Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Locating the source of volcanic tremor at stromboli volcano, italy

We have developed a method for locating sources of volcanic tremor and applied it to a dataset recorded on Stromboli volcano before and after the onset of the February 27th 2007 effusive eruption. Volcanic tremor has attracted considerable attention by seismologists because of its potential value as a tool for forecasting eruptions and for better understanding the physical processes that occur inside active volcanoes. Commonly used methods to locate volcanic tremor sources are: 1) array techniques, 2) semblance based methods, 3) calculation of wave field amplitude. We have choosen the third approach, using a quantitative modeling of the seismic wavefield. For this purpose, we have calculated the Green Functions (GF) in the frequency domain with the Finite Element Method (FEM). We have used this method because it is well suited to solve elliptic problems, as the elastodynamics in the Fourier domain. The volcanic tremor source is located by determining the source function over a regular grid of points. The best fit point is choosen as the tremor source location. The source inversion is performed in the frequency domain, using only the wavefield amplitudes. We illustrate the method and its validation over a synthetic dataset. We show some preliminary results on the Stromboli dataset, evidencing temporal variations of the volcanic tremor sources.

Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Morphogenesis of follicular epithelium in Drosophila melanogaster: function of von Hippel-Lindau tumour suppressor gene

During my PhD I have been involved in several projects regarding the morphogenesis of the follicular epithelium, such as the analysis of the pathways that correlate follicular epithelium patterning and eggshell genes expression. Moreover, I used the follicular epithelium as a model system to analyze the function of the Drosophila homolog of the human von Hippel-Lindau (d-VHL) during oogenesis, in order to gain insight into the role of h-VHL for the pathogenesis of VHL disease. h-VHL is implicated in a variety of processes and there is now a greater appreciation of HIF-independent h-VHL functions that are relevant to tumour development, including maintenance and organization of the primary cilium, maintenance of the differentiated phenotype in renal cells and regulation of epithelial-mesenchymal transition. However, the function of h-VHL gene during development has not been fully understood. It was previously shown that d-VHL down-regulates the motility of tubular epithelial cells (tracheal cells) during embryogenesis. Epithelial morphogenesis is important for organogenesis and pivotal for carcinogenesis, but mechanisms that control it are poorly understood. The Drosophila follicular epithelium is a genetically tractable model to understand these mechanisms in vivo. Therefore, to examine whether d-VHL has a role in epithelial morphogenesis and maintenance, I performed genetic and molecular analyses by using in vivo and in vitro approaches. From my analysis, I determined that d-VHL binds to and stabilizes microtubules. Loss of d-VHL depolymerizes the microtubule network during oogenesis, leading to a possible deregulation in the subcellular trafficking transport of polarity markers from Golgi apparatus to the different domains in which follicle cells are divided. The analysis carried out has allowed to establish a significant role of d-VHL in the maintenance of the follicular epithelium integrity.

Complexity of N-Myc transcriptional function in childhood neuroblastoma

Myc is a transcription factor that can activate transcription of several hundreds genes by direct binding to their promoters at specific DNA sequences (E-box). However, recent studies have also shown that it can exert its biological role by repressing transcription. Such studies collectively support a model in which c-Myc-mediated repression occurs through interactions with transcription factors bound to promoter DNA regions but not through direct recognition of typical E-box sequences. Here, we investigated whether N-Myc can also repress gene transcription, and how this is mechanistically achieved. We used human neuroblastoma cells as a model system in that N-MYC amplification/over-expression represents a key prognostic marker of this tumour. By means of transcription profile analyses we could identify at least 5 genes (TRKA, p75NTR, ABCC3, TG2, p21) that are specifically repressed by N-Myc. Through a dual-step-ChIP assay and genetic dissection of gene promoters, we found that N-Myc is physically associated with gene promoters in vivo, in proximity of the transcription start site. N-Myc association with promoters requires interaction with other proteins, such as Sp1 and Miz1 transcription factors. Furthermore, we found that N-Myc may repress gene expression by interfering directly with Sp1 and/or with Miz1 activity (i.e. TRKA, p75NTR, ABCC3, p21) or by recruiting Histone Deacetylase 1 (Hdac1) (i.e. TG2). In vitro analyses show that distinct N-Myc domains can interact with Sp1, Miz1 and Hdac1, supporting the idea that Myc may participate in distinct repression complexes by interacting specifically with diverse proteins. Finally, results show that N-Myc, through repressed genes, affects important cellular functions, such as apoptosis, growth, differentiation and motility. Overall, our results support a model in which N-Myc, like c-Myc, can repress gene transcription by direct interaction with Sp1 and/or Miz1, and provide further lines of evidence on the importance of transcriptional repression by Myc factors in tumour biology.

