On the Wick product and Wong-Zakai approximations.

This thesis is a compilation of 6 papers that the author has written together with Alberto Lanconelli (chapters 3, 5 and 8) and Hyun-Jung Kim (ch 7). The logic thread that link all these chapters together is the interest to analyze and approximate the solutions of certain stochastic differential equations using the so called Wick product as the basic tool. In the first chapter we present arguably the most important achievement of this thesis; namely the generalization to multiple dimensions of a Wick-Wong-Zakai approximation theorem proposed by Hu and Oksendal. By exploiting the relationship between the Wick product and the Malliavin derivative we propose an original reduction method which allows us to approximate semi-linear systems of stochastic differential equations of the Itô type. Furthermore in chapter 4 we present a non-trivial extension of the aforementioned results to the case in which the system of stochastic differential equations are driven by a multi-dimensional fraction Brownian motion with Hurst parameter bigger than 1/2. In chapter 5 we employ our approach and present a “short time” approximation for the solution of the Zakai equation from non-linear filtering theory and provide an estimation of the speed of convergence. In chapters 6 and 7 we study some properties of the unique mild solution for the Stochastic Heat Equation driven by spatial white noise of the Wick-Skorohod type. In particular by means of our reduction method we obtain an alternative derivation of the Feynman-Kac representation for the solution, we find its optimal Hölder regularity in time and space and present a Feynman-Kac-type closed form for its spatial derivative. Chapter 8 treats a somewhat different topic; in particular we investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of semi-linear stochastic differential equations describing a predator-prey model perturbed by Gaussian noise.

Impatto di rifaximina sul microbiota intestinale: selezione di bifidobatteri antibiotico resistenti

The ideal approach for the long term treatment of intestinal disorders, such as inflammatory bowel disease (IBD), is represented by a safe and well tolerated therapy able to reduce mucosal inflammation and maintain homeostasis of the intestinal microbiota. A combined therapy with antimicrobial agents, to reduce antigenic load, and immunomodulators, to ameliorate the dysregulated responses, followed by probiotic supplementation has been proposed. Because of the complementary mechanisms of action of antibiotics and probiotics, a combined therapeutic approach would give advantages in terms of enlargement of the antimicrobial spectrum, due to the barrier effect of probiotic bacteria, and limitation of some side effects of traditional chemiotherapy (i.e. indiscriminate decrease of aggressive and protective intestinal bacteria, altered absorption of nutrient elements, allergic and inflammatory reactions). Rifaximin (4-deoxy-4’-methylpyrido[1’,2’-1,2]imidazo[5,4-c]rifamycin SV) is a product of synthesis experiments designed to modify the parent compound, rifamycin, in order to achieve low gastrointestinal absorption while retaining good antibacterial activity. Both experimental and clinical pharmacology clearly show that this compound is a non systemic antibiotic with a broad spectrum of antibacterial action, covering Gram-positive and Gram-negative organisms, both aerobes and anaerobes. Being virtually non absorbed, its bioavailability within the gastrointestinal tract is rather high with intraluminal and faecal drug concentrations that largely exceed the MIC values observed in vitro against a wide range of pathogenic microorganisms. The gastrointestinal tract represents therefore the primary therapeutic target and gastrointestinal infections the main indication. The little value of rifaximin outside the enteric area minimizes both antimicrobial resistance and systemic adverse events. Fermented dairy products enriched with probiotic bacteria have developed into one of the most successful categories of functional foods. Probiotics are defined as “live microorganisms which, when administered in adequate amounts, confer a health benefit on the host” (FAO/WHO, 2002), and mainly include Lactobacillus and Bifidobacterium species. Probiotic bacteria exert a direct effect on the intestinal microbiota of the host and contribute to organoleptic, rheological and nutritional properties of food. Administration of pharmaceutical probiotic formula has been associated with therapeutic effects in treatment of diarrhoea, constipation, flatulence, enteropathogens colonization, gastroenteritis, hypercholesterolemia, IBD, such as ulcerative colitis (UC), Crohn’s disease, pouchitis and irritable bowel syndrome. Prerequisites for probiotics are to be effective and safe. The characteristics of an effective probiotic for gastrointestinal tract disorders are tolerance to upper gastrointestinal environment (resistance to digestion by enteric or pancreatic enzymes, gastric acid and bile), adhesion on intestinal surface to lengthen the retention time, ability to prevent the adherence, establishment and/or replication of pathogens, production of antimicrobial substances, degradation of toxic catabolites by bacterial detoxifying enzymatic activities, and modulation of the host immune responses. This study was carried out using a validated three-stage fermentative continuous system and it is aimed to investigate the effect of rifaximin on the colonic microbial flora of a healthy individual, in terms of bacterial composition and production of fermentative metabolic end products. Moreover, this is the first study that investigates in vitro the impact of the simultaneous administration of the antibiotic rifaximin and the probiotic B. lactis BI07 on the intestinal microbiota. Bacterial groups of interest were evaluated using culture-based methods and molecular culture-independent techniques (FISH, PCR-DGGE). Metabolic outputs in terms of SCFA profiles were determined by HPLC analysis. Collected data demonstrated that rifaximin as well as antibiotic and probiotic treatment did not change drastically the intestinal microflora, whereas bacteria belonging to Bifidobacterium and Lactobacillus significantly increase over the course of the treatment, suggesting a spontaneous upsurge of rifaximin resistance. These results are in agreement with a previous study, in which it has been demonstrated that rifaximin administration in patients with UC, affects the host with minor variations of the intestinal microflora, and that the microbiota is restored over a wash-out period. In particular, several Bifidobacterium rifaximin resistant mutants could be isolated during the antibiotic treatment, but they disappeared after the antibiotic suspension. Furthermore, bacteria belonging to Atopobium spp. and E. rectale/Clostridium cluster XIVa increased significantly after rifaximin and probiotic treatment. Atopobium genus and E. rectale/Clostridium cluster XIVa are saccharolytic, butyrate-producing bacteria, and for these characteristics they are widely considered health-promoting microorganisms. The absence of major variations in the intestinal microflora of a healthy individual and the significant increase in probiotic and health-promoting bacteria concentrations support the rationale of the administration of rifaximin as efficacious and non-dysbiosis promoting therapy and suggest the efficacy of an antibiotic/probiotic combined treatment in several gut pathologies, such as IBD. To assess the use of an antibiotic/probiotic combination for clinical management of intestinal disorders, genetic, proteomic and physiologic approaches were employed to elucidate molecular mechanisms determining rifaximin resistance in Bifidobacterium, and the expected interactions occurring in the gut between these bacteria and the drug. The ability of an antimicrobial agent to select resistance is a relevant factor that affects its usefulness and may diminish its useful life. Rifaximin resistance phenotype was easily acquired by all bifidobacteria analyzed [type strains of the most representative intestinal bifidobacterial species (B. infantis, B. breve, B. longum, B. adolescentis and B. bifidum) and three bifidobacteria included in a pharmaceutical probiotic preparation (B. lactis BI07, B. breve BBSF and B. longum BL04)] and persisted for more than 400 bacterial generations in the absence of selective pressure. Exclusion of any reversion phenomenon suggested two hypotheses: (i) stable and immobile genetic elements encode resistance; (ii) the drug moiety does not act as an inducer of the resistance phenotype, but enables selection of resistant mutants. Since point mutations in rpoB have been indicated as representing the principal factor determining rifampicin resistance in E. coli and M. tuberculosis, whether a similar mechanism also occurs in Bifidobacterium was verified. The analysis of a 129 bp rpoB core region of several wild-type and resistant bifidobacteria revealed five different types of miss-sense mutations in codons 513, 516, 522 and 529. Position 529 was a novel mutation site, not previously described, and position 522 appeared interesting for both the double point substitutions and the heterogeneous profile of nucleotide changes. The sequence heterogeneity of codon 522 in Bifidobacterium leads to hypothesize an indirect role of its encoded amino acid in the binding with the rifaximin moiety. These results demonstrated the chromosomal nature of rifaximin resistance in Bifidobacterium, minimizing risk factors for horizontal transmission of resistance elements between intestinal microbial species. Further proteomic and physiologic investigations were carried out using B. lactis BI07, component of a pharmaceutical probiotic preparation, as a model strain. The choice of this strain was determined based on the following elements: (i) B. lactis BI07 is able to survive and persist in the gut; (ii) a proteomic overview of this strain has been recently reported. The involvement of metabolic changes associated with rifaximin resistance was investigated by proteomic analysis performed with two-dimensional electrophoresis and mass spectrometry. Comparative proteomic mapping of BI07-wt and BI07-res revealed that most differences in protein expression patterns were genetically encoded rather than induced by antibiotic exposure. In particular, rifaximin resistance phenotype was characterized by increased expression levels of stress proteins. Overexpression of stress proteins was expected, as they represent a common non specific response by bacteria when stimulated by different shock conditions, including exposure to toxic agents like heavy metals, oxidants, acids, bile salts and antibiotics. Also, positive transcription regulators were found to be overexpressed in BI07-res, suggesting that bacteria could activate compensatory mechanisms to assist the