Implementation of network entropy algorithms on hpc machines, with application to high-dimensional experimental data

Network Theory is a prolific and lively field, especially when it approaches Biology. New concepts from this theory find application in areas where extensive datasets are already available for analysis, without the need to invest money to collect them. The only tools that are necessary to accomplish an analysis are easily accessible: a computing machine and a good algorithm. As these two tools progress, thanks to technology advancement and human efforts, wider and wider datasets can be analysed. The aim of this paper is twofold. Firstly, to provide an overview of one of these concepts, which originates at the meeting point between Network Theory and Statistical Mechanics: the entropy of a network ensemble. This quantity has been described from different angles in the literature. Our approach tries to be a synthesis of the different points of view. The second part of the work is devoted to presenting a parallel algorithm that can evaluate this quantity over an extensive dataset. Eventually, the algorithm will also be used to analyse high-throughput data coming from biology.

Approccio network-based alla discriminant analysis mediante HPC per la ricerca di signature ottimali in dati ad alta dimensionalità

Il presente lavoro di tesi si inserisce nell’ambito della classificazione di dati ad alta dimensionalità, sviluppando un algoritmo basato sul metodo della Discriminant Analysis. Esso classifica i campioni attraverso le variabili prese a coppie formando un network a partire da quelle che hanno una performance sufficientemente elevata. Successivamente, l’algoritmo si avvale di proprietà topologiche dei network (in particolare la ricerca di subnetwork e misure di centralità di singoli nodi) per ottenere varie signature (sottoinsiemi delle variabili iniziali) con performance ottimali di classificazione e caratterizzate da una bassa dimensionalità (dell’ordine di 101, inferiore di almeno un fattore 103 rispetto alle variabili di partenza nei problemi trattati). Per fare ciò, l’algoritmo comprende una parte di definizione del network e un’altra di selezione e riduzione della signature, calcolando ad ogni passaggio la nuova capacità di classificazione operando test di cross-validazione (k-fold o leave- one-out). Considerato l’alto numero di variabili coinvolte nei problemi trattati – dell’ordine di 104 – l’algoritmo è stato necessariamente implementato su High-Performance Computer, con lo sviluppo in parallelo delle parti più onerose del codice C++, nella fattispecie il calcolo vero e proprio del di- scriminante e il sorting finale dei risultati. L’applicazione qui studiata è a dati high-throughput in ambito genetico, riguardanti l’espressione genica a livello cellulare, settore in cui i database frequentemente sono costituiti da un numero elevato di variabili (104 −105) a fronte di un basso numero di campioni (101 −102). In campo medico-clinico, la determinazione di signature a bassa dimensionalità per la discriminazione e classificazione di campioni (e.g. sano/malato, responder/not-responder, ecc.) è un problema di fondamentale importanza, ad esempio per la messa a punto di strategie terapeutiche personalizzate per specifici sottogruppi di pazienti attraverso la realizzazione di kit diagnostici per l’analisi di profili di espressione applicabili su larga scala. L’analisi effettuata in questa tesi su vari tipi di dati reali mostra che il metodo proposto, anche in confronto ad altri metodi esistenti basati o me- no sull’approccio a network, fornisce performance ottime, tenendo conto del fatto che il metodo produce signature con elevate performance di classifica- zione e contemporaneamente mantenendo molto ridotto il numero di variabili utilizzate per questo scopo.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Numerical simulation of interdigitated back contact hetero-junction solar cells

