Visibility has an encompassing importance in humans' perception of the landscape, since the first encounter with a new environment normally occurs through sight. In historical and archaeological studies, two main methods (i.e., the geometric method and the Geographical Information System [GIS] computation) have been employed to determine the distance from which an object can be recognized. However, neither is exhaustive when applied to a maritime context, where the main factor affecting the visibility radius is weather.

An Ermakov-Pinney-like equation associated with the scalar wave equation in curved space-time is here studied. The example of Schwarzschild space-time considered in the present work shows that this equation can be viewed more as a "model equation," with interesting applications in black hole physics. Other applications studied involve cosmological space-times (de Sitter) and pulse of plane gravitational waves: in all these cases the evolution of the Ermakov-Pinney field seems to be consistent with a rapid blow-up, unlike the Schwarzschild case where spatially damped oscillations are allowed.

In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

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.

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 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.

Background: Mutations of the mitochondrial protein paraplegin cause hereditary spastic paraplegia type 7 (SPG7), a so-far untreatable degenerative disease of the upper motoneuron with still undefined pathomechanism. The intermittent mitochondrial permeability transition pore (mPTP) opening, called flickering, is an essential process that operates to maintain mitochondrial homeostasis by reducing intra-matrix Ca and reactive oxygen species (ROS) concentration, and is critical for efficient synaptic function.

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission.