Interpretable Convolutional Neural Networks for Decoding and Analyzing Neural Time Series Data

Machine learning is widely adopted to decode multi-variate neural time series, including electroencephalographic (EEG) and single-cell recordings. Recent solutions based on deep learning (DL) outperformed traditional decoders by automatically extracting relevant discriminative features from raw or minimally pre-processed signals. Convolutional Neural Networks (CNNs) have been successfully applied to EEG and are the most common DL-based EEG decoders in the state-of-the-art (SOA). However, the current research is affected by some limitations. SOA CNNs for EEG decoding usually exploit deep and heavy structures with the risk of overfitting small datasets, and architectures are often defined empirically. Furthermore, CNNs are mainly validated by designing within-subject decoders. Crucially, the automatically learned features mainly remain unexplored; conversely, interpreting these features may be of great value to use decoders also as analysis tools, highlighting neural signatures underlying the different decoded brain or behavioral states in a data-driven way. Lastly, SOA DL-based algorithms used to decode single-cell recordings rely on more complex, slower to train and less interpretable networks than CNNs, and the use of CNNs with these signals has not been investigated. This PhD research addresses the previous limitations, with reference to P300 and motor decoding from EEG, and motor decoding from single-neuron activity. CNNs were designed light, compact, and interpretable. Moreover, multiple training strategies were adopted, including transfer learning, which could reduce training times promoting the application of CNNs in practice. Furthermore, CNN-based EEG analyses were proposed to study neural features in the spatial, temporal and frequency domains, and proved to better highlight and enhance relevant neural features related to P300 and motor states than canonical EEG analyses. Remarkably, these analyses could be used, in perspective, to design novel EEG biomarkers for neurological or neurodevelopmental disorders. Lastly, CNNs were developed to decode single-neuron activity, providing a better compromise between performance and model complexity.

Development of functional MRI protocols in the study of neurodegenerative diseases: MRI study in patients with REM sleep behavior disorder, idiopathic Parkinson's disease and multisystem atrophy

In the central nervous system, iron in several proteins is involved in many important processes: oxygen transportation, oxidative phosphorylation, mitochondrial respiration, myelin production, the synthesis and metabolism of neurotransmitters. Abnormal iron homoeostasis can induce cellular damage through hydroxyl radical production, which can cause the oxidation, modification of lipids, proteins, carbohydrates, and DNA, lead to neurotoxicity. Moreover increased levels of iron are harmful and iron accumulations are typical hallmarks of brain ageing and several neurodegenerative disorders particularly PD. Numerous studies on post mortem tissue report on an increased amount of total iron in the substantia nigra in patients with PD also supported by large body of in vivo findings from Magnetic Resonance Imaging (MRI) studies. The importance and approaches for in vivo brain iron assessment using multiparametric MRI is increased over last years. Quantitative MRI may provide useful biomarkers for brain integrity assessment in iron-related neurodegeneration. Particularly, a prominent change in iron- sensitive T2* MRI contrast within the sub areas of the SN overlapping with nigrosome 1 were shown to be a hallmark of Parkinson's Disease with high diagnostic accuracy. Moreover, differential diagnosis between Parkinson's Disease (PD) and atypical parkinsonian syndromes (APS) remains challenging, mainly in the early phases of the disease. Advanced brain MR imaging enables to detect the pathological changes of nigral and extranigral structures at the onset of clinical manifestations and during the course of the disease. The Nigrosome-1 (N1) is a substructure of the healthy Substantia Nigra pars compacta enriched by dopaminergic neurons; their loss in Parkinson’s disease and atypical parkinsonian syndromes is related to the iron accumulation. N1 changes are supportive MR biomarkers for diagnosis of these neurodegenerative disorders, but its detection is hard with conventional sequences, also using high field (3T) scanner. Quantitative susceptibility mapping (QSM), an iron-sensitive technique, enables the direct detection of Neurodegeneration

Oceanic Near-inertial internal waves generation, propagation and interaction with mesoscale dynamics

Oceans play a key role in the climate system, being the largest heat sinks on Earth. Part of the energy balance of ocean circulation is driven by the Near-inertial internal waves (NIWs). Strong NIWs are observed during a multi-platform, multi-disciplinary and multi-scale campaign led by the NATO-STO CMRE in autumn 2017 in the Ligurian Sea (northwestern Mediterranean Sea). The objectives of this work are as follows: characterise the studied area at different scales; study the NIWs generation and their propagation; estimate the NIWs properties; study the interaction between NIWs and mesoscale structures. This work provides, to the author’s knowledge, the first characterization of NIWs in the Mediterranean Sea. The near-surface NIWs observed at the fixed moorings are locally generated by wind bursts while the deeper waves originate in other regions and arrive at the moorings several days later. Most of the observed NIWs energy propagates downward with a mean vertical group velocity of (2.2±0.3) ⋅10-4 m s-1. On average, the NIWs have an amplitude of 0.13 m s-1 and mean horizontal and vertical wavelengths of 43±25 km and 125±35 m, while shorter wavelengths are observed at the near-coastal mooring, 36±2 km and 33±2 m, respectively. Most of the observed NIWs are blue shifted and reach a value 9% higher than the local inertial frequency. Only two observed NIWs are characterised by a redshift (up to 3% lower than the local inertial frequency). In support of the in situ observations, a high resolution numerical model is implemented using NEMO (Madec et al., 2019). Results show that anticyclones (cyclones) shift the frequency of NIWs to lower (higher) frequencies with respect to the local inertial frequency. Anticyclones facilitate the downward propagation of NIW energy, while cyclones dampen it. Absence of NIWs energy within an anticyclone is also investigated.

Towards a logical foundation of randomized computation

This dissertation investigates the relations between logic and TCS in the probabilistic setting. It is motivated by two main considerations. On the one hand, since their appearance in the 1960s-1970s, probabilistic models have become increasingly pervasive in several fast-growing areas of CS. On the other, the study and development of (deterministic) computational models has considerably benefitted from the mutual interchanges between logic and CS. Nevertheless, probabilistic computation was only marginally touched by such fruitful interactions. The goal of this thesis is precisely to (start) bring(ing) this gap, by developing logical systems corresponding to specific aspects of randomized computation and, therefore, by generalizing standard achievements to the probabilistic realm. To do so, our key ingredient is the introduction of new, measure-sensitive quantifiers associated with quantitative interpretations. The dissertation is tripartite. In the first part, we focus on the relation between logic and counting complexity classes. We show that, due to our classical counting propositional logic, it is possible to generalize to counting classes, the standard results by Cook and Meyer and Stockmeyer linking propositional logic and the polynomial hierarchy. Indeed, we show that the validity problem for counting-quantified formulae captures the corresponding level in Wagner's hierarchy. In the second part, we consider programming language theory. Type systems for randomized \lambda-calculi, also guaranteeing various forms of termination properties, were introduced in the last decades, but these are not "logically oriented" and no Curry-Howard correspondence is known for them. Following intuitions coming from counting logics, we define the first probabilistic version of the correspondence. Finally, we consider the relationship between arithmetic and computation. We present a quantitative extension of the language of arithmetic able to formalize basic results from probability theory. This language is also our starting point to define randomized bounded theories and, so, to generalize canonical results by Buss.