596 resultados para discontinuity


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Pós-graduação em Educação - IBRC

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Patterns of geographic variation of the canid Cerdocyon thous have historically been obscured by its remarkable intraspecific morphological variability. The observed distribution is highly associated with phytophysiognomy, a feature considered highly dynamic along geological time. In the present study, we tested whether vegetation distribution during the Holocene Glacial Maximum of South America (HGM) explains the patterns of morphological variation within Cerdocyon thous. The species was divided in groups according to paleohabitats that could support their presence during the HGM, and then tested for differences in skull morphometrics. The results obtained demonstrate that the climatic changes during the HGM influenced the population structure of this species, resulting in the establishment of geographical groups with different degrees of morphological cohesion. Higher morphological cohesion found in the Northern group might be explained by the marked discontinuity between its geographical range and the rest of the species`distribution. The Eastern and Southern morphological divergence is less striking and, although this could be related to past vegetation distribution, the disappearance of those barriers leads to a population structure that could be slowly breaking down. (C) 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98, 77-84.

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Nasal gliomas are rare benign congenital midline tumors composed of heterotopic neuroglial tissue. They have potential for intracranial extension through a bony defect in the skull base. Neuroimaging is essential for identifying nasal lesions and for determining their exact location and any possible intracranial extension. Computed tomography is often the initial imaging study obtained because it provides good visualization of the bony landmarks of the skull base; it is not, however, well suited for soft tissue imaging. Magnetic resonance imaging has better soft tissue resolution and may be the best initial study in patients seen early in life because the anterior skull base consists of an unossified cartilage and may falsely appear as if there is a bony dehiscence on computed tomography. A frontal craniotomy approach is recommended if intracranial extension is identified, followed by a transnasal endoscopic approach for intranasal glioma. A case is presented of a huge fetal facial mass that was shown by ultrasound that protruded through the left nostril at 33 weeks of gestation. Computed tomography of the neonate suggested a transethmoidal encephalocele. Magnetic resonance imaging showed a huge mass occupying the nasopharynx and the nasal cavity and protruding externally to the face but ruled out bony discontinuity in the skull base and, therefore, any intracranial connection. The infant underwent an endoscopic resection of the mass via oral and nasal routes and pathologic examination revealed intranasal glioma. (C) 2012 Elsevier Inc. All rights reserved.

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Background: In an aging population an increasing number of elderly caregivers will be called upon to provide care over a long period, during which time they will be burdened both by caregiving and by the physiological effects of their own aging. Among them there will be more aged male caregivers, who will probably be less prepared than women to become caregivers. The aim of this study was to investigate the relationship between caregivers' gender, age, family income, living arrangements and social support as independent variables, and depressive symptoms, comorbidities, level of frailty, grip strength, walking speed and social isolation, as dependent variables. Methods: 176 elderly people (123 women) were selected from a sample of a population-based study on frailty (n = 900), who had cared for a spouse (79.3%) and/or parents (31.4%) in the past five years (mean age = 71.8 +/- 4.86 years; mean monthly family income in minimum wages = 4.64 +/- 5.14). The study used questionnaires and self-report scales, grip strength and walking speed tests. Results: 65% of participants evaluated caregiving as being very stressful. Univariate analyses of regression showed low family income as a risk factor for depression; being female and low perceived social support as a risk for comorbidities; being 80 years of age and above for low grip strength; and being male for social isolation indicated by discontinuity of activities and social roles. In multivariate analyses of regression, poverty arose as a risk factor for depression and being female for comorbidities. Conclusions: Gender roles, age, income and social support interacted with physical and emotional health, and with the continuity of social participation of elderly caregivers. Special attention must be given to male caregivers.

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Oxygen-deficient TiO2 films with enhanced visible and near-infrared optical absorption have been deposited by reactive sputtering using a planar diode radio frequency magnetron configuration. It is observed that the increase in the absorption coefficient is more effective when the O-2 gas supply is periodically interrupted rather than by a decrease of the partial O-2 gas pressure in the deposition plasma. The optical absorption coefficient at 1.5 eV increases from about 1 x 10(2) cm(-1) to more than 4 x 10(3) cm(-1) as a result of the gas flow discontinuity. A red-shift of similar to 0.24 eV in the optical absorption edge is also observed. High resolution transmission electron microscopy with composition analysis shows that the films present a dense columnar morphology, with estimated mean column width of 40nm. Moreover, the interruptions of the O-2 gas flow do not produce detectable variations in the film composition along its growing direction. X-ray diffraction and micro-Raman experiments indicate the presence of the TiO2 anatase, rutile, and brookite phases. The anatase phase is dominant, with a slight increment of the rutile and brookite phases in films deposited under discontinued O-2 gas flow. The increase of optical absorption in the visible and near-infrared regions has been attributed to a high density of defects in the TiO2 films, which is consistent with density functional theory calculations that place oxygen-related vacancy states in the upper third of the optical bandgap. The electronic structure calculation results, along with the adopted deposition method and experimental data, have been used to propose a mechanism to explain the formation of the observed oxygen-related defects in TiO2 thin films. The observed increase in sub-bandgap absorption and the modeling of the corresponding changes in the electronic structure are potentially useful concerning the optimization of efficiency of the photocatalytic activity and the magnetic doping of TiO2 films. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4724334]

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The visual system is particularly sensitive to methylmercury (MeHg) exposure and, therefore, provides a useful model for investigating the fundamental mechanisms that direct toxic effects. During a period of 70 days, adult of a freshwater fish species Hoplias malabaricus were fed with fish prey previously labeled with two different doses of methylmercury (0.075 and 0.75 mu g g(-1)) to determine the mercury distribution and morphological changes in the retina. Mercury deposits were found in the photoreceptor layer, in the inner plexiform layer and in the outer plexiform layer, demonstrating a dose-dependent bioaccumulation. The ultrastructure analysis of retina revealed a cellular deterioration in the photoreceptor layer, morphological changes in the inner and outer segments of rods, structural changes in the plasma membrane of rods and double cones, changes in the process of removal of membranous discs and a structural discontinuity. These results lead to the conclusion that methylmercury is able to cross the blood-retina barrier, accumulate in the cells and layers of retina and induce changes in photoreceptors of H. malabaricus even under subchronic exposure. (c) 2012 Elsevier Inc. All rights reserved.

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Esta pesquisa investiga os fatores que estão relacionados à descontinuidade do tratamento da tuberculose em Rio Branco-Acre e foi realizada com uma contribuição da etnografia para uma apreensão da realidade a ser estudada. Foi desenvolvida em duas etapas de mapeamento: na primeira, procedeu-se à busca de informações na base de dados do SINAN (Sistema de Notificação de Agravos Nacional) e na Coordenação Municipal do Programa de Tuberculose, a segunda etapa procurou registrar fatos a partir da observação do atendimento numa unidade de saúde que presta assistência aos portadores de tuberculose em tratamento, e entrevistas com eles, assim como de profissionais que prestavam assistência. Na análise das observações, coletas de narrativas e entrevistas, observou-se que os profissionais dos serviços de saúde caracterizam algumas pessoas como propícias a descontinuarem o tratamento e não consideram os diferentes modos de vida na abordagem de seus pacientes, dificultando, assim, a formação do vínculo e favorecendo a descontinuidade ou o abandono. Identificou-se também que as pessoas que faziam o tratamento da tuberculose tinham várias formas de lidar com as limitações que foram geradas pela doença, como a restrição para o trabalho, entre outras, e as pessoas que o descontinuaram levavam em consideração seu sistema de crenças e valores, bem como a própria percepção de saúde/doença, devido a estarem se sentindo curados quando o interromperam.

