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. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, effective one-body, and Delaunay averaging. We determine the full functional structure of the 5PN Hamiltonian (which involves 95 nonzero numerical coefficients), except for two undetermined coefficients proportional to the cube of the symmetric mass ratio, and to the fifth and sixth power of the gravitational constant, G. We present not only the 5PN-accurate, 3PM contribution to the scattering angle but also its 6PN-accurate generalization. Both results agree with the corresponding truncations of the recent 3PM result of Bern et al. [Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019)]. We also compute the 5PN-accurate, fourth-post-Minkowskian (4PM) contribution to the scattering angle, including its nonlocal contribution, thereby offering checks for future 4PM calculations. We point out a remarkable hidden simplicity of the gauge-invariant functional relation between the radial action and the effective-one-body energy and angular momentum.

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. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders G(3) and G(4), and the derived O(G(3)) scattering angle agrees, within our 6PN accuracy, with the computation of [Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.

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. The former is computed as a large-angular-momentum expansion (given here to next-to-next-to-leading order), while the latter is given as a small-eccentricity expansion (given here to the tenth order). We note the appearance of zeta(3) in the nonlocal part of the scattering angle. The averaged Hamiltonian for ellipticlike motions then yields two more gauge-invariant observables: the energy and the periastron precession as functions of orbital frequencies. We point out the existence of a hidden simplicity in the mass-ratio dependence of the gravitational-wave energy loss of a two-body system. We include a Supplemental Material that gives the explicit analytic form of a scattering integral which we could only evaluate numerically.

Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the Godel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described through an eccentricity-semi-latus rectum parametrization, familiar from the Newtonian dynamics of a two-body system. However, changing coordinates such planar geodesics all become explicitly circular, as exhibited by Kundt's form of the Godel metric. We derive here a one-to-one correspondence between the constants of the motion along these geodesics as well as between the parameter spaces of elliptic-like versus circular geodesics. We also show how to connect the two equivalent descriptions of particle motion by introducing a pair of complex coordinates in the 2-planes orthogonal to the symmetry axis, which brings the metric into a form which is invariant under Mobius transformations preserving the symmetries of the orbit, i.e., taking circles to circles.

The paper deals with de la Vallee Poussin type interpolation on the square at tensor product Chebyshev zeros of the first kind. The approximation is studied in the space of locally continuous functions with possible algebraic singularities on the boundary, equipped with weighted uniform norms. In particular, simple necessary and sufficient conditions are proved for the uniform boundedness of the related Lebesgue constants. Error estimates in some Sobolev-type spaces are also given. Pros and cons of such a kind of filtered interpolation are analyzed in comparison with the Lagrange polynomials interpolating at the same Chebyshev grid or at the equal number of Padua nodes. The advantages in reducing the Gibbs phenomenon are shown by means of some numerical experiments. (C) 2020 Elsevier Inc. All rights reserved.

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [-1,1] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on l1-regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods discussed in literature that learn the edges and the corresponding link parameters one node at a time, in this work we propose a method that learns all the edges and corresponding link parameters simultaneously for all nodes. The idea behind this proposal is to exploit the reciprocal information of the nodes between each other during the estimation process. Numerical experiments highlight the advantage of this technique and confirm the intuition behind it. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Let P and (P) over tilde be the laws of two discrete-time stochastic processes defined on the sequence space S-N,where S is a finite set of points. In this paper we derive a bound on the total variation distance d(TV)(P, (P) over tilde) in terms of the cylindrical projections of P and (P) over tilde. We apply the result to Markov chains with finite state space and random walks on Z with not necessarily independent increments, and we consider several examples. Our approach relies on the general framework of stochastic analysis for discrete-time obtuse random walks and the proof of our main result makes use of the predictable representation of multidimensional normal martingales. Along the way, we obtain a sufficient condition for the absolute continuity of (P) over tilde with respect to P which is of interest in its own right.