The goal of this thesis is the application of an opto-electronic numerical simulation to heterojunction silicon solar cells featuring an all back contact architecture (Interdigitated Back Contact Hetero-Junction IBC-HJ). The studied structure exhibits both metal contacts, emitter and base, at the back surface of the cell with the objective to reduce the optical losses due to the shadowing by front contact of conventional photovoltaic devices. Overall, IBC-HJ are promising low-cost alternatives to monocrystalline wafer-based solar cells featuring front and back contact schemes, in fact, for IBC-HJ the high concentration doping diffusions are replaced by low-temperature deposition processes of thin amorphous silicon layers. Furthermore, another advantage of IBC solar cells with reference to conventional architectures is the possibility to enable a low-cost assembling of photovoltaic modules, being all contacts on the same side. A preliminary extensive literature survey has been helpful to highlight the specific critical aspects of IBC-HJ solar cells as well as the state-of-the-art of their modeling, processing and performance of practical devices. In order to perform the analysis of IBC-HJ devices, a two-dimensional (2-D) numerical simulation flow has been set up. A commercial device simulator based on finite-difference method to solve numerically the whole set of equations governing the electrical transport in semiconductor materials (Sentuarus Device by Synopsys) has been adopted. The first activity carried out during this work has been the definition of a 2-D geometry corresponding to the simulation domain and the specification of the electrical and optical properties of materials. In order to calculate the main figures of merit of the investigated solar cells, the spatially resolved photon absorption rate map has been calculated by means of an optical simulator. Optical simulations have been performed by using two different methods depending upon the geometrical features of the front interface of the solar cell: the transfer matrix method (TMM) and the raytracing (RT). The first method allows to model light prop-agation by plane waves within one-dimensional spatial domains under the assumption of devices exhibiting stacks of parallel layers with planar interfaces. In addition, TMM is suitable for the simulation of thin multi-layer anti reflection coating layers for the reduction of the amount of reflected light at the front interface. Raytracing is required for three-dimensional optical simulations of upright pyramidal textured surfaces which are widely adopted to significantly reduce the reflection at the front surface. The optical generation profiles are interpolated onto the electrical grid adopted by the device simulator which solves the carriers transport equations coupled with Poisson and continuity equations in a self-consistent way. The main figures of merit are calculated by means of a postprocessing of the output data from device simulation. After the validation of the simulation methodology by means of comparison of the simulation result with literature data, the ultimate efficiency of the IBC-HJ architecture has been calculated. By accounting for all optical losses, IBC-HJ solar cells result in a theoretical maximum efficiency above 23.5% (without texturing at front interface) higher than that of both standard homojunction crystalline silicon (Homogeneous Emitter HE) and front contact heterojuction (Heterojunction with Intrinsic Thin layer HIT) solar cells. However it is clear that the criticalities of this structure are mainly due to the defects density and to the poor carriers transport mobility in the amorphous silicon layers. Lastly, the influence of the most critical geometrical and physical parameters on the main figures of merit have been investigated by applying the numerical simulation tool set-up during the first part of the present thesis. Simulations have highlighted that carrier mobility and defects level in amorphous silicon may lead to a potentially significant reduction of the conversion efficiency.

Numerical Analysis and Redesign of a High Speed Linear Cascade Wind Tunnel for Aircraft Gas Turbine Engines Testing

Linear cascade testing serves a fundamental role in the research, development, and design of turbomachines as it is a simple yet very effective way to compute the performance of a generic blade geometry. These kinds of experiments are usually carried out in specialized wind tunnel facilities. This thesis deals with the numerical characterization and subsequent partial redesign of the S-1/C Continuous High Speed Wind Tunnel of the Von Karman Institute for Fluid Dynamics. The current facility is powered by a 13-stage axial compressor that is not powerful enough to balance the energy loss experienced when testing low turning airfoils. In order to address this issue a performance assessment of the wind tunnel was performed under several flow regimes via numerical simulations. After that, a redesign proposal aimed at reducing the pressure loss was investigated. This consists of a linear cascade of turning blades to be placed downstream of the test section and designed specifically for the type of linear cascade being tested. An automatic design procedure was created taking as input parameters those measured at the outlet of the cascade. The parametrization method employed Bézier curves to produce an airfoil geometry that could be imported into a CAD software so that a cascade could be designed. The proposal was simulated via CFD analysis and proved to be effective in reducing pressure losses up to 41%. The same tool developed in this thesis could be adopted to design similar apparatuses and could also be optimized and specialized for the design of turbomachines components.

Characterization of in-gap electronic states in two-dimensional single crystal PEA2PbBr4 perovskite for X-ray detection

Hybrid Organic-Inorganic Halide Perovskites (HOIPs) include a large class of materials described with the general formula ABX3, where A is an organic cation, B an inorganic cation and X an halide anion. HOIPs show excellent optoelectronic characteristics such as tunable band gap, high adsorption coefficient and great mobility life-time. A subclass of these materials, the so-called two- dimensional (2D) layered HOIPs, have emerged as potential alternatives to traditional 3D analogs to enhance the stability and increase performance of perovskite devices, with particular regard in the area of ionizing radiation detectors, where these materials have reached truly remarkable milestones. One of the key challenges for future development of efficient and stable 2D perovskite X-ray detector is a complete understanding of the nature of defects that lead to the formation of deep states. Deep states act as non-radiative recombination centers for charge carriers and are one of the factors that most hinder the development of efficient 2D HOIPs-based X-ray detectors. In this work, deep states in PEA2PbBr4 were studied through Photo-Induced Current Transient Spectroscopy (PICTS), a highly sensitive spectroscopic technique capable of detecting the presence of deep states in highly resistive ohmic materials, and characterizing their activation energy, capture cross section and, under stringent conditions, the concentration of these states. The evolution of deep states in PEA 2 PbBr 4 was evaluated after exposure of the material to high doses of ionizing radiation and during aging (one year). The data obtained allowed us to evaluate the contribution of ion migration in PEA2PbBr4. This work represents an important starting point for a better understanding of transport and recombination phenomena in 2D perovskites. To date, the PICTS technique applied to 2D perovskites has not yet been reported in the scientific literature.