Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

Models and methods for damage and quantitative risk assessment of Natech scenarios

Natural events are a widely recognized hazard for industrial sites where relevant quantities of hazardous substances are handled, due to the possible generation of cascading events resulting in severe technological accidents (Natech scenarios). Natural events may damage storage and process equipment containing hazardous substances, that may be released leading to major accident scenarios called Natech events. The need to assess the risk associated with Natech scenarios is growing and methodologies were developed to allow the quantification of Natech risk, considering both point sources and linear sources as pipelines. A key element of these procedures is the use of vulnerability models providing an estimation of the damage probability of equipment or pipeline segment as a result of the impact of the natural event. Therefore, the first aim of the PhD project was to outline the state of the art of vulnerability models for equipment and pipelines subject to natural events such as floods, earthquakes, and wind. Moreover, the present PhD project also aimed at the development of new vulnerability models in order to fill some gaps in literature. In particular, a vulnerability model for vertical equipment subject to wind and to flood were developed. Finally, in order to improve the calculation of Natech risk for linear sources an original methodology was developed for Natech quantitative risk assessment methodology for pipelines subject to earthquakes. Overall, the results obtained are a step forward in the quantitative risk assessment of Natech accidents. The tools developed open the way to the inclusion of new equipment in the analysis of Natech events, and the methodology for the assessment of linear risk sources as pipelines provides an important tool for a more accurate and comprehensive assessment of Natech risk.