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.

3D probability tomography: theoretical developments and applications to high-resolution geophysical prospecting

The theory of the 3D multipole probability tomography method (3D GPT) to image source poles, dipoles, quadrupoles and octopoles, of a geophysical vector or scalar field dataset is developed. A geophysical dataset is assumed to be the response of an aggregation of poles, dipoles, quadrupoles and octopoles. These physical sources are used to reconstruct without a priori assumptions the most probable position and shape of the true geophysical buried sources, by determining the location of their centres and critical points of their boundaries, as corners, wedges and vertices. This theory, then, is adapted to the geoelectrical, gravity and self potential methods. A few synthetic examples using simple geometries and three field examples are discussed in order to demonstrate the notably enhanced resolution power of the new approach. At first, the application to a field example related to a dipole–dipole geoelectrical survey carried out in the archaeological park of Pompei is presented. The survey was finalised to recognize remains of the ancient Roman urban network including roads, squares and buildings, which were buried under the thick pyroclastic cover fallen during the 79 AD Vesuvius eruption. The revealed anomaly structures are ascribed to wellpreserved remnants of some aligned walls of Roman edifices, buried and partially destroyed by the 79 AD Vesuvius pyroclastic fall. Then, a field example related to a gravity survey carried out in the volcanic area of Mount Etna (Sicily, Italy) is presented, aimed at imaging as accurately as possible the differential mass density structure within the first few km of depth inside the volcanic apparatus. An assemblage of vertical prismatic blocks appears to be the most probable gravity model of the Etna apparatus within the first 5 km of depth below sea level. Finally, an experimental SP dataset collected in the Mt. Somma-Vesuvius volcanic district (Naples, Italy) is elaborated in order to define location and shape of the sources of two SP anomalies of opposite sign detected in the northwestern sector of the surveyed area. The modelled sources are interpreted as the polarization state induced by an intense hydrothermal convective flow mechanism within the volcanic apparatus, from the free surface down to about 3 km of depth b.s.l..

A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Low Correlated Sequences & Architectures and Algorithms for Analog-to-Information Converters: Theory, Design, Implementation and Applications.

Most electronic systems can be described in a very simplified way as an assemblage of analog and digital components put all together in order to perform a certain function. Nowadays, there is an increasing tendency to reduce the analog components, and to replace them by operations performed in the digital domain. This tendency has led to the emergence of new electronic systems that are more flexible, cheaper and robust. However, no matter the amount of digital process implemented, there will be always an analog part to be sorted out and thus, the step of converting digital signals into analog signals and vice versa cannot be avoided. This conversion can be more or less complex depending on the characteristics of the signals. Thus, even if it is desirable to replace functions carried out by analog components by digital processes, it is equally important to do so in a way that simplifies the conversion from digital to analog signals and vice versa. In the present thesis, we have study strategies based on increasing the amount of processing in the digital domain in such a way that the implementation of analog hardware stages can be simplified. To this aim, we have proposed the use of very low quantized signals, i.e. 1-bit, for the acquisition and for the generation of particular classes of signals.

Non-Equilibrium Atmospheric Plasma As A Novel Route To Nanomaterial Synthesis And Processing For Biomedical Applications

Since last century, the rising interest of value-added and advanced functional materials has spurred a ceaseless development in terms of industrial processes and applications. Among the emerging technologies, thanks to their unique features and versatility in terms of supported processes, non-equilibrium plasma discharges appear as a key solvent-free, high-throughput and cost-efficient technique. Nevertheless, applied research studies are needed with the aim of addressing plasma potentialities optimizing devices and processes for future industrial applications. In this framework, the aim of this dissertation is to report on the activities carried out and the results achieved concerning the development and optimization of plasma techniques for nanomaterial synthesis and processing to be applied in the biomedical field. In the first section, the design and investigation of a plasma assisted process for the production of silver (Ag) nanostructured multilayer coatings exhibiting anti-biofilm and anti-clot properties is described. With the aim on enabling in-situ and on-demand deposition of Ag nanoparticles (NPs), the optimization of a continuous in-flight aerosol process for particle synthesis is reported. The stability and promising biological performances of deposited coatings spurred further investigation through in-vitro and in-vivo tests which results are reported and discussed. With the aim of addressing the unanswered questions and tuning NPs functionalities, the second section concerns the study of silver containing droplet conversion in a flow-through plasma reactor. The presented results, obtained combining different analysis techniques, support a formation mechanism based on droplet to particle conversion driven by plasma induced precursor reduction. Finally, the third section deals with the development of a simulative and experimental approach used to investigate the in-situ droplet evaporation inside the plasma discharge addressing the main contributions to liquid evaporation in the perspective of process industrial scale up.

