CFD modeling of two-phase boiling flows in the slug flow regime with an interface capturing technique

The objective of this thesis was to improve the commercial CFD software Ansys Fluent to obtain a tool able to perform accurate simulations of flow boiling in the slug flow regime. The achievement of a reliable numerical framework allows a better understanding of the bubble and flow dynamics induced by the evaporation and makes possible the prediction of the wall heat transfer trends. In order to save computational time, the flow is modeled with an axisymmetrical formulation. Vapor and liquid phases are treated as incompressible and in laminar flow. By means of a single fluid approach, the flow equations are written as for a single phase flow, but discontinuities at the interface and interfacial effects need to be accounted for and discretized properly. Ansys Fluent provides a Volume Of Fluid technique to advect the interface and to map the discontinuous fluid properties throughout the flow domain. The interfacial effects are dominant in the boiling slug flow and the accuracy of their estimation is fundamental for the reliability of the solver. Self-implemented functions, developed ad-hoc, are introduced within the numerical code to compute the surface tension force and the rates of mass and energy exchange at the interface related to the evaporation. Several validation benchmarks assess the better performances of the improved software. Various adiabatic configurations are simulated in order to test the capability of the numerical framework in modeling actual flows and the comparison with experimental results is very positive. The simulation of a single evaporating bubble underlines the dominant effect on the global heat transfer rate of the local transient heat convection in the liquid after the bubble transit. The simulation of multiple evaporating bubbles flowing in sequence shows that their mutual influence can strongly enhance the heat transfer coefficient, up to twice the single phase flow value.

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system.

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

X-Ray studies of the physics of matter around super-massive black-holes in nearby Seyfert galaxies

Seyfert galaxies are the closest active galactic nuclei. As such, we can use them to test the physical properties of the entire class of objects. To investigate their general properties, I took advantage of different methods of data analysis. In particular I used three different samples of objects, that, despite frequent overlaps, have been chosen to best tackle different topics: the heterogeneous BeppoS AX sample was thought to be optimized to test the average hard X-ray (E above 10 keV) properties of nearby Seyfert galaxies; the X-CfA was thought the be optimized to compare the properties of low-luminosity sources to the ones of higher luminosity and, thus, it was also used to test the emission mechanism models; finally, the XMM–Newton sample was extracted from the X-CfA sample so as to ensure a truly unbiased and well defined sample of objects to define the average properties of Seyfert galaxies. Taking advantage of the broad-band coverage of the BeppoS AX MECS and PDS instruments (between ~2-100 keV), I infer the average X-ray spectral propertiesof nearby Seyfert galaxies and in particular the photon index (~1.8), the high-energy cut-off (~290 keV), and the relative amount of cold reflection (~1.0). Moreover the unified scheme for active galactic nuclei was positively tested. The distribution of isotropic indicators used here (photon index, relative amount of reflection, high-energy cut-off and narrow FeK energy centroid) are similar in type I and type II objects while the absorbing column and the iron line equivalent width significantly differ between the two classes of sources with type II objects displaying larger absorbing columns. Taking advantage of the XMM–Newton and X–CfA samples I also deduced from measurements that 30 to 50% of type II Seyfert galaxies are Compton thick. Confirming previous results, the narrow FeK line is consistent, in Seyfert 2 galaxies, with being produced in the same matter responsible for the observed obscuration. These results support the basic picture of the unified model. Moreover, the presence of a X-ray Baldwin effect in type I sources has been measured using for the first time the 20-100 keV luminosity (EW proportional to L(20-100)^(−0.22±0.05)). This finding suggests that the torus covering factor may be a function of source luminosity, thereby suggesting a refinement of the baseline version of the unifed model itself. Using the BeppoSAX sample, it has been also recorded a possible correlation between the photon index and the amount of cold reflection in both type I and II sources. At a first glance this confirms the thermal Comptonization as the most likely origin of the high energy emission for the active galactic nuclei. This relation, in fact, naturally emerges supposing that the accretion disk penetrates, depending to the accretion rate, the central corona at different depths (Merloni et al. 2006): the higher accreting systems hosting disks down to the last stable orbit while the lower accreting systems hosting truncated disks. On the contrary, the study of the well defined X–C f A sample of Seyfert galaxies has proved that the intrinsic X-ray luminosity of nearby Seyfert galaxies can span values between 10^(38−43) erg s^−1, i.e. covering a huge range of accretion rates. The less efficient systems have been supposed to host ADAF systems without accretion disk. However, the study of the X–CfA sample has also proved the existence of correlations between optical emission lines and X-ray luminosity in the entire range of L_(X) covered by the sample. These relations are similar to the ones obtained if high-L objects are considered. Thus the emission mechanism must be similar in luminous and weak systems. A possible scenario to reconcile these somehow opposite indications is assuming that the ADAF and the two phase mechanism co-exist with different relative importance moving from low-to-high accretion systems (as suggested by the Gamma vs. R relation). The present data require that no abrupt transition between the two regimes is present. As mentioned above, the possible presence of an accretion disk has been tested using samples of nearby Seyfert galaxies. Here, to deeply investigate the flow patterns close to super-massive black-holes, three case study objects for which enough counts statistics is available have been analysed using deep X-ray observations taken with XMM–Newton. The obtained results have shown that the accretion flow can significantly differ between the objects when it is analyzed with the appropriate detail. For instance the accretion disk is well established down to the last stable orbit in a Kerr system for IRAS 13197-1627 where strong light bending effect have been measured. The accretion disk seems to be formed spiraling in the inner ~10-30 gravitational radii in NGC 3783 where time dependent and recursive modulation have been measured both in the continuum emission and in the broad emission line component. Finally, the accretion disk seems to be only weakly detectable in rk 509, with its weak broad emission line component. Finally, blueshifted resonant absorption lines have been detected in all three objects. This seems to demonstrate that, around super-massive black-holes, there is matter which is not confined in the accretion disk and moves along the line of sight with velocities as large as v~0.01-0.4c (whre c is the speed of light). Wether this matter forms winds or blobs is still matter of debate together with the assessment of the real statistical significance of the measured absorption lines. Nonetheless, if confirmed, these phenomena are of outstanding interest because they offer new potential probes for the dynamics of the innermost regions of accretion flows, to tackle the formation of ejecta/jets and to place constraints on the rate of kinetic energy injected by AGNs into the ISM and IGM. Future high energy missions (such as the planned Simbol-X and IXO) will likely allow an exciting step forward in our understanding of the flow dynamics around black holes and the formation of the highest velocity outflows.

Peak-to-Peak Output Current Ripple Analysis in Multiphase and Multilevel Inverters

Analysis of the peak-to-peak output current ripple amplitude for multiphase and multilevel inverters is presented in this PhD thesis. The current ripple is calculated on the basis of the alternating voltage component, and peak-to-peak value is defined by the current slopes and application times of the voltage levels in a switching period. Detailed analytical expressions of peak-to-peak current ripple distribution over a fundamental period are given as function of the modulation index. For all the cases, reference is made to centered and symmetrical switching patterns, generated either by carrier-based or space vector PWM. Starting from the definition and the analysis of the output current ripple in three-phase two-level inverters, the theoretical developments have been extended to the case of multiphase inverters, with emphasis on the five- and seven-phase inverters. The instantaneous current ripple is introduced for a generic balanced multiphase loads consisting of series RL impedance and ac back emf (RLE). Simplified and effective expressions to account for the maximum of the output current ripple have been defined. The peak-to-peak current ripple diagrams are presented and discussed. The analysis of the output current ripple has been extended also to multilevel inverters, specifically three-phase three-level inverters. Also in this case, the current ripple analysis is carried out for a balanced three-phase system consisting of series RL impedance and ac back emf (RLE), representing both motor loads and grid-connected applications. The peak-to-peak current ripple diagrams are presented and discussed. In addition, simulation and experimental results are carried out to prove the validity of the analytical developments in all the cases. The cases with different phase numbers and with different number of levels are compared among them, and some useful conclusions have been pointed out. Furthermore, some application examples are given.

An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.

