Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

Spectral-Element and Adjoint 3D Full-Wave Tomography for the Lithosphere of Central Italy

The primary objective of this thesis is to obtain a better understanding of the 3D velocity structure of the lithosphere in central Italy. To this end, I adopted the Spectral-Element Method to perform accurate numerical simulations of the complex wavefields generated by the 2009 Mw 6.3 L’Aquila event and by its foreshocks and aftershocks together with some additional events within our target region. For the mainshock, the source was represented by a finite fault and different models for central Italy, both 1D and 3D, were tested. Surface topography, attenuation and Moho discontinuity were also accounted for. Three-component synthetic waveforms were compared to the corresponding recorded data. The results of these analyses show that 3D models, including all the known structural heterogeneities in the region, are essential to accurately reproduce waveform propagation. They allow to capture features of the seismograms, mainly related to topography or to low wavespeed areas, and, combined with a finite fault model, result into a favorable match between data and synthetics for frequencies up to ~0.5 Hz. We also obtained peak ground velocity maps, that provide valuable information for seismic hazard assessment. The remaining differences between data and synthetics led us to take advantage of SEM combined with an adjoint method to iteratively improve the available 3D structure model for central Italy. A total of 63 events and 52 stations in the region were considered. We performed five iterations of the tomographic inversion, by calculating the misfit function gradient - necessary for the model update - from adjoint sensitivity kernels, constructed using only two simulations for each event. Our last updated model features a reduced traveltime misfit function and improved agreement between data and synthetics, although further iterations, as well as refined source solutions, are necessary to obtain a new reference 3D model for central Italy tomography.

Variability analysis of discrete event series and wavefront patterns in surface electrocardiogram: contributions to psychophysiological and clinical research

The surface electrocardiogram (ECG) is an established diagnostic tool for the detection of abnormalities in the electrical activity of the heart. The interest of the ECG, however, extends beyond the diagnostic purpose. In recent years, studies in cognitive psychophysiology have related heart rate variability (HRV) to memory performance and mental workload. The aim of this thesis was to analyze the variability of surface ECG derived rhythms, at two different time scales: the discrete-event time scale, typical of beat-related features (Objective I), and the “continuous” time scale of separated sources in the ECG (Objective II), in selected scenarios relevant to psychophysiological and clinical research, respectively. Objective I) Joint time-frequency and non-linear analysis of HRV was carried out, with the goal of assessing psychophysiological workload (PPW) in response to working memory engaging tasks. Results from fourteen healthy young subjects suggest the potential use of the proposed indices in discriminating PPW levels in response to varying memory-search task difficulty. Objective II) A novel source-cancellation method based on morphology clustering was proposed for the estimation of the atrial wavefront in atrial fibrillation (AF) from body surface potential maps. Strong direct correlation between spectral concentration (SC) of atrial wavefront and temporal variability of the spectral distribution was shown in persistent AF patients, suggesting that with higher SC, shorter observation time is required to collect spectral distribution, from which the fibrillatory rate is estimated. This could be time and cost effective in clinical decision-making. The results held for reduced leads sets, suggesting that a simplified setup could also be considered, further reducing the costs. In designing the methods of this thesis, an online signal processing approach was kept, with the goal of contributing to real-world applicability. An algorithm for automatic assessment of ambulatory ECG quality, and an automatic ECG delineation algorithm were designed and validated.

Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

Discrete Event Systems based Design Patterns for Diagnosability Analysis of Automated Manufacturing Systems

The main goal of this thesis is to facilitate the process of industrial automated systems development applying formal methods to ensure the reliability of systems. A new formulation of distributed diagnosability problem in terms of Discrete Event Systems theory and automata framework is presented, which is then used to enforce the desired property of the system, rather then just verifying it. This approach tackles the state explosion problem with modeling patterns and new algorithms, aimed for verification of diagnosability property in the context of the distributed diagnosability problem. The concepts are validated with a newly developed software tool.

Seismic tomographic full-waveform inversion for the Vrancea sinking lithosphere structure using the adjoint method.

The Vrancea region, at the south-eastern bend of the Carpathian Mountains in Romania, represents one of the most puzzling seismically active zones of Europe. Beside some shallow seismicity spread across the whole Romanian territory, Vrancea is the place of an intense seismicity with the presence of a cluster of intermediate-depth foci placed in a narrow nearly vertical volume. Although large-scale mantle seismic tomographic studies have revealed the presence of a narrow, almost vertical, high-velocity body in the upper mantle, the nature and the geodynamic of this deep intra-continental seismicity is still questioned. High-resolution seismic tomography could help to reveal more details in the subcrustal structure of Vrancea. Recent developments in computational seismology as well as the availability of parallel computing now allow to potentially retrieve more information out of seismic waveforms and to reach such high-resolution models. This study was aimed to evaluate the application of a full waveform inversion tomography at regional scale for the Vrancea lithosphere using data from the 1999 six months temporary local network CALIXTO. Starting from a detailed 3D Vp, Vs and density model, built on classical travel-time tomography together with gravity data, I evaluated the improvements obtained with the full waveform inversion approach. The latter proved to be highly problem dependent and highly computational expensive. The model retrieved after the first two iterations does not show large variations with respect to the initial model but remains in agreement with previous tomographic models. It presents a well-defined downgoing slab shape high velocity anomaly, composed of a N-S horizontal anomaly in the depths between 40 and 70km linked to a nearly vertical NE-SW anomaly from 70 to 180km.

A new 3D modelling paradigm for discrete model

Until few years ago, 3D modelling was a topic confined into a professional environment. Nowadays technological innovations, the 3D printer among all, have attracted novice users to this application field. This sudden breakthrough was not supported by adequate software solutions. The 3D editing tools currently available do not assist the non-expert user during the various stages of generation, interaction and manipulation of 3D virtual models. This is mainly due to the current paradigm that is largely supported by two-dimensional input/output devices and strongly affected by obvious geometrical constraints. We have identified three main phases that characterize the creation and management of 3D virtual models. We investigated these directions evaluating and simplifying the classic editing techniques in order to propose more natural and intuitive tools in a pure 3D modelling environment. In particular, we focused on freehand sketch-based modelling to create 3D virtual models, interaction and navigation in a 3D modelling environment and advanced editing tools for free-form deformation and objects composition. To pursuing these goals we wondered how new gesture-based interaction technologies can be successfully employed in a 3D modelling environments, how we could improve the depth perception and the interaction in 3D environments and which operations could be developed to simplify the classical virtual models editing paradigm. Our main aims were to propose a set of solutions with which a common user can realize an idea in a 3D virtual model, drawing in the air just as he would on paper. Moreover, we tried to use gestures and mid-air movements to explore and interact in 3D virtual environment, and we studied simple and effective 3D form transformations. The work was carried out adopting the discrete representation of the models, thanks to its intuitiveness, but especially because it is full of open challenges.