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising in stochastic geometry. As a consequence, we provide almost sure central limit theorems for (i) the total edge length of the k-nearest neighbors random graph. (ii) the clique count in random geometric graphs. and (iii) the volume of the set approximation via the Poisson-Voronoi tessellation.

We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes. (C) 2020 Elsevier B.V. All rights reserved.

Sparse solvers are one of the building blocks of any technology for reliable and high-performance scientific and engineering computing. In this paper we present a software package which implements an efficient multigrid sparse solver running on Graphics Processing Units. The package is a branch of a wider initiative of software development for sparse Linear Algebra computations on emergent HPC architectures involving a large research group working in many application projects over the last ten years.

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. StructuRly aims to resolve this problem by offering a complete environment for population analysis. In particular, StructuRly combines the statistical power of the R language with the friendly interfaces implemented using the shiny libraries to provide a novel tool for performing population clustering, evaluating several genetic indexes, and comparing results. Moreover, graphical representations are interactive and can be easily personalized. StructuRly is available either as R package on GitHub, with detailed information for its installation and use and as shinyapps.io servers for those users who are not familiar with R and the RStudio IDE. The application has been tested on Linux, macOS and Windows operative systems and can be launched as a shiny app in every web browser.

Si considera l'interpolazione di una funzione di due variabili su una griglia di nodi di Chebyshev di I specie mediante polinomi di approssimazione filtrata basati sul classico filtro di de la Vallée Poussin. Tale problema trova applicazioni sia nell'analisi delle immagini che nella risoluzione numerica di equazioni integrali singolari. Vengono mostrate stime dell'errore in norma uniforme pesata che dipendono dai diversi gradi di regolarità della funzione approssimante. Inoltre confronti con l'interpolazione di Lagrange sugli stessi nodi e con l'interpolazione sullo stesso numero di Padua points, mostrano i vantaggi dell'interpolazione filtrata di de la Vallée Poussin in particolare nella riduzione del fenomeno di Gibbs. xx

Il capitolo è interamente dedicato alle analisi dei dati relativi al personale T.I. e T.D. del CNR, con particolare attenzione alle serie storiche relative alle carriere dei ricercatori e tecnologi, al salario accessorio dei tecnici ed amministrativi, alle differenze che si possono notare all'interno dei vari Dipartimenti e della Sede Centrale. Questa analisi rimane un unicum nel panorama delle analisi dei dati di genere del più grande Ente di Ricerca, perché analizza e confronta l'evolversi della situazione nell'arco di un intero decennio.

Nel paragrafo si analizzano e si elaborano i dati relativi ai progetti di telelavoro nei bienni 2017-18 e 2019-20 e si pongono in evidenza i risultati di queste analisi che confermano le considerazioni generali indicate in precedenza.

Si presenta qui una breve sintesi del Progetto "La Ricerca del tempo Guadagnato" finanziato nell'ambito del POR-FSE 2007-2013 della Regione Campania e che ha visto la realizzazione, tra l'altro, di una Ludoteca aziendale presso l'Area di Ricerca Napoli1

Coronavirus disease 2019 (COVID-19) death rate differs depending on sex. Some hypotheses can be put forward on the basis of current knowledge on gender differences in respiratory viral diseases.

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. Moreover, well-balanced properties are shown to be preserved when applying IMEX time-integrators in the diffusive scaling. Numerical tests confirm these theoretical findings.

The aim of this preliminary study is to understand and simulate the hydric behaviour of a porous material in the presence of protective treatments. In particular, here the limestone Lumaquela deAjarte is considered before and after the application of the silane-based product ANC. A recently developed mathematical model was applied in order to describe the capillary rise of water in stone specimens. The model was calibrated by using experimental data concerning the water absorption by capillarity in both treated and untreated stone specimens. With a suitable calibration of the main parameters of the model and of the boundary conditions, it was possible to reproduce the main features of the experimentally observed phenomenon.

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.