performances with different noise levels. Results show the robustness of the HLSVD filter and its capability to extract easily and effciently the useful crystallographic information. These characteristics make the filter an interesting and user-friendly tool for processing of XRD data.

A reliable and automatic method is applied to crystallographic data for tissue typing. The technique is based on canonical correlation analysis, a statistical method which makes use of the spectral-spatial information characterizing X-ray diffraction data measured from bone samples with implanted tissues. The performance has been compared with a standard crystallographic technique in terms of accuracy and automation. The proposed approach is able to provide reliable tissue classification with a direct tissue visualization without requiring any user interaction.

A thermal lattice Boltzmann model for a van der Waals fluid is proposed. In the continuum, the model reproduces at second order of a Chapman-Enskog expansion, the theory recently introduced by A. Onuki (Phys. Rev. Lett. 94, 054501 2005). Phase separation has been studied in a system quenched by contact with external walls. Pressure waves favor the thermalization of the system at initial times and the temperature, soon with respect to typical times of phase separation, becomes homogeneous in the bulk. Alternate layers of liquid and vapor form on the walls and disappear at late times.

Motivation: Epstein-Barr virus (EBV) infects greater than 90% of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative analysis; however, there is no applicable animal model. Computer models may provide a virtual environment to perform experiments not possible in human volunteers. Results: We report the application of a relatively simple stochastic cellular automaton (C-ImmSim) to the modeling of EBV infection. Infected B-cell dynamics in the acute and chronic phases of infection correspond well to clinical data including the establishment of a long term persistent infection (up to 10 years) that is absolutely dependent on access of latently infected B cells to the peripheral pool where they are not subject to immunosurveillance. In the absence of this compartment the infection is cleared. Availability: The latest version 6 of C-ImmSim is available under the GNU General Public License and is downloadable from www.iac. cnr.it/filippo/cimmsim.html Contact: david.thorley-lawson@tufts.edu

A simple and efficient numerical method for solving the advection equation on the spherical surface is presented. To overcome the well-known ‘pole problem’ related to the polar singularity of spherical coordinates, the space discretization is performed on a geodesic grid derived by a uniform triangulation of the sphere; the time discretization uses a semi-Lagrangian approach. These two choices, efficiently combined in a substepping procedure, allow us to easily determine the departure points of the characteristic lines, avoiding any computationally expensive tree-search. Moreover, suitable interpolation procedures on such geodesic grid are presented and compared. The performance of the method in terms of accuracy and efficiency is assessed on two standard test cases: solid-body rotation and a deformation flow.

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.

In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In the first part an $O(p^2n)$ solver for a semiseparable matrix of semiseparability rank $ p$ is derived, and in a second part we derive an $O(l^2n) $solver for a band matrix with bandwidth $ 2l + 1.$ Both solvers are constructed in a similar way: firstly a Yule–Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side. Finally, a combination of the above methods is presented to solve linear systems with semiseparable plus band coefficient matrices. The overall complexity of this solver is $6(l + p)^2 n $ plus lower order terms. In the final section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods.