Probabilistic tomography of atmospheric parameters from GNSS data

The objective of the work is the evaluation of the potential capabilities of navigation satellite signals to retrieve basic atmospheric parameters. A capillary study have been performed on the assumptions more or less explicitly contained in the common processing steps of navigation signals. A probabilistic procedure has been designed for measuring vertical discretised profiles of pressure, temperature and water vapour and their associated errors. Numerical experiments on a synthetic dataset have been performed with the main objective of quantifying the information that could be gained from such approach, using entropy and relative entropy as testing parameters. A simulator of phase delay and bending of a GNSS signal travelling across the atmosphere has been developed to this aim.

Implicit computational complexity and probabilistic classes

The thesis applies the ICC tecniques to the probabilistic polinomial complexity classes in order to get an implicit characterization of them. The main contribution lays on the implicit characterization of PP (which stands for Probabilistic Polynomial Time) class, showing a syntactical characterisation of PP and a static complexity analyser able to recognise if an imperative program computes in Probabilistic Polynomial Time. The thesis is divided in two parts. The first part focuses on solving the problem by creating a prototype of functional language (a probabilistic variation of lambda calculus with bounded recursion) that is sound and complete respect to Probabilistic Prolynomial Time. The second part, instead, reverses the problem and develops a feasible way to verify if a program, written with a prototype of imperative programming language, is running in Probabilistic polynomial time or not. This thesis would characterise itself as one of the first step for Implicit Computational Complexity over probabilistic classes. There are still open hard problem to investigate and try to solve. There are a lot of theoretical aspects strongly connected with these topics and I expect that in the future there will be wide attention to ICC and probabilistic classes.

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.

A probabilistic approach to classify the levee reliability

This work aims to evaluate the reliability of these levee systems, calculating the probability of “failure” of determined levee stretches under different loads, using probabilistic methods that take into account the fragility curves obtained through the Monte Carlo Method. For this study overtopping and piping are considered as failure mechanisms (since these are the most frequent) and the major levee system of the Po River with a primary focus on the section between Piacenza and Cremona, in the lower-middle area of the Padana Plain, is analysed. The novelty of this approach is to check the reliability of individual embankment stretches, not just a single section, while taking into account the variability of the levee system geometry from one stretch to another. This work takes also into consideration, for each levee stretch analysed, a probability distribution of the load variables involved in the definition of the fragility curves, where it is influenced by the differences in the topography and morphology of the riverbed along the sectional depth analysed as it pertains to the levee system in its entirety. A type of classification is proposed, for both failure mechanisms, to give an indication of the reliability of the levee system based of the information obtained by the fragility curve analysis. To accomplish this work, an hydraulic model has been developed where a 500-year flood is modelled to determinate the residual hazard value of failure for each stretch of levee near the corresponding water depth, then comparing the results with the obtained classifications. This work has the additional the aim of acting as an interface between the world of Applied Geology and Environmental Hydraulic Engineering where a strong collaboration is needed between the two professions to resolve and improve the estimation of hydraulic risk.

The arcuate fasciculus: an along-tract analysis with white matter probabilistic tractography

Il cervello umano è composto da una rete complessa, formata da fasci di assoni, che connettono le diverse aree cerebrali. Il fascio arcuato collega l’area imputata alla com- prensione del linguaggio con quella dedicata alla sua produzione. Il fascio arcuato è presente in entrambi gli emisferi cerebrali, anche se spesso è utilizzato prevalente- mente il sinistro. In questa tesi sono state valutate, in un campione di soggetti sani, le differenze tra fascio arcuato destro e sinistro, utilizzando la trattografia, metodica avanzata e non invasiva che permette la ricostruzione della traiettoria delle fibre con immagini RM (Risonanza Magnetica) pesate in diffusione. A questo scopo ho utilizzato un algoritmo probabilistico, che permette la stima di probabilità di connessione della fibra in oggetto con le diverse aree cerebrali, anche nelle sedi di incrocio con fibre di fasci diversi. Grazie all’implementazione di questo metodo, è stato possibile ottenere una ricostruzione accurata del fascio arcuato, an- che nell’emisfero destro dove è spesso critica, tanto da non essere possibile con altri algoritmi trattografici. Parametrizzando poi la geometria del tratto ho diviso il fascio arcuato in venti seg- menti e ho confrontato i parametri delle misure di diffusione, valutate nell’emisfero destro e sinistro. Da queste analisi emerge un’ampia variabilità nella geometria dell’arcuato, sia tra diversi soggetti che diversi emisferi. Nell’emisfero destro l’arcuato incrocia maggiormente fibre appartenenti ad altri fasci. Nell’emisfero sinistro le fibre dell’arcuato sono più compatte e si misura anche una maggiore connettività con altre aree del cervello coinvolte nelle funzioni linguistiche. Nella seconda fase dello studio ho applicato la stessa metodica in due pazienti con lesioni cerebrali, con l’obiettivo di testare il danno del fascio arcuato ipsilaterale alla lesione e stimare se nell’emisfero controlaterale si innescassero meccanismi di plastic- ità strutturale. Questa metodica può essere implementata, in un gruppo di pazienti omogenei, per identificare marcatori RM diagnostici nella fase di pianificazione pre- chirurgica e marcatori RM prognostici di recupero funzionale del linguaggio.

Future storm surge impacts on insurable losses for the North Sea region

The influence of climate change on storm surges including increased mean sea level change and the associated insurable losses are assessed for the North Sea basin. In doing so, the newly developed approach couples a dynamical storm surge model with a loss model. The key element of the approach is the generation of a probabilistic storm surge event set. Together with parametrizations of the inland propagation and the coastal protection failure probability this enables the estimation of annual expected losses. The sensitivity to the parametrizations is rather weak except when the assumption of high level of increased mean sea level change is made. Applying this approach to future scenarios shows a substantial increase of insurable losses with respect to the present day. Superimposing different mean sea level changes shows a nonlinear behavior at the country level, as the future storm surge changes are higher for Germany and Denmark. Thus, the study exhibits the necessity to assess the socio-economic impacts of coastal floods by combining the expected sea level rise with storm surge projections.

Utilization of Probabilistic Models in Short Read Assembly from Second-Generation Sequencing

With the advent of cheaper and faster DNA sequencing technologies, assembly methods have greatly changed. Instead of outputting reads that are thousands of base pairs long, new sequencers parallelize the task by producing read lengths between 35 and 400 base pairs. Reconstructing an organism’s genome from these millions of reads is a computationally expensive task. Our algorithm solves this problem by organizing and indexing the reads using n-grams, which are short, fixed-length DNA sequences of length n. These n-grams are used to efficiently locate putative read joins, thereby eliminating the need to perform an exhaustive search over all possible read pairs. Our goal was develop a novel n-gram method for the assembly of genomes from next-generation sequencers. Specifically, a probabilistic, iterative approach was utilized to determine the most likely reads to join through development of a new metric that models the probability of any two arbitrary reads being joined together. Tests were run using simulated short read data based on randomly created genomes ranging in lengths from 10,000 to 100,000 nucleotides with 16 to 20x coverage. We were able to successfully re-assemble entire genomes up to 100,000 nucleotides in length.