Stochastic differential equations with rough coefficients

This thesis deals with the study of the stochastic continuity equation (SCE) on R^d under low regularity assumptions on the coefficients. This is the equations for the mass associated to an SDE on R^d. In the first chapter Wiener pathwise uniqueness (i.e. uniqueness for solutions adapted to Brownian filtration) is proved for the SCE,. We use Wiener chaos to reduce Wiener uniqueness for the SCE to uniqueness for the Fokker-Planck equation (FPE). The method consists of projecting the equation on the Wiener chaos spaces and using the shift effect of the projectors in order to discard the Ito integral. The second chapter deals with the SCE for flows, following Le Jan- Raimond’s approach. Here we need that the FPE admits a particular semigroup as solution, which is guaranteed by the theory of Dirichlet forms under mild assumptions on the coefficients. Wiener chaos gives Wiener uniqueness (as before) and also existence. Another method of existence is based on filtering a weak solution X of the associated SDE with respect to a certain cylindrical Brownian motion W. In the third chapter, we consider the case of a rough drift . Here a phenomenon of regularization by noise can be observed: the results in the first chapter give immediately Wiener uniqueness for the SCE, while uniqueness does not hold in the deterministic case without additional hypotheses on the drift. We cite an example of this phenomenon. We prove also that, in many cases, strong uniqueness (i.e. Uniqueness with respect to every filtration, not only Brownian filtration) holds for the SCE. This is not surprising since a strong uniqueness result (due to Krylov- Röckner) holds for the SDE. First, extending Ambrosio’s approach, we associate to every measure-valued solution of the SCE a superposition solution N. Then, starting from N, we build a weak solution of the SDE. This correspondence and Krylov-Röckner’s result imply strong uniqueness for the SCE. The last chapter is about a particular class of generalized flows, the isotropic Brownian flows (IBFs). An IBF is a family of Brownian motions, indexed by their starting points in Rd , which are invariant in law for translation and rotation; it can be found as (possibly generalized) solution S of an SCE with isotropic infinitesimal covariance function K. Here we consider K’s driven by two parameters α and η, related respectively to the correlation of the two-point motion and to the compressibility of the flow. Studying the distance between the motions of two points (which is a 1-dimensional diffusion), we find that coalescence and/or splitting occur, depending of the values of α, η and d. This analysis makes rigorous the results for a simple model of turbulence and shows that this situation cannot be described classically, thus motivating the theory of generalized flows. Finally two appendices recall preliminaries and technical results

The enhanced Sanov theorem and propagation of chaos

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in rough path spaces and allows for a robust subsequent analysis of the particle system and its McKean-Vlasov type limit, as shown in two corollaries.Comment: 42 page

Valorization of chestnut shells for hydrogen production by Clostridium butyricum fermentation

Chestnut shell s (CS) is an agronomic waste generated from the peeling process of the chestnut fruit. It is well-known that the extract of CS contains high amounts of tannins, which are polyphenolic antioxidants1, but this agronomic residue also contains about 36% sugars in form of polysaccharides, and no utilization of chestnut shells as potential source of fermentable sugars has been considered so far. As consequence, this waste represents an interesting exploitable source for monosaccharides production, and in this study we evaluated the potential of biohydrogen production from CS hydrolyzate

Comparison of faecal techniques including FLOTAC for copromicroscopic detection of first stage larvae of Angiostrongylus vasorum

Angiostrongylus vasorum is a metastrongylid nematode that resides in the pulmonary arteries and the right heart chambers. In dogs, infection results in respiratory, bleeding and neurological disorders and further clinical signs. In the present study, FLOTAC was evaluated for the detection of first-stage larvae (L1) of A. vasorum in canine faecal samples. This technique is based on the counting of parasitic stages (eggs, larvae, oocysts and cysts) in chambers after spinning of faecal samples onto a surface. In a first step, nine flotation solutions were evaluated using faeces of two experimentally infected dogs. Zinc sulphate (specific gravity (s.g.) 1.2) and zinc sulphate plus potassium iodomercurate (s.g. 1.45) gave good results. However, with the latter technique, the larvae were slightly deformed. Subsequently, FLOTAC, using zinc sulphate, was compared through a randomisation technique with McMaster, flotation in tube and Baermann-Wetzel technique. The mean larvae per gramme (LPG) obtained by the FLOTAC for both dogs was significantly higher (P < 0.05) than those obtained by the other three techniques (the means of the other techniques all lie below the 95% CI of the mean LPG of the FLOTAC technique). In addition, the FLOTAC results were consistent across replicates with only Poisson (or random) variation between individual replicates. The other techniques appear to be less consistent with evidence of extra-Poisson variation in at least one of the two dogs across the replicates within each technique. The FLOTAC technique may contribute to an improvement of the ability to diagnose canine lungworm infections and represent a valuable alternative for larval counting of A. vasorum in faecal samples, especially following transport or storage where there may be limited larvae viability, and larval migration techniques cannot be use

