Computational Methods in Biophysics and Medicinal Chemistry: Applications and Challenges

In this thesis I described the theory and application of several computational methods in solving medicinal chemistry and biophysical tasks. I pointed out to the valuable information which could be achieved by means of computer simulations and to the possibility to predict the outcome of traditional experiments. Nowadays, computer represents an invaluable tool for chemists. In particular, the main topics of my research consisted in the development of an automated docking protocol for the voltage-gated hERG potassium channel blockers, and the investigation of the catalytic mechanism of the human peptidyl-prolyl cis-trans isomerase Pin1.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Bioinformatic methods in applied genomic research

Here I will focus on three main topics that best address and include the projects I have been working in during my three year PhD period that I have spent in different research laboratories addressing both computationally and practically important problems all related to modern molecular genomics. The first topic is the use of livestock species (pigs) as a model of obesity, a complex human dysfunction. My efforts here concern the detection and annotation of Single Nucleotide Polymorphisms. I developed a pipeline for mining human and porcine sequences. Starting from a set of human genes related with obesity the platform returns a list of annotated porcine SNPs extracted from a new set of potential obesity-genes. 565 of these SNPs were analyzed on an Illumina chip to test the involvement in obesity on a population composed by more than 500 pigs. Results will be discussed. All the computational analysis and experiments were done in collaboration with the Biocomputing group and Dr.Luca Fontanesi, respectively, under the direction of prof. Rita Casadio at the Bologna University, Italy. The second topic concerns developing a methodology, based on Factor Analysis, to simultaneously mine information from different levels of biological organization. With specific test cases we develop models of the complexity of the mRNA-miRNA molecular interaction in brain tumors measured indirectly by microarray and quantitative PCR. This work was done under the supervision of Prof. Christine Nardini, at the “CAS-MPG Partner Institute for Computational Biology” of Shangai, China (co-founded by the Max Planck Society and the Chinese Academy of Sciences jointly) The third topic concerns the development of a new method to overcome the variety of PCR technologies routinely adopted to characterize unknown flanking DNA regions of a viral integration locus of the human genome after clinical gene therapy. This new method is entirely based on next generation sequencing and it reduces the time required to detect insertion sites, decreasing the complexity of the procedure. This work was done in collaboration with the group of Dr. Manfred Schmidt at the Nationales Centrum für Tumorerkrankungen (Heidelberg, Germany) supervised by Dr. Annette Deichmann and Dr. Ali Nowrouzi. Furthermore I add as an Appendix the description of a R package for gene network reconstruction that I helped to develop for scientific usage (http://www.bioconductor.org/help/bioc-views/release/bioc/html/BUS.html).

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

New Methods in Organocatalysis

In the following chapters new methods in organocatalysis are described. The design of new catalysts is explored starting from the synthesis and the study of ion tagged prolines to their applications and recycle, then moving to the synthesis of new bicyclic diarylprolinol silyl ethers and their use in organocatalytic transformations. The study of new organocatalytic reaction is also investigated, in particular bifunctional thioureas are employed to catalyse the conjugate addition of nitro compounds to 3-yilidene oxindoles in sequential and domino reactions. Finally, preliminary results on photochemical organocatalytic atom transfer radical addition to alkenes are discussed in the last chapter.

Novel investigation methods in Computational Social Dynamics and Complex Systems

In this thesis the evolution of the techno-social systems analysis methods will be reported, through the explanation of the various research experience directly faced. The first case presented is a research based on data mining of a dataset of words association named Human Brain Cloud: validation will be faced and, also through a non-trivial modeling, a better understanding of language properties will be presented. Then, a real complex system experiment will be introduced: the WideNoise experiment in the context of the EveryAware european project. The project and the experiment course will be illustrated and data analysis will be displayed. Then the Experimental Tribe platform for social computation will be introduced . It has been conceived to help researchers in the implementation of web experiments, and aims also to catalyze the cumulative growth of experimental methodologies and the standardization of tools cited above. In the last part, three other research experience which already took place on the Experimental Tribe platform will be discussed in detail, from the design of the experiment to the analysis of the results and, eventually, to the modeling of the systems involved. The experiments are: CityRace, about the measurement of human traffic-facing strategies; laPENSOcosì, aiming to unveil the political opinion structure; AirProbe, implemented again in the EveryAware project framework, which consisted in monitoring air quality opinion shift of a community informed about local air pollution. At the end, the evolution of the technosocial systems investigation methods shall emerge together with the opportunities and the threats offered by this new scientific path.