Reverse genetic studies of Benyvirus - Polymyxa betae molecular interaction: Role of the RNA4-encoded protein in virus transmission

Beet necrotic yellow vein virus (BNYVV), the leading infectious agent that affects sugar beet, is included within viruses transmitted through the soil from plasmodiophorid as Polymyxa betae. BNYVV is the causal agent of Rhizomania, which induces abnormal rootlet proliferation and is widespread in the sugar beet growing areas in Europe, Asia and America; for review see (Peltier et al., 2008). In this latter continent, Beet soil-borne mosaic virus (BSBMV) has been identified (Lee et al., 2001) and belongs to the benyvirus genus together with BNYVV, both vectored by P. betae. BSBMV is widely distributed only in the United States and it has not been reported yet in others countries. It was first identified in Texas as a sugar beet virus morphologically similar but serologically distinct to BNYVV. Subsequent sequence analysis of BSBMV RNAs evidenced similar genomic organization to that of BNYVV but sufficient molecular differences to distinct BSBMV and BNYVV in two different species (Rush et al., 2003). Benyviruses field isolates usually consist of four RNA species but some BNYVV isolates contain a fifth RNA. RNAs -1 contains a single long ORF encoding polypeptide that shares amino acid homology with known viral RNA-dependent RNA polymerases (RdRp) and helicases. RNAs -2 contains six ORFs: capsid protein (CP), one readthrough protein, triple gene block proteins (TGB) that are required for cell-to-cell virus movement and the sixth 14 kDa ORF is a post-translation gene silencing suppressor. RNAs -3 is involved on disease symptoms and is essential for virus systemic movement. BSBMV RNA-3 can be trans-replicated, trans-encapsidated by the BNYVV helper strain (RNA-1 and -2) (Ratti et al., 2009). BNYVV RNA-4 encoded one 31 kDa protein and is essential for vector interactions and virus transmission by P. betae (Rahim et al., 2007). BNYVV RNA-5 encoded 26 kDa protein that improve virus infections and accumulation in the hosts. We are interest on BSBMV effect on Rhizomania studies using powerful tools as full-length infectious cDNA clones. B-type full-length infectious cDNA clones are available (Quillet et al., 1989) as well as A/P-type RNA-3, -4 and -5 from BNYVV (unpublished). A-type BNYVV full-length clones are also available, but RNA-1 cDNA clone still need to be modified. During the PhD program, we start production of BSBMV full-length cDNA clones and we investigate molecular interactions between plant and Benyviruses exploiting biological, epidemiological and molecular similarities/divergences between BSBMV and BNYVV. During my PhD researchrs we obtained full length infectious cDNA clones of BSBMV RNA-1 and -2 and we demonstrate that they transcripts are replicated and packaged in planta and able to substitute BNYVV RNA-1 or RNA-2 in a chimeric viral progeny (BSBMV RNA-1 + BNYVV RNA-2 or BNYVV RNA-1 + BSBMV RNA-2). During BSBMV full-length cDNA clones production, unexpected 1,730 nts long form of BSBMV RNA-4 has been detected from sugar beet roots grown on BSBMV infected soil. Sequence analysis of the new BSBMV RNA-4 form revealed high identity (~100%) with published version of BSBMV RNA-4 sequence (NC_003508) between nucleotides 1-608 and 1,138-1,730, however the new form shows 528 additionally nucleotides between positions 608-1,138 (FJ424610). Two putative ORFs has been identified, the first one (nucleotides 383 to 1,234), encode a protein with predicted mass of 32 kDa (p32) and the second one (nucleotides 885 to 1,244) express an expected product of 13 kDa (p13). As for BSBMV RNA-3 (Ratti et al., 2009), full-length BSBMV RNA-4 cDNA clone permitted to obtain infectious transcripts that BNYVV viral machinery (Stras12) is able to replicate and to encapsidate in planta. Moreover, we demonstrated that BSBMV RNA-4 can substitute BNYVV RNA-4 for an efficient transmission through the vector P. betae in Beta vulgaris plants, demonstrating a very high correlation between BNYVV and BSBMV. At the same time, using BNYVV helper strain, we studied BSBMV RNA-4’s protein expression in planta. We associated a local necrotic lesions phenotype to the p32 protein expression onto mechanically inoculated C. quinoa. Flag or GFP-tagged sequences of p32 and p13 have been expressed in viral context, using Rep3 replicons, based on BNYVV RNA-3. Western blot analyses of local lesions contents, using FLAG-specific antibody, revealed a high molecular weight protein, which suggest either a strong interaction of BSBMV RNA4’s protein with host protein(s) or post translational modifications. GFP-fusion sequences permitted the subcellular localization of BSBMV RNA4’s proteins. Moreover we demonstrated the absence of self-activation domains on p32 by yeast two hybrid system approaches. We also confirmed that p32 protein is essential for virus transmission by P. betae using BNYVV helper strain and BNYVV RNA-3 and we investigated its role by the use of different deleted forms of p32 protein. Serial mechanical inoculation of wild-type BSBMV on C. quinoa plants were performed every 7 days. Deleted form of BSBMV RNA-4 (1298 bp) appeared after 14 passages and its sequence analysis shows deletion of 433 nucleotides between positions 611 and 1044 of RNA-4 new form. We demonstrated that this deleted form can’t support transmission by P. betae using BNYVV helper strain and BNYVV RNA-3, moreover we confirmed our hypothesis that BSBMV RNA-4 described by Lee et al. (2001) is a deleted form. Interesting after 21 passages we identifed one chimeric form of BSBMV RNA-4 and BSBMV RNA-3 (1146 bp). Two putative ORFs has been identified on its sequence, the first one (nucleotides 383 to 562), encode a protein with predicted mass of 7 kDa (p7), corresponding to the N-terminal of p32 protein encoded by BSBMV RNA-4; the second one (nucleotides 562 to 789) express an expected product of 9 kDa (p9) corresponding to the C-terminal of p29 encoded by BSBMV RNA-3. Results obtained by our research in this topic opened new research lines that our laboratories will develop in a closely future. In particular BSBMV p32 and its mutated forms will be used to identify factors, as host or vector protein(s), involved in the virus transmission through P. betae. The new results could allow selection or production of sugar beet plants able to prevent virus transmission then able to reduce viral inoculum in the soil.

