Processi di semi-Markov a tempo discreto

Studio della teoria dei processi di semi-Markov nella modellizzazione a tempo discreto. Introduzione delle catene di rinnovo di Markov, del nucleo di semi-Markov e delle catene di semi-Markov, risultati ad essi relativi. Analisi delle equazioni di rinnovo di Markov, caratterizzazione degli stati di una catena di semi-Markov, teorema di esistenza e unicità dell'equazione di rinnovo di Markov. Un esempio concreto.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

New markov chain based methods for single and cross-domain sentiment classification

Nowadays communication is switching from a centralized scenario, where communication media like newspapers, radio, TV programs produce information and people are just consumers, to a completely different decentralized scenario, where everyone is potentially an information producer through the use of social networks, blogs, forums that allow a real-time worldwide information exchange. These new instruments, as a result of their widespread diffusion, have started playing an important socio-economic role. They are the most used communication media and, as a consequence, they constitute the main source of information enterprises, political parties and other organizations can rely on. Analyzing data stored in servers all over the world is feasible by means of Text Mining techniques like Sentiment Analysis, which aims to extract opinions from huge amount of unstructured texts. This could lead to determine, for instance, the user satisfaction degree about products, services, politicians and so on. In this context, this dissertation presents new Document Sentiment Classification methods based on the mathematical theory of Markov Chains. All these approaches bank on a Markov Chain based model, which is language independent and whose killing features are simplicity and generality, which make it interesting with respect to previous sophisticated techniques. Every discussed technique has been tested in both Single-Domain and Cross-Domain Sentiment Classification areas, comparing performance with those of other two previous works. The performed analysis shows that some of the examined algorithms produce results comparable with the best methods in literature, with reference to both single-domain and cross-domain tasks, in $2$-classes (i.e. positive and negative) Document Sentiment Classification. However, there is still room for improvement, because this work also shows the way to walk in order to enhance performance, that is, a good novel feature selection process would be enough to outperform the state of the art. Furthermore, since some of the proposed approaches show promising results in $2$-classes Single-Domain Sentiment Classification, another future work will regard validating these results also in tasks with more than $2$ classes.

Conditional entropy and predictability for non-reversible Markov systems

The purpose of this thesis is to clarify the role of non-equilibrium stationary currents of Markov processes in the context of the predictability of future states of the system. Once the connection between the predictability and the conditional entropy is established, we provide a comprehensive approach to the definition of a multi-particle Markov system. In particular, starting from the well-known theory of random walk on network, we derive the non-linear master equation for an interacting multi-particle system under the one-step process hypothesis, highlighting the limits of its tractability and the prop- erties of its stationary solution. Lastly, in order to study the impact of the NESS on the predictability at short times, we analyze the conditional entropy by modulating the intensity of the stationary currents, both for a single-particle and a multi-particle Markov system. The results obtained analytically are numerically tested on a 5-node cycle network and put in correspondence with the stationary entropy production. Furthermore, because of the low dimensionality of the single-particle system, an analysis of its spectral properties as a function of the modulated stationary currents is performed.

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.