Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Synthesis and conformational analysis of heteroaromatic atropisomeric systems

The research work reported in this Thesis was held along two main lines of research. The first and main line of research is about the synthesis of heteroaromatic compounds with increasing steric hindrance, with the aim of preparing stable atropisomers. The main tools used for the study of these dynamic systems, as described in the Introduction, are DNMR, coupled with line shape simulation and DFT calculations, aimed to the conformational analysis for the prediction of the geometries and energy barriers to the trasition states. This techniques have been applied to the research projects about: • atropisomers of arylmaleimides; • atropisomers of 4-arylpyrazolo[3,4-b]pyridines; • study of the intramolecular NO2/CO interaction in solution; • study on 2-arylpyridines. Parallel to the main project, in collaboration with other groups, the research line about determination of the absolute configuration was followed. The products, deriving form organocatalytic reactions, in many cases couldn’t be analyzed by means of X-Ray diffraction, making necessary the development of a protocol based on spectroscopic methodologies: NMR, circular dichroism and computational tools (DFT, TD-DFT) have been implemented in this scope. In this Thesis are reported the determination of the absolute configuration of: • substituted 1,2,3,4-tetrahydroquinolines; • compounds from enantioselective Friedel-Crafts alkylation-acetalization cascade of naphthols with α,β-unsaturated cyclic ketones; • substituted 3,4-annulated indoles.

Dynamics and control issues of multi-rotor platforms

This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.

Genetic basis of variation for root traits and response to heat stress in durum wheat

Durum wheat is the second most important wheat species worldwide and the most important crop in several Mediterranean countries including Italy. Durum wheat is primarily grown under rainfed conditions where episodes of drought and heat stress are major factors limiting grain yield. The research presented in this thesis aimed at the identification of traits and genes that underlie root system architecture (RSA) and tolerance to heat stress in durum wheat, in order to eventually contribute to the genetic improvement of this species. In the first two experiments we aimed at the identification of QTLs for root trait architecture at the seedling level by studying a bi-parental population of 176 recombinant inbred lines (from the cross Meridiano x Claudio) and a collection of 183 durum elite accessions. Forty-eight novel QTLs for RSA traits were identified in each of the two experiments, by means of linkage- and association mapping-based QTL analysis, respectively. Important QTLs controlling the angle of root growth in the seedling were identified. In a third experiment, we investigated the phenotypic variation of root anatomical traits by means of microscope-based analysis of root cross sections in 10 elite durum cultivars. The results showed the presence of sizeable genetic variation in aerenchyma-related traits, prompting for additional studies aimed at mapping the QTLs governing such variation and to test the role of aerenchyma in the adaptive response to abiotic stresses. In the fourth experiment, an association mapping experiment for cell membrane stability at the seedling stage (as a proxy trait for heat tolerance) was carried out by means of association mapping. A total of 34 QTLs (including five major ones), were detected. Our study provides information on QTLs for root architecture and heat tolerance which could potentially be considered in durum wheat breeding programs.

Modelling the dynamic response of rockfall protection barriers

Mountainous areas are prone to natural hazards like rockfalls. Among the many countermeasures, rockfall protection barriers represent an effective solution to mitigate the risk. They are metallic structures designed to intercept rocks falling from unstable slopes, thus dissipating the energy deriving from the impact. This study aims at providing a better understanding of the response of several rockfall barrier types, through the development of rather sophisticated three-dimensional numerical finite elements models which take into account for the highly dynamic and non-linear conditions of such events. The models are built considering the actual geometrical and mechanical properties of real systems. Particular attention is given to the connecting details between the structural components and to their interactions. The importance of the work lies in being able to support a wide experimental activity with appropriate numerical modelling. The data of several full-scale tests carried out on barrier prototypes, as well as on their structural components, are combined with results of numerical simulations. Though the models are designed with relatively simple solutions in order to obtain a low computational cost of the simulations, they are able to reproduce with great accuracy the test results, thus validating the reliability of the numerical strategy proposed for the design of these structures. The developed models have shown to be readily applied to predict the barrier performance under different possible scenarios, by varying the initial configuration of the structures and/or of the impact conditions. Furthermore, the numerical models enable to optimize the design of these structures and to evaluate the benefit of possible solutions. Finally it is shown they can be also used as a valuable supporting tool for the operators within a rockfall risk assessment procedure, to gain crucial understanding of the performance of existing barriers in working conditions.

