Automated Segmentation and Non-Rigid Registration for the Quantitative Evaluation of Myocardial Perfusion from Magnetic Resonance Images

Myocardial perfusion quantification by means of Contrast-Enhanced Cardiac Magnetic Resonance images relies on time consuming frame-by-frame manual tracing of regions of interest. In this Thesis, a novel automated technique for myocardial segmentation and non-rigid registration as a basis for perfusion quantification is presented. The proposed technique is based on three steps: reference frame selection, myocardial segmentation and non-rigid registration. In the first step, the reference frame in which both endo- and epicardial segmentation will be performed is chosen. Endocardial segmentation is achieved by means of a statistical region-based level-set technique followed by a curvature-based regularization motion. Epicardial segmentation is achieved by means of an edge-based level-set technique followed again by a regularization motion. To take into account the changes in position, size and shape of myocardium throughout the sequence due to out of plane respiratory motion, a non-rigid registration algorithm is required. The proposed non-rigid registration scheme consists in a novel multiscale extension of the normalized cross-correlation algorithm in combination with level-set methods. The myocardium is then divided into standard segments. Contrast enhancement curves are computed measuring the mean pixel intensity of each segment over time, and perfusion indices are extracted from each curve. The overall approach has been tested on synthetic and real datasets. For validation purposes, the sequences have been manually traced by an experienced interpreter, and contrast enhancement curves as well as perfusion indices have been computed. Comparisons between automatically extracted and manually obtained contours and enhancement curves showed high inter-technique agreement. Comparisons of perfusion indices computed using both approaches against quantitative coronary angiography and visual interpretation demonstrated that the two technique have similar diagnostic accuracy. In conclusion, the proposed technique allows fast, automated and accurate measurement of intra-myocardial contrast dynamics, and may thus address the strong clinical need for quantitative evaluation of myocardial perfusion.

Leopoli-Cencelle beyond virtual reality Documentazione, interpretazione e comprensione di una città medievale

La città medievale di Leopoli-Cencelle (fondata da Papa Leone IV nell‘854 d.C. non lontano da Civitavecchia) è stata oggetto di studio e di periodiche campagne di scavo a partire dal 1994. Le stratigrafie investigate con metodi tradizionali, hanno portato alla luce le numerose trasformazioni che la città ha subìto nel corso della sua esistenza in vita. Case, torri, botteghe e strati di vissuto, sono stati interpretati sin dall’inizio dello scavo basandosi sulla documentazione tradizionale e bi-dimensionale, legata al dato cartaceo e al disegno. Il presente lavoro intende re-interpretare i dati di scavo con l’ausilio delle tecnologie digitali. Per il progetto sono stati utilizzati un laser scanner, tecniche di Computer Vision e modellazione 3D. I tre metodi sono stati combinati in modo da poter visualizzare tridimensionalmente gli edifici abitativi scavati, con la possibilità di sovrapporre semplici modelli 3D che permettano di formulare ipotesi differenti sulla forma e sull’uso degli spazi. Modellare spazio e tempo offrendo varie possibilità di scelta, permette di combinare i dati reali tridimensionali, acquisiti con un laser scanner, con semplici modelli filologici in 3D e offre l’opportunità di valutare diverse possibili interpretazioni delle caratteristiche dell’edificio in base agli spazi, ai materiali, alle tecniche costruttive. Lo scopo del progetto è andare oltre la Realtà Virtuale, con la possibilità di analizzare i resti e di re-interpretare la funzione di un edificio, sia in fase di scavo che a scavo concluso. Dal punto di vista della ricerca, la possibilità di visualizzare le ipotesi sul campo favorisce una comprensione più profonda del contesto archeologico. Un secondo obiettivo è la comunicazione a un pubblico di “non-archeologi”. Si vuole offrire a normali visitatori la possibilità di comprendere e sperimentare il processo interpretativo, fornendo loro qualcosa in più rispetto a una sola ipotesi definitiva.

