Advanced neuroimaging methodologies to improve connectivity detection in normal and abnormal language brain networks

The language connectome was in-vivo investigated using multimodal non-invasive quantitative MRI. In PPA patients (n=18) recruited by the IRCCS ISNB, Bologna, cortical thickness measures showed a predominant reduction on the left hemisphere (p<0.005) with respect to matched healthy controls (HC) (n=18), and an accuracy of 86.1% in discrimination from Alzheimer’s disease patients (n=18). The left temporal and para-hippocampal gyri significantly correlated (p<0.01) with language fluency. In PPA patients (n=31) recruited by the Northwestern University Chicago, DTI measures were longitudinally evaluated (2-years follow-up) under the supervision of Prof. M. Catani, King’s College London. Significant differences with matched HC (n=27) were found, tract-localized at baseline and widespread in the follow-up. Language assessment scores correlated with arcuate (AF) and uncinate (UF) fasciculi DTI measures. In left-ischemic stroke patients (n=16) recruited by the NatBrainLab, King’s College London, language recovery was longitudinally evaluated (6-months follow-up). Using arterial spin labelling imaging a significant correlation (p<0.01) between language recovery and cerebral blood flow asymmetry, was found in the middle cerebral artery perfusion, towards the right. In HC (n=29) recruited by the DIBINEM Functional MR Unit, University of Bologna, an along-tract algorithm was developed suitable for different tractography methods, using the Laplacian operator. A higher left superior temporal gyrus and precentral operculum AF connectivity was found (Talozzi L et al., 2018), and lateralized UF projections towards the left dorsal orbital cortex. In HC (n=50) recruited in the Human Connectome Project, a new tractography-driven approach was developed for left association fibres, using a principal component analysis. The first component discriminated cortical areas typically connected by the AF, suggesting a good discrimination of cortical areas sharing a similar connectivity pattern. The evaluation of morphological, microstructural and metabolic measures could be used as in-vivo biomarkers to monitor language impairment related to neurodegeneration or as surrogate of cognitive rehabilitation/interventional treatment efficacy.

Characterization of DNA sequence properties through network and statistical approaches

In this thesis we will see that the DNA sequence is constantly shaped by the interactions with its environment at multiple levels, showing footprints of DNA methylation, of its 3D organization and, in the case of bacteria, of the interaction with the host organisms. In the first chapter, we will see that analyzing the distribution of distances between consecutive dinucleotides of the same type along the sequence, we can detect epigenetic and structural footprints. In particular, we will see that CG distance distribution allows to distinguish among organisms of different biological complexity, depending on how much CG sites are involved in DNA methylation. Moreover, we will see that CG and TA can be described by the same fitting function, suggesting a relationship between the two. We will also provide an interpretation of the observed trend, simulating a positioning process guided by the presence and absence of memory. In the end, we will focus on TA distance distribution, characterizing deviations from the trend predicted by the best fitting function, and identifying specific patterns that might be related to peculiar mechanical properties of the DNA and also to epigenetic and structural processes. In the second chapter, we will see how we can map the 3D structure of the DNA onto its sequence. In particular, we devised a network-based algorithm that produces a genome assembly starting from its 3D configuration, using as inputs Hi-C contact maps. Specifically, we will see how we can identify the different chromosomes and reconstruct their sequences by exploiting the spectral properties of the Laplacian operator of a network. In the third chapter, we will see a novel method for source clustering and source attribution, based on a network approach, that allows to identify host-bacteria interaction starting from the detection of Single-Nucleotide Polymorphisms along the sequence of bacterial genomes.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.