We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential if , if , 0 if .

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 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.

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.

Single-cell RNA-seq (scRNAseq) is a powerful tool to study heterogeneity of cells. Recently, several clustering based methods have been proposed to identify distinct cell populations. These methods are based on different statistical models and usually require to perform several additional steps, such as preprocessing or dimension reduction, before applying the clustering algorithm. Individual steps are often controlled by method-specific parameters, permitting the method to be used in different modes on the same datasets, depending on the user choices.

Background: Immune system conditions of the patient is a key factor in COVID-19 infection survival. A growing number of studies have focused on immunological determinants to develop better biomarkers for therapies. Aim: Studies of the insurgence of immunity is at the core of both SARS-CoV-2 vaccine development and therapies. This paper attempts to describe the insurgence (and the span) of immunity in COVID-19 at the population level by developing an in-silico model.

Pervasive mobile and low-end wireless technologies, such as radio-frequency identification (RFID), wireless sensor networks and the impending vehicular ad-hoc networks (VANETs), make the wireless scenario exciting and in full transformation. For all the above (and similar) technologies to fully unleash their potential in the industry and society, there are two pillars that cannot be overlooked: security and privacy. Both properties are especially relevant if we focus on ad-hoc wireless networks, where devices are required to cooperate - e.g.

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.

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer.

We consider two-dimensional zero-temperature systems of N particles to which we associate an energy of the form E[V](X):=?1?i<j?NV(|X(i)-X(j)|),where X(j) ? R represents the position of the particle j and V(r) ? R is the pairwise interaction energy potential of two particles placed at distance r. We show that under suitable assumptions on the single-well potential V, the ground state energy per particle converges to an explicit constant E¯ [V] , which is the same as the energy per particle in the square lattice infinite configuration.