We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besid
es real pixels noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the $mathtt{SMICA}$ map we found ${f}_{rm ,NL} = 33 pm 23$, at $1sigma$ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval ${f}_{rm ,NL} in [33, 41]$, concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixels noise intensities.
The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not
exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter fNL. We apply it to these sets of CMB maps and find gtrsim 98% of chance of positive detection, even for small intensity local non-Gaussianity like fNL = 38 +/- 18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities and find out that our method successfully classifies ~ 95% of the tested maps. Furthermore, we analyze the foreground-cleaned Planck maps obtaining constraints for non-Gaussianity at large-angles that are in good agreement with recent constraints. Finally, we also test the robustness of our estimator including cut-sky masks and realistic noise maps measured by Planck, obtaining successful results as well.
The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the
underlying combinational aspects. SU(2) recoupling theory, involving Wigners 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, play nowadays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory -and of its extension to other Lie and quantum group- by using the collective term of `spin networks. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey Scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper we list and discuss some aspects of these developments -such as for instance the hyperquantization algorithm- as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.
We investigate the large-scale angular distribution of the short-Gamma ray bursts (SGRBs) from BATSE experiment, using a new coordinates-free method. The analyses performed take into account the angular correlations induced by the non-uniform sky exp
osure during the experiment, and the uncertainty in the measured angular coordinates. Comparising the large-scale angular correlations from the data with those expected from simulations using the exposure function we find similar features. Additionally, confronting the large-angle correlations computed from the data with those obtained from simulated maps produced under the assumption of statistical isotropy we found that they are incompatible at 95% confidence level. However, such differences are restricted to the angular scales 36o - 45o, which are likely to be due to the non-uniform sky exposure. This result strongly suggests that the set of SGRBs from BATSE are intrinsically isotropic. Moreover, we also investigated a possible large-angle correlation of these data with the supergalactic plane. No evidence for such large-scale anisotropy was found.
We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of
4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.