Studies of OPA1 pathogenic mechanisms in Dominant Optic Atrophy and novel protein function in mitochondrial DNA stability

The mitochondrion is an essential cytoplasmic organelle that provides most of the energy necessary for eukaryotic cell physiology. Mitochondrial structure and functions are maintained by proteins of both mitochondrial and nuclear origin. These organelles are organized in an extended network that dynamically fuses and divides. Mitochondrial morphology results from the equilibrium between fusion and fission processes, controlled by a family of “mitochondria-shaping” proteins. It is becoming clear that defects in mitochondrial dynamics can impair mitochondrial respiration, morphology and motility, leading to apoptotic cell death in vitro and more or less severe neurodegenerative disorders in vivo in humans. Mutations in OPA1, a nuclear encoded mitochondrial protein, cause autosomal Dominant Optic Atrophy (DOA), a heterogeneous blinding disease characterized by retinal ganglion cell degeneration leading to optic neuropathy (Delettre et al., 2000; Alexander et al., 2000). OPA1 is a mitochondrial dynamin-related guanosine triphosphatase (GTPase) protein involved in mitochondrial network dynamics, cytochrome c storage and apoptosis. This protein is anchored or associated on the inner mitochondrial membrane facing the intermembrane space. Eight OPA1 isoforms resulting from alternative splicing combinations of exon 4, 4b and 5b have been described (Delettre et al., 2001). These variants greatly vary among diverse organs and the presence of specific isoforms has been associated with various mitochondrial functions. The different spliced exons encode domains included in the amino-terminal region and contribute to determine OPA1 functions (Olichon et al., 2006). It has been shown that exon 4, that is conserved throughout evolution, confers functions to OPA1 involved in maintenance of the mitochondrial membrane potential and in the fusion of the network. Conversely, exon 4b and exon 5b, which are vertebrate specific, are involved in regulation of cytochrome c release from mitochondria, and activation of apoptosis, a process restricted to vertebrates (Olichon et al., 2007). While Mgm1p has been identified thanks to its role in mtDNA maintenance, it is only recently that OPA1 has been linked to mtDNA stability. Missense mutations in OPA1 cause accumulation of multiple deletions in skeletal muscle. The syndrome associated to these mutations (DOA-1 plus) is complex, consisting of a combination of dominant optic atrophy, progressive external ophtalmoplegia, peripheral neuropathy, ataxia and deafness (Amati- Bonneau et al., 2008; Hudson et al., 2008). OPA1 is the fifth gene associated with mtDNA “breakage syndrome” together with ANT1, PolG1-2 and TYMP (Spinazzola et al., 2009). In this thesis we show for the first time that specific OPA1 isoforms associated to exon 4b are important for mtDNA stability, by anchoring the nucleoids to the inner mitochondrial membrane. Our results clearly demonstrate that OPA1 isoforms including exon 4b are intimately associated to the maintenance of the mitochondrial genome, as their silencing leads to mtDNA depletion. The mechanism leading to mtDNA loss is associated with replication inhibition in cells where exon 4b containing isoforms were down-regulated. Furthermore silencing of exon 4b associated isoforms is responsible for alteration in mtDNA-nucleoids distribution in the mitochondrial network. In this study it was evidenced that OPA1 exon 4b isoform is cleaved to provide a 10kd peptide embedded in the inner membrane by a second transmembrane domain, that seems to be crucial for mitochondrial genome maintenance and does correspond to the second transmembrane domain of the yeasts orthologue encoded by MGM1 or Msp1, which is also mandatory for this process (Diot et al., 2009; Herlan et al., 2003). Furthermore in this thesis we show that the NT-OPA1-exon 4b peptide co-immuno-precipitates with mtDNA and specifically interacts with two major components of the mitochondrial nucleoids: the polymerase gamma and Tfam. Thus, from these experiments the conclusion is that NT-OPA1- exon 4b peptide contributes to the nucleoid anchoring in the inner mitochondrial membrane, a process that is required for the initiation of mtDNA replication and for the distribution of nucleoids along the network. These data provide new crucial insights in understanding the mechanism involved in maintenance of mtDNA integrity, because they clearly demonstrate that, besides genes implicated in mtDNA replications (i.e. polymerase gamma, Tfam, twinkle and genes involved in the nucleotide pool metabolism), OPA1 and mitochondrial membrane dynamics play also an important role. Noticeably, the effect on mtDNA is different depending on the specific OPA1 isoforms down-regulated, suggesting the involvement of two different combined mechanisms. Over two hundred OPA1 mutations, spread throughout the coding region of the gene, have been described to date, including substitutions, deletions or insertions. Some mutations are predicted to generate a truncated protein inducing haploinsufficiency, whereas the missense nucleotide substitutions result in aminoacidic changes which affect conserved positions of the OPA1 protein. So far, the functional consequences of OPA1 mutations in cells from DOA patients are poorly understood. Phosphorus MR spectroscopy in patients with the c.2708delTTAG deletion revealed a defect in oxidative phosphorylation in muscles (Lodi et al., 2004). An energetic impairment has been also show in fibroblasts with the severe OPA1 R445H mutation (Amati-Bonneau et al., 2005). It has been previously reported by our group that OPA1 mutations leading to haploinsufficiency are associated in fibroblasts to an oxidative phosphorylation dysfunction, mainly involving the respiratory complex I (Zanna et al., 2008). In this study we have evaluated the energetic efficiency of a panel of skin fibroblasts derived from DOA patients, five fibroblast cell lines with OPA1 mutations causing haploinsufficiency (DOA-H) and two cell lines bearing mis-sense aminoacidic substitutions (DOA-AA), and compared with control fibroblasts. Although both types of DOA fibroblasts maintained a similar ATP content when incubated in a glucose-free medium, i.e. when forced to utilize the oxidative phosphorylation only to produce ATP, the mitochondrial ATP synthesis through complex I, measured in digitonin-permeabilized cells, was significantly reduced in cells with OPA1 haploinsufficiency only, whereas it was similar to controls in cells with the missense substitutions. Furthermore, evaluation of the mitochondrial membrane potential (DYm) in the two fibroblast lines DOA-AA and in two DOA-H fibroblasts, namely those bearing the c.2819-2A>C mutation and the c.2708delTTAG microdeletion, revealed an anomalous depolarizing response to oligomycin in DOA-H cell lines only. This finding clearly supports the hypothesis that these mutations cause a significant alteration in the respiratory chain function, which can be unmasked only when the operation of the ATP synthase is prevented. Noticeably, oligomycin-induced depolarization in these cells was almost completely prevented by preincubation with cyclosporin A, a well known inhibitor of the permeability transition pore (PTP). This results is very important because it suggests for the first time that the voltage threshold for PTP opening is altered in DOA-H fibroblasts. Although this issue has not yet been addressed in the present study, several are the mechanisms that have been proposed to lead to PTP deregulation, including in particular increased reactive oxygen species production and alteration of Ca2+ homeostasis, whose role in DOA fibroblasts PTP opening is currently under investigation. Identification of the mechanisms leading to altered threshold for PTP regulation will help our understanding of the pathophysiology of DOA, but also provide a strategy for therapeutic intervention.

