Networks are pervasive in computer science and in real world applications. It is often useful to leverage distinctive node features to regroup such data in clusters, by making use of a single representative node per cluster. Such contracted graphs can help identify features of the original networks that were not visible before. As an example, we can identify contiguous nodes having the same discrete property in a social network. Contracting a graph allows a more scalable analysis of the interactions and structure of the network nodes.

This manuscript relates to the exploiting of the abstract calculus pattern (ACP) for the (numerical) solution of ordinary differential equation (ODEs) systems, which are ubiquitous mathematical formulations of many physical (dynamical) phenomena. We present FOODIE, a software suite aimed to numerically solve ODE problems by means of a clear, concise, and efficient abstract interface.

Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print.

Machine learning (ML) is increasingly used in cognitive, computational and clinical neuroscience. The reliable and efficient application of ML requires a sound understanding of its subtleties and limitations. Training ML models on datasets with imbalanced classes is a particularly common problem, and it can have severe consequences if not adequately addressed.

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.

Advanced persistent threats (APTs) have rocketed over the last years. Unfortunately, their technical characterization is incomplete--it is still unclear if they are advanced usages of regular malware or a different form of malware. This is key to develop an effective cyberdefense. To address this issue, in this paper we analyze the techniques and tactics at stake for both regular and APT-linked malware. To enable reproducibility, our approach leverages only publicly available datasets and analysis tools. Our study involves 11,651 regular malware and 4686 APT-linked ones.

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ?. Under the classical Miles-Howard stability condition on the Richardson number, we prove that the system experiences a shear-buoyancy instability: the density variation and velocity undergo an O(t-1/2) inviscid damping while the vorticity and density gradient grow as O(t1/2). The result holds at least until the natural, nonlinear timescale t??-2.