transcription process in the presence of RNA polymerase inhibitors. Other differences in expression profiles were related to proteins involved in central metabolism; these modifications suggest metabolic disadvantages of resistant mutants in comparison with sensitive bifidobacteria in the gut environment, without selective pressure, explaining their disappearance from faeces of patients with UC after interruption of antibiotic treatment. The differences observed between BI07-wt e BI07-res proteomic patterns, as well as the high frequency of silent mutations reported for resistant mutants of Bifidobacterium could be the consequences of an increased mutation rate, mechanism which may lead to persistence of resistant bacteria in the population. However, the in vivo disappearance of resistant mutants in absence of selective pressure, allows excluding the upsurge of compensatory mutations without loss of resistance. Furthermore, the proteomic characterization of the resistant phenotype suggests that rifaximin resistance is associated with a reduced bacterial fitness in B. lactis BI07-res, supporting the hypothesis of a biological cost of antibiotic resistance in Bifidobacterium. The hypothesis of rifaximin inactivation by bacterial enzymatic activities was verified by using liquid chromatography coupled with tandem mass spectrometry. Neither chemical modifications nor degradation derivatives of the rifaximin moiety were detected. The exclusion of a biodegradation pattern for the drug was further supported by the quantitative recovery in BI07-res culture fractions of the total rifaximin amount (100 μg/ml) added to the culture medium. To confirm the main role of the mutation on the β chain of RNA polymerase in rifaximin resistance acquisition, transcription activity of crude enzymatic extracts of BI07-res cells was evaluated. Although the inhibition effects of rifaximin on in vitro transcription were definitely higher for BI07-wt than for BI07-res, a partial resistance of the mutated RNA polymerase at rifaximin concentrations > 10 μg/ml was supposed, on the basis of the calculated differences in inhibition percentages between BI07-wt and BI07-res. By considering the resistance of entire BI07-res cells to rifaximin concentrations > 100 μg/ml, supplementary resistance mechanisms may take place in vivo. A barrier for the rifaximin uptake in BI07-res cells was suggested in this study, on the basis of the major portion of the antibiotic found to be bound to the cellular pellet respect to the portion recovered in the cellular lysate. Related to this finding, a resistance mechanism involving changes of membrane permeability was supposed. A previous study supports this hypothesis, demonstrating the involvement of surface properties and permeability in natural resistance to rifampicin in mycobacteria, isolated from cases of human infection, which possessed a rifampicin-susceptible RNA polymerase. To understand the mechanism of membrane barrier, variations in percentage of saturated and unsaturated FAs and their methylation products in BI07-wt and BI07-res membranes were investigated. While saturated FAs confer rigidity to membrane and resistance to stress agents, such as antibiotics, a high level of lipid unsaturation is associated with high fluidity and susceptibility to stresses. Thus, the higher percentage of saturated FAs during the stationary phase of BI07-res could represent a defence mechanism of mutant cells to prevent the antibiotic uptake. Furthermore, the increase of CFAs such as dihydrosterculic acid during the stationary phase of BI07-res suggests that this CFA could be more suitable than its isomer lactobacillic acid to interact with and prevent the penetration of exogenous molecules including rifaximin. Finally, the impact of rifaximin on immune regulatory functions of the gut was evaluated. It has been suggested a potential anti-inflammatory effect of rifaximin, with reduced secretion of IFN-γ in a rodent model of colitis. Analogously, it has been reported a significant decrease in IL-8, MCP-1, MCP-3 e IL-10 levels in patients affected by pouchitis, treated with a combined therapy of rifaximin and ciprofloxacin. Since rifaximin enables in vivo and in vitro selection of Bifidobacterium resistant mutants with high frequency, the immunomodulation activities of rifaximin associated with a B. lactis resistant mutant were also taken into account. Data obtained from PBMC stimulation experiments suggest the following conclusions: (i) rifaximin does not exert any effect on production of IL-1β, IL-6 and IL-10, whereas it weakly stimulates production of TNF-α; (ii) B. lactis appears as a good inducer of IL-1β, IL-6 and TNF-α; (iii) combination of BI07-res and rifaximin exhibits a lower stimulation effect than BI07-res alone, especially for IL-6. These results confirm the potential anti-inflammatory effect of rifaximin, and are in agreement with several studies that report a transient pro-inflammatory response associated with probiotic administration. The understanding of the molecular factors determining rifaximin resistance in the genus Bifidobacterium assumes an applicative significance at pharmaceutical and medical level, as it represents the scientific basis to justify the simultaneous use of the antibiotic rifaximin and probiotic bifidobacteria in the clinical treatment of intestinal disorders.

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.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.