Longitudinal evolution of cognitive functions in patients with multiple system atrophy: a prospective study

Introduction and Background: Multiple system atrophy (MSA) is a sporadic, adult-onset, progressive neurodegenerative disease characterized clinically by parkinsonism, cerebellar ataxia, and autonomic failure. We investigated cognitive functions longitudinally in a group of probable MSA patients, matching data with sleep parameters. Patients and Methods: 10 patients (7m/3f) underwent a detailed interview, a general and neurological examination, laboratory exams, MRI scans, a cardiovascular reflexes study, a battery of neuropsychological tests, and video-polysomnographic recording (VPSG). Patients were revaluated (T1) a mean of 16±5 (range: 12-28) months after the initial evaluation (T0). At T1, the neuropsychological assessment and VPSG were repeated. Results: The mean patient age was 57.8±6.4 years (range: 47-64) with a mean age at disease onset of 53.2±7.1 years (range: 43-61) and symptoms duration at T0 of 60±48 months (range: 12-144). At T0, 7 patients showed no cognitive deficits while 3 patients showed isolated cognitive deficits. At T1, 1 patient worsened developing multiple cognitive deficits from a normal condition. At T0 and T1, sleep efficiency was reduced, REM latency increased, NREM sleep stages 1-2 slightly increased. Comparisons between T1 and T0 showed a significant worsening in two tests of attention and no significant differences of VPSG parameters. No correlation was found between neuropsychological results and VPSG findings or RBD duration. Discussion and Conclusions: The majority of our patients do not show any cognitive deficits at T0 and T1, while isolated cognitive deficits are present in the remaining patients. Attention is the cognitive function which significantly worsened. Our data confirm the previous findings concerning the prevalence, type and the evolution of cognitive deficits in MSA. Regarding the developing of a condition of dementia, our data did not show a clear-cut diagnosis of dementia. We confirm a mild alteration of sleep structure. RBD duration does not correlate with neuropsychological findings.

