Real-world facility planning problems often require to tackle simultaneously network connectivity and zonal requirements, in order to guarantee an equitable provision of services and an efficient flow of goods, people and information among the facilities. Nonetheless, such challenges have not been addressed jointly so far. In this paper we explore the introduction of advanced network connectivity features and spatial-related requirements within Covering Location Problems.

This article is concerned with the rigorous justification of the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main peculiarity of this work with respect to previous studies is that no (regularizing) viscosity contribution is added to the fluid-dynamics equations and only diffusivity effects are included.

We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in ?H1- (R2) ? ?H s(R2) with s > 3 and for any 0 < < 1. Such result improves the existing literature, where the asymptotic stability is proved for initial perturbations belonging at least to H20(R2). More precisely, the aim of the article is threefold. First, we provide a simplified and improved proof of global-in-time well-posedness of the Boussinesq equations with strongly damped vorticity in H1- (R2)?

We present a mathematical model describing the evolution of sea ice and meltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h(x,t) and pond depth w(x,t) fields. The model is similar, in principle, to the one put forward by Luthije et al. (2006), but it features i) a modified melting term, ii) a non-uniform seepage rate of meltwater through the porous ice medium and a minimal coupling with the atmosphere via a surface wind shear term, ?s (Scagliarini et al. 2020).

In a subsoil bioremediation intervention air or oxygen is injected in the polluted region and then a model for unsaturated porous media it is required, based on the theory of the dynamics of multiphase fluids in porous media. In order to optmize the costs of the intervention it is useful to consider the gas as compressible and this fact introduces nonlinearity in the mathematical model. The physical problem is described by a system of equations and the unknowns are: pollutant; bacteria concentration; oxygen saturation and oxygen pressure.

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes.

We study the consistency and the oracle properties of the adaptive Lasso estimator for the coefficients of a linear AR(p) time series with a strictly stationary white noise (not necessarily described by i.i.d. r.v.'s). We apply the results to INAR(p) time series and to the non-parametric inference of the fertility function of a Hawkes point process. We present some numerical simulations to emphasize the advantages of the proposed procedure with respect to more classical ones and finally we apply it to a set of epidemiological data

This paper investigates the model for pedestrian flow firstly proposed in [Cristiani, Priuli, and Tosin, SIAM J. Appl. Math., 75:605-629, 2015]. The model assumes that each individual in the crowd moves in a known domain, aiming at minimizing a given cost functional. Both the pedestrian dynamics and the cost functional itself depend on the position of the whole crowd. In addition, pedestrians are assumed to have predictive abilities, but limited in time.