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.

Using a recently introduced method [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a nonlocal-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging.

Using the new methodology introduced in a recent paper [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian level. We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics.

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 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.

In order to solve Prandtl--type equations we propose a collocation--quadrature method based on de la Vallée Poussin (briefly VP) filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder--Zygmund spaces of locally continuous functions. With respect to classical methods based on Lagrange interpolation at the same collocation nodes, we succeed in reproducing the optimal convergence rates of the L2 case and cut off the typical log factor which seemed inevitable dealing with uniform norms.

Population genetics focuses on the analysis of genetic differences within and between-group of individuals and the inference of the populations' structure. These analyses are usually carried out using Bayesian clustering or maximum likelihood estimation algorithms that assign individuals to a given population depending on specific genetic patterns. Although several tools were developed to perform population genetics analysis, their standard graphical outputs may not be sufficiently informative for users lacking interactivity and complete information.

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the epsilon-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis.

Tumor resistance to chemotherapy represents an important challenge in modern oncology. Although platinum (Pt)-based drugs have demonstrated excellent therapeutic potential, their effectiveness in a wide range of tumors is limited by the development of resistance mechanisms. One of these mechanisms includes increased cisplatin sequestration/efflux by the copper-transporting ATPase, ATP7B. However, targeting ATP7B to reduce Pt tolerance in tumors could represent a serious risk because suppression of ATP7B might compromise copper homeostasis, as happens in Wilson disease.