Drug of abuse analysis: new methods in herbal and biological matrices for medicinal chemistry and forensic investigation

In this Ph.D. project, original and innovative approaches for the quali-quantitative analysis of abuse substances, as well as therapeutic agents with abuse potential and related compounds were designed, developed and validated for application to different fields such as forensics, clinical and pharmaceutical. All the parameters involved in the developed analytical workflows were properly and accurately optimised, from sample collection to sample pretreatment up to the instrumental analysis. Advanced dried blood microsampling technologies have been developed, able of bringing several advantages to the method as a whole, such as significant reduction of solvent use, feasible storage and transportation conditions and enhancement of analyte stability. At the same time, the use of capillary blood allows to increase subject compliance and overall method applicability by exploiting such innovative technologies. Both biological and non-biological samples involved in this project were subjected to optimised pretreatment techniques developed ad-hoc for each target analyte, making also use of advanced microextraction techniques. Finally, original and advanced instrumental analytical methods have been developed based on high and ultra-high performance liquid chromatography (HPLC,UHPLC) coupled to different detection means (mainly mass spectrometry, but also electrochemical, and spectrophotometric detection for screening purpose), and on attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) for solid-state analysis. Each method has been designed to obtain highly selective, sensitive yet sustainable systems and has been validated according to international guidelines. All the methods developed herein proved to be suitable for the analysis of the compounds under investigation and may be useful tools in medicinal chemistry, pharmaceutical analysis, within clinical studies and forensic investigations.

Perturbative and non perturbative effects in the Standard Model and orbifolded ADS/CFT based theories

We study some perturbative and nonperturbative effects in the framework of the Standard Model of particle physics. In particular we consider the time dependence of the Higgs vacuum expectation value given by the dynamics of the StandardModel and study the non-adiabatic production of both bosons and fermions, which is intrinsically non-perturbative. In theHartree approximation, we analyze the general expressions that describe the dissipative dynamics due to the backreaction of the produced particles. Then, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vacuum expectation value (vev). As perturbative effects, we consider the leading logarithmic resummation in small Bjorken x QCD, concentrating ourselves on the Nc dependence of the Green functions associated to reggeized gluons. Here the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the large Nc limit (planar limit) case where the problem becomes integrable. In this contest we consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. In particular we study the depencence of the spectrum of thesemodelswith respect to the number of colors andmake comparisons with the planar limit case. In the final part we move on the study of theories beyond the Standard Model, considering models built on AdS5 S5/Γ orbifold compactifications of the type IIB superstring, where Γ is the abelian group Zn. We present an appealing three family N = 0 SUSY model with n = 7 for the order of the orbifolding group. This result in a modified Pati–Salam Model which reduced to the StandardModel after symmetry breaking and has interesting phenomenological consequences for LHC.

Effects of environmental complexity on neurogenesis in the hippocampal dentate gyrus

