New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Gwas analysis for the identification of molecular basis responsible for yield related traits and disease resistance in durum wheat

The PhD thesis was developed in the framework of Innovar H2020 project. This project aimed at using genomics, transcriptomics and phenotyping techniques to update varietal registration procedure used in Europe for Value of Cultivation and Use (VCU) and Distinctiness Uniformity and Stability (DUS) protocols. The phenotypic and genotypic diversity of a durum wheat panel were assessed for different agronomic traits, connected with wheat development, disease resistance and spike fertility. A panel of 253 durum wheat varieties was characterized for VCU and DUS traits and genotyped with Illumina 90K SNP Chip array (Wang et al., 2014). GWAS analysis was performed, detecting strong QTLs confirmed also by literature review. Candidate genes were identified for each trait and molecular markers will be developed to be used for marker assisted selection in breeding programs. As for disease resistance, the panel was evaluated for resistance to Soil-Borne-Cereal-Mosaic-Virus (SBCMV). A major QTL, sbm2, was detected on chromosome 2B responsible for durum wheat resistance (Maccaferri et al., 2011). The sbm2 interval was explored by fine mapping on segregant population using KASP markers and by RNASeq analysis, detecting candidate genes involved in plant-pathogen reaction. As regards yield related traits, detailed analysis was performed on the GNI-2A QTL (Milner et al., 2016), responsible for increased number spike fertility. Fine mapping analysis was performed on durum panel identifying hox2 a strong candidate gene, codifying for transcription factor protein. The gene is paralogue of GNI-1 (Sakuma et al., 2019), and it has a 4 kbp deletion responsible for increased number of florets per spikelet. To conclude, the herein reported thesis shows a complete characterization of agronomic and disease resistance traits in modern durum wheat varieties. The results obtained will augment available information for each variety, identifying informative molecular markers for breeding purposes and QTLs/candidate genes responsible for different agronomic traits.

Characterization of an international tetraploid wheat germplasm including landraces and primitive wheat towards improved resilience to abiotic and biotic stresses and quality

This thesis aimed to characterise two large tetraploid germplasm collections. The Global Durum Panel, involving modern cultivars and landrances and the Tetraploid Global Collection which comprises all the tetraploid wheat subgroups. Two distinct parallel studies were carried out. The first is focused on the characterisation of both collection for yield and quality related traits. The panel were phenotyped for two consecutive years each. In this phase the following traits were collected: the number of fertile spikelets per spike, the number of fertile florets of central spikelet for the spike-related traits. The following grain related traits were also phenotyped: the thousand kernel weight, the average grain area, average grain length, average grain width, grain brightness, grain redness, grain yellowness. GWAS analysis were performed for each collected trait and major QTLs were subjected to candidate gene analysis. Major QTLs emerging from GWA study were located on chromosome 2A with a strong bibliographic evidence for grain number-related traits such as the fertile spikelet number, the number of fertile florets per central spikelet. On the other hand two evident peaks were detected on chromosomes 6A and 7B for grain size and weight related traits. The second work was focused on the characterisation of the Global Durum Panel for root system architecture components, namely the root growth angle. GWAS analysis was perfomed and three major QTLs were detected on chromosome 2A, 6A and 7A. These three QTLs all have a bibliographic evidence.

Uncovering the encoding and transmission of behaviourally relevant information in neural activity

Most cognitive functions require the encoding and routing of information across distributed networks of brain regions. Information propagation is typically attributed to physical connections existing between brain regions, and contributes to the formation of spatially correlated activity patterns, known as functional connectivity. While structural connectivity provides the anatomical foundation for neural interactions, the exact manner in which it shapes functional connectivity is complex and not yet fully understood. Additionally, traditional measures of directed functional connectivity only capture the overall correlation between neural activity, and provide no insight on the content of transmitted information, limiting their ability in understanding neural computations underlying the distributed processing of behaviorally-relevant variables. In this work, we first study the relationship between structural and functional connectivity in simulated recurrent spiking neural networks with spike timing dependent plasticity. We use established measures of time-lagged correlation and overall information propagation to infer the temporal evolution of synaptic weights, showing that measures of dynamic functional connectivity can be used to reliably reconstruct the evolution of structural properties of the network. Then, we extend current methods of directed causal communication between brain areas, by deriving an information-theoretic measure of Feature-specific Information Transfer (FIT) quantifying the amount, content and direction of information flow. We test FIT on simulated data, showing its key properties and advantages over traditional measures of overall propagated information. We show applications of FIT to several neural datasets obtained with different recording methods (magneto and electro-encephalography, spiking activity, local field potentials) during various cognitive functions, ranging from sensory perception to decision making and motor learning. Overall, these analyses demonstrate the ability of FIT to advance the investigation of communication between brain regions, uncovering the previously unaddressed content of directed information flow.

Numerical simulation of the flow and performance evaluation of an aerospike engine

The main focus of this work is to define a numerical methodology to simulate an aerospike engine and then to analyse the performance of DemoP1, which is a small aerospike demonstrator built by Pangea Aerospace. The aerospike is a promising solution to build more efficient engine than the actual one. Its main advantage is the expansion adaptation that allows to reach the optimal expansion in a wide range of ambient pressures delivering more thrust than an equivalent bell-shaped nozzle. The main drawbacks are the cooling system design and the spike manufacturing but nowadays, these issues seem to be overcome with the use of the additive manufacturing method. The simulations are performed with dbnsTurbFoam which is a solver of OpenFOAM. It has been designed to simulate a supersonic compressible turbulent flow. This work is divided in four chapters. The first one is a short introduction. The second one shows a brief summary of the theoretical performance of the aerospike. The third one introduces the numerical methodology to simulate a compressible supersonic flow. In the fourth chapter, the solver has been verified with an experiment found in literature. And in the fifth chapter, the simulations on DemoP1 engine are illustrated.