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This study has investigated the question of relation between literacy practices in and out of school in rural Tanzania. By using the perspective of linguistic anthropology, literacy practices in five villages in Karagwe district in the northwest of Tanzania have been analysed. The outcome may be used as a basis for educational planning and literacy programs. The analysis has revealed an intimate relation between language, literacy and power. In Karagwe, traditional élites have drawn on literacy to construct and reconstruct their authority, while new élites, such as individual women and some young people have been able to use literacy as one tool to get access to power. The study has also revealed a high level of bilingualism and a high emphasis on education in the area, which prove a potential for future education in the area. At the same time discontinuity in language use, mainly caused by stigmatisation of what is perceived as local and traditional, such as the mother-tongue of the majority of the children, and the high status accrued to all that is perceived as Western, has turned out to constitute a great obstacle for pupils’ learning. The use of ethnographic perspectives has enabled comparisons between interactional patterns in schools and outside school. This has revealed communicative patterns in school that hinder pupils’ learning, while the same patterns in other discourses reinforce learning. By using ethnography, relations between explicit and implicit language ideologies and their impact in educational contexts may be revealed. This knowledge may then be used to make educational plans and literacy programmes more relevant and efficient, not only in poor post-colonial settings such as Tanzania, but also elsewhere, such as in Western settings.

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In this work a multidisciplinary study of the December 26th, 2004 Sumatra earthquake has been carried out. We have investigated both the effect of the earthquake on the Earth rotation and the stress field variations associated with the seismic event. In the first part of the work we have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earth’s pole path and on the length-of-day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with some preliminary instrumental evidences on the pole path perturbation (which has not been confirmed yet) registered just after the occurrence of the earthquake, which showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the perturbation induced by the tsunami on the instantaneous rotational pole is characterized by a step-like discontinuity, which is compatible with the observations but its magnitude turns out to be almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties. In the second part of this work of thesis we modeled the coseismic and postseismic stress evolution following the Sumatra earthquake. By means of a semi-analytical, viscoelastic, spherical model of global postseismic deformation and a numerical finite-element approach, we performed an analysis of the stress diffusion following the earthquake in the near and far field of the mainshock source. We evaluated the stress changes due to the Sumatra earthquake by projecting the Coulomb stress over the sequence of aftershocks taken from various catalogues in a time window spanning about two years and finally analyzed the spatio-temporal pattern. The analysis performed with the semi-analytical and the finite-element modeling gives a complex picture of the stress diffusion, in the area under study, after the Sumatra earthquake. We believe that the results obtained with the analytical method suffer heavily for the restrictions imposed, on the hypocentral depths of the aftershocks, in order to obtain the convergence of the harmonic series of the stress components. On the contrary we imposed no constraints on the numerical method so we expect that the results obtained give a more realistic description of the stress variations pattern.

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Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

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In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

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This PhD thesis aims at providing an evaluation of EU Cohesion policy impact on regional growth. It employs methodologies and data sources never before applied for this purpose. Main contributions to the literature concerning EU regional policy effectiveness have been extensively analysed. Moreover, having carried out an overview of the current literature on Cohesion Policy, we deduce that this work introduces innovative features in the field. The work enriches the current literature with regards to two aspects. The first aspect concerns the use of the instrument of Regression Discontinuity Design in order to examine the presence of a different outcome in terms of growth between Objectives 1 regions and non-Objective 1 regions at the cut-off point (75 percent of EU-15 GDP per capita in PPS) during the two programming periods, 1994-1999 and 2000-2006. The results confirm a significant difference higher than 0.5 percent per year between the two groups. The other empirical evaluation regards the study of a cross-section regression model based on the convergence theory that analyses the dependence relation between regional per capita growth and EU Cohesion policy expenditure in several fields of interventions. We have built a very fine dataset of spending variables (certified expenditure), using sources of data directly provided from the Regional Policy Directorate of the European Commission.

