Stochastic modeling of bacterial protein domains distribution to predict horizontal gene transfer

In questo elaborato, abbiamo tentato di modellizzare i processi che regolano la presenza dei domini proteici. I domini proteici studiati in questa tesi sono stati ottenuti dai genomi batterici disponibili nei data base pubblici (principalmente dal National Centre for Biotechnology Information: NCBI) tramite una procedura di simulazione computazionale. Ci siamo concentrati su organismi batterici in quanto in essi la presenza di geni trasmessi orizzontalmente, ossia che parte del materiale genetico non provenga dai genitori, e assodato che sia presente in una maggiore percentuale rispetto agli organismi più evoluti. Il modello usato si basa sui processi stocastici di nascita e morte, con l'aggiunta di un parametro di migrazione, usato anche nella descrizione dell'abbondanza relativa delle specie in ambito delle biodiversità ecologiche. Le relazioni tra i parametri, calcolati come migliori stime di una distribuzione binomiale negativa rinormalizzata e adattata agli istogrammi sperimentali, ci induce ad ipotizzare che le famiglie batteriche caratterizzate da un basso valore numerico del parametro di immigrazione abbiano contrastato questo deficit con un elevato valore del tasso di nascita. Al contrario, ipotizziamo che le famiglie con un tasso di nascita relativamente basso si siano adattate, e in conseguenza, mostrano un elevato valore del parametro di migrazione. Inoltre riteniamo che il parametro di migrazione sia direttamente proporzionale alla quantità di trasferimento genico orizzontale effettuato dalla famiglia batterica.

A framework for risk analysis in automotive cybersecurity

We address the problem of automotive cybersecurity from the point of view of Threat Analysis and Risk Assessment (TARA). The central question that motivates the thesis is the one about the acceptability of risk, which is vital in taking a decision about the implementation of cybersecurity solutions. For this purpose, we develop a quantitative framework in which we take in input the results of risk assessment and define measures of various facets of a possible risk response; we then exploit the natural presence of trade-offs (cost versus effectiveness) to formulate the problem as a multi-objective optimization. Finally, we develop a stochastic model of the future evolution of the risk factors, by means of Markov chains; we adapt the formulations of the optimization problems to this non-deterministic context. The thesis is the result of a collaboration with the Vehicle Electrification division of Marelli, in particular with the Cybersecurity team based in Bologna; this allowed us to consider a particular instance of the problem, deriving from a real TARA, in order to test both the deterministic and the stochastic framework in a real world application. The collaboration also explains why in the work we often assume the point of view of a tier-1 supplier; however, the analyses performed can be adapted to any other level of the supply chain.

Data analysis and hydrological modelling of rainfall and discharge extremes along the Tione River: implications for the design of water structures

There are many natural events that can negatively affect the urban ecosystem, but weather-climate variations are certainly among the most significant. The history of settlements has been characterized by extreme events like earthquakes and floods, which repeat themselves at different times, causing extensive damage to the built heritage on a structural and urban scale. Changes in climate also alter various climatic subsystems, changing rainfall regimes and hydrological cycles, increasing the frequency and intensity of extreme precipitation events (heavy rainfall).  From an hydrological risk perspective, it is crucial to understand future events that could occur and their magnitude in order to design safer infrastructures. Unfortunately, it is not easy to understand future scenarios as the complexity of climate is enormous.  For this thesis, precipitation and discharge extremes were primarily used as data sources. It is important to underline that the two data sets are not separated: changes in rainfall regime, due to climate change, could significantly affect overflows into receiving water bodies. It is imperative that we understand and model climate change effects on water structures to support the development of adaptation strategies.   The main purpose of this thesis is to search for suitable water structures for a road located along the Tione River. Therefore, through the analysis of the area from a hydrological point of view, we aim to guarantee the safety of the infrastructure over time.   The observations made have the purpose to underline how models such as a stochastic one can improve the quality of an analysis for design purposes, and influence choices.

Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Mimicking the one-dimensional marginal distributions of stochastic diffusions

In the large maturity limit, we compute explicitly the Local Volatility surface for Heston, through Dupire’s formula, with Fourier pricing of the respective derivatives of the call price. Than we verify that the prices of European call options produced by the Heston model, concide with those given by the local volatility model where the Local Volatility is computed as said above.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

A deep learning model via thermodynamics and condensed matter physics

Deep Learning architectures give brilliant results in a large variety of fields, but a comprehensive theoretical description of their inner functioning is still lacking. In this work, we try to understand the behavior of neural networks by modelling in the frameworks of Thermodynamics and Condensed Matter Physics. We approach neural networks as in a real laboratory and we measure the frequency spectrum and the entropy of the weights of the trained model. The stochasticity of the training occupies a central role in the dynamics of the weights and makes it difficult to assimilate neural networks to simple physical systems. However, the analogy with Thermodynamics and the introduction of a well defined temperature leads us to an interesting result: if we eliminate from a CNN the "hottest" filters, the performance of the model remains the same, whereas, if we eliminate the "coldest" ones, the performance gets drastically worst. This result could be exploited in the realization of a training loop which eliminates the filters that do not contribute to loss reduction. In this way, the computational cost of the training will be lightened and more importantly this would be done by following a physical model. In any case, beside important practical applications, our analysis proves that a new and improved modeling of Deep Learning systems can pave the way to new and more efficient algorithms.

Stochastic physics and representation of El Niño Southern Oscillation in climate models

El Niño-Southern Oscillation (ENSO) è il maggiore fenomeno climatico che avviene a livello dell’Oceano Pacifico tropicale e che ha influenze ambientali, climatiche e socioeconomiche a larga scala. In questa tesi si ripercorrono i passi principali che sono stati fatti per tentare di comprendere un fenomeno così complesso. Per prima cosa, si sono studiati i meccanismi che ne governano la dinamica, fino alla formulazione del modello matematico chiamato Delayed Oscillator (DO) model, proposto da Suarez e Schopf nel 1988. In seguito, per tenere conto della natura caotica del sistema studiato, si è introdotto nel modello lo schema chiamato Stochastically Perturbed Parameterisation Tendencies (SPPT). Infine, si sono portati due esempi di soluzione numerica del DO, sia con che senza l’introduzione della correzione apportata dallo schema SPPT, e si è visto in che misura SPPT porta reali miglioramenti al modello studiato.