Non-standard signatures from Cosmic Microwave Background polarisation

In this Thesis we focus on non-standard signatures from CMB polarisation, which might hint at the existence of new phenomena beyond the standard models for Cosmology and Particle physics. With the Planck ESA mission, CMB temperature anisotropies have been observed at the cosmic variance limit, but polarisation remains to be further investigated. CMB polarisation data are important not only because they contribute to provide tighter constraints of cosmological parameters but also because they allow the investigation of physical processes that would be precluded if just the CMB temperature maps were considered. We take polarisation data into account to assess the statistical significance of the anomalies currently observed only in the CMB temperature map and to constrain the Cosmic Birefringence (CB) effect, which is expected in parity-violating extensions of the standard electromagnetism. In particular, we propose a new one-dimensional estimator for the lack of power anomaly capable of taking both temperature and polarisation into account jointly. With the aim of studying the anisotropic CB we develop and perform two different and complementary methods able to evaluate the power spectrum of the CB. Finally, by employing these estimators and methodologies on Planck data we provide new constraints beyond what already known in literature. The measure of CMB polarisation represents a technological challenge and to make accurate estimates, one has to keep an exquisite control of the systematic effects. In order to investigate the impact of spurious signal in forthcoming CMB polarisation experiments, we study the interplay between half-wave plates (HWP) non-idealities and the beams. Our analysis suggests that certain HWP configurations, depending on the complexity of Galactic foregrounds and the beam models, significantly impacts the B-mode reconstruction fidelity and could limit the capabilities of next-generation CMB experiments. We provide also a first study of the impact of non-ideal HWPs on CB.

A Semantic-based Framework for Digital Survey of Architectural Heritage

The research aims at developing a framework for semantic-based digital survey of architectural heritage. Rooted in knowledge-based modeling which extracts mathematical constraints of geometry from architectural treatises, as-built information of architecture obtained from image-based modeling is integrated with the ideal model in BIM platform. The knowledge-based modeling transforms the geometry and parametric relation of architectural components from 2D printings to 3D digital models, and create large amount variations based on shape grammar in real time thanks to parametric modeling. It also provides prior knowledge for semantically segmenting unorganized survey data. The emergence of SfM (Structure from Motion) provides access to reconstruct large complex architectural scenes with high flexibility, low cost and full automation, but low reliability of metric accuracy. We solve this problem by combing photogrammetric approaches which consists of camera configuration, image enhancement, and bundle adjustment, etc. Experiments show the accuracy of image-based modeling following our workflow is comparable to that from range-based modeling. We also demonstrate positive results of our optimized approach in digital reconstruction of portico where low-texture-vault and dramatical transition of illumination bring huge difficulties in the workflow without optimization. Once the as-built model is obtained, it is integrated with the ideal model in BIM platform which allows multiple data enrichment. In spite of its promising prospect in AEC industry, BIM is developed with limited consideration of reverse-engineering from survey data. Besides representing the architectural heritage in parallel ways (ideal model and as-built model) and comparing their difference, we concern how to create as-built model in BIM software which is still an open area to be addressed. The research is supposed to be fundamental for research of architectural history, documentation and conservation of architectural heritage, and renovation of existing buildings.

Sostanzialismo e relazionalismo dello spaziotempo alla luce della relatività generale

