The method of simulated quantiles is extended to a general multivariate framework and to provide sparse estimation of the scaling matrix. The method is based on the minimisation of a distance between appropriate statistics evaluated on the true and synthetic data simulated from the postulated model. Those statistics are functions of the quantiles providing an effective way to deal with distributions that do not admit moments of any order like the α–Stable or the Tukey lambda distribution. The lack of a natural ordering represents the major challenge for the extension of the method to the multivariate framework, which is addressed by considering the notion of projectional quantile. The SCAD 1–penalty is then introduced in order to achieve sparse estimation of the scaling matrix which is mostly responsible for the curse of dimensionality. The asymptotic properties of the proposed estimator have been discussed and the method is illustrated and tested on several synthetic datasets simulated from the Elliptical Stable distribution for which alternative methods are recognised to perform poorly.

How can Science be told in, and with comics, if ever? In recent years, the CNR Edizioni Comics&Science label tried to answer this question with a variety of projects, all spawned by the all-time classic comic book format. Let us recapitulate, with an open eye on future developments.

We consider a variational model analyzed in March and Riey (Inverse Probl Imag 11(6): 997-1025, 2017) for simultaneous video inpainting and motion estimation. The model has applications in the field of recovery of missing data in archive film materials. A gray-value video content is reconstructed in a spatiotemporal region where the video data is lost. A variational method for motion compensated video inpainting is used, which is based on the simultaneous estimation of apparent motion in the video data. Apparent motion is mathematically described by a vector field of velocity, denoted optical flow, which is estimated through gray-value variations of the video data. The functional to be minimized is defined on a space of vector valued functions of bounded variation and the relaxation method of the Calculus of Variations is used. We introduce in the functional analyzed in March and Riey(Inverse Probl Imag 11(6): 997-1025, 2017) a suitable positive weight, and we show that diagonal minimizing sequences of the functional converge, up to subsequences as the weight tends to infinity, to minimizers of an appropriate limit functional. Such a limit functional is the relaxed version of a functional, modified with suitable improvements, proposed by Lauze and Nielsen (2004) and which permits an accurate joint reconstruction both of the optical flow and of the video content.

In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs. The results are based on a general convergence analysis theory applied to the class of AMG methods employing unsmoothed aggregation and identifying a quality measure for the coarsening; similar quality measures were originally introduced and applied to other methods as tools to obtain good quality aggregates leading to optimal convergence for M-matrices. The analysis, as well as the coarsening procedure, is purely algebraic and, in our case, allows an a posteriori evaluation of the quality of the aggregation procedure which we apply to analyze the impact of approximate algorithms for matching computation and the definition of graph edge weights. We also explore the connection between the choice of the aggregates and the compatible relaxation convergence, confirming the consistency between theories for designing coarsening procedures in purely algebraic multigrid methods and the effectiveness of the coarsening based on compatible weighted matching. We discuss various completely automatic algorithmic approaches to obtain aggregates for which good convergence properties are achieved on various test cases.

A reaction-diffusion system governing the prey-predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

In this study, we computationally corroborate the flow of rock glaciers against borehole measurements, within the context of a model previously developed (2020). The model is, here, tested against the simulation of the sliding motion of the Murtel-Corvatsch alpine glacier, which is characterized in detail in the literature with internal structure description and borehole deformations measurement. The capability of the model to take into account the composition of the rock glacier, as a mixture of ice and rock and sand grains with the local impact of pressure and heat transfer, results in the accurate detection of the internal sliding. With careful calibration of the model parameters, the computed numerical solution of the model reports a relative error of 1.8% and of 0.3% in the reproduction of the measured shear zone velocity and of the ratio of measured shear zone deformation over top surface deformation, respectively. Furthermore a deeper understanding of the role of the model parameters involved in the simulation of such a process is also gained and we discuss the same in detail.

