Statistical characterization of polychromatic absolute and differential squared visibilities obtained from AMBER/VLTI instrument

In optical interferometry, the visibility squared modulus are generally assumed to follow a Gaussian distribution and to be independent of each other. A quantitative analysis of the relevance of such assumptions is important to help improving the exploitation of existing and upcoming multi-wavelength interferometric instruments. Analyze the statistical behaviour of both the absolute and the colour-differential squared visibilities: distribution laws, correlations and cross-correlations between different baselines. We use observations of stellar calibrators obtained with AMBER instrument on VLTI in different instrumental and observing configurations, from which we extract the frame-by-frame transfer function. Statistical hypotheses tests and diagnostics are then systematically applied. For both absolute and differential squared visibilities and under all instrumental and observing conditions, we find a better fit for the Student distribution than for the Gaussian, log-normal and Cauchy distributions. We find and analyze clear correlation effects caused by atmospheric perturbations. The differential squared visibilities allow to keep a larger fraction of data with respect to selected absolute squared visibilities and thus benefit from reduced temporal dispersion, while their distribution is more clearly characterized. The frame selection based on the criterion of a fixed SNR value might result in either a biased sample of frames or in a too severe selection.Comment: A&A, 13 pages and 9 figure

Bakry-\'Emery and Ollivier Ricci Curvature of Cayley Graphs

In this article we study two discrete curvature notions, Bakry-\'Emery curvature and Ollivier Ricci curvature, on Cayley graphs. We introduce Right Angled Artin-Coxeter Hybrids (RAACHs) generalizing Right Angled Artin and Coxeter groups (RAAGs and RACGs) and derive the curvatures of Cayley graphs of certain RAACHs. Moreover, we show for general finitely presented groups $\Gamma = \langle S \, \mid\, R \rangle$ that addition of relators does not lead to a decrease the weighted curvatures of their Cayley graphs with adapted weighting schemes

Bakry-\'Emery curvature sharpness and curvature flow in finite weighted graphs. I. Theory

In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-\'Emery calculus. The flow is described via a time-continuous evolution through the weighting schemes. By adapting this flow to preserve the Markovian property, its limits turn out to be curvature sharp. Our aim is to present the flow in the most general case of not necessarily reversible random walks allowing laziness, including vanishing transition probabilities along some edges ("degenerate" edges). This approach requires to extend all concepts (in particular, the Bakry-\'Emery curvature related notions) to this general case and it leads to a distinction between the underlying topology (a mixed combinatorial graph) and the weighting scheme (given by transition rates). We present various results about curvature sharp vertices and weighted graphs as well as some fundamental properties of this new curvature flow. This paper is accompanied by a second paper discussing the curvature flow implementation in Python for practical use. In this second paper we present examples and exhibit further properties of the flow

Differential Hebbian learning with time-continuous signals for active noise reduction

Spike timing-dependent plasticity, related to differential Hebb-rules, has become a leading paradigm in neuronal learning, because weights can grow or shrink depending on the timing of pre- and post-synaptic signals. Here we use this paradigm to reduce unwanted (acoustic) noise. Our system relies on heterosynaptic differential Hebbian learning and we show that it can efficiently eliminate noise by up to -140 dB in multi-microphone setups under various conditions. The system quickly learns, most often within a few seconds, and it is robust with respect to different geometrical microphone configurations, too. Hence, this theoretical study demonstrates that it is possible to successfully transfer differential Hebbian learning, derived from the neurosciences, into a technical domain