The daily exposure of social media users to propaganda and disinformation campaigns has reinvigorated the need to investigate the local and global patterns of diffusion of different (mis)information content on social media. Echo chambers and influencers are often deemed responsible of both the polarization of users in online social networks and the success of propaganda and disinformation campaigns. This article adopts a data-driven approach to investigate the structuration of communities and propaganda networks on Twitter in order to assess the correctness of these imputations.

The containment of the invasive species is a widespread problem in the environmental management, with a significant economic impact. We analyze an optimal control model which aims to find the best temporal resource allocation strategy for the removal of an invasive species. We derive the optimality system in the state and control variables and we use the phase-space analysis to provide qualitative insights about the behavior of the optimal solution.

An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s -> 0+ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz-Sobolev spaces associated with Young functions satisfying the \Delta2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.

Some recent results on the theory of fractional Orlicz-Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter s in (0, 1) tends to either of the endpoints of its range are also discussed. This note is based on the papers [1, 2, 3, 4], where additional material and proofs can be found.

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s in (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.

TEOBResumS and SEOBNRv4 are the two existing semianalytical gravitational waveform models for spin-aligned coalescing black hole binaries based on the effective-one-body (EOB) approach. They are informed by numerical relativity simulations and provide the relative dynamics and waveforms from early inspiral to plunge, merger, and ringdown. The central building block of each model is the EOB resummed Hamiltonian. The two models implement different Hamiltonians that are both deformations of the Hamiltonian of a test spinning black hole moving around a Kerr black hole.

In this paper we provide emission estimates due to vehicular traffic via Generic Second Order Models. We generalize them to model road networks with merge and diverge junctions. The procedure consists on solving the Riemann Problem at junction assuming the maximization of the flow and a priority rule for the incoming roads. We provide some numerical results for a single-lane roundabout and we propose an application of the given procedure to estimate the production of nitrogen oxides (NOx) emission rates.

Dissipative kinetic models inspired by neutron transport are studied in a (1+1)-dimensional context: first, in the two-stream approximation, then in the general case of continuous velocities. Both are known to relax, in the diffusive scaling, toward a damped heat equation. Accordingly, it is shown that "uniformly accurate" L-splines discretizations of this parabolic asymptotic equation emerge from well-balanced schemes involving scattering S-matrices for the kinetic models.

We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions.