Markov Constraints for Generating Texts with Style

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Halogenated aliphatic and aromatic aerobic biodegradation via direct metabolism and cometabolism: batch and continuous tests

In this thesis the application of biotechnological processes based on microbial metabolic degradation of halogenated compound has been investigated. Several studies showed that most of these pollutants can be biodegraded by single bacterial strains or mixed microbial population via aerobic direct metabolism or cometabolism using as a growth substrates aromatic or aliphatic hydrocarbons. The enhancement of two specific processes has been here object of study in relation with its own respective scenario described as follow: 1st) the bioremediation via aerobic cometabolism of soil contaminated by a high chlorinated compound using a mixed microbial population and the selection and isolation of consortium specific for the compound. 2nd) the implementation of a treatment technology based on direct metabolism of two pure strains at the exact point source of emission, preventing dilution and contamination of large volumes of waste fluids polluted by several halogenated compound minimizing the environmental impact. In order to verify the effect of these two new biotechnological application to remove halogenated compound and purpose them as a more efficient alternative continuous and batch tests have been set up in the experimental part of this thesis. Results obtained from the continuous tests in the second scenario have been supported by microbial analysis via Fluorescence in situ Hybridisation (FISH) and by a mathematical model of the system. The results showed that both process in its own respective scenario offer an effective solutions for the biological treatment of chlorinate compound pollution.

Continuous geochemical monitoring by mass-spectometer in the Campi Flegrei geothermal area. An application at Pisciarelli-Solfatara (diffuse and fumarolic gases) and at the mud gases during drilling of the CFDDP pilot hole

During this work has been developed an innovative methodology for continuous and in situ gas monitoring (24/24 h) of fumarolic and soil diffusive emissions applied to the geothermal and volcanic area of Pisciarelli near Agnano inside the Campi Flegrei caldera (CFc). In literature there are only scattered and in discrete data of the geochemical gas composition of fumarole at Campi Flegrei; it is only since the early ’80 that exist a systematic record of fumaroles with discrete sampling at Solfatara (Bocca Grande and Bocca Nuova fumaroles) and since 1999, even at the degassing areas of Pisciarelli. This type of sampling has resulted in a time series of geochemical analysis with discontinuous periods of time set (in average 2-3 measurements per month) completely inadequate for the purposes of Civil Defence in such high volcanic risk and densely populated areas. For this purpose, and to remedy this lack of data, during this study was introduced a new methodology of continuous and in situ sampling able to continuously detect data related and from its soil diffusive degassing. Due to its high sampling density (about one measurement per minute therefore producing 1440 data daily) and numerous species detected (CO2, Ar, 36Ar, CH4, He, H2S, N2, O2) allowing a good statistic record and the reconstruction of the gas composition evolution of the investigated area. This methodology is based on continuous sampling of fumaroles gases and soil degassing using an extraction line, which after undergoing a series of condensation processes of the water vapour content - better described hereinafter - is analyzed through using a quadrupole mass spectrometer

A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.