In network analysis, many community detection algorithms have been developed. However, their implementation leaves unaddressed the question of the statistical validation of the results. Here, we present robin (ROBustness In Network), an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability.

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori.

Spectral emissivity is a key property of the Earth surface of which only very few measurements exist so far in the far-infrared (FIR) spectral region, even though recent work has shown its FIR contribution is important for accurate modelling of global climate. The European Space Agency's 9th Earth Explorer, FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) will provide the first global spectrally resolved measurements of the Earth's top-of-the-atmosphere (TOA) spectrum in the FIR.

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.

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents.

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.

We numerically study the dynamics of a polydisperse double emulsion under a symmetric shear flow. We show that both dispersity and shear rate crucially affect the behavior of the innermost drops and of the surrounding shell.

Convergence of new quadrature rules for approximating the Hilbert transform are given. Numerical tests show the goodness of such approximations