Pyramid wavefront sensors for astronomy and for the human eye

WaveFront Sensors (WFSs) may be defined as the heart of an adaptive optics system since they analyze the radiation coming from reference sources and allow to quantify the distortion of a wavefront. Among the varieties of existing WFSs, my PhD research thesis focuses especially on innovative optical systems taking advantage of the peculiarities of the Pyramid WFS. In my PhD project I have designed, implemented, characterized or studied three different applications characterized by the fact that one or multiple pyramid WFSs play a major role. They extend from WATERFALL, an application for the human eye (8 mm), to a Very-Linear (and very sensitive) WFS (VL-WFS), part of a concept for a 40 meter telescope adaptive optics, passing through a very complex system featuring more than 100 degrees of freedom, to be mounted on 8.4 m x 2 LBT telescope (Ground-layer WFS for LINC-NIRVANA). WATERFALL concerns the design and successful realization of a prototype for opthalmologic application for industrial commercialization to measure dioptric power of Intra-Ocular Lenses. GWS for NIRVANA works includes the definition of tolerances to be met and the detailed description of its alignment, integration phase and successful verification, leading it toward its on-sky commissioning phase in the Pathfinder experiment. The VL-WFS is in its very early phase, concepts and new ideas (mostly coming from our group) have to be organized in order to make a real proposal of a Global MCAO instrument for the E-ELT. The projects briefly presented are all based on the same optical concepts and if the ophthalmology application might at first sight look unrelated to astronomy, it is, in fact, representing a simple SCAO system applied to an optical system which is the eye, proving how the interaction between different research field can lead to successful results

Beyond topological persistence: Starting from networks

Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to significant data types as simple graphs and quivers. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness such as clique communities, $k$-vertex and $k$-edge connectedness directly on simple graphs and monic coherent categories.Comment: arXiv admin note: text overlap with arXiv:1707.0967

Principal Regression Analysis and the index leverage effect

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.Comment: 10 pages, 7 figure

Measuring Mindfulness: First Steps Towards the Development of a Comprehensive Mindfulness Scale

The present study describes the development of and results obtained from the first version of a new mindfulness scale: the Comprehensive Inventory of Mindfulness Experiences beta (CHIME-β). The aim of the present analysis was to investigate two relevant open questions in mindfulness assessment: (1) the coverage of aspects of mindfulness and (2) the type of interrelationships among these aspects. A review of the aspects of mindfulness assessed by eight currently available mindfulness questionnaires led to the identification of nine aspects of mindfulness. The CHIME-β was constructed in order to cover each of these aspects in a balanced way. Initially, principal component and confirmatory factor analyses, as well as reliability and validity analyses, were performed in the entire sample (n = 313) of individuals from the general population and mindfulness-based stress reduction (MBSR) groups. The factor structure that emerged from this analysis was further investigated in meditation-trained individuals (n = 144) who had just completed an MBSR intervention. Results suggested a four-factor structure underlying the nine aspects proposed. The relationship between these mindfulness factors appears to be influenced by the degree of meditation experience. In fact, the mindfulness factors showed a greater interconnectedness among mediation-trained participants. Finally, data suggest that a non-avoidant stance plays a central role in mindfulness, while the capacity to put inner experiences into words may be related to mindfulness rather than a component of the construc