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.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Fluid dynamic analysis and modelling of industrial chemical equipment

The research is aimed at contributing to the identification of reliable fully predictive Computational Fluid Dynamics (CFD) methods for the numerical simulation of equipment typically adopted in the chemical and process industries. The apparatuses selected for the investigation, specifically membrane modules, stirred vessels and fluidized beds, were characterized by a different and often complex fluid dynamic behaviour and in some cases the momentum transfer phenomena were coupled with mass transfer or multiphase interactions. Firs of all, a novel modelling approach based on CFD for the prediction of the gas separation process in membrane modules for hydrogen purification is developed. The reliability of the gas velocity field calculated numerically is assessed by comparison of the predictions with experimental velocity data collected by Particle Image Velocimetry, while the applicability of the model to properly predict the separation process under a wide range of operating conditions is assessed through a strict comparison with permeation experimental data. Then, the effect of numerical issues on the RANS-based predictions of single phase stirred tanks is analysed. The homogenisation process of a scalar tracer is also investigated and simulation results are compared to original passive tracer homogenisation curves determined with Planar Laser Induced Fluorescence. The capability of a CFD approach based on the solution of RANS equations is also investigated for describing the fluid dynamic characteristics of the dispersion of organics in water. Finally, an Eulerian-Eulerian fluid-dynamic model is used to simulate mono-disperse suspensions of Geldart A Group particles fluidized by a Newtonian incompressible fluid as well as binary segregating fluidized beds of particles differing in size and density. The results obtained under a number of different operating conditions are compared with literature experimental data and the effect of numerical uncertainties on axial segregation is also discussed.

Magnetic fields around radio galaxies from Faraday rotation measure analysis

The purpose of this thesis is to investigate the strength and structure of the magnetized medium surrounding radio galaxies via observations of the Faraday effect. This study is based on an analysis of the polarization properties of radio galaxies selected to have a range of morphologies (elongated tails, or lobes with small axial ratios) and to be located in a variety of environments (from rich cluster core to small group). The targets include famous objects like M84 and M87. A key aspect of this work is the combination of accurate radio imaging with high-quality X-ray data for the gas surrounding the sources. Although the focus of this thesis is primarily observational, I developed analytical models and performed two- and three-dimensional numerical simulations of magnetic fields. The steps of the thesis are: (a) to analyze new and archival observations of Faraday rotation measure (RM) across radio galaxies and (b) to interpret these and existing RM images using sophisticated two and three-dimensional Monte Carlo simulations. The approach has been to select a few bright, very extended and highly polarized radio galaxies. This is essential to have high signal-to-noise in polarization over large enough areas to allow computation of spatial statistics such as the structure function (and hence the power spectrum) of rotation measure, which requires a large number of independent measurements. New and archival Very Large Array observations of the target sources have been analyzed in combination with high-quality X-ray data from the Chandra, XMM-Newton and ROSAT satellites. The work has been carried out by making use of: 1) Analytical predictions of the RM structure functions to quantify the RM statistics and to constrain the power spectra of the RM and magnetic field. 2) Two-dimensional Monte Carlo simulations to address the effect of an incomplete sampling of RM distribution and so to determine errors for the power spectra. 3) Methods to combine measurements of RM and depolarization in order to constrain the magnetic-field power spectrum on small scales. 4) Three-dimensional models of the group/cluster environments, including different magnetic field power spectra and gas density distributions. This thesis has shown that the magnetized medium surrounding radio galaxies appears more complicated than was apparent from earlier work. Three distinct types of magnetic-field structure are identified: an isotropic component with large-scale fluctuations, plausibly associated with the intergalactic medium not affected by the presence of a radio source; a well-ordered field draped around the front ends of the radio lobes and a field with small-scale fluctuations in rims of compressed gas surrounding the inner lobes, perhaps associated with a mixing layer.

Methods for Clearance Influence Analysis in Planar and Spatial Mechanisms

This doctoral dissertation presents a new method to asses the influence of clearancein the kinematic pairs on the configuration of planar and spatial mechanisms. The subject has been widely investigated in both past and present scientific literature, and is approached in different ways: a static/kinetostatic way, which looks for the clearance take-up due to the external loads on the mechanism; a probabilistic way, which expresses clearance-due displacements using probability density functions; a dynamic way, which evaluates dynamic effects like the actual forces in the pairs caused by impacts, or the consequent vibrations. This dissertation presents a new method to approach the problem of clearance. The problem is studied from a purely kinematic perspective. With reference to a given mechanism configuration, the pose (position and orientation) error of the mechanism link of interest is expressed as a vector function of the degrees of freedom introduced in each pair by clearance: the presence of clearance in a kinematic pair, in facts, causes the actual pair to have more degrees of freedom than the theoretical clearance-free one. The clearance-due degrees of freedom are bounded by the pair geometry. A proper modelling of clearance-affected pairs allows expressing such bounding through analytical functions. It is then possible to study the problem as a maximization problem, where a continuous function (the pose error of the link of interest) subject to some constraints (the analytical functions bounding clearance- due degrees of freedom) has to be maximize. Revolute, prismatic, cylindrical, and spherical clearance-affected pairs have been analytically modelled; with reference to mechanisms involving such pairs, the solution to the maximization problem has been obtained in a closed form.

Analysis of charge-transport properties in GST materials for next generation phase-change memory devices

The quest for universal memory is driving the rapid development of memories with superior all-round capabilities in non-volatility, high speed, high endurance and low power. The memory subsystem accounts for a significant cost and power budget of a computer system. Current DRAM-based main memory systems are starting to hit the power and cost limit. To resolve this issue the industry is improving existing technologies such as Flash and exploring new ones. Among those new technologies is the Phase Change Memory (PCM), which overcomes some of the shortcomings of the Flash such as durability and scalability. This alternative non-volatile memory technology, which uses resistance contrast in phase-change materials, offers more density relative to DRAM, and can help to increase main memory capacity of future systems while remaining within the cost and power constraints. Chalcogenide materials can suitably be exploited for manufacturing phase-change memory devices. Charge transport in amorphous chalcogenide-GST used for memory devices is modeled using two contributions: hopping of trapped electrons and motion of band electrons in extended states. Crystalline GST exhibits an almost Ohmic I(V) curve. In contrast amorphous GST shows a high resistance at low biases while, above a threshold voltage, a transition takes place from a highly resistive to a conductive state, characterized by a negative differential-resistance behavior. A clear and complete understanding of the threshold behavior of the amorphous phase is fundamental for exploiting such materials in the fabrication of innovative nonvolatile memories. The type of feedback that produces the snapback phenomenon is described as a filamentation in energy that is controlled by electron–electron interactions between trapped electrons and band electrons. The model thus derived is implemented within a state-of-the-art simulator. An analytical version of the model is also derived and is useful for discussing the snapback behavior and the scaling properties of the device.

Social housing: interventions of densification in urban regeneration (1995-2010). Critical analysis of strategies adopted in Milan, London, São Paulo

The prospect of the continuous multiplication of life styles, the obsolescence of the traditional typological diagrams, the usability of spaces on different territorial scales, imposes on contemporary architecture the search for new models of living. Limited densities in urban development have produced the erosion of territory, the increase of the harmful emissions and energy consumption. High density housing cannot refuse the social emergency to ensure high quality and low cost dwellings, to a new people target: students, temporary workers, key workers, foreign, young couples without children, large families and, in general, people who carry out public services. Social housing strategies have become particularly relevant in regenerating high density urban outskirts. The choice of this research topic derives from the desire to deal with the recent accommodation emergency, according to different perspectives, with a view to give a contribution to the current literature, by proposing some tools for a correct design of the social housing, by ensuring good quality, cost-effective, and eco-sustainable solutions, from the concept phase, through management and maintenance, until the end of the building life cycle. The purpose of the thesis is defining a framework of guidelines that become effective instruments to be used in designing the social housing. They should also integrate the existing regulations and are mainly thought for those who work in this sector. They would aim at supporting students who have to cope with this particular residential theme, and also the users themselves. The scientific evidence of either the recent specialized literature or the solutions adopted in some case studies within the selected metropolitan areas of Milan, London and São Paulo, it is possible to identify the principles of this new design approach, in which the connection between typology, morphology and technology pursues the goal of a high living standard.

Carcinoma polmonare non a piccole cellule T1aN0M0: Ruolo prognostico della Microvessel Density