The Fokker--Planck approximation for an elementary linear, two-dimensional kinetic model endowed with a mass-preserving integral collision process is numerically studied, along with its diffusive limit. In order to set up a well-balanced discretization relying on an $S$-matrix, exact steady states of the continuous equation are derived. The ability of the scheme to keep these stationary solutions invariant produces the discretization of the local differential operator which mimics the collision process. The aforementioned scheme can be reformulated as an implicit-explicit one, which is proved to be both well-balanced and asymptotic-preserving in the diffusion limit. Several numerical benchmarks, computed on coarse grids, are displayed so as to illustrate the results.

First-degree relatives (FDRs) of type 2 diabetics (T2D) feature dysfunction of subcutaneous adipose tissue (SAT) long before T2D onset. miRNAs have a role in adipocyte precursor cells (APC) differentiation and in adipocyte identity. Thus, impaired miRNA expression may contribute to SAT dysfunction in FDRs. In the present work, we have explored changes in miRNA expression associated with T2D family history which may affect gene expression in SAT APCs from FDRs. Small RNA-seq was performed in APCs from healthy FDRs and matched controls and omics data were validated by qPCR. Integrative analyses of APC miRNome and transcriptome from FDRs revealed down-regulated hsa-miR-23a-5p, -193a-5p and -193b-5p accompanied by up-regulated Insulin-like Growth Factor 2 (IGF2) gene which proved to be their direct target. The expression changes in these marks were associated with SAT adipocyte hypertrophy in FDRs. APCs from FDRs further demonstrated reduced capability to differentiate into adipocytes. Treatment with IGF2 protein decreased APC adipogenesis, while over-expression of hsa-miR-23a-5p, -193a-5p and -193b-5p enhanced adipogenesis by IGF2 targeting. Indeed, IGF2 increased the Wnt Family Member 10B gene expression in APCs. Down-regulation of the three miRNAs and IGF2 up-regulation was also observed in Peripheral Blood Leukocytes (PBLs) from FDRs. In conclusion, APCs from FDRs feature a specific miRNA/gene profile, which associates with SAT adipocyte hypertrophy and appears to contribute to impaired adipogenesis. PBL detection of this profile may help in identifying adipocyte hypertrophy in individuals at high risk of T2D.

Mass spectrometry is a widely applied technology with a strong impact in the proteomics field. MALDI-TOF is a combined technology in mass spectrometry with many applications in characterizing biological samples from different sources, such as the identification of cancer biomarkers, the detection of food frauds, the identification of doping substances in athletes' fluids, and so on. The massive quantity of data, in the form of mass spectra, are often biased and altered by different sources of noise. Therefore, extracting the most relevant features that characterize the samples is often challenging and requires combining several computational methods. Here, we present GeenaR, a novel web tool that provides a complete workflow for pre-processing, analyzing, visualizing, and comparing MALDI-TOF mass spectra. GeenaR is user-friendly, provides many different functionalities for the analysis of the mass spectra, and supports reproducible research since it produces a human-readable report that contains function parameters, results, and the code used for processing the mass spectra. First, we illustrate the features available in GeenaR. Then, we describe its internal structure. Finally, we prove its capabilities in analyzing oncological datasets by presenting two case studies related to ovarian cancer and colorectal cancer. GeenaR is available at http://proteomics.hsanmartino.it/geenar/.

The present work is inspired by the recent developments in laboratory experiments madeon chips, where the culturing of multiple cell species was possible. The model is based on coupledreaction-diffusion-transport equations with chemotaxis and takes into account the interactions amongcell populations and the possibility of drug administration for drug testing effects. Our effort isdevoted to the development of a simulation tool that is able to reproduce the chemotactic movementand the interactions between different cell species (immune and cancer cells) living in a microfluidicchip environment. The main issues faced in this work are the introduction of mass-preserving andpositivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passingthrough interfaces between 2D and 1D domains of the chip and the development of mass-preservingand positivity preserving numerical conditions at the external boundaries and at the interfacesbetween 2D and 1D domains.