Streptococcus agalactiae adapts to glucose stress conditions by modulating gene expression profile

Diabetes mellitus is considered a risk factor for Group B Streptococcus (GBS) infections. Typically, this pathology is associated to high glucose levels in the bloodstream. Although clinical evidences support this notion, the physiological mechanisms underlying GBS adaptation to such conditions are not yet defined. In the attempt to address this issue, we performed comparative global gene expression analysis of GBS grown under glucose-stress conditions and observed that a number of metabolic and virulence genes was differentially regulated. Of importance, we also demonstrated that by knocking-out the csrRS locus the transcription profile of GBS grown in high-glucose conditions was profoundly affected, with more than a third of glucose-dependent genes, including the virulence factor bibA, found to be controlled by this two-component system. Furthermore, in vitro molecular analysis showed that CsrR specifically binds to the bibA promoter and the phosphorilation increases the affinity of the regulator to this promoter region. Moreover, we demonstrated that CsrR acts as a repressor of bibA expression by binding to its promoter in vivo. In conclusion, this work by elucidating both the response of GBS to pathological glucose conditions and the underlined molecular mechanisms will set the basis for a better understanding of GBS pathogenesis.

Heuristic algorithms for the Capacitated Location-Routing Problem and the Multi-Depot Vehicle Routing Problem

The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot. This thesis addresses heuristics algorithms based on the well-know granular search idea introduced by Toth and Vigo (2003) to solve the CLRP and the MDVRP. Extensive computational experiments on benchmark instances for both problems have been performed to determine the effectiveness of the proposed algorithms. This work is organized as follows: Chapter 1 describes a detailed overview and a methodological review of the literature for the the Capacitated Location-Routing Problem (CLRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). Chapter 2 describes a two-phase hybrid heuristic algorithm to solve the CLRP. Chapter 3 shows a computational comparison of heuristic algorithms for the CLRP. Chapter 4 presents a hybrid granular tabu search approach for solving the MDVRP.

