No abstract

Deviations from statistical isotropy can be modeled in various ways, for instance, anisotropic cosmological models (Bianchi models), compact topologies, and presence of primordial magnetic field. Signature of anisotropy manifests itself in cosmic microwave background correlation patterns. Here we explore the symmetries of the correlation function and its implications on the observable measures constructed within the bipolar harmonic formalism for these variety of models. Different quantifiers within the bipolar harmonic representation are used to distinguish between plausible models of breakdown of statistical isotropy and as a spectroscopic tool for discriminating between distinct cosmic topology.

Gaussianity of temperature fluctuations in the Cosmic Microwave Background(CMB) implies that the statistical properties of the temperature field can be completely characterized by its two point correlation function. The two point correlation function can be expanded in full generality in the bipolar spherical harmonic(BipoSH) basis. Looking for significant deviations from zero for Bipolar Spherical Harmonic(BipoSH) Coefficients derived from observed CMB maps forms the basis of the strategy used to detect isotropy violation. In order to quantify "significant deviation" we need to understand the distributions of these coefficients. We analytically evaluate the moments and the distribution of the coefficients of expansion(A LM l 1 l 2 ), using characteristic function approach. We show that for BipoSH coefficients with M = 0 an analytical form for the moments up to any arbitrary order can be derived. For the remaining BipoSH coefficients with M = 0, the moments derived using the characteristic function approach need to be supplemented with a correction term. The correction term is found to be important particularly at low multipoles. We provide a general prescription for calculating these corrections, however we restrict the explicit calculations only up to kurtosis. We confirm our results with measurements of BipoSH coefficients on numerically simulated statistically isotropic CMB maps.

AbstractAutomatic sleep stage scoring based on deep neural networks has come into focus of sleep researchers and physicians, as a reliable method able to objectively classify sleep stages, would save human resources and thus would simplify clinical routines. Due to novel open-source software libraries for Machine Learning in combination with enormous progress in hardware development in recent years a paradigm shift in the field of sleep research towards automatic diagnostics could be observed. We argue that modern Machine Learning techniques are not just a tool to perform automatic sleep stage classification but are also a creative approach to find hidden properties of sleep physiology. We have already developed and established algorithms to visualize and cluster EEG data, in a way so that we can already make first assessments on sleep health in terms of sleep-apnea and consequently daytime vigilance. In the following study, we further developed our method by the innovative approach to analyze cortical activity during sleep by computing vectorial cross-correlations of different EEG channels represented by hypnodensity graphs. We can show that this measure serves to estimate the period length of sleep cycles and thus can help to find disturbances due to pathological conditions.