The exotic fraction among unassociated Fermi sources

Revealing the nature of unassociated high-energy (> 100 MeV) gamma-ray sources remains a challenge 35 years after their discovery. Of the 934 gamma-ray sources at high Galactic latitude (|b| > 15 degrees) in the First Fermi-LAT catalogue (1FGL), 316 have no obvious associations at other wavelengths. In this paper, we apply the K-means unsupervised classification algorithm to isolate potential counterparts for 18 unassociated Fermi sources contained within a 3000 square degree `overlap region' of the sky intensively covered in radio and optical wavelengths. Combining our results with previous works, we reach potential associations for 119 out of the 128 Fermi sources within said region. If these associations are correct, we estimate that less than 20% of all remaining unassociated 1FGL sources at high Galactic latitude (|b| > 15 degrees) might host `exotic' counterparts distinct from known classes of gamma-ray emitters. Potentially even these outliers could be explained by high-redshift/dust-obscured analogues of the associated sample or by intrinsically faint radio objects. Although such estimate leaves some room for novel discoveries, it severely restricts the possibility of detecting dark matter subhaloes and other unconventional types of gamma-ray emitters in the 1FGL. In closing, we argue that the identification of Fermi sources at the low end of the flux density distribution will be a complex process that might only be achieved through a clever combination of refined classification algorithms, multi-wavelength efforts, and dedicated optical spectroscopy.Comment: 7 pages, 5 figures, 2 table

Using complete measurement statistics for optimal device-independent randomness evaluation

The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the joint probabilities characterizing the measurement outcomes of a Bell test are richer than just the degree of violation of a single Bell inequality. In this work we show how to take this extra information into account in a systematic manner in order to optimally evaluate the randomness that can be certified from non-local correlations. We further show that taking into account the complete set of outcome probabilities is equivalent to optimizing over all possible Bell inequalities, thereby allowing us to determine the optimal Bell inequality for certifying the maximal amount of randomness from a given set of non-local correlations.Comment: 12 pages, 4 figures. v2, v3, v4: minor corrections. See also the related independent work arXiv:1309.389

Integrability, Supersymmetry and Coherent States. A volume in honour of Professor Véronique Hussin

ISBN 978-3-030-20087-

Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates

Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the literature, but here they are characterized in full generality together with their integrability properties. Some of these systems are defined only in a region of $\mathbb R^n$, and in general they do not include bounded solutions. The quantum symmetries and potentials are shown to reduce to their superintegrable classical analogs in the $\hbar \to0$ limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit

Towards an Ashtekar formalism in eight dimensions

We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M-theory via matroid theory.Comment: 15 pages, Latex, minor changes, to appear in Class. Quantum Gra

Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri

Using MacDowell-Mansouri theory, in this work, we investigate a superfield description of the self-dual supergravity a la Ashtekar. We find that in order to reproduce previous results on supersymmetric Ashtekar formalism, it is necessary to properly combine the supersymmetric field-strength in the Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar formalism in eight dimensions.Comment: 19 pages, Latex; section 6 improve

Equivalence between various versions of the self-dual action of the Ashtekar formalism

Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions.Comment: 10 pages, Latex, minor correction