Field-free control of magnetism in nanostructured materials probed with high resolution X-ray microscopy

Magnetic memories are a backbone of today's digital data storage technology, where the digital information is stored as the magnetic configuration of nanostructured ferromagnetic bits. Currently, the writing of the digital information on the magnetic memory is carried out with the help of magnetic fields. This approach, while viable, is not optimal due to its intrinsically high energy consumption and relatively poor scalability. For this reason, the research for different mechanisms that can be used to manipulate the magnetic configuration of a material is of interest. In this thesis, the control of the magnetization of different nanostructured materials with field-free mechanisms is investigated. The magnetic configuration of these nanostructured materials was imaged directly with high resolution x-ray magnetic microscopy. rnFirst of all, the control of the magnetic configuration of nanostructured ferromagnetic Heusler compounds by fabricating nanostructures with different geometries was analyzed. Here, it was observed that the magnetic configuration of the nanostructured elements is given by the competition of magneto-crystalline and shape anisotropy. By fabricating elements with different geometries, we could alter the point where these two effects equilibrate, allowing for the possibility to tailor the magnetic configuration of these nanostructured elements to the required necessities.rnThen, the control of the magnetic configuration of Ni nanostructures fabricated on top of a piezoelectric material with the magneto-elastic effect (i.e. by applying a piezoelectric strain to the Ni nanostructures) was investigated. Here, the magneto-elastic coupling effect gives rise to an additional anisotropy contribution, proportional to the strain applied to the magnetic material. For this system, a reproducible and reversible control of the magnetic configuration of the nanostructured Ni elements with the application of an electric field across the piezoelectric material was achieved.rnFinally, the control of the magnetic configuration of La0.7Sr0.3MnO3 (LSMO) nanostructures with spin-polarized currents was studied. Here, the spin-transfer torque effect was employed to achieve the displacement of magnetic domain walls in the LSMO nanostructures. A high spin-transfer torque efficiency was observed for LSMO at low temperatures, and a Joule-heating induced hopping of the magnetic domain walls was observed at room temperatures, allowing for the analysis of the energetics of the domain walls in LSMO.rnThe results presented in this thesis give thus an overview on the different field-free approaches that can be used to manipulate and tailor the magnetization configuration of a nanostructured material to the various technological requirements, opening up novel interesting possibilities for these materials.

Atropisomeric xanthines: Synthesis, stereodynamics and absolute configuration

During the thesis period a new class of atropisomeric xanthine derivatives has been studied. We decided to focus our attention on these purine bases because of their various biological activities, that could play an important role in the discovery of new bioactive atropisomers. The synthesized compounds bear an Aryl-N chiral axis in position 1 of the xanthine scaffold, around which the rotation is prevented by the presence of bulky ortho substituents. Through a retro synthetic analysis we synthesized three atropisomeric structures bearing in position 1 of the purine scaffold respectively an o-tolyl, o-nitrophenyl and a 1-naphthyl group. The conformational studies by DFT simulations showed that the interconversion energy barrier between the two available skewed conformations is higher enough to obtain thermally stable atropisomers. After the separation of the atropisomers, the experimental energy of interconversion was investigated by means of kinetic studies following the thermal racemization process using an enantioselective HPLC column. The absolute configuration of each atropisomer was assigned by experimental ECD analysis and TD-DFT simulations of the ECD spectra.

Synthesis and dynamic study of atropisomeric compounds containing boron-carbon bond

In this thesis we studied the stereodynamic behavior of 1,2-azaborines variously substituted on boron (7a, 7b, 13). Depending on the hindrance of the asymmetric aryl substituent the resulting conformations could be stereolabile or configurationally stable. Through dynamic NMR and lineshape simulation, the energy rotational barriers of the different conformers are obtained. When the barrier is higher than 22-23 kcal/mol stable atropisomers that are fisically separable could be obtained (case of compound 13) and the free activation energy barrier is determinable by kinetic analysis. Absolute configuration of two atropisomers were assigned by comparison between computational calculations and experimental ECD. Isosteric compound 21 is then synthesized in order to compare the rotational barrier around B-Caryl with the one around Cnaphth-Caryl bond.

