In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs.

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.

Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external force. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of autonomous propulsion and agent-agent interactions determine the collective dynamics of the system.

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.

Recent years have witnessed a massive push towards reproducible research in neuroscience. Unfortunately, this endeavor is often challenged by the large diversity of tools used, project-specific custom code and the difficulty to track all user-defined parameters. NeuroPycon is an open-source multi-modal brain data analysis toolkit which provides Python-based template pipelines for advanced multi-processing of MEG, EEG, functional and anatomical MRI data, with a focus on connectivity and graph theoretical analyses.

Current theories of schizophrenia emphasize the role of altered information integration as the core dysfunction of this illness. While ample neuroimaging evidence for such accounts comes from investigations of spatial connectivity, understanding temporal disruptions is important to fully capture the essence of dysconnectivity in schizophrenia.

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.

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.

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.