A theory on power in networks

The eigenvector centrality equation $\lambda x = A \, x$ is a successful compromise between simplicity and expressivity. It claims that central actors are those connected with central others. For at least 70 years, this equation has been explored in disparate contexts, including econometrics, sociometry, bibliometrics, Web information retrieval, and network science. We propose an equally elegant counterpart: the power equation $x = A x^{\div}$, where $x^{\div}$ is the vector whose entries are the reciprocal of those of $x$. It asserts that power is in the hands of those connected with powerless others. It is meaningful, for instance, in bargaining situations, where it is advantageous to be connected to those who have few options. We tell the parallel, mostly unexplored story of this intriguing equation

SFXTs versus classical SgXBs: Does the difference lie in the companion wind?

We present a comparative study of stellar winds in classical supergiant high mass X-ray binaries (SgXBs) and supergiant fast X-ray transients (SFXTs) based on the analysis of publicly available out-of-eclipse observations performed with Suzaku and XMM-Newton. Our data-set includes 55 observations of classical SgXBs and 21 observations of SFXTs. We found that classical SgXBs are characterized by a systematically higher absorption and luminosity compared to the SFXTs, confirming the results of previous works in the literature. Additionally, we show that the equivalent width of the fluorescence K{\alpha} iron line in the classical SgXBs is significantly larger than that of the SFXTs (outside X-ray eclipses). Based on our current understanding of the physics of accretion in these systems, we conclude that the most likely explanation of these differences is to be ascribed to the presence of mechanisms inhibiting accretion for most of the time in the SFXTs and leading to a much less efficient photoionization of the stellar wind compared to classical SgXBs.We do not find evidence for the previously reported anti-correlation between the equivalent width of the fluorescence iron line and the luminosity of SgXBs.Comment: 12 pages, 8 figures, 2 tables, Accepted for publication in A&

Arbitrarily regularizable graphs

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative regularizable graphs have been thoroughly investigated in the literature. In this work, we propose and study arbitrarily regularizable graphs. In particular, we investigate necessary and sufficient regularization conditions on the topology of the graph and of the corresponding adjacency matrix. Moreover, we study the computational complexity of the regularization problem and characterize it as a linear programming model

LOFT: the Large Observatory For X-ray Timing

LOFT, the large observatory for X-ray timing, is a new mission concept competing with other four candidates for a launch opportunity in 2022-2024. LOFT will be performing high-time resolution X-ray observations of compact objects, combining for the first time an unprecedented large collecting area for X-ray photons and a spectral resolution approaching that of CCD-based X-ray instruments (down to 200 eV FWHM at 6 keV). The operating energy range is 2-80 keV. The main science goals of LOFT are the measurement of the neutron stars equation of states and the test of General Relativity in the strong field regime. The breakthrough capabilities of the instruments on-board LOFT will permit to open also new discovery windows for a wide range of Galactic and extragalactic X-ray sources. In this contribution, we provide a general description of the mission concept and summarize its main scientific capabilitie

The Sylvester–Kac matrix space

AbstractThe Sylvester–Kac matrix is a tridiagonal matrix with integer entries and integer eigenvalues that appears in a variety of applicative problems. We show that it belongs to a four dimensional linear space of tridiagonal matrices that can be simultaneously reduced to triangular form. We name this space after the matrix

The temporalized Massey's method

We propose and throughly investigate a temporalized version of the popular Massey's technique for rating actors in sport competitions. The method can be described as a dynamic temporal process in which team ratings are updated at every match according to their performance during the match and the strength of the opponent team. Using the Italian soccer dataset, we empirically show that the method has a good foresight prediction accuracy