Until recently the debate on the ontology of spacetime had only a philosophical significance, since, from a physical point of view, General Relativity has been made "immune" to the consequences of the "Hole Argument" simply by reducing the subject to the assertion that solutions of Einstein equations which are mathematically different and related by an active diffeomorfism are physically equivalent. From a technical point of view, the natural reading of the consequences of the "Hole Argument” has always been to go further and say that the mathematical representation of spacetime in General Relativity inevitably contains a “superfluous structure” brought to light by the gauge freedom of the theory. This position of apparent split between the philosophical outcome and the physical one has been corrected thanks to a meticulous and complicated formal analysis of the theory in a fundamental and recent (2006) work by Luca Lusanna and Massimo Pauri entitled “Explaining Leibniz equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events”. The main result of this article is that of having shown how, from a physical point of view, point-events of Einstein empty spacetime, in a particular class of models considered by them, are literally identifiable with the autonomous degrees of freedom of the gravitational field (the Dirac observables, DO). In the light of philosophical considerations based on realism assumptions of the theories and entities, the two authors then conclude by saying that spacetime point-events have a degree of "weak objectivity", since they, depending on a NIF (non-inertial frame), unlike the points of the homogeneous newtonian space, are plunged in a rich and complex non-local holistic structure provided by the “ontic part” of the metric field. Therefore according to the complex structure of spacetime that General Relativity highlights and within the declared limits of a methodology based on a Galilean scientific representation, we can certainly assert that spacetime has got "elements of reality", but the inevitably relational elements that are in the physical detection of point-events in the vacuum of matter (highlighted by the “ontic part” of the metric field, the DO) are closely dependent on the choice of the global spatiotemporal laboratory where the dynamics is expressed (NIF). According to the two authors, a peculiar kind of structuralism takes shape: the point structuralism, with common features both of the absolutist and substantival tradition and of the relationalist one. The intention of this thesis is that of proposing a method of approaching the problem that is, at least at the beginning, independent from the previous ones, that is to propose an approach based on the possibility of describing the gravitational field at three distinct levels. In other words, keeping the results achieved by the work of Lusanna and Pauri in mind and following their underlying philosophical assumptions, we intend to partially converge to their structuralist approach, but starting from what we believe is the "foundational peculiarity" of General Relativity, which is that characteristic inherent in the elements that constitute its formal structure: its essentially geometric nature as a theory considered regardless of the empirical necessity of the measure theory. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now "visible" no longer in terms of its autonomous degrees of freedom (the DO), which, in fact, do not have a tensorial and, therefore, nor geometric nature, but it is analyzable through three levels: a first one, called the potential level (which the theory identifies with the components of the metric tensor), a second one, known as the connections level (which in the theory determine the forces acting on the mass and, as such, offer a level of description related to the one that the newtonian gravitation provides in terms of components of the gravitational field) and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part” of the metric field. It is then shown how to this last level it is possible to establish a “primitive level of objectivity” of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor. The convergence towards the affirmation by Lusanna and Pauri that the existence of a holistic, non-local and relational structure from which the properties quantitatively identified of point-events depend (in addition to their own intrinsic detection), even if it is obtained from different considerations, is realized, in our opinion, in the assignment of a crucial role to the degree of curvature of spacetime that is defined by the Weyl tensor even in the case of empty spacetimes (as in the analysis conducted by Lusanna and Pauri). In the end, matter, regarded as the physical counterpart of spacetime curvature, whose expression is the Weyl tensor, changes the value of this tensor even in spacetimes without matter. In this way, going back to the approach of Lusanna and Pauri, it affects the DOs evolution and, consequently, the physical identification of point-events (as our authors claim). In conclusion, we think that it is possible to see the holistic, relational, and non-local structure of spacetime also through the "behavior" of the Weyl tensor in terms of the Riemann tensor. This "behavior" that leads to geometrical effects of curvature is characterized from the beginning by the fact that it concerns extensive domains of the manifold (although it should be pointed out that the values of the Weyl tensor change from point to point) by virtue of the fact that the action of matter elsewhere indefinitely acts. Finally, we think that the characteristic relationality of spacetime structure should be identified in this "primitive level of organization" of spacetime.

Biomechanics of sprint running: a methodological contribution

Sports biomechanics describes human movement from a performance enhancement and an injury reduction perspective. In this respect, the purpose of sports scientists is to support coaches and physicians with reliable information about athletes’ technique. The lack of methods allowing for in-field athlete evaluation as well as for accurate joint force estimates represents, to date, the main limitation to this purpose. The investigations illustrated in the present thesis aimed at providing a contribution towards the development of the above mentioned methods. Two complementary approaches were adopted: a Low Resolution Approach – related to performance assessment – where the use of wearable inertial measurement units is exploited during different phases of sprint running, and a High Resolution Approach – related to joint kinetics estimate for injury prevention – where subject-specific, non-rigid constraints for knee joint kinematic modelling used in multi-body optimization techniques are defined. Results obtained using the Low Resolution Approach indicated that, due to their portability and inexpensiveness, inertial measurement systems are a valid alternative to laboratory-based instrumentation for in-field performance evaluation of sprint running. Using acceleration and angular velocity data, the following quantities were estimated: trunk inclination and angular velocity, instantaneous horizontal velocity and displacement of a point approximating the centre of mass, and stride and support phase durations. As concerns the High Resolution Approach, results indicated that the length of the anterior cruciate and lateral collateral ligaments decreased, while that of the deep bundle of the medial collateral ligament increased significantly during flexion. Variations of the posterior cruciate and the superficial bundle of the medial collateral ligament lengths were concealed by the experimental indeterminacy. A mathematical model was provided that allowed the estimate of subject-specific ligament lengths as a function of knee flexion and that can be integrated in a multi-body optimization procedure.

