The Hitchin map for one-nodal base curves of compact type

Studying moduli spaces of semistable Higgs bundles (E, \phi) of rank n on a smooth curve C, a key role is played by the spectral curve X (Hitchin), because an important result by Beauville-Narasimhan-Ramanan allows us to study isomorphism classes of such Higgs bundles in terms of isomorphism classes of rank-1 torsion-free sheaves on X. This way, the generic fibre of the Hitchin map, which associates to any semistable Higgs bundle the coefficients of the characteristic polynomial of \phi, is isomorphic to the Jacobian of X. Focusing on rank-2 Higgs data, this construction was extended by Barik to the case in which the curve C is reducible, one-nodal, having two smooth components. Such curve is called of compact type because its Picard group is compact. In this work, we describe and clarify the main points of the construction by Barik and we give examples, especially concerning generic fibres of the Hitchin map. Referring to Hausel-Pauly, we consider the case of SL(2,C)-Higgs bundles on a smooth base curve, which are such that the generic fibre of the Hitchin map is a subvariety of the Jacobian of X, the Prym variety. We recall the description of special loci, called endoscopic loci, such that the associated Prym variety is not connected. Then, letting G be an affine reductive group having underlying Lie algebra so(4,C), we consider G-Higgs bundles on a smooth base curve. Starting from the construction by Bradlow-Schaposnik, we discuss the associated endoscopic loci. By adapting these studies to a one-nodal base curve of compact type, we describe the fibre of the SL(2,C)-Hitchin map and of the G-Hitchin map, together with endoscopic loci. In the Appendix, we give an interpretation of generic spectral curves in terms of families of double covers.

Sulforaphane as a multifunctional neuroprotective molecule to prevent and slow down the progression of Alzheimer’s disease

Oxidative stress has been implicated in the pathogenesis of a number of diseases including neurodegenerative disorders, cancer, ischemia, etc. Alzheimer’s disease (AD) is histopathologically characterized by the presence of extracellular senile plaque (SP), predominantly consisting of fibrillar amyloid-peptide (Aβ), intracellular neurofibrillary tangles (NFTs), composed of hyperphosphorylated tau protein, and cell loss in the selected regions of the brain. However, the pathogenesis of AD remains largely unknown, but a number of hypothesis were proposed for AD mechanisms, which include: the amyloid cascade, excitotoxicity, oxidative stress and inflammation hypothesis, and all of them are based, to some extent on the role of A. Accumulated evidence indicates that the increased levels of ROS may act as important mediators of synaptic loss and eventually promote formation of neurofibrillary tangles and senile plaques. Therefore a vicious circle between ROS and Aaccumulation may accelerate progression of AD. For these reasons, growing attention has focused on oxidative mechanism of Atoxicity as well as the search for novel neuroprotective agents. A strategy to prevent the oxidative stress in neurons may be the use of chemopreventive agents as inducers of antioxidant and phase 2 enzymes. Sulforaphane (SF), derived from corresponding glucoraphanin, glucosinolate found in abundance in cruciferous vegetables, has recently gained attention as a potential neuroprotective compound inducer of antioxidant phase 2 enzymes. Consistent with this evidence, the study is aimed at identifying the SF ability to prevent and counteract the oxidative damage inducted by oligomers of Aβ (1-42) in terms of impairment in the intracellular redox state and cellular death in differentiated human neuroblastoma and microglia primary cultures. In addition we will evaluated the mechanism underlying the SF neuroprotection activity.

Role of Reactive Oxygen Species in signalling and oxidative stress

Results reported in this Thesis contribute to the comprehension of the complicated world of “redox biology”. ROS regulate signalling pathways both in physiological responses and in pathogenesis and progression of diseases. In cancer cells, the increase in ROS generation from metabolic abnormalities and oncogenic signalling may trigger a redox adaptation response, leading to an up-regulation of antioxidant capacity in order to maintain the ROS level below the toxic threshold. Thus, cancer cells would be more dependent on the antioxidant system and more vulnerable to further oxidative stress induced by exogenous ROS-generating agents or compounds that inhibit the antioxidant system. Results here reported indicate that the development of new drugs targeting specific Nox isoforms, responsible for intracellular ROS generation, or AQP isoforms, involved in the transport of extracellular H2O2 toward intracellular targets, might be an interesting novel anti-leukaemia strategy. Furthermore, also the use of CSD peptide, which simulate the VEGFR-2 segregation into caveolae in the inactive form, might be a strategy to stop the cellular response to VEGF signalling. As above stated, in the understanding of the redox biology, it is also important to identify and distinguish the molecular effectors that maintain normal biological and physiological responses, such as agents that stimulate our adaptation systems and elevate our endogenous antioxidant defences or other protective systems. Data here reported indicate that the nutraceutical compound sulforaphane and the Klotho protein are able to stimulate the HO-1 and Prx-1 expression, as well as the GSH levels, confirming their antioxidant and protective role. Finally, results here reported demonstrated that Stevia extracts are involved in insulin regulated glucose metabolism, suggesting that the use of these compounds goes beyond their sweetening power and may also offer therapeutic benefits hence improving the quality of life.