Parasitic infections in dogs involved in animal-assisted interventions

Animal Assisted Interventions (AAIs) programmes have been considered useful in different settings, such as hospital, therapeutic, educational and assisted living environments. In these contexts, all animals, and particularly dogs, should be subjected to appropriate health controls to prevent a potential risk of transmission of zoonotic agents. Domestic dogs are reservoirs of many zoonotic pathogens including several gastrointestinal parasites (protozoa and helminths). Therefore, the aim of the present study was to investigate the presence of the protozoan Giardia duodenalis and zoonotic gastrointestinal nematodes (geohelminths) in dogs hosted in a dog educational centre in the city of Naples (southern Italy) where the animals were trained to AAI. Between April and June 2016, 74 dog faecal samples were analysed using the FLOTAC dual technique to detect G. duodenalis cysts and other parasitic elements. Out of the 74 faecal samples examined, 18 (24.3%; 95% CI = 15.4–35.9) were positive for parasitic elements. Specifically, 8 were positive for G. duodenalis (44.4%; 95% CI = 22.4–68.7). In addition, some co-infections were also found: one sample (5.6%; 95% CI = 0.3–29.4) resulted positive to both Toxocara canis and Trichuris vulpis and two samples (11.1%; 95% CI = 1.9–36.1) were positive to both G. duodenalis and Ancylostomidae. Given that children, young adults and immunocompromised individuals are among the main users of the AAIs, specific guidelines targeting G. duodenalis and other gastrointestinal zoonotic parasites should be formulated in order to develop effective control and prevention strategies and reduce the zoonotic risk favoured by the human-dog interaction

Early MicroRNA expression profile as a prognostic biomarker for the development of pelvic inflammatory disease in a mouse model of chlamydial genital infection

It is not currently possible to predict the probability of whether a woman with a chlamydial genital infection will develop pelvic inflammatory disease (PID). To determine if specific biomarkers may be associated with distinct chlamydial pathotypes, we utilized two Chlamydia muridarum variants (C. muridarum Var001 [CmVar001] and CmVar004) that differ in their abilities to elicit upper genital tract pathology in a mouse model. CmVar004 has a lower growth rate in vitro and induces pathology in only 20% of C57BL/6 mouse oviducts versus 83.3% of oviducts in CmVar001-infected mice. To determine if chemokine and cytokine production within 24 h of infection is associated with the outcome of pathology, levels of 15 chemokines and cytokines were measured. CmVar004 infection induced significantly lower levels of CXCL1, CXCL2, tumor necrosis factor alpha (TNF-α), and CCL2 in comparison to CmVar001 infection with similar rRNA (rs16) levels for Chlamydiae. A combination of microRNA (miRNA) sequencing and quantitative real-time PCR (qRT-PCR) analysis of 134 inflammation-related miRNAs was performed 24 h postinfection to determine if the chemokine/cytokine responses would also be reflected in miRNA expression profiles. Interestingly, 12 miRNAs (miR-135a-5p, miR298-5p, miR142-3p, miR223-3p, miR299a-3p, miR147-3p, miR105, miR325-3p, miR132-3p, miR142-5p, miR155-5p, and miR-410-3p) were overexpressed during CmVar004 infection compared to CmVar001 infection, inversely correlating with the respective chemokine/cytokine responses. To our knowledge, this is the first report demonstrating that early biomarkers elicited in the host can differentiate between two pathological variants of chlamydiae and be predictive of upper tract disease. © 2014 Yeruva et al

Changes in training load, running performance, lower body power and biochemical characteristics of back players throughout a professional Rugby Union season

The aim of this study was to observe and quantify changes in training load (TL), running performance, lower body power and biochemical characteristics of professional rugby union back players over an entire season. Eight professional players (age: 25.8 ± 4.6 y) participated in this study. Session-RPE (S-RPE) and microtechnologies (GPS) were used for assessing training load (TL). During the season, running performance was monitored using the YoYo Recovery Test Level-2 (YYRT2) and lower body power performance using the drop jump (DJ) test. Changes in hematological, endocrine and muscle damage parameters were examined through 3 blood samples taken at separate times throughout the season. TL progressively and significantly (p < 0.001) decreased throughout the season particularly due to the decrease in the training volume. The last blood sample of the season revealed a significant (p < 0.001) increase in hematological parameters and a significant increase (p < 0.01) in cortisol blood concentration without change in the testosterone/cortisol ratio. No significant change in YYRT2 performance was observed over the season, while DJ test performance was significantly lower during the first 2 blocks of the season compared to other blocks. The training volume showed a significant negative correlation with DJ-test performances (TD: r = -0.49 and S-RPE: r = -0.40, p < 0.001). Although there was a decrease in training volume throughout the season, there was no significant changes in running performance. Furthermore, lower body power production showed a significant increase in particular during the last part of the season

Non-explosion by Stratonovich noise for ODEs

We show that the addition of a suitable Stratonovich noise prevents the explosion for ODEs with drifts of super-linear growth, in dimension $d\ge 2$. We also show the existence of an invariant measure and the geometric ergodicity for the corresponding SDE.Comment: 16 page