Local Earthquake Tomography by trans-dimensional Monte Carlo Sampling

In this study a new, fully non-linear, approach to Local Earthquake Tomography is presented. Local Earthquakes Tomography (LET) is a non-linear inversion problem that allows the joint determination of earthquakes parameters and velocity structure from arrival times of waves generated by local sources. Since the early developments of seismic tomography several inversion methods have been developed to solve this problem in a linearized way. In the framework of Monte Carlo sampling, we developed a new code based on the Reversible Jump Markov Chain Monte Carlo sampling method (Rj-McMc). It is a trans-dimensional approach in which the number of unknowns, and thus the model parameterization, is treated as one of the unknowns. I show that our new code allows overcoming major limitations of linearized tomography, opening a new perspective in seismic imaging. Synthetic tests demonstrate that our algorithm is able to produce a robust and reliable tomography without the need to make subjective a-priori assumptions about starting models and parameterization. Moreover it provides a more accurate estimate of uncertainties about the model parameters. Therefore, it is very suitable for investigating the velocity structure in regions that lack of accurate a-priori information. Synthetic tests also reveal that the lack of any regularization constraints allows extracting more information from the observed data and that the velocity structure can be detected also in regions where the density of rays is low and standard linearized codes fails. I also present high-resolution Vp and Vp/Vs models in two widespread investigated regions: the Parkfield segment of the San Andreas Fault (California, USA) and the area around the Alto Tiberina fault (Umbria-Marche, Italy). In both the cases, the models obtained with our code show a substantial improvement in the data fit, if compared with the models obtained from the same data set with the linearized inversion codes.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

The reconstruction of skeletal movement: the soft tissue artefact issue

In 3D human movement analysis performed using stereophotogrammetric systems and skin markers, bone pose can only be estimated in an indirect fashion. During a movement, soft tissue deformations make the markers move with respect to the underlying bone generating soft tissue artefact (STA). STA has devastating effects on bone pose estimation and its compensation remains an open question. The aim of this PhD thesis was to contribute to the solution of this crucial issue. Modelling STA using measurable trial-specific variables is a fundamental prerequisite for its removal from marker trajectories. Two STA model architectures are proposed. Initially, a thigh marker-level artefact model is presented. STA was modelled as a linear combination of joint angles involved in the movement. This model was calibrated using ex-vivo and in-vivo STA invasive measures. The considerable number of model parameters led to defining STA approximations. Three definitions were proposed to represent STA as a series of modes: individual marker displacements, marker-cluster geometrical transformations (MCGT), and skin envelope shape variations. Modes were selected using two criteria: one based on modal energy and another on the selection of modes chosen a priori. The MCGT allows to select either rigid or non-rigid STA components. It was also empirically demonstrated that only the rigid component affects joint kinematics, regardless of the non-rigid amplitude. Therefore, a model of thigh and shank STA rigid component at cluster-level was then defined. An acceptable trade-off between STA compensation effectiveness and number of parameters can be obtained, improving joint kinematics accuracy. The obtained results lead to two main potential applications: the proposed models can generate realistic STAs for simulation purposes to compare different skeletal kinematics estimators; and, more importantly, focusing only on the STA rigid component, the model attains a satisfactory STA reconstruction with less parameters, facilitating its incorporation in an pose estimator.