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An integrated array of analytical methods -including clay mineralogy, vitrinite reflectance, Raman spectroscopy on carbonaceous material, and apatite fission-track analysis- was employed to constrain the thermal and thermochronological evolution of selected portions of the Pontides of northern Turkey. (1) A multimethod investigation was applied for the first time to characterise the thermal history of the Karakaya Complex, a Permo-Triassic subduction-accretion complex cropping out throughout the Sakarya Zone. The results indicate two different thermal regimes: the Lower Karakaya Complex (Nilüfer Unit) -mostly made of metabasite and marble- suffered peak temperatures of 300-500°C (greenschist facies); the Upper Karakaya Complex (Hodul and the Orhanlar Units) –mostly made of greywacke and arkose- yielded heterogeneous peak temperatures (125-376°C), possibly the result of different degree of involvement of the units in the complex dynamic processes of the accretionary wedge. Contrary to common belief, the results of this study indicate that the entire Karakaya Complex suffered metamorphic conditions. Moreover, a good degree of correlation among the results of these methods demonstrate that Raman spectroscopy on carbonaceous material can be applied successfully to temperature ranges of 200-330°C, thus extending the application of this method from higher grade metamorphic contexts to lower grade metamorphic conditions. (2) Apatite fission-track analysis was applied to the Sakarya and the İstanbul Zones in order to constrain the exhumation history and timing of amalgamation of these two exotic terranes. AFT ages from the İstanbul and Sakarya terranes recorded three distinct episodes of exhumation related to the complex tectonic evolution of the Pontides. (i) Paleocene - early Eocene ages (62.3-50.3 Ma) reflect the closure of the İzmir-Ankara ocean and the ensuing collision between the Sakarya terrane and the Anatolide-Tauride Block. (ii) Late Eocene - earliest Oligocene (43.5-32.3 Ma) ages reflect renewed tectonic activity along the İzmir-Ankara. (iii) Late Oligocene- Early Miocene ages reflect the onset and development of the northern Aegean extension. The consistency of AFT ages, both north and south of the tectonic contact between the İstanbul and Sakarya terranes, suggest that such terranes were amalgamated in pre-Cenozoic times. (3) Fission-track analysis was also applied to rock samples from the Marmara region, in an attempt to constrain the inception and development of the North Anatolian Fault system in the region. The results agree with those from the central Pontides. The youngest AFT ages (Late Oligocene - early Miocene) were recorded in the western portion of the Marmara Sea region and reflect the onset and development of northern Aegean extension. Fission-track data from the eastern Marmara Sea region indicate rapid Early Eocene exhumation induced by the development of the İzmir-Ankara orogenic wedge. Thermochronological data along the trace of the Ganos Fault –a segment of the North Anatolian Fault system- indicate the presence of a tectonic discontinuity active by Late Oligocene time, i.e. well before the arrival of the North Anatolian Fault system in the area. The integration of thermochronologic data with preexisting structural data point to the existence of a system of major E-W-trending structural discontinuities active at least from the Late Oligocene. In the Early Pliocene, inception of the present-day North Anatolian Fault system in the Marmara region occurred by reactivation of these older tectonic structures. 


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In this thesis Marsili back-arc basin and Palinuro Volcanic Complex (Southern Tyrrhenian Sea) have been investigated by using magnetic, bathymetric and gravimetric data. A new velocity model of opening of the Marsili basin has been proposed, highlighting the transition from the horizontal spreading of the back-arc to the vertical accretion of the Marsili seamount. Introducing gravity data, Marsili's internal structure has been modeled and a huge portion of the volcano with low density and vanishing magnetization has been detected. Forward modeling of Palinuro Volcanic Complex showed as Palinuro represents the shallowest evidence of a deep tectonic discontinuity and the possible transition domain between the oceanic crust of Marsili Basin and the continental crust related to the Appenninic chain.

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Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.