Meningocerebral angiodysplasia with metanephric induction failure: Broadening the spectrum of an emerging maldevelopmental syndrome

The uncommon simultaneous occurrence of an exuberant, angioma-like proliferation of superficial cerebral microvessels along with absence of the kidneys has been proposed to constitute a syndromic complex for which the term "meningocerebral angiodysplasia (or angiomatosis) with renal agenesis" (MCA-RA) is being descriptively used. We observed this constellation in one of a pair of dichorionic male twins following postpartal death in the 38th week of pregnancy. General autopsy revealed rudimentary metanephric anlagen made up of few residual glomeruli, cysts lined by flattened tubular epithelium, and islands of cartilage - corresponding to renal aplastic dysplasia. Largely inconspicuous with respect to its gyral pattern, as well as the configuration of the ventricular system, the brain microscopically showed extensive replacement of the cortex by a lattice of proliferating capillaries with necrosis of the intervening parenchyma. Minute foci of calcified necrosis were scattered in the deep subcortical white matter as well, while the ventricular ependyma and the subventricular germ cell layer remained remarkably intact. The cerebellum and brain stem appeared unaffected as well. Karyotyping of skin fibroblasts indicated a normal chromosome set of 46XY without gross structural anomalies. We interpret these findings as ones apt to being reasonably accommodated within the spectrum of MCA-RA. Although exceedingly rare, accurate identification of individual cases of MCA-RA is relevant both to differential diagnosis from its prognostically different look-alike "proliferative vasculopathy and hydranencephaly-hydrocephaly" (PVHH), and to refine the nosology of unconventional pediatric vascular malformations, for which the rather nonspecific label "angiodysgenetic necrotizing encephalopathy" is still commonly used.

Development of a high performance parallel computing platform and its use in the study of nanostructures : clusters, sheets and tubes .

Small clusters of gallium oxide, technologically important high temperature ceramic, together with interaction of nucleic acid bases with graphene and small-diameter carbon nanotube are focus of first principles calculations in this work. A high performance parallel computing platform is also developed to perform these calculations at Michigan Tech. First principles calculations are based on density functional theory employing either local density or gradient-corrected approximation together with plane wave and gaussian basis sets. The bulk Ga2O3 is known to be a very good candidate for fabricating electronic devices that operate at high temperatures. To explore the properties of Ga2O3 at nonoscale, we have performed a systematic theoretical study on the small polyatomic gallium oxide clusters. The calculated results find that all lowest energy isomers of GamOn clusters are dominated by the Ga-O bonds over the metal-metal or the oxygen-oxygen bonds. Analysis of atomic charges suggest the clusters to be highly ionic similar to the case of bulk Ga2O3. In the study of sequential oxidation of these slusters starting from Ga2O, it is found that the most stable isomers display up to four different backbones of constituent atoms. Furthermore, the predicted configuration of the ground state of Ga2O is recently confirmed by the experimental result of Neumark's group. Guided by the results of calculations the study of gallium oxide clusters, performance related challenge of computational simulations, of producing high performance computers/platforms, has been addressed. Several engineering aspects were thoroughly studied during the design, development and implementation of the high performance parallel computing platform, rama, at Michigan Tech. In an attempt to stay true to the principles of Beowulf revolutioni, the rama cluster was extensively customized to make it easy to understand, and use - for administrators as well as end-users. Following the results of benchmark calculations and to keep up with the complexity of systems under study, rama has been expanded to a total of sixty four processors. Interest in the non-covalent intereaction of DNA with carbon nanotubes has steadily increased during past several years. This hybrid system, at the junction of the biological regime and the nanomaterials world, possesses features which make it very attractive for a wide range of applicatioins. Using the in-house computational power available, we have studied details of the interaction between nucleic acid bases with graphene sheet as well as high-curvature small-diameter carbon nanotube. The calculated trend in the binding energies strongly suggests that the polarizability of the base molecules determines the interaction strength of the nucleic acid bases with graphene. When comparing the results obtained here for physisorption on the small diameter nanotube considered with those from the study on graphene, it is observed that the interaction strength of nucleic acid bases is smaller for the tube. Thus, these results show that the effect of introducing curvature is to reduce the binding energy. The binding energies for the two extreme cases of negligible curvature (i.e. flat graphene sheet) and of very high curvature (i.e. small diameter nanotube) may be considered as upper and lower bounds. This finding represents an important step towards a better understanding of experimentally observed sequence-dependent interaction of DNA with Carbon nanotubes.