Introduction. Postnatal neurogenesis in the hippocampal dentate gyrus, can be modulated by numerous determinants, such as hormones, transmitters and stress. Among the factors positively interfering with neurogenesis, the complexity of the environment appears to play a particularly striking role. Adult mice reared in an enriched environment produce more neurons and exhibit better performance in hippocampus-specific learning tasks. While the effects of complex environments on hippocampal neurogenesis are well documented, there is a lack of information on the effects of living under socio-sensory deprivation conditions. Due to the immaturity of rats and mice at birth, studies dealing with the effects of environmental enrichment on hippocampal neurogenesis were carried out in adult animals, i.e. during a period of relatively low rate of neurogenesis. The impact of environment is likely to be more dramatic during the first postnatal weeks, because at this time granule cell production is remarkably higher than at later phases of development. The aim of the present research was to clarify whether and to what extent isolated or enriched rearing conditions affect hippocampal neurogenesis during the early postnatal period, a time window characterized by a high rate of precursor proliferation and to elucidate the mechanisms underlying these effects. The experimental model chosen for this research was the guinea pig, a precocious rodent, which, at 4-5 days of age can be independent from maternal care. Experimental design. Animals were assigned to a standard (control), an isolated, or an enriched environment a few days after birth (P5-P6). On P14-P17 animals received one daily bromodeoxyuridine (BrdU) injection, to label dividing cells, and were sacrificed either on P18, to evaluate cell proliferation or on P45, to evaluate cell survival and differentiation. Methods. Brain sections were processed for BrdU immunhistochemistry, to quantify the new born and surviving cells. The phenotype of the surviving cells was examined by means of confocal microscopy and immunofluorescent double-labeling for BrdU and either a marker of neurons (NeuN) or a marker of astrocytes (GFAP). Apoptotic cell death was examined with the TUNEL method. Serial sections were processed for immunohistochemistry for i) vimentin, a marker of radial glial cells, ii) BDNF (brain-derived neurotrofic factor), a neurotrophin involved in neuron proliferation/survival, iii) PSA-NCAM (the polysialylated form of the neural cell adhesion molecule), a molecule associated with neuronal migration. Total granule cell number in the dentate gyrus was evaluated by stereological methods, in Nissl-stained sections. Results. Effects of isolation. In P18 isolated animals we found a reduced cell proliferation (-35%) compared to controls and a lower expression of BDNF. Though in absolute terms P45 isolated animals had less surviving cells than controls, they showed no differences in survival rate and phenotype percent distribution compared to controls. Evaluation of the absolute number of surviving cells of each phenotype showed that isolated animals had a reduced number of cells with neuronal phenotype than controls. Looking at the location of the new neurons, we found that while in control animals 76% of them had migrated to the granule cell layer, in isolated animals only 55% of the new neurons had reached this layer. Examination of radial glia cells of P18 and P45 animals by vimentin immunohistochemistry showed that in isolated animals radial glia cells were reduced in density and had less and shorter processes. Granule cell count revealed that isolated animals had less granule cells than controls (-32% at P18 and -42% at P45). Effects of enrichment. In P18 enriched animals there was an increase in cell proliferation (+26%) compared to controls and a higher expression of BDNF. Though in both groups there was a decline in the number of BrdU-positive cells by P45, enriched animals had more surviving cells (+63) and a higher survival rate than controls. No differences were found between control and enriched animals in phenotype percent distribution. Evaluation of the absolute number of cells of each phenotype showed that enriched animals had a larger number of cells of each phenotype than controls. Looking at the location of cells of each phenotype we found that enriched animals had more new neurons in the granule cell layer and more astrocytes and cells with undetermined phenotype in the hilus. Enriched animals had a higher expression of PSA-NCAM in the granule cell layer and hilus Vimentin immunohistochemistry showed that in enriched animals radial glia cells were more numerous and had more processes.. Granule cell count revealed that enriched animals had more granule cells than controls (+37% at P18 and +31% at P45). Discussion. Results show that isolation rearing reduces hippocampal cell proliferation but does not affect cell survival, while enriched rearing increases both cell proliferation and cell survival. Changes in the expression of BDNF are likely to contribute to he effects of environment on precursor cell proliferation. The reduction and increase in final number of granule neurons in isolated and enriched animals, respectively, are attributable to the effects of environment on cell proliferation and survival and not to changes in the differentiation program. As radial glia cells play a pivotal role in neuron guidance to the granule cell layer, the reduced number of radial glia cells in isolated animals and the increased number in enriched animals suggests that the size of radial glia population may change dynamically, in order to match changes in neuron production. The high PSA-NCAM expression in enriched animals may concur to favor the survival of the new neurons by facilitating their migration to the granule cell layer. Conclusions. By using a precocious rodent we could demonstrate that isolated/enriched rearing conditions, at a time window during which intense granule cell proliferation takes place, lead to a notable decrease/increase of total granule cell number. The time-course and magnitude of postnatal granule cell production in guinea pigs are more similar to the human and non-human primate condition than in rats and mice. Translation of current data to humans would imply that exposure of children to environments poor/rich of stimuli may have a notably large impact on dentate neurogenesis and, very likely, on hippocampus dependent memory functions.