A (2+2)-dimensional kinetic equation, directly inspired by the run-and-tumble modelingof chemotaxis dynamics is studied so as to derive a both ''2D well-balanced'' and''asymptotic-preserving'' numerical approximation. To this end, exact stationary regimesare expressed by means of Laplace transforms of Fourier-Bessel solutions of associatedelliptic equations. This yields a scattering S-matrix which permits to formulate a timemarchingscheme in the form of a convex combination in kinetic scaling. Then, in thediffusive scaling, an IMEX-type discretization follows, for which the ''2D well-balancedproperty'' still holds, while the consistency with the asymptotic drift-diffusion equation ischecked. Numerical benchmarks, involving ''nonlocal gradients'' (or finite samplingradius), carried out in both scalings, assess theoretical findings. Nonlocal gradients appearto inhibit blowup phenomena.

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. Under the standard hypothesis of Gaussian additive noise, we model the signals by the RADWT and the anomalies as additive in each signal. Then we perform AD imposing a double penalty on the multiple regression model we obtained, promoting group sparsity both on the regression coefficients and on the anomalies. The first constraint preserves a common structure on the underlying signal components; the second one aims to identify the presence/absence of anomalies. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case.

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix's symmetry and the graphs' joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator's consistency property. Finally, we illustrate our estimator's performance through simulated and real data examples on gene regulatory networks.

This article deals with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with bilinear estimates and interpolation inequalities for handling the nonlinearity.

We introduce a new class of robust M-estimators for performing simultaneous parameter estimation and variable selection in high-dimensional regression models. We first explain the motivations for the key ingredient of our procedures which are inspired by regularization methods used in wavelet thresholding in noisy signal processing. The derived penalized estimation procedures are shown to enjoy theoretically the oracle property both in the classical finite dimensional case as well as the high-dimensional case when the number of variables p is not fixed but can grow with the sample size n, and to achieve optimal asymptotic rates of convergence. A fast accelerated proximal gradient algorithm, of coordinate descent type, is proposed and implemented for computing the estimates and appears to be surprisingly efficient in solving the corresponding regularization problems including the case for ultra high-dimensional data where p>> n. Finally, a very extensive simulation study and some real data analysis, compare several recent existing M-estimation procedures with the ones proposed in the paper, and demonstrate their utility and their advantages.

The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a QR sweep and part of a QL sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method.

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded weak solutions by means of a viscous regularization and refined compensated compactness arguments. Second, we investigate the smooth setting by providing a de- tailed description of the impact of the singular pressure on the breakdown of the solutions. In this smooth framework, we rigorously justify the singular limit towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.

We provide a framework to extend the relative entropy method to a class of diffusive relaxation systems with discrete velocities. The methodology is detailed in the toy case of the 1D Jin-Xin model under the diffusive scaling, and provides a direct proof of convergence to the limit parabolic equation in any interval of time, in the regime where the solutions are smooth. Recently, the same approach has been successfully used to show the strong convergence of a vector-BGK model to the 2D incompressible Navier-Stokes equations.

Internal waves describe the (linear) response of an incompressible sta- bly stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the slope has the same inclination as the group velocity. In this paper, we prove that in this critical geometry the weakly viscous and weakly nonlinear wave equations have actually a solution which is well approximated by the sum of the in- cident wave packet, a reflected second harmonic and some boundary layer terms. This result confirms the prediction by Dauxois and Young, and provides precise estimates on the time of validity of this approximation.

In this paper we revisit the problem of performing a QZ step with a so-called perfect shift, which is an exact eigenvalue of a given regular pencil lambdaB-A in unreduced Hessenberg triangular form. In exact arithmetic, the QZ step moves that eigenvalue to the bottom of the pencil, while the rest of the pencil is maintained in Hessenberg triangular form, which then yields a deflation of the given eigenvalue. But in finite precision the QZ step gets blurred and precludes the deflation of the given eigenvalue. In this paper we show that when we first compute the corresponding eigenvector to sufficient accuracy, then the QZ step can be constructed using this eigenvector, so that the deflation is also obtained in finite precision. An important application of this technique is the computation of the index of a system of differential algebraic equations, since an exact deflation of the infinite eigenvalues is needed to impose correctly the algebraic constraints of such differential equations.