Evaluation of seismic losses of RC buildings: the case of the industrial areas after the 2012 Emilia Earthquake

The topic of seismic loss assessment not only incorporates many aspects of the earthquake engineering, but also entails social factors, public policies and business interests. Because of its multidisciplinary character, this process may be complex to challenge, and sound discouraging to neophytes. In this context, there is an increasing need of deriving simplified methodologies to streamline the process and provide tools for decision-makers and practitioners. This dissertation investigates different possible applications both in the area of modelling of seismic losses, both in the analysis of observational seismic data. Regarding the first topic, the PRESSAFE-disp method is proposed for the fast evaluation of the fragility curves of precast reinforced-concrete (RC) structures. Hence, a direct application of the method to the productive area of San Felice is studied to assess the number of collapses under a specific seismic scenario. In particular, with reference to the 2012 events, two large-scale stochastic models are outlined. The outcomes of the framework are promising, in good agreement with the observed damage scenario. Furthermore, a simplified displacement-based methodology is outlined to estimate different loss performance metrics for the decision-making phase of the seismic retrofit of a single RC building. The aim is to evaluate the seismic performance of different retrofit options, for a comparative analysis of their effectiveness and the convenience. Finally, a contribution to the analysis of the observational data is presented in the last part of the dissertation. A specific database of losses of precast RC buildings damaged by the 2012 Earthquake is created. A statistical analysis is performed, allowing deriving several consequence functions. The outcomes presented may be implemented in probabilistic seismic risk assessments to forecast the losses at the large scale. Furthermore, these may be adopted to establish retrofit policies to prevent and reduce the consequences of future earthquakes in industrial areas.

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

Neurogeometry of stereo vision

This work aims to develop a neurogeometric model of stereo vision, based on cortical architectures involved in the problem of 3D perception and neural mechanisms generated by retinal disparities. First, we provide a sub-Riemannian geometry for stereo vision, inspired by the work on the stereo problem by Zucker (2006), and using sub-Riemannian tools introduced by Citti-Sarti (2006) for monocular vision. We present a mathematical interpretation of the neural mechanisms underlying the behavior of binocular cells, that integrate monocular inputs. The natural compatibility between stereo geometry and neurophysiological models shows that these binocular cells are sensitive to position and orientation. Therefore, we model their action in the space R3xS2 equipped with a sub-Riemannian metric. Integral curves of the sub-Riemannian structure model neural connectivity and can be related to the 3D analog of the psychophysical association fields for the 3D process of regular contour formation. Then, we identify 3D perceptual units in the visual scene: they emerge as a consequence of the random cortico-cortical connection of binocular cells. Considering an opportune stochastic version of the integral curves, we generate a family of kernels. These kernels represent the probability of interaction between binocular cells, and they are implemented as facilitation patterns to define the evolution in time of neural population activity at a point. This activity is usually modeled through a mean field equation: steady stable solutions lead to consider the associated eigenvalue problem. We show that three-dimensional perceptual units naturally arise from the discrete version of the eigenvalue problem associated to the integro-differential equation of the population activity.

Neurogeometry of reaching

The purpose of the thesis is to develop a model for the functional behaviour of neurons in the primary motor cortex (M1) responsible for arm reaching movements. From Georgopoulos neurophysiological data, we provide a first bundle structure compatible with the hypercolumnar organization and with the position-direction selectivity of motor cortical cells. We then extend this model to encode the direction of arm movement which varies in time, as experimentally measured by Hatsopoulos by introducing the notion of movement fragments. We provide a sub-Riemannian model which describes the time-dependent directional selectivity of cells though integral curves of the geometric structure we set up. The sub-Riemannian distance we define allows to implement a grouping algorithm able to detect a set of hand motor trajectories. These paths, identified by using a kernel defined in terms of kinematic variables, are compatible with the motor primitives obtained from neurophysiological results by spectral analysis applied directly on cortical variables. In a second part of the work, we propose geodesics in this space as an alternative model of models for arm movement trajectories. We define a special class of curves, called admissible, on which to study the geodesics problem: we provide a connectivity property in terms of admissible paths and the existence of normal length minimizers. Admissible geodesics are used as a model of reaching paths, finding a first validation through Flash and Hogan minimizing trajectories.

