We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length h of integration and that it recovers the continuous dynamic as h tends to zero.

Personalized medicine (PM) moves at the same pace of data and technology and calls for important changes in healthcare. New players are participating, providing impulse to PM. We review the conceptual foundations for PM and personalized healthcare and their evolution through scientific publications where a clear definition and the features of the different formulations are identifiable. We then examined PM policy documents of the International Consortium for Personalised Medicine and related initiatives to understand how PM stakeholders have been changing.

We consider here a cell-centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity, a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations.

We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of s-fractional perimeter, defined for 0<s<1, to the case s>=1. We show that, as the core-radius vanishes, such core-radius regularized s-fractional perimeters, suitably scaled, ?-converge to the standard Euclidean perimeter.

The Dirichlet-Ferguson measure is a random probability measure that has seen widespread use in Bayesian nonparametrics. Our main results can be seen as a first step towards the development of a stochastic analysis of the Dirichlet-Ferguson measure. We define a gradient that acts on functionals of the measure and derive its adjoint. The corresponding integration by parts formula is used to prove a covariance representation formula for square integrable functionals of the Dirichlet-Ferguson measure and to provide a quantitative central limit theorem for the first chaos.

The COVID-19 pandemic triggered a global research effort to define and assess timely and effective containment policies. Understanding the role that specific venues play in the dynamics of epidemic spread is critical to guide the implementation of fine-grained non-pharmaceutical interventions (NPIs). In this paper, we present a new model of context-dependent interactions that integrates information about the surrounding territory and the social fabric.

Network embedding, also known as network representation learning, aims at defining low-dimensional, continuous vector representation of nodes to maximally preserve the network structure. Recent efforts attempt to extend network embedding to attributed networks where nodes are enriched with descriptors, to enhance interpretability. However, most of these efforts seldom consider the additional knowledge relevant to the aim of the downstream network analysis, i.e. task-related information. When they do, they are analysis-specific and thus lack adaptability to alternative tasks.

Here some issues are studied, related to the numerical solution of Richards' equation in a one dimensional spatial domain by a technique based on the Transversal Method of Lines (TMoL). The core idea of TMoL approach is to semi-discretize the time derivative of Richards' equation: afterward a system of second order differential equations in the space variable is derived as an initial value problem. The computational framework of this method requires both Dirichlet and Neumann boundary conditions at the top of the column. The practical motivation for choosing such a condition is argued.

This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by epsilon the length scale parameter in such models, we focus on the vertical bar log epsilon VERBAR; energy regime.

The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy, the dissipation, and the squared H -1 distance to a kink.