Il Senato come camera di rappresentanza territoriale

La riforma del bicameralismo rappresenta nell’ordinamento italiano una delle tematiche più dibattute sin dalla “concessione” dello Statuto Albertino. In Assemblea Costituente, infatti, l’opzione tra monocamerali e bicameralismo - prima - e il dibattito su che tipo di bicameralismo si sarebbe dovuto adottare - poi - hanno dato vita ad una parte organizzativa particolarmente debole e in gran parte antiquata rispetto alle esigenze della prima parte della Costituzione che, al contrario, ha rappresentato il precipitato di una profonda consonanza di ideali. La tesi si propone dunque l’obiettivo di dimostrare che l’esigenza di procedere ad una riforma del sistema bicamerale in Italia sia oggi quanto mai attuale e necessaria. Da un lato, infatti, essa favorirebbe il superamento delle inefficienze del sistema parlamentare e potrebbe rappresentare uno strumento per ovviare alla debole razionalizzazione della forma di governo che, da sempre, ha determinato la strutturale instabilità degli esecutivi. Dall’altro lato, la riforma servirebbe soprattutto a realizzare quella connessione organica tra Stato e regioni necessaria per completare il disegno regionalistico che si ricava dalla Costituzione stessa. Esigenza questa che, peraltro, si è notevolmente rafforzata con la riforma del titolo V della Costituzione, la cui portata innovativa è stata sostanzialmente svuotata di contenuto a causa delle difficoltà che si sono incontrate nella sua attuazione.

Analysis and mathematical modeling of wave-structure interaction

The aim of this thesis, included within the THESEUS project, is the development of a mathematical model 2DV two-phase, based on the existing code IH-2VOF developed by the University of Cantabria, able to represent together the overtopping phenomenon and the sediment transport. Several numerical simulations were carried out in order to analyze the flow characteristics on a dike crest. The results show that the seaward/landward slope does not affect the evolution of the flow depth and velocity over the dike crest whereas the most important parameter is the relative submergence. Wave heights decrease and flow velocities increase while waves travel over the crest. In particular, by increasing the submergence, the wave height decay and the increase of the velocity are less marked. Besides, an appropriate curve able to fit the variation of the wave height/velocity over the dike crest were found. Both for the wave height and for the wave velocity different fitting coefficients were determined on the basis of the submergence and of the significant wave height. An equation describing the trend of the dimensionless coefficient c_h for the wave height was derived. These conclusions could be taken into consideration for the design criteria and the upgrade of the structures. In the second part of the thesis, new equations for the representation of the sediment transport in the IH-2VOF model were introduced in order to represent beach erosion while waves run-up and overtop the sea banks during storms. The new model allows to calculate sediment fluxes in the water column together with the sediment concentration. Moreover it is possible to model the bed profile evolution. Different tests were performed under low-intensity regular waves with an homogeneous layer of sand on the bottom of a channel in order to analyze the erosion-deposition patterns and verify the model results.

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.

Decoding Agc1 deficiency: bioinformatics approaches to unveil the functional implications of Slc25a12 on the transcriptome and epigenome

In the brain, mutations in SLC25A12 gene encoding AGC1 cause an ultra-rare genetic disease reported as a developmental and epileptic encephalopathy associated with global cerebral hypomyelination. Symptoms of the disease include diffused hypomyelination, arrested psychomotor development, severe hypotonia, seizures and are common to other neurological and developmental disorders. Amongst the biological components believed to be most affected by AGC1 deficiency are oligodendrocytes, glial cells responsible for myelination. Recent studies (Poeta et al, 2022) have also shown how altered levels of transcription factors and epigenetic modifications greatly affect proliferation and differentiation in oligodendrocyte precursor cells (OPCs). In this study we explore the transcriptomic landscape of Agc1 in two different system models: OPCs silenced for Agc1 and iPSCs from human patients differentiated to neural progenitors. Analyses range from differential expression analysis, alternative splicing, master regulator analysis. ATAC-seq results on OPCs were integrated with results from RNA-Seq to assess the activity of a TF based on the accessibility data from its putative targets, which allows to integrate RNA-Seq data to infer their role as either activators or repressors. All the findings for this model were also integrated with early data from iPSCs RNA-seq results, looking for possible commonalities between the two different system models, among which we find a downregulation in genes encoding for SREBP, a transcription factor regulating fatty acids biosynthesis, a key process for myelination which could explain the hypomyelinated state of patients. We also find that in both systems cells tend to form more neurites, likely losing their ability to differentiate, considering their progenitor state. We also report several alterations in the chromatin state of cells lacking Agc1, which confirms the hypothesis for which Agc1 is not a disease restricted only to metabolic alterations in the cells, but there is a profound shift of the regulatory state of these cells.