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.

Study of a new method for high energy top tagging at the ATLAS experiment

Since its discovery, top quark has represented one of the most investigated field in particle physics. The aim of this thesis is the reconstruction of hadronic top with high transverse momentum (boosted) with the Template Overlap Method (TOM). Because of the high energy, the decay products of boosted tops are partially or totally overlapped and thus they are contained in a single large radius jet (fat-jet). TOM compares the internal energy distributions of the candidate fat-jet to a sample of tops obtained by a MC simulation (template). The algorithm is based on the definition of an overlap function, which quantifies the level of agreement between the fat-jet and the template, allowing an efficient discrimination of signal from the background contributions. A working point has been decided in order to obtain a signal efficiency close to 90% and a corresponding background rejection at 70%. TOM performances have been tested on MC samples in the muon channel and compared with the previous methods present in literature. All the methods will be merged in a multivariate analysis to give a global top tagging which will be included in ttbar production differential cross section performed on the data acquired in 2012 at sqrt(s)=8 TeV in high phase space region, where new physics processes could be possible. Due to its peculiarity to increase the pT, the Template Overlap Method will play a crucial role in the next data taking at sqrt(s)=13 TeV, where the almost totality of the tops will be produced at high energy, making the standard reconstruction methods inefficient.

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.