Synthesis of bicyclo-DNA nucleosides with additional functionalization in the carbocyclic ring

Two novel bicyclo nucleoside isomers carrying the base thymine in the furanose ring and an ester substituent in the carbocyclic ring were synthesized from a common bicyclic sugar precursor via a cyclopropanation/fragmentation pathway in nine steps. The relative configuration of the ester substituent in both isomers as well as the anomeric configuration in one nucleoside was determined by 1H-NMR difference NOE spectroscopy.

The absence of angiopoietin-2 leads to abnormal vascular maturation and persistent proliferative retinopathy

Angiopoietin-2 (Ang-2) antagonises the maturing effect of angiopoietin-1 (Ang-1) on blood vessels, and cooperates with VEGF to induce neovascularisation. In knockout mice, Ang-2 displayed a specific role in postnatal angiogenic remodelling. Here, we demonstrate that mice deficient in Ang-2 fail to form a proper spatial retinal vascular network. The retinal vasculature was characterised by reduced large vessel numbers and defects forming the superficial periphery mostly on the arteriolar site, and the secondary and tertiary deep capillary network. Hypoxia in the retinal periphery induced a four-fold VEGF upregulation and active endothelial proliferation for up to 60 days. Concomitantly, retinal digest preparations showed increased arteriolar (+33%) and capillary diameters (+90%), and fluorescein angiograms revealed leakiness of neovascular front. At one year of age, persistent preretinal vessels were non-leaky in accordance with a relative increase in the ratio of Ang-1 to VEGF. Taken together, the data suggest that Ang-2 has an important function in the spatial configuration of the three-dimensional retinal vasculature. Secondarily, prolonged VEGF activity results in a model of persistent proliferative retinopathy.

Gain-of-function mutation S422L in the KCNJ8-encoded cardiac K(ATP) channel Kir6.1 as a pathogenic substrate for J-wave syndromes.

BACKGROUND J-wave syndromes have emerged conceptually to encompass the pleiotropic expression of J-point abnormalities including Brugada syndrome (BrS) and early repolarization syndrome (ERS). KCNJ8, which encodes the cardiac K(ATP) Kir6.1 channel, recently has been implicated in ERS following identification of the functionally uncharacterized missense mutation S422L. OBJECTIVE The purpose of this study was to further explore KCNJ8 as a novel susceptibility gene for J-wave syndromes. METHODS Using polymerase chain reaction, denaturing high-performance liquid chromatography, and direct DNA sequencing, comprehensive open reading frame/splice site mutational analysis of KCNJ8 was performed in 101 unrelated patients with J-wave syndromes, including 87 with BrS and 14 with ERS. Six hundred healthy individuals were examined to assess the allelic frequency for all variants detected. KCNJ8 mutation(s) was engineered by site-directed mutagenesis and coexpressed heterologously with SUR2A in COS-1 cells. Ion currents were recorded using whole-cell configuration of the patch-clamp technique. RESULTS One BrS case and one ERS case hosted the identical missense mutation S422L, which was reported previously. KCNJ8-S422L involves a highly conserved residue and was absent in 1,200 reference alleles. Both cases were negative for mutations in all known BrS and ERS susceptibility genes. K(ATP) current of the Kir6.1-S422L mutation was increased significantly over the voltage range from 0 to 40 mV compared to Kir6.1-WT channels (n = 16-21; P <.05). CONCLUSION These findings further implicate KCNJ8 as a novel J-wave syndrome susceptibility gene and a marked gain of function in the cardiac K(ATP) Kir6.1 channel secondary to KCNJ8-S422L as a novel pathogenic mechanism for the phenotypic expression of both BrS and ERS.