Kernel Methods for Tree Structured Data

Machine learning comprises a series of techniques for automatic extraction of meaningful information from large collections of noisy data. In many real world applications, data is naturally represented in structured form. Since traditional methods in machine learning deal with vectorial information, they require an a priori form of preprocessing. Among all the learning techniques for dealing with structured data, kernel methods are recognized to have a strong theoretical background and to be effective approaches. They do not require an explicit vectorial representation of the data in terms of features, but rely on a measure of similarity between any pair of objects of a domain, the kernel function. Designing fast and good kernel functions is a challenging problem. In the case of tree structured data two issues become relevant: kernel for trees should not be sparse and should be fast to compute. The sparsity problem arises when, given a dataset and a kernel function, most structures of the dataset are completely dissimilar to one another. In those cases the classifier has too few information for making correct predictions on unseen data. In fact, it tends to produce a discriminating function behaving as the nearest neighbour rule. Sparsity is likely to arise for some standard tree kernel functions, such as the subtree and subset tree kernel, when they are applied to datasets with node labels belonging to a large domain. A second drawback of using tree kernels is the time complexity required both in learning and classification phases. Such a complexity can sometimes prevents the kernel application in scenarios involving large amount of data. This thesis proposes three contributions for resolving the above issues of kernel for trees. A first contribution aims at creating kernel functions which adapt to the statistical properties of the dataset, thus reducing its sparsity with respect to traditional tree kernel functions. Specifically, we propose to encode the input trees by an algorithm able to project the data onto a lower dimensional space with the property that similar structures are mapped similarly. By building kernel functions on the lower dimensional representation, we are able to perform inexact matchings between different inputs in the original space. A second contribution is the proposal of a novel kernel function based on the convolution kernel framework. Convolution kernel measures the similarity of two objects in terms of the similarities of their subparts. Most convolution kernels are based on counting the number of shared substructures, partially discarding information about their position in the original structure. The kernel function we propose is, instead, especially focused on this aspect. A third contribution is devoted at reducing the computational burden related to the calculation of a kernel function between a tree and a forest of trees, which is a typical operation in the classification phase and, for some algorithms, also in the learning phase. We propose a general methodology applicable to convolution kernels. Moreover, we show an instantiation of our technique when kernels such as the subtree and subset tree kernels are employed. In those cases, Direct Acyclic Graphs can be used to compactly represent shared substructures in different trees, thus reducing the computational burden and storage requirements.

Welfare provision in Sweden and the dominant position of the Sap

There have been almost fifty years since Harry Eckstein' s classic monograph, A Theory of Stable Democracy (Princeton, 1961), where he sketched out the basic tenets of the “congruence theory”, which was to become one of the most important and innovative contributions to understanding democratic rule. His next work, Division and Cohesion in Democracy, (Princeton University Press: 1966) is designed to serve as a plausibility probe for this 'theory' (ftn.) and is a case study of a Northern democratic system, Norway. What is more, this line of his work best exemplifies the contribution Eckstein brought to the methodology of comparative politics through his seminal article, “ “Case Study and Theory in Political Science” ” (in Greenstein and Polsby, eds., Handbook of Political Science, 1975), on the importance of the case study as an approach to empirical theory. This article demonstrates the special utility of “crucial case studies” in testing theory, thereby undermining the accepted wisdom in comparative research that the larger the number of cases the better. Although not along the same lines, but shifting the case study unit of research, I intend to take up here the challenge and build upon an equally unique political system, the Swedish one. Bearing in mind the peculiarities of the Swedish political system, my unit of analysis is going to be further restricted to the Swedish Social Democratic Party, the Svenska Arbetare Partiet. However, my research stays within the methodological framework of the case study theory inasmuch as it focuses on a single political system and party. The Swedish SAP endurance in government office and its electoral success throughout half a century (ftn. As of the 1991 election, there were about 56 years - more than half century - of interrupted social democratic "reign" in Sweden.) are undeniably a performance no other Social Democrat party has yet achieved in democratic conditions. Therefore, it is legitimate to inquire about the exceptionality of this unique political power combination. Which were the different components of this dominance power position, which made possible for SAP's governmental office stamina? I will argue here that it was the end-product of a combination of multifarious factors such as a key position in the party system, strong party leadership and organization, a carefully designed strategy regarding class politics and welfare policy. My research is divided into three main parts, the historical incursion, the 'welfare' part and the 'environment' part. The first part is a historical account of the main political events and issues, which are relevant for my case study. Chapter 2 is devoted to the historical events unfolding in the 1920-1960 period: the Saltsjoebaden Agreement, the series of workers' strikes in the 1920s and SAP's inception. It exposes SAP's ascent to power in the mid 1930s and the party's ensuing strategies for winning and keeping political office, that is its economic program and key economic goals. The following chapter - chapter 3 - explores the next period, i.e. the period from 1960s to 1990s and covers the party's troubled political times, its peak and the beginnings of the decline. The 1960s are relevant for SAP's planning of a long term economic strategy - the Rehn Meidner model, a new way of macroeconomic steering, based on the Keynesian model, but adapted to the new economic realities of welfare capitalist societies. The second and third parts of this study develop several hypotheses related to SAP's 'dominant position' (endurance in politics and in office) and test them afterwards. Mainly, the twin issues of economics and environment are raised and their political relevance for the party analyzed. On one hand, globalization and its spillover effects over the Swedish welfare system are important causal factors in explaining the transformative social-economic challenges the party had to put up with. On the other hand, Europeanization and environmental change influenced to a great deal SAP's foreign policy choices and its domestic electoral strategies. The implications of globalization on the Swedish welfare system will make the subject of two chapters - chapters four and five, respectively, whereupon the Europeanization consequences will be treated at length in the third part of this work - chapters six and seven, respectively. Apparently, at first sight, the link between foreign policy and electoral strategy is difficult to prove and uncanny, in the least. However, in the SAP's case there is a bulk of literature and public opinion statistical data able to show that governmental domestic policy and party politics are in a tight dependence to foreign policy decisions and sovereignty issues. Again, these country characteristics and peculiar causal relationships are outlined in the first chapters and explained in the second and third parts. The sixth chapter explores the presupposed relationship between Europeanization and environmental policy, on one hand, and SAP's environmental policy formulation and simultaneous agenda-setting at the international level, on the other hand. This chapter describes Swedish leadership in environmental policy formulation on two simultaneous fronts and across two different time spans. The last chapter, chapter eight - while trying to develop a conclusion, explores the alternative theories plausible in explaining the outlined hypotheses and points out the reasons why these theories do not fit as valid alternative explanation to my systemic corporatism thesis as the main causal factor determining SAP's 'dominant position'. Among the alternative theories, I would consider Traedgaardh L. and Bo Rothstein's historical exceptionalism thesis and the public opinion thesis, which alone are not able to explain the half century social democratic endurance in government in the Swedish case.

