Semiclassical analysis of systems of Schrödinger equations

The scalar Schrödinger equation models the probability density distribution for a particle to be found in a point x given a certain potential V(x) forming a well with respect to a fixed energy level E_0. Formally two real inversion points a,b exist such that V(a)=V(b)=E_0, V(x)<0 in (a,b) and V(x)>0 for xb. Following the work made by D.Yafaev and performing a WKB approximation we obtain solutions defined on specific intervals. The aim of the first part of the thesis is to find a condition on E, which belongs to a neighbourhood of E_0, such that it is an eigenvalue of the Schrödinger operator, obtaining in this way global and linear dependent solutions in L2. In quantum mechanics this condition is known as Bohr-Sommerfeld quantization. In the second part we define a Schrödinger operator referred to two potential wells and we study the quantization conditions on E in order to have a global solution in L2xL2 with respect to the mutual position of the potentials. In particular their wells can be disjoint,can have an intersection, can be included one into the other and can have a single point intersection. For these cases we refer to the works of A.Martinez, S. Fujiié, T. Watanabe, S. Ashida.

Experimental evaluation of the z-resolution in different clinical Digital Breast Tomosynthesis systems using commercial phantoms

Digital Breast Tomosynthesis (DBT) is an advanced mammography technique based on the reconstruction of a pseudo-volumetric image. To date, image quality represents the most deficient section of DBT quality control protocols. In fact, related tests are not yet characterized by either action levels or typical values. This thesis work focuses on the evaluation of one aspect of image quality: the z-resolution. The latter is studied in terms of Artifact Spread Function (ASF), a function that describes the signal spread of a detail along the reconstructed focal planes. To quantify the ASF numerically, its Full Width at Half Maximum (FWHM) is calculated and used as a representative index of z-resolution. Experimental measurements were acquired in 24 DBT systems, of 7 different models, currently in use in 20 hospital facilities in Italy. The analysis, performed on the clinical reconstructed images, of 5 different commercial phantoms, lead to the identification of characteristic FWHM values for each type of DBT system. The ASF clearly showed a dependence on the size of the detail, providing higher FWHM values for larger objects. The z-resolution was found to be positively influenced by the acquisition angle: Fujifilm sistematically showed wider ASF profiles in ST mode (15°) than in HR mode (40°). However, no clear relationship was found between angular range and ASF, among different DBT systems, due to the influence of the peculiarities of each reconstruction algorithm. The experimental approach shown in this thesis work can be proposed as a z-resolution quality control test procedure. Contextually, the values found could be used as a starting point for identifying typical values to be included in the test, in a DBT protocol. Clearly, a statistically significant number of images is needed to do this. The equipment involved in this work is located in hospitals and is not available for research purposes, so only a limited amount of data was acquired and processed.

Use of isotopes for studying nitrogen processes in a wetland within the Venice Lagoon watershed

The present study is based on the use of isotopes for evaluating the efficiency of nutrients removal of a wetland, in particular nitrogen and nitrates, also between the different habitats present in the wetland. Nutrients like nitrogen and phosphorus, normally distributed as fertilizers, are among the principal causes of diffuse pollution. This is particularly important in the Adriatic Sea, which is frequently subjected to eutrophication phenomena. So it is very crucial requalification of wetland, in which there are naturally depurative processes such as denitrification and plant uptake, which allow the reduction of pollutant loads that flow in water bodies. In this study nutrient reduction is analyzed in the wetland of the Comuna drain, which waters flow in the Venice lagoon. Chemical and isotopical analyses were performed on samples of water, vegetation, soil and sediments taken in the wetlands of the Comuna drain in four different periods of the year and on data of nitrogen and phosphorus concentration obtained by the LASA of the University of Padova. Values of total nitrogen and nitrates were obtained in order to evaluate the reduction within the different systems of the wetland. Instead, the isotopic values of nitrogen and carbon were used to evaluate which process influence more nitrogen reduction and to understand the origin of the nutrient, if it is from fertilizers, waste water or sewage. To conclude, the most important process in the wetland of the Comuna drain is plant uptake, in facts the bigger percentage of nitrogen reduction was in the period of vegetative growth. So it is important the study of isotopes in plant tissues and water residence time, whose increase would allow a greater reduction of nutrients.

Modelling and simulating in systems biology: an approach based on multi-agent systems

Systems Biology is an innovative way of doing biology recently raised in bio-informatics contexts, characterised by the study of biological systems as complex systems with a strong focus on the system level and on the interaction dimension. In other words, the objective is to understand biological systems as a whole, putting on the foreground not only the study of the individual parts as standalone parts, but also of their interaction and of the global properties that emerge at the system level by means of the interaction among the parts. This thesis focuses on the adoption of multi-agent systems (MAS) as a suitable paradigm for Systems Biology, for developing models and simulation of complex biological systems. Multi-agent system have been recently introduced in informatics context as a suitabe paradigm for modelling and engineering complex systems. Roughly speaking, a MAS can be conceived as a set of autonomous and interacting entities, called agents, situated in some kind of nvironment, where they fruitfully interact and coordinate so as to obtain a coherent global system behaviour. The claim of this work is that the general properties of MAS make them an effective approach for modelling and building simulations of complex biological systems, following the methodological principles identified by Systems Biology. In particular, the thesis focuses on cell populations as biological systems. In order to support the claim, the thesis introduces and describes (i) a MAS-based model conceived for modelling the dynamics of systems of cells interacting inside cell environment called niches. (ii) a computational tool, developed for implementing the models and executing the simulations. The tool is meant to work as a kind of virtual laboratory, on top of which kinds of virtual experiments can be performed, characterised by the definition and execution of specific models implemented as MASs, so as to support the validation, falsification and improvement of the models through the observation and analysis of the simulations. A hematopoietic stem cell system is taken as reference case study for formulating a specific model and executing virtual experiments.

Acute stress regulates vasotocinergic and isotocinergic systems in the gilthead sea bream (Sparus aurata L.).

The hypothalamus-pituitary-interrenal axis is involved in stress response regulation. In addition, arginine vasotocin (AVT) and isotocin (IT) are also considered as important players in this stress regulation. The present study assessed, using the teleost gilthead sea bream (Sparus aurata) as a biological model, hypothalamic mRNA expression changes of AVT and IT and their receptors at hepatic level after an acute stress situation. Specimens were submitted to air for 3 min and place back in their respective tanks after that, being sampled at different times (15 min, 30 min, 1, 2, 4 and 8 hours post-stress) in order to study the time course response. Plasma cortisol values increased after few minutes post-exposure, decreasing during the experimental time while a metabolic reorganization occurred in both plasmatic and hepatic levels. At hypothalamic level, acute stress affects mRNA expression of AVT and IT precursors, as well as hepatic expression of their receptors, suggesting the involvement of both vasotocinergic and isotocinergic systems in the acute stress response. Our results demonstrate the activation and involvement of both endocrine pathways in the regulation of metabolic and stress systems of Sparus aurata, which is stated, at least, through changes in mRNA expression levels of these genes analysed.