Deep learning and embeddings for problems of computational biology

The development of Next Generation Sequencing promotes Biology in the Big Data era. The ever-increasing gap between proteins with known sequences and those with a complete functional annotation requires computational methods for automatic structure and functional annotation. My research has been focusing on proteins and led so far to the development of three novel tools, DeepREx, E-SNPs&GO and ISPRED-SEQ, based on Machine and Deep Learning approaches. DeepREx computes the solvent exposure of residues in a protein chain. This problem is relevant for the definition of structural constraints regarding the possible folding of the protein. DeepREx exploits Long Short-Term Memory layers to capture residue-level interactions between positions distant in the sequence, achieving state-of-the-art performances. With DeepRex, I conducted a large-scale analysis investigating the relationship between solvent exposure of a residue and its probability to be pathogenic upon mutation. E-SNPs&GO predicts the pathogenicity of a Single Residue Variation. Variations occurring on a protein sequence can have different effects, possibly leading to the onset of diseases. E-SNPs&GO exploits protein embeddings generated by two novel Protein Language Models (PLMs), as well as a new way of representing functional information coming from the Gene Ontology. The method achieves state-of-the-art performances and is extremely time-efficient when compared to traditional approaches. ISPRED-SEQ predicts the presence of Protein-Protein Interaction sites in a protein sequence. Knowing how a protein interacts with other molecules is crucial for accurate functional characterization. ISPRED-SEQ exploits a convolutional layer to parse local context after embedding the protein sequence with two novel PLMs, greatly surpassing the current state-of-the-art. All methods are published in international journals and are available as user-friendly web servers. They have been developed keeping in mind standard guidelines for FAIRness (FAIR: Findable, Accessible, Interoperable, Reusable) and are integrated into the public collection of tools provided by ELIXIR, the European infrastructure for Bioinformatics.

Characterisation of RNase Y in H. pylori: a non-essential enzyme involved in the processing of cag-PAI non coding RNA 1 (CncR1) sRNA

The importance of Helicobacter pylori as a human pathogen is underlined by the plethora of diseases it is responsible for. The capacity of H. pylori to adapt to the restricted host-associated environment andto evade the host immune response largely depends on a streamlined signalling network. The peculiar H. pylori small genome size combined with its paucity of transcriptional regulators highlights the relevance of post-transcriptional regulatory mechanisms as small non-coding RNAs (sRNAs). However, among the 8 RNases represented in H. pylori genome, a regulator guiding sRNAs metabolism is still not well studied. We investigated for the first time the physiological role in H. pylori G27 strain of the RNase Y enzyme. In the first line of research we provide a comprehensive characterization of the RNase Y activity by analysing its genomic organization and the factors that orchestrate its expression. Then, based on bioinformatic prediction models, we depict the most relevant determinants of RNase Y function, demonstrating a correlation of both structure and domain organization with orthologues represented in Gram-positive bacteria. To unveil the post-transcriptional regulatory effect exerted by the RNase Y, we compared the transcriptome of an RNase Y knock-out mutant to the parental wild type strain by RNA-seq approach. In the second line of research we characterized the activity of this single strand specific endoribonuclease on cag-PAI non coding RNA 1 (CncR1) sRNA. We found that deletion or inactivation of RNase Y led to the accumulation of a 3’-extended CncR1 (CncR1-L) transcript over time. Moreover, beneath its increased half-life, CncR1-L resembled a CncR1 inactive phenotype. Finally, we focused on the characterization of the in vivo interactome of CncR1. We set up a preliminary MS2-affinity purification coupled with RNA-sequencing (MAPS) approach and we evaluated the enrichment of specific targets, demonstrating the suitability of the technique in the H. pylori G27 strain.

Development of machine learning methods for multi-modal biomarkers detection and integration

In medicine, innovation depends on a better knowledge of the human body mechanism, which represents a complex system of multi-scale constituents. Unraveling the complexity underneath diseases proves to be challenging. A deep understanding of the inner workings comes with dealing with many heterogeneous information. Exploring the molecular status and the organization of genes, proteins, metabolites provides insights on what is driving a disease, from aggressiveness to curability. Molecular constituents, however, are only the building blocks of the human body and cannot currently tell the whole story of diseases. This is why nowadays attention is growing towards the contemporary exploitation of multi-scale information. Holistic methods are then drawing interest to address the problem of integrating heterogeneous data. The heterogeneity may derive from the diversity across data types and from the diversity within diseases. Here, four studies conducted data integration using customly designed workflows that implement novel methods and views to tackle the heterogeneous characterization of diseases. The first study devoted to determine shared gene regulatory signatures for onco-hematology and it showed partial co-regulation across blood-related diseases. The second study focused on Acute Myeloid Leukemia and refined the unsupervised integration of genomic alterations, which turned out to better resemble clinical practice. In the third study, network integration for artherosclerosis demonstrated, as a proof of concept, the impact of network intelligibility when it comes to model heterogeneous data, which showed to accelerate the identification of new potential pharmaceutical targets. Lastly, the fourth study introduced a new method to integrate multiple data types in a unique latent heterogeneous-representation that facilitated the selection of important data types to predict the tumour stage of invasive ductal carcinoma. The results of these four studies laid the groundwork to ease the detection of new biomarkers ultimately beneficial to medical practice and to the ever-growing field of Personalized Medicine.