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.

The role of biological processes in affecting the dynamics and fate of microplastics in coastal marine systems

Microplastics (MP) are omnipresent contaminants in the marine environment. Ingestion of MP has been reported for a wide range of marine biota, but to what extent the uptake by organisms affects the dynamics and fate of MP in the marine system has received little attention. My thesis explored this topic by integrating laboratory tests and experiments, field quantitative surveys of MP distribution and dynamics, and the use of specialised analytical techniques such as Attenuated-Total-Reflectance- (ATR) and imaging- Fourier Transformed Infrared Spectroscopy (FTIR). I compared different methodologies to extract MP from wild invertebrate specimens, and selected the use of potassium hydroxide (KOH) as the most cost-effective approach. I used this approach to analyse the MP contamination in various invertebrate species with different ecological traits from European salt marshes. I found that 96% of the analysed specimens (330) did not contain any MP. As preliminary environmental analyses showed high levels of environmental MP contamination, I hypothesised that most MP do not accumulate into organisms but are rather fast egested. I subsequently used laboratory multi-trophic experiments and a long-term field experiment using the filter-feeding mussel Mytilus galloprovincialis and the detritus feeding polychaete Hediste diversicolor to test the aforementioned hypothesis. Overall, results showed that MP are ingested but rapidly egested by marine invertebrates, which may limit MP transfer via predator-prey interactions but at the same time enhance their transfer via detrital pathways in the sediments. These processes seem to be extremely variable over time, with potential unexplored environmental consequences. This rapid dynamics also limits the conclusions that can be derived from static observations of MP contents in marine organisms, not fully capturing the real levels of potential contaminations by marine species. This emphasises the need to consider such dynamics in future work to measure the uptake rates by organisms in natural systems.

Improvement of photon transport model by including coupled photon-electron transport and kernel refinement

The first part of this work deals with the inverse problem solution in the X-ray spectroscopy field. An original strategy to solve the inverse problem by using the maximum entropy principle is illustrated. It is built the code UMESTRAT, to apply the described strategy in a semiautomatic way. The application of UMESTRAT is shown with a computational example. The second part of this work deals with the improvement of the X-ray Boltzmann model, by studying two radiative interactions neglected in the current photon models. Firstly it is studied the characteristic line emission due to Compton ionization. It is developed a strategy that allows the evaluation of this contribution for the shells K, L and M of all elements with Z from 11 to 92. It is evaluated the single shell Compton/photoelectric ratio as a function of the primary photon energy. It is derived the energy values at which the Compton interaction becomes the prevailing process to produce ionization for the considered shells. Finally it is introduced a new kernel for the XRF from Compton ionization. In a second place it is characterized the bremsstrahlung radiative contribution due the secondary electrons. The bremsstrahlung radiation is characterized in terms of space, angle and energy, for all elements whit Z=1-92 in the energy range 1–150 keV by using the Monte Carlo code PENELOPE. It is demonstrated that bremsstrahlung radiative contribution can be well approximated with an isotropic point photon source. It is created a data library comprising the energetic distributions of bremsstrahlung. It is developed a new bremsstrahlung kernel which allows the introduction of this contribution in the modified Boltzmann equation. An example of application to the simulation of a synchrotron experiment is shown.

Harnessing the power of Drosophila model to obtain new insights on MYC and ABCC1 cellular functions: from neuroblastoma to autism spectrum disorder

MYCN amplification is a genetic hallmark of the childhood tumour neuroblastoma. MYCN-MAX dimers activate the expression of genes promoting cell proliferation. Moreover, MYCN seems to transcriptionally repress cell differentiation even in absence of MAX. We adopted the Drosophila eye as model to investigate the effect of high MYC to MAX expression ratio on cells. We found that dMyc overexpression in eye cell precursors inhibits cell differentiation and induces the ectopic expression of Antennapedia (the wing Hox gene). The further increase of MYC/MAX ratio results in an eye-to-wing homeotic transformation. Notably, dMyc overexpression phenotype is suppressed by low levels of transcriptional co-repressors and MYCN associates to the promoter of Deformed (the eye Hox gene) in proximity to repressive sites. Hence, we envisage that, in presence of high MYC/MAX ratio, the “free MYC” might inhibit Deformed expression, leading in turn to the ectopic expression of Antennapedia. This suggests that MYCN might reinforce its oncogenic role by affecting the physiological homeotic program. Furthermore, poor neuroblastoma outcome associates with a high level of the MRP1 protein, encoded by the ABCC1 gene and known to promote drug efflux in cancer cells. Intriguingly, this correlation persists regardless of chemotherapy and ABCC1 overexpression enhances neuroblastoma cell motility. We found that Drosophila dMRP contributes to the adhesion between the dorsal and ventral epithelia of the wing by inhibiting the function of integrin receptors, well known regulators of cell adhesion and migration. Besides, integrins play a crucial role during synaptogenesis and ABCC1 locus is included in a copy number variable region of the human genome (16p13.11) involved in neuropsychiatric diseases. Interestingly, we found that the altered dMRP/MRP1 level affects nervous system development in Drosophila embryos. These preliminary findings point out novel ABCC1 functions possibly defining ABCC1 contribution to neuroblastoma and to the pathogenicity of 16p13.11 deletion/duplication

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.

