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.

Consider the problem of computing an approximate solution of an overdetermined system of linear equations. The usual approach to the problem is least squares, in which the 2--norm of the residual isminimized. This produces the minimum variance unbiased estimator of the solution when the errors in the observations are independent and normally distributed with mean 0 and constant variance. It is well known, however, that the least squares solution is not robust if outliers occur, i.e., if some of the observations are contaminated by large error. In this case, alternate approaches have been proposed which judge the size of the residual in a way that is less sensitive to these components. These include the Huber M-function, the Talwar function, the logistic function, the Fair function, and the $\ell_1$ norm. In this paper, new algorithms are proposed to compute the solution to these problems efficiently, in particular when the matrix $A$ has small displacement rank. Matrices with small displacement rank include matrices that are Toeplitz, block-Toeplitz, block-Toeplitz with Toeplitz blocks, Toeplitz plus Hankel, and a variety of other forms. For exposition, only Toeplitz matrices are considered here, but the ideas apply to all matrices with small displacement rank. Algorithms are also presented to compute the solution efficiently when a regularization term is included to handle the case when the matrix of the coefficients is ill-conditioned or rank-deficient. The techniques are illustrated on a problem of FIR system identification.

In this paper we will present a general framework for solving linear systems of equations. The solver is based on the Levinson-idea for solving Toeplitz systems of equations. We will consider a general class of matrices, defined as the class of simple $ (p_1,p_2)$-Levinson conform matrices. This class incorporates, for instance, semiseparable, band, companion, arrowhead and many other matrices. For this class, we will derive a solver of complexity $O(p_1 p_2 n).$ The system solver is written inductively, and uses in every step k, the solution of a so-called $k$-th order Yule-Walker-like equation. The algorithm obtained first has complexity algorithm $O(p_1 p_2 n^2).$ Based, however on the specific structure of the simple $ (p_1,p_2)$-Levinson conform matrices, we will be able to further reduce the complexity of the presented method, and get an order $O(p_1 p_2 n)$ algoritm. Different examples of matrices are given for this algorithm. Examples are presented for: general dense matrices, upper triangular matrices, higher order generator semiseparable matrices, quasiseparable matrices, Givens-vector representable semiseparable matrices, band matrices, companion matrices, confederate matrices, arrowhead matrices, fellow matrices and many more. Finally, the relation between this method and an upper triangular factorization of the original matrix is given and also details concerning possible look ahead methods are presented.

Magnetic resonance spectroscopic imaging (MRSI) provides information about the spatial metabolic heterogeneity of an organ in the human body. In this way, MRSI can be used to detect tissue regions with abnormal metabolism, e.g. tumor tissue. The main drawback of MRSI in clinical practice is that the analysis of the data requires a lot of expertise from the radiologists. In this article, we present an automatic method that assigns each voxel of a spectroscopic image of the brain to a histopathological class. The method is based on Canonical Correlation Analysis (CCA), which has recently been shown to be a robust technique for tissue typing. In CCA, the spectral as well as the spatial information about the voxel is used to assign it to a class. This has advantages over other methods that only use spectral information since histopathological classes are normally covering neighbouring voxels. In this paper, a new CCA-based method is introduced in which MRSI and MR imaging information is integrated. The performance of tissue typing is compared for CCA applied to the whole MR spectra and to sets of features obtained from the spectra. Tests on simulated and in vivo MRSI data show that the new method is very accurate in terms of classification and segmentation. The results also show the advantage of combining spectroscopic and imaging data.

The physical behavior of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudopotential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100).

We consider pointwise mean squared errors of several known Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coe±cients is a mixture of an atom of probability zero and a Gaussian density. We show that for the properly chosen hyperparameters of the prior, all the three estimators are (up to a log-factor) asymptotically minimax within any prescribed Besov ball. We discuss the Bayesian paradox and compare the results for the pointwise squared risk with those for the global mean squared error