La perdita di chance nel prisma del danno non patrimoniale

Il danno da perdita di chance rappresenta la categoria giuridica di cui la giurisprudenza si serve per ampliare i confini della tutela risarcitoria, in diversi casi in cui, alla stregua dell’impostazione dogmatica tradizionale, non potrebbe dirsi configurabile un danno-conseguenza (né sotto forma di danno emergente, né sotto forma di lucro cessante). Lo studio, una volta delimitato il campo dell’indagine e dato conto delle opinioni dottrinali sulla ricostruzione della figura, ha preso le mosse dall’illustrazione degli orientamenti della giurisprudenza, la quale, a partire dagli anni ’80 del secolo scorso, è andata via via applicando l’istituto nei settori del diritto del lavoro, della responsabilità professionale (in particolare dell’avvocato), e del danno alla persona (nel quale ultimo si è messo in luce come il danno da perdita di chance possa rivestire funzione unicamente descrittiva di tipologie di pregiudizio riconducibili alle “tradizionali” voci di danno). Nel secondo capitolo si è analiticamente esaminata la fattispecie del danno da perdita di chance, alla luce delle categorie e dei principi generali della responsabilità civile, vagliando i margini di “armonizzabilità” dell’istituto rispetto alle classificazioni in termini di danno emergente/lucro cessante, danno presente/futuro, danno-evento/danno-conseguenza, nonché rispetto alle regole sulla causalità, al requisito dell’ingiustizia del danno, e alle tecniche di liquidazione del danno. Nell’ultimo capitolo, si è proceduto, poi, a “calare” l’istituto del danno da perdita di chance nel “sottosettore” della responsabilità sanitaria, sottoponendo a verifica la “tenuta teorica” della sua “variante” non patrimoniale al cospetto della recente novella legislativa rappresentata dalla l. n. 24/17, nonché degli orientamenti giurisprudenziali che, negli ultimi due anni, hanno interessato i temi dell’onere della prova del nesso causale e dello stesso danno da perdita di chance non patrimoniale. A conclusione dello studio, si sono svolte, infine, alcune considerazioni sulle criticità che precludono un’armonica “riconduzione a sistema” dell’istituto, consigliandone il definitivo abbandono.

Memory hierarchy and data communication in heterogeneous reconfigurable SoCs

The miniaturization race in the hardware industry aiming at continuous increasing of transistor density on a die does not bring respective application performance improvements any more. One of the most promising alternatives is to exploit a heterogeneous nature of common applications in hardware. Supported by reconfigurable computation, which has already proved its efficiency in accelerating data intensive applications, this concept promises a breakthrough in contemporary technology development. Memory organization in such heterogeneous reconfigurable architectures becomes very critical. Two primary aspects introduce a sophisticated trade-off. On the one hand, a memory subsystem should provide well organized distributed data structure and guarantee the required data bandwidth. On the other hand, it should hide the heterogeneous hardware structure from the end-user, in order to support feasible high-level programmability of the system. This thesis work explores the heterogeneous reconfigurable hardware architectures and presents possible solutions to cope the problem of memory organization and data structure. By the example of the MORPHEUS heterogeneous platform, the discussion follows the complete design cycle, starting from decision making and justification, until hardware realization. Particular emphasis is made on the methods to support high system performance, meet application requirements, and provide a user-friendly programmer interface. As a result, the research introduces a complete heterogeneous platform enhanced with a hierarchical memory organization, which copes with its task by means of separating computation from communication, providing reconfigurable engines with computation and configuration data, and unification of heterogeneous computational devices using local storage buffers. It is distinguished from the related solutions by distributed data-flow organization, specifically engineered mechanisms to operate with data on local domains, particular communication infrastructure based on Network-on-Chip, and thorough methods to prevent computation and communication stalls. In addition, a novel advanced technique to accelerate memory access was developed and implemented.

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.