Design and testing of innovative, artificial intelligence-based techniques to model and control the combustion process and to reduce the Co2 emissions in modern, high-performance, gasoline direct injection engines

This work deals with the development of calibration procedures and control systems to improve the performance and efficiency of modern spark ignition turbocharged engines. The algorithms developed are used to optimize and manage the spark advance and the air-to-fuel ratio to control the knock and the exhaust gas temperature at the turbine inlet. The described work falls within the activity that the research group started in the previous years with the industrial partner Ferrari S.p.a. . The first chapter deals with the development of a control-oriented engine simulator based on a neural network approach, with which the main combustion indexes can be simulated. The second chapter deals with the development of a procedure to calibrate offline the spark advance and the air-to-fuel ratio to run the engine under knock-limited conditions and with the maximum admissible exhaust gas temperature at the turbine inlet. This procedure is then converted into a model-based control system and validated with a Software in the Loop approach using the engine simulator developed in the first chapter. Finally, it is implemented in a rapid control prototyping hardware to manage the combustion in steady-state and transient operating conditions at the test bench. The third chapter deals with the study of an innovative and cheap sensor for the in-cylinder pressure measurement, which is a piezoelectric washer that can be installed between the spark plug and the engine head. The signal generated by this kind of sensor is studied, developing a specific algorithm to adjust the value of the knock index in real-time. Finally, with the engine simulator developed in the first chapter, it is demonstrated that the innovative sensor can be coupled with the control system described in the second chapter and that the performance obtained could be the same reachable with the standard in-cylinder pressure sensors.

Access to climate justice: the main procedural hurdles, and possible solutions, within the italian legal framework and the IBA Model Statute

The thesis deals with standing and justiciability in climate litigation against governments and the private sector. The first part addresses the impacts of climate change on human rights, the major developments in international climate law, and the historical reasons for climate litigation. The second part analyses several cases, divided into categories. It then draws to a comparative conclusion with regard to each category. The third part deals with the Italian legal tradition on standing and justiciability – starting from the historical roots of such rules. The fourth part introduces the ‘Model Statute’ drafted by the International Bar Association, arguing that the 'ratio legis' of this proposal could be implemented in Italy or the EU. The thesis develops arguments, based on the existing legal framework, to help plaintiffs establish standing and justiciability in proceedings pending before Italian courts. It further proposes the idea that 'citizen suits' are consistent with the Italian and EU legal tradition and that the EU could rely on citizen suits to privately enforce its climate law and policies under the ‘European Green Deal.’

A 3D biomimetic in vitro model: a novel strategy to investigate glioma biology

Gliomas are one of the most frequent primary malignant brain tumors. Acquisition of stem-like features likely contributes to the malignant nature of high-grade gliomas and may be responsible for the initiation, growth, and recurrence of these tumors. In this regard, although the traditional 2D cell culture system has been widely used in cancer research, it shows limitations in maintaining the stemness properties of cancer and in mimicking the in vivo microenvironment. In order to overcome these limitations, different three-dimensional (3D) culture systems have been developed to mimic better the tumor microenvironment. Cancer cells cultured in 3D structures may represent a more reliable in vitro model due to increased cell-cell and cell-extracellular matrix (ECM) interaction. Several attempts to recreate brain cancer tissue in vitro are described in literature. However, to date, it is still unclear which main characteristics the ideal model should reproduce. The overall goal of this project was the development of a 3D in vitro model able to reproduce the brain ECM microenvironment and to recapitulate pathological condition for the study of tumor stroma interactions, tumor invasion ability, and molecular phenotype of glioma cells. We performed an in silico bioinformatic analysis using GEPIA2 Software to compare the expression level of seven matrix protein in the LGG tumors with healthy tissues. Then, we carried out a FFPE retrospective study in order to evaluate the percentage of expression of selected proteins. Thus, we developed a 3D scaffold composed by Hyaluronic Acid and Collagen IV in a ratio of 50:50. We used two astrocytoma cell lines, HTB-12 and HTB-13. In conclusion, we developed an in vitro 3D model able to reproduce the composition of brain tumor ECM, demonstrating that it is a feasible platform to investigate the interaction between tumor cells and the matrix.