Obiettivi. Valutare l’angiogenesi tumorale mediante la Microvessel density (MVD) come fattore predittivo di mortalità per tumore polmonare non a piccole cellule (NSCLC) pT1aN0M0 trattato chirurgicamente. Metodi. I dati demografici, clinici e istopatologici sono stati registrati per 82 pazienti (60 maschi, 22 femmine) sottoposti a resezione chirurgica in due diverse Chirurgie Toraciche tra gennaio 2002 e dicembre 2007 per tumori polmonari non a piccole cellule pT1AN0M0. La MVD è stata valutata mediante il conteggio visivo dei microvasi positivi alla colorazione immunoistochimica con anticorpo monoclonale anti-CD31 e definita come il numero medio di microvasi per 1 mm2 di campo ottico. Risultati. Sono state eseguite 59 lobectomie (72%) e 23 resezioni sublobari (28%). Reperti istopatologici: 43 adenocarcinomi (52%) e 39 neoplasie non- adenocarcinoma (48%) pT1aN0M0; MVD media: 161 (CD31/mm2); mediana: 148; range 50-365, cut-off=150. Una MVD elevata (> 150 CD31/mm2) è stata osservata in 40 pazienti (49%), una MVD ridotta ( ≤ 150 CD31/mm2 ) in 42 pazienti (51%). Sopravvivenze a 5 anni: 70 % e 95%, rispettivamente per il gruppo ad elevata MVD vs il gruppo a ridotta MVD con una p = 0,0041, statisticamente significativa. Il tipo di resezione chirurgica, il diametro del tumore, le principali comorbidità e l’istotipo nono sono stati fattori predittivi significativi di mortalità correlata alla malattia. La MVD è risultata essere superiore nel gruppo “Adenocarcinoma” (MVD mediana=180) rispetto al gruppo “Non-Adenocarcinoma (MVD mediana=125), con un test di Mann-Whitney statisticamente significativo (p < 0,0001). Nel gruppo “Adenocarcinoma” la sopravvivenza a 5 anni è stata del 66% e 93 %, rispettivamente per i pazienti con MVD elevata e ridotta (p = 0.043. Conclusioni. Il nostro studio ha mostrato che la Microvessel density valutata con la colorazione immunoistochimica per CD31 ha un valore prognostico rilevante nel carcinoma polmonare in stadio precoce pT1aN0M0.

Hydrodynamic induced by an array of wave energy converters. Experimental and numerical analysis

The thesis analyses the hydrodynamic induced by an array of Wave energy Converters (WECs), under an experimental and numerical point of view. WECs can be considered an innovative solution able to contribute to the green energy supply and –at the same time– to protect the rear coastal area under marine spatial planning considerations. This research activity essentially rises due to this combined concept. The WEC under exam is a floating device belonging to the Wave Activated Bodies (WAB) class. Experimental data were performed at Aalborg University in different scales and layouts, and the performance of the models was analysed under a variety of irregular wave attacks. The numerical simulations performed with the codes MIKE 21 BW and ANSYS-AQWA. Experimental results were also used to calibrate the numerical parameters and/or to directly been compared to numerical results, in order to extend the experimental database. Results of the research activity are summarized in terms of device performance and guidelines for a future wave farm installation. The device length should be “tuned” based on the local climate conditions. The wave transmission behind the devices is pretty high, suggesting that the tested layout should be considered as a module of a wave farm installation. Indications on the minimum inter-distance among the devices are provided. Furthermore, a CALM mooring system leads to lower wave transmission and also larger power production than a spread mooring. The two numerical codes have different potentialities. The hydrodynamics around single and multiple devices is obtained with MIKE 21 BW, while wave loads and motions for a single moored device are derived from ANSYS-AQWA. Combining the experimental and numerical it is suggested –for both coastal protection and energy production– to adopt a staggered layout, which will maximise the devices density and minimize the marine space required for the installation.

Exploring host-pathogen interactions through protein microarray. Large-scale protein microarray analysis revealed novel human receptors for the staphylococcal immune evasion protein FLIPr and for the neisserial adhesin NadA

Adhesion, immune evasion and invasion are key determinants during bacterial pathogenesis. Pathogenic bacteria possess a wide variety of surface exposed and secreted proteins which allow them to adhere to tissues, escape the immune system and spread throughout the human body. Therefore, extensive contacts between the human and the bacterial extracellular proteomes take place at the host-pathogen interface at the protein level. Recent researches emphasized the importance of a global and deeper understanding of the molecular mechanisms which underlie bacterial immune evasion and pathogenesis. Through the use of a large-scale, unbiased, protein microarray-based approach and of wide libraries of human and bacterial purified proteins, novel host-pathogen interactions were identified. This approach was first applied to Staphylococcus aureus, cause of a wide variety of diseases ranging from skin infections to endocarditis and sepsis. The screening led to the identification of several novel interactions between the human and the S. aureus extracellular proteomes. The interaction between the S. aureus immune evasion protein FLIPr (formyl-peptide receptor like-1 inhibitory protein) and the human complement component C1q, key players of the offense-defense fighting, was characterized using label-free techniques and functional assays. The same approach was also applied to Neisseria meningitidis, major cause of bacterial meningitis and fulminant sepsis worldwide. The screening led to the identification of several potential human receptors for the neisserial adhesin A (NadA), an important adhesion protein and key determinant of meningococcal interactions with the human host at various stages. The interaction between NadA and human LOX-1 (low-density oxidized lipoprotein receptor) was confirmed using label-free technologies and cell binding experiments in vitro. Taken together, these two examples provided concrete insights into S. aureus and N. meningitidis pathogenesis, and identified protein microarray coupled with appropriate validation methodologies as a powerful large scale tool for host-pathogen interactions studies.