Motion control and real-time systems: an approach to trajectory rebuilding in non-deterministic networks

Motion control is a sub-field of automation, in which the position and/or velocity of machines are controlled using some type of device. In motion control the position, velocity, force, pressure, etc., profiles are designed in such a way that the different mechanical parts work as an harmonious whole in which a perfect synchronization must be achieved. The real-time exchange of information in the distributed system that is nowadays an industrial plant plays an important role in order to achieve always better performance, better effectiveness and better safety. The network for connecting field devices such as sensors, actuators, field controllers such as PLCs, regulators, drive controller etc., and man-machine interfaces is commonly called fieldbus. Since the motion transmission is now task of the communication system, and not more of kinematic chains as in the past, the communication protocol must assure that the desired profiles, and their properties, are correctly transmitted to the axes then reproduced or else the synchronization among the different parts is lost with all the resulting consequences. In this thesis, the problem of trajectory reconstruction in the case of an event-triggered communication system is faced. The most important feature that a real-time communication system must have is the preservation of the following temporal and spatial properties: absolute temporal consistency, relative temporal consistency, spatial consistency. Starting from the basic system composed by one master and one slave and passing through systems made up by many slaves and one master or many masters and one slave, the problems in the profile reconstruction and temporal properties preservation, and subsequently the synchronization of different profiles in network adopting an event-triggered communication system, have been shown. These networks are characterized by the fact that a common knowledge of the global time is not available. Therefore they are non-deterministic networks. Each topology is analyzed and the proposed solution based on phase-locked loops adopted for the basic master-slave case has been improved to face with the other configurations.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Transposable elements: structure and dynamic of the autonomous retrotransposon R2 in Arthropoda with non-canonical reproduction

Eukaryotic ribosomal DNA constitutes a multi gene family organized in a cluster called nucleolar organizer region (NOR); this region is composed usually by hundreds to thousands of tandemly repeated units. Ribosomal genes, being repeated sequences, evolve following the typical pattern of concerted evolution. The autonomous retroelement R2 inserts in the ribosomal gene 28S, leading to defective 28S rDNA genes. R2 element, being a retrotransposon, performs its activity in the genome multiplying its copy number through a “copy and paste” mechanism called target primed reverse transcription. It consists in the retrotranscription of the element’s mRNA into DNA, then the DNA is integrated in the target site. Since the retrotranscription can be interrupted, but the integration will be carried out anyway, truncated copies of the element will also be present in the genome. The study of these truncated variants is a tool to examine the activity of the element. R2 phylogeny appears, in general, not consistent with that of its hosts, except some cases (e.g. Drosophila spp. and Reticulitermes spp.); moreover R2 is absent in some species (Fugu rubripes, human, mouse, etc.), while other species have more R2 lineages in their genome (the turtle Mauremys reevesii, the Japanese beetle Popilia japonica, etc). R2 elements here presented are isolated in 4 species of notostracan branchiopods and in two species of stick insects, whose reproductive strategies range from strict gonochorism to unisexuality. From sequencing data emerges that in Triops cancriformis (Spanish gonochoric population), in Lepidurus arcticus (two putatively unisexual populations from Iceland) and in Bacillus rossius (gonochoric population from Capalbio) the R2 elements are complete and encode functional proteins, reflecting the general features of this family of transposable elements. On the other hand, R2 from Italian and Austrian populations of T. cancriformis (respectively unisexual and hermaphroditic), Lepidurus lubbocki (two elements within the same Italian population, gonochoric but with unfunctional males) and Bacillus grandii grandii (gonochoric population from Ponte Manghisi) have sequences that encode incomplete or non-functional proteins in which it is possible to recognize only part of the characteristic domains. In Lepidurus couesii (Italian gonochoric populations) different elements were found as in L. lubbocki, and the sequencing is still in progress. Two hypothesis are given to explain the inconsistency of R2/host phylogeny: vertical inheritance of the element followed by extinction/diversification or horizontal transmission. My data support previous study that state the vertical transmission as the most likely explanation; nevertheless horizontal transfer events can’t be excluded. I also studied the element’s activity in Spanish populations of T. cancriformis, in L. lubbocki, in L. arcticus and in gonochoric and parthenogenetic populations of B. rossius. In gonochoric populations of T. cancriformis and B. rossius I found that each individual has its own private set of truncated variants. The situation is the opposite for the remaining hermaphroditic/parthenogenetic species and populations, all individuals sharing – in the so far analyzed samples - the majority of variants. This situation is very interesting, because it isn’t concordant with the Muller’s ratchet theory that hypothesizes the parthenogenetic populations being either devoided of transposable elements or TEs overloaded. My data suggest a possible epigenetic mechanism that can block the retrotransposon activity, and in this way deleterious mutations don’t accumulate.