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.

This paper provides a unified point of view on fractional perimeters and Riesz potentials. Denoting byH? - for ? 2 .0; 1/ - the ?-fractional perimeter and by J ? - for ? 2 .(d; 0)- the ?-Riesz energies acting on characteristic functions, we prove that both functionals can be seen as limits of renormalized self-attractive energies as well as limits of repulsive interactions between a set and its complement. We also show that the functionals H? and J ? , up to a suitable additive renormalization diverging when ? ? 0, belong to a continuous one-parameter family of functionals, which for ? D 0 gives back a new object we refer to as 0-fractional perimeter. All the convergence results with respect to the parameter ? and to the renormalization procedures are obtained in the framework of A-convergence. As a byproduct of our analysis, we obtain the isoperimetric inequality for the 0-fractional perimeter.

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.

Up-to-date computational glaciology is very often basing its investigations about glacier flow on the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and on the "brute force" adaptation of the Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, a modelling effort is worth in order to include the normal stress gradient effects which are not covered by such a power law model and are indeed physically significant in the case of moraine ice and rock glaciers. In this trend Kannan, Mansutti and Rajagopal have proposed (2021) a mathematical numerical model which has been successfully challenged on the reproduction of borehole deformation measurements of the Murtel-Corvatsch rock glacier on the Grisons Alps, Switzerland. This case, and possibly other numerical results at the present time in progress, will be discussed.

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.

In this paper, we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidence. In addition, it permits us to investigate in detail the hydrodynamic phenomena occurring during breakup stages. Finally, a suitable deformation parameter is introduced and analyzed to characterize the state of deformation of the system by inspecting pairs of interacting droplets flowing in the narrow channel.

We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle $\theta$. The ratio between deterministic and stochastic rupture times, though, decreases with $\theta$. Finally, we discuss the case of fluctuating thin film dewetting on chemically patterned substrates and its dependence on the form of the wettability gradients.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by Brownian multi-particle collision dynamics. Different scenarios will be considered: tethered polymers subject to an external force, chains under steady shear flow [1], and filaments with either both [2] or one fixed end [3] under oscillatory shear flow. The results of the numerical studies will be presented and discussed. [1] A. Lamura and R. G. Winkler, Semiflexible polymers under external fields confined to two dimensions, J. Chem. Phys. 137, 244909 (2012) [2] A. Lamura and R. G. Winkler, Tethered semiflexible polymer under large amplitude oscillatory shear, Polymers 11, 737 (2019) [3] A. Lamura, R. G. Winkler, and G. Gompper, Wall-anchored semiflexible polymer under oscillating shear flow, pre-print (2020)

A mm thick free-standing gel containing lipid vesicles made of 2-oleoyl-1-palmitoyl-sn-glycero-3-phosphocholine (POPC) was studied by scanning Small Angle X-ray Scattering (SAXS) and X-ray Transmission (XT) microscopies. Raster scanning relatively large volumes, besides reducing the risk of radiation damage, allows signal integration, improving the signal-to-noise ratio (SNR), as well as high statistical significance of the dataset. The persistence of lipid vesicles in gel was demonstrated, while mapping their spatial distribution and concentration gradients. Information about lipid aggregation and packing, as well as about gel density gradients, was obtained.A posterioriconfirmation of lipid presence in well-defined sample areas was obtained by studying the dried sample, featuring clear Bragg peaks from stacked bilayers. The comparison between wet and dry samples allowed it to be proved that lipids do not significantly migrate within the gel even upon drying, whereas bilayer curvature is lost by removing water, resulting in lipids packed in ordered lamellae. Suitable algorithms were successfully employed for enhancing transmission microscopy sensitivity to low absorbing objects, and allowing full SAXS intensity normalization as a general approach. In particular, data reduction includes normalization of the SAXS intensity against the local sample thickness derived from absorption contrast maps. The proposed study was demonstrated by a room-sized instrumentation, although equipped with a high brilliance X-ray micro-source, and is expected to be applicable to a wide variety of organic, inorganic, and multicomponent systems, including biomaterials. The employed routines for data reduction and microscopy, including Gaussian filter for contrast enhancement of low absorbing objects and a region growing segmentation algorithm to exclude no-sample regions, have been implemented and made freely available through the updated in-house developed software SUNBIM.

Background: The high contagiousness and rapid spreading of the coronavirus disease 2019 (COVID-19) has caused a high number of critical to severe life-threatening cases, which required urgent hospital admission and treatment in intensive care units (ICUs). The pandemic has been a tough test for all European national health systems and their capability to provide an adequate reaction. Methods: The present work aims to reveal correlations between parameters such as COVID-19 incidence, ICU bed occupancy, ICU excess area, and mortality in Italian regions. Public data for the period of March 1 to July 16, 2020, were analyzed using several mathematical and statistical methods. Results: The analysis defined two separate groups of Italian regions. The examined variables considered within these groups were interlinked and dependent on each other. The regions of the two groups shared the same kind of fitted model (linear) explaining mortality as a function of cumulative incidence, but with higher value of the constant in one group, so characterized by a high intrinsic "strength" of the pandemic, certainly playing a major role in the generation of a large number of severe and life-threatening cases. These results are confirmed at European level. Other factors may condition mortality and be linked to incidence, such as ICU saturation and excess. Conclusions: These quantitative results could be a very helpful tool to set up preventive measures and optimize biomedical interventions before the pandemic, in its recurrent waves, could overcome the reaction capacity of any public health system.