Harnack inequalities in sub-Riemannian settings

In the present thesis, we discuss the main notions of an axiomatic approach for an invariant Harnack inequality. This procedure, originated from techniques for fully nonlinear elliptic operators, has been developed by Di Fazio, Gutiérrez, and Lanconelli in the general settings of doubling Hölder quasi-metric spaces. The main tools of the approach are the so-called double ball property and critical density property: the validity of these properties implies an invariant Harnack inequality. We are mainly interested in the horizontally elliptic operators, i.e. some second order linear degenerate-elliptic operators which are elliptic with respect to the horizontal directions of a Carnot group. An invariant Harnack inequality of Krylov-Safonov type is still an open problem in this context. In the thesis we show how the double ball property is related to the solvability of a kind of exterior Dirichlet problem for these operators. More precisely, it is a consequence of the existence of some suitable interior barrier functions of Bouligand-type. By following these ideas, we prove the double ball property for a generic step two Carnot group. Regarding the critical density, we generalize to the setting of H-type groups some arguments by Gutiérrez and Tournier for the Heisenberg group. We recognize that the critical density holds true in these peculiar contexts by assuming a Cordes-Landis type condition for the coefficient matrix of the operator. By the axiomatic approach, we thus prove an invariant Harnack inequality in H-type groups which is uniform in the class of the coefficient matrices with prescribed bounds for the eigenvalues and satisfying such a Cordes-Landis condition.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Secondary Microseisms Characterization and Green’s Function Extraction at the Larderello-Travale Geothermal Field (Italy)

Over the past ten years, the cross-correlation of long-time series of ambient seismic noise (ASN) has been widely adopted to extract the surface-wave part of the Green’s Functions (GF). This stochastic procedure relies on the assumption that ASN wave-field is diffuse and stationary. At frequencies <1Hz, the ASN is mainly composed by surface-waves, whose origin is attributed to the sea-wave climate. Consequently, marked directional properties may be observed, which call for accurate investigation about location and temporal evolution of the ASN-sources before attempting any GF retrieval. Within this general context, this thesis is aimed at a thorough investigation about feasibility and robustness of the noise-based methods toward the imaging of complex geological structures at the local (∼10-50km) scale. The study focused on the analysis of an extended (11 months) seismological data set collected at the Larderello-Travale geothermal field (Italy), an area for which the underground geological structures are well-constrained thanks to decades of geothermal exploration. Focusing on the secondary microseism band (SM;f>0.1Hz), I first investigate the spectral features and the kinematic properties of the noise wavefield using beamforming analysis, highlighting a marked variability with time and frequency. For the 0.1-0.3Hz frequency band and during Spring- Summer-time, the SMs waves propagate with high apparent velocities and from well-defined directions, likely associated with ocean-storms in the south- ern hemisphere. Conversely, at frequencies >0.3Hz the distribution of back- azimuths is more scattered, thus indicating that this frequency-band is the most appropriate for the application of stochastic techniques. For this latter frequency interval, I tested two correlation-based methods, acting in the time (NCF) and frequency (modified-SPAC) domains, respectively yielding esti- mates of the group- and phase-velocity dispersions. Velocity data provided by the two methods are markedly discordant; comparison with independent geological and geophysical constraints suggests that NCF results are more robust and reliable.

Identificazione di possibili unita' di stock di Anguilla anguilla mediante analisi microchimica e morfometrica degli otoliti

L’anguilla europea, è una specie eurialina catadroma con un complesso ciclo biologico: l’area di riproduzione, unica, si trova molto distante da quella di distribuzione. La specie necessita di una gestione dello stock a fini conservazionistici. Il problema è europeo: lo stock è unico, distribuito in Europa e nell’Africa settentrionale, si riproduce in Atlantico ed è panmittico. C’è preoccupazione per il declino del reclutamento e delle catture di adulti. Lo scopo del progetto è di individuare possibili unità di stock nella penisola italiana. La ricerca è basata sullo studio degli otoliti mediante analisi morfometrica e microchimica. I contorni degli otoliti sono sottoposti ad analisi ellittica di Fourier per individuare eventuali gruppi. Gli otoliti sono stati levigati per effettuare: letture d’età, indagini microstrutturali al SEM delle fasi larvali, analisi microchimiche LA-ICP-MS del nucleo, studiarne l’origine e valutare l’ambiente di sviluppo. Le indagini morfometriche mostrano evidenti pattern ontogenetici, ma non legati ocorrelati alla località, sesso o anno di nascita. Le indagini microstrutturali hanno evidenziano l’alto contenuto organico nucleare, un pattern comune di crescita ed eventi chiave delle fasi larvali, con una media di 212 anelli giornalieri. La microchimica rivela che le larve si sviluppano in acque salate fino alla metamorfosi, poi migrano verso acque meno salate. Le analisi su campioni nati nello stesso anno, evidenziano due gruppi: individui di rimonta naturale e individui di ripopolamento. I profili nucleo bordo evidenziano la permanenza a salinità intermedie degli adulti. L’attività di ricerca si è dimostrata proficua dal punto di vista tecnico con la messa a punto di protocolli innovativi e con forti ricadute sulla riduzione dei tempi e costi d’analisi. Il debole segnale di possibili unità di stock andrà verificato in futuro mediante analisi più dettagliate discriminando meglio la storia di ogni singolo individuo.