Caratteristiche ortopediche-ortodontiche in pazienti affetti da Sindrome di Nooan

La sindrome di Noonan (SN) è una patologia a trasmissione autosomica dominante caratterizzata da bassa statura, difetti cardiaci congeniti, dismorfia facciale. In letteratura sono stati pubblicati pochi case reports riguardanti le condizioni orali-facciali in pazienti affetti da SN. Obiettivo. Individuare patologie di pertinenza ortopedico-ortodontica caratteristiche della sindrome utilizzando un campione di pazienti con diagnosi di SN. Metodi. Un gruppo di 10 pazienti affetti da SN è stato sottoposto a esame obiettivo extraorale ed intraorale, ortopantomografia, teleradiografia latero-laterale, impronte delle arcate dentarie. Le misurazioni sulle TLL sono state effettuate sulla base dell'analisi MBT; i valori palatali provengono dai modelli di studio dell’arcata superiore. È stata utilizzato il test t-Student per mettere a confronto il gruppo di studio e il gruppo di controllo riguardo le misure cefalometriche e i valori palatali. Risultati. Nel gruppo di studio sono state rilevate anomalie di numero (un dente deciduo soprannumerario e una agenesia di un dente permanente). Il test t-Student rivela differenze statisticamente significative per 7 variabili cefalometriche su 13 e per 2 variabili palatali. Conclusioni. Basandosi su questo studio è possibile concludere che i pazienti con SN mostrano II classe scheletrica di tipo mandibolare, crescita iperdivergente, tendenza al morso aperto scheletrico, palatoversione degli incisivi superiori, palato stretto. Questi risultati possono fornire informazioni utili sia per la diagnosi di SN sia per la pianificazione del corretto trattamento ortodontico.

Resonances in the two centers Coulomb system

In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.

Employing Distances in Design-based Spatial Estimation

In the last couple of decades we assisted to a reappraisal of spatial design-based techniques. Usually the spatial information regarding the spatial location of the individuals of a population has been used to develop efficient sampling designs. This thesis aims at offering a new technique for both inference on individual values and global population values able to employ the spatial information available before sampling at estimation level by rewriting a deterministic interpolator under a design-based framework. The achieved point estimator of the individual values is treated both in the case of finite spatial populations and continuous spatial domains, while the theory on the estimator of the population global value covers the finite population case only. A fairly broad simulation study compares the results of the point estimator with the simple random sampling without replacement estimator in predictive form and the kriging, which is the benchmark technique for inference on spatial data. The Monte Carlo experiment is carried out on populations generated according to different superpopulation methods in order to manage different aspects of the spatial structure. The simulation outcomes point out that the proposed point estimator has almost the same behaviour as the kriging predictor regardless of the parameters adopted for generating the populations, especially for low sampling fractions. Moreover, the use of the spatial information improves substantially design-based spatial inference on individual values.