Landscape connectivity, habitat structure and activity of bat guilds in farmland-dominated matrices

Agricultural intensification has caused a decline in structural elements in European farmland, where natural habitats are increasingly fragmented. The loss of habitat structures has a detrimental effect on biodiversity and affects bat species that depend on vegetation structures for foraging and commuting. We investigated the impact of connectivity and configuration of structural landscape elements on flight activity, species richness and diversity of insectivorous bats and distinguished three bat guilds according to species-specific bioacoustic characteristics. We tested whether bats with shorter-range echolocation were more sensitive to habitat fragmentation than bats with longer-range echolocation. We expected to find different connectivity thresholds for the three guilds and hypothesized that bats prefer linear over patchy landscape elements. Bat activity was quantified using repeated acoustic monitoring in 225 locations at 15 study plots distributed across the Swiss Central Plateau, where connectivity and the shape of landscape elements were determined by spatial analysis (GIS). Spectrograms of bat calls were assigned to species with the software batit by means of image recognition and statistical classification algorithms. Bat activity was significantly higher around landscape elements compared to open control areas. Short- and long-range echolocating bats were more active in well-connected landscapes, but optimal connectivity levels differed between the guilds. Species richness increased significantly with connectivity, while species diversity did not (Shannon's diversity index). Total bat activity was unaffected by the shape of landscape elements. Synthesis and applications. This study highlights the importance of connectivity in farmland landscapes for bats, with shorter-range echolocating bats being particularly sensitive to habitat fragmentation. More structurally diverse landscape elements are likely to reduce population declines of bats and could improve conditions for other declining species, including birds. Activity was highest around optimal values of connectivity, which must be evaluated for the different guilds and spatially targeted for a region's habitat configuration. In a multi-species approach, we recommend the reintroduction of structural elements to increase habitat heterogeneity should become part of agri-environment schemes.

Intracoronary Optical Coherence Tomography and Histology of Overlapping Everolimus-Eluting Bioresorbable Vascular Scaffolds in a Porcine Coronary Artery Model

OBJECTIVES: This study sought to assess the vascular response of overlapping Absorb stents compared with overlapping newer-generation everolimus-eluting metallic platform stents (Xience V [XV]) in a porcine coronary artery model. BACKGROUND: The everolimus-eluting bioresorbable vascular scaffold (Absorb) is a novel approach to treating coronary lesions. A persistent inflammatory response, fibrin deposition, and delayed endothelialization have been reported with overlapping first-generation drug-eluting stents. METHODS: Forty-one overlapping Absorb and overlapping Xience V (XV) devices (3.0 × 12 mm) were implanted in the main coronary arteries of 17 nonatherosclerotic pigs with 10% overstretch. Implanted coronary arteries were evaluated by optical coherence tomography (OCT) at 28 days (Absorb n = 11, XV n = 7) and 90 days (Absorb n = 11, XV n = 8), with immediate histological evaluation following euthanasia at the same time points. One animal from each time point was evaluated with scanning electron microscopy alone. A total of 1,407 cross sections were analyzed by OCT and 148 cross sections analyzed histologically. RESULTS: At 28 days in the overlap, OCT analyses indicated 80.1% of Absorb struts and 99.4% of XV struts to be covered (p < 0.0001), corresponding to histological observations of struts with cellular coverage of 75.4% and 99.6%, respectively (p < 0.001). Uncovered struts were almost exclusively related to the presence of "stacked" Absorb struts, that is, with a direct overlay configuration. At 90 days, overlapping Absorb and overlapping XV struts demonstrated >99% strut coverage by OCT and histology, with no evidence of a significant inflammatory process, and comparable % volume obstructions. CONCLUSIONS: In porcine coronary arteries implanted with overlapping Absorb or overlapping XV struts, strut coverage is delayed at 28 days in overlapping Absorb, dependent on the overlay configuration of the thicker Absorb struts. At 90 days, both overlapping Absorb and overlapping XV have comparable strut coverage. The implications of increased strut thickness may have important clinical and design considerations for bioresorbable platforms.