New methodologies in CT perfusion and MRI analysis to develop cancer imaging biomarkers

Quantitative imaging in oncology aims at developing imaging biomarkers for diagnosis and prediction of cancer aggressiveness and therapy response before any morphological change become visible. This Thesis exploits Computed Tomography perfusion (CTp) and multiparametric Magnetic Resonance Imaging (mpMRI) for investigating diverse cancer features on different organs. I developed a voxel-based image analysis methodology in CTp and extended its use to mpMRI, for performing precise and accurate analyses at single-voxel level. This is expected to improve reproducibility of measurements and cancer mechanisms’ comprehension and clinical interpretability. CTp has not entered the clinical routine yet, although its usefulness in the monitoring of cancer angiogenesis, due to different perfusion computing methods yielding unreproducible results. Instead, machine learning applications in mpMRI, useful to detect imaging features representative of cancer heterogeneity, are mostly limited to clinical research, because of results’ variability and difficult interpretability, which make clinicians not confident in clinical applications. In hepatic CTp, I investigated whether, and under what conditions, two widely adopted perfusion methods, Maximum Slope (MS) and Deconvolution (DV), could yield reproducible parameters. To this end, I developed signal processing methods to model the first pass kinetics and remove any numerical cause hampering the reproducibility. In mpMRI, I proposed a new approach to extract local first-order features, aiming at preserving spatial reference and making their interpretation easier. In CTp, I found out the cause of MS and DV non-reproducibility: MS and DV represent two different states of the system. Transport delays invalidate MS assumptions and, by correcting MS formulation, I have obtained the voxel-based equivalence of the two methods. In mpMRI, the developed predictive models allowed (i) detecting rectal cancers responding to neoadjuvant chemoradiation showing, at pre-therapy, sparse coarse subregions with altered density, and (ii) predicting clinically significant prostate cancers stemming from the disproportion between high- and low- diffusivity gland components.

Computing the structural and vibrational properties of polymorphic organic molecular crystals through van der Waals corrected density functional theory and the electronic properties of organic thin films through microelectrostatic calculations.

The present Thesis reports on the various research projects to which I have contributed during my PhD period, working with several research groups, and whose results have been communicated in a number of scientific publications. The main focus of my research activity was to learn, test, exploit and extend the recently developed vdW-DFT (van der Waals corrected Density Functional Theory) methods for computing the structural, vibrational and electronic properties of ordered molecular crystals from first principles. A secondary, and more recent, research activity has been the analysis with microelectrostatic methods of Molecular Dynamics (MD) simulations of disordered molecular systems. While only very unreliable methods based on empirical models were practically usable until a few years ago, accurate calculations of the crystal energy are now possible, thanks to very fast modern computers and to the excellent performance of the best vdW-DFT methods. Accurate energies are particularly important for describing organic molecular solids, since they often exhibit several alternative crystal structures (polymorphs), with very different packing arrangements but very small energy differences. Standard DFT methods do not describe the long-range electron correlations which give rise to the vdW interactions. Although weak, these interactions are extremely sensitive to the packing arrangement, and neglecting them used to be a problem. The calculations of reliable crystal structures and vibrational frequencies has been made possible only recently, thanks to development of some good representations of the vdW contribution to the energy (known as “vdW corrections”).

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Numerical and experimental analysis of 3D printed smart structures and systems

Three dimensional (3D) printers of continuous fiber reinforced composites, such as MarkTwo (MT) by Markforged, can be used to manufacture such structures. To date, research works devoted to the study and application of flexible elements and CMs realized with MT printer are only a few and very recent. A good numerical and/or analytical tool for the mechanical behavior analysis of the new composites is still missing. In addition, there is still a gap in obtaining the material properties used (e.g. elastic modulus) as it is usually unknown and sensitive to printing parameters used (e.g. infill density), making the numerical simulation inaccurate. Consequently, the aim of this thesis is to present several work developed. The first is a preliminary investigation on the tensile and flexural response of Straight Beam Flexures (SBF) realized with MT printer and featuring different interlayer fiber volume-fraction and orientation, as well as different laminate position within the sample. The second is to develop a numerical analysis within the Carrera' s Unified Formulation (CUF) framework, based on component-wise (CW) approach, including a novel preprocessing tool that has been developed to account all regions printed in an easy and time efficient way. Among its benefits, the CUF-CW approach enables building an accurate database for collecting first natural frequencies modes results, then predicting Young' s modulus based on an inverse problem formulation. To validate the tool, the numerical results are compared to the experimental natural frequencies evaluated using a digital image correlation method. Further, we take the CUF-CW model and use static condensation to analyze smart structures which can be decomposed into a large number of similar components. Third, the potentiality of MT in combination with topology optimization and compliant joints design (CJD) is investigated for the realization of automated machinery mechanisms subjected to inertial loads.