Synthesis, multiscale-multiphase characterization and applications of thiophene-based biohybrids

Biohybrid derivatives of π-conjugated materials are emerging as powerful tools to study biological events through the (opto)electronic variations of the π-conjugated moieties, as well as to direct and govern the self-assembly properties of the organic materials through the organization principles of the bio component. So far, very few examples of thiophene-based biohybrids have been reported. The aim of this Ph. D thesis has been the development of oligothiophene-oligonucleotide hybrid derivatives as tools, on one side, to detect DNA hybridisation events and, on the other, as model compounds to investigate thiophene-nucleobase interactions in the solid state. To obtain oligothiophene bioconjugates with the required high level of purity, we first developed new synthetic ecofriendly protocols for the synthesis of thiophene oligomers. Our innovative heterogeneous Suzuki coupling methodology, carried out in EtOH/water or isopropanol under microwave irradiation, allowed us to obtain alkyl substituted oligothiophenes and thiophene based co-oligomers in high yields and very short reaction times, free from residual metals and with improved film forming properties. These methodologies were subsequently applied in the synthesis of oligothiophene-oligonucleotide conjugates. Oligothiophene-5-labeled deoxyuridines were synthesized and incorporated into 19-meric oligonucletide sequences. We showed that the oligothiophene-labeled oligonucletide sequences obtained can be used as probes to detect a single nucleotide polymorphism (SNP) in complementary DNA target sequences. In fact, all the probes showed marked variations in emission intensity upon hybridization with a complementary target sequence. The observed variations in emitted light were comparable or even superior to those reported in similar studies, showing that the biohybrids can potentially be useful to develop biosensors for the detection of DNA mismatches. Finally, water-soluble, photoluminescent and electroactive dinucleotide-hybrid derivatives of quaterthiophene and quinquethiophene were synthesized. By means of a combination of spectroscopy and microscopy techniques, electrical characterizations, microfluidic measurements and theoretical calculations, we were able to demonstrate that the self-assembly modalities of the biohybrids in thin films are driven by the interplay of intra and intermolecular interactions in which the π-stacking between the oligothiophene and nucleotide bases plays a major role.

Internal Model Principle: extension to the switching case and applications

This thesis deals with a novel control approach based on the extension of the well-known Internal Model Principle to the case of periodic switched linear exosystems. This extension, inspired by power electronics applications, aims to provide an effective design method to robustly achieve the asymptotic tracking of periodic references with an infinite number of harmonics. In the first part of the thesis the basic components of the novel control scheme are described and preliminary results on stabilization are provided. In the second part, advanced control methods for two applications coming from the world high energy physics are presented.

Metaheuristics for Search Problems in Genomics - New Algorithms and Applications

In this thesis we made the first steps towards the systematic application of a methodology for automatically building formal models of complex biological systems. Such a methodology could be useful also to design artificial systems possessing desirable properties such as robustness and evolvability. The approach we follow in this thesis is to manipulate formal models by means of adaptive search methods called metaheuristics. In the first part of the thesis we develop state-of-the-art hybrid metaheuristic algorithms to tackle two important problems in genomics, namely, the Haplotype Inference by parsimony and the Founder Sequence Reconstruction Problem. We compare our algorithms with other effective techniques in the literature, we show strength and limitations of our approaches to various problem formulations and, finally, we propose further enhancements that could possibly improve the performance of our algorithms and widen their applicability. In the second part, we concentrate on Boolean network (BN) models of gene regulatory networks (GRNs). We detail our automatic design methodology and apply it to four use cases which correspond to different design criteria and address some limitations of GRN modeling by BNs. Finally, we tackle the Density Classification Problem with the aim of showing the learning capabilities of BNs. Experimental evaluation of this methodology shows its efficacy in producing network that meet our design criteria. Our results, coherently to what has been found in other works, also suggest that networks manipulated by a search process exhibit a mixture of characteristics typical of different dynamical regimes.

Sulfanyl Radical Addition to Alkynes: Revisiting an Old Reaction to Enter the Novel Realms of Green Chemistry, Bioconjugation, and Material Chemistry

In the last decade considerable attention has been devoted to the rewarding use of Green Chemistry in various synthetic processes and applications. Green Chemistry is of special interest in the synthesis of expensive pharmaceutical products, where suitable adoption of “green” reagents and conditions is highly desirable. Our project especially focused in a search for new green radical processes which might also find useful applications in the industry. In particular, we have explored the possible adoption of green solvents in radical Thiol-Ene and Thiol-Yne coupling reactions, which to date have been normally performed in “ordinary” organic solvents such as benzene and toluene, with the primary aim of applying those coupling reactions to the construction of biological substrates. We have additionally tuned adequate reaction conditions which might enable achievement of highly functionalised materials and/or complex bioconjugation via homo/heterosequence. Furthermore, we have performed suitable theoretical studies to gain useful chemical information concerning mechanistic implications of the use of green solvents in the radical Thiol-Yne coupling reactions.

Novel tools for conservation genetics in marine fish: population structure and evolution of the European hake (Merluccius merluccius) inferred by SNP variation and applications to traceability

The research presented in my PhD thesis is part of a wider European project, FishPopTrace, focused on traceability of fish populations and products. My work was aimed at developing and analyzing novel genetic tools for a widely distributed marine fish species, the European hake (Merluccius merluccius), in order to investigate population genetic structure and explore potential applications to traceability scenarios. A total of 395 SNPs (Single Nucleotide Polymorphisms) were discovered from a massive collection of Expressed Sequence Tags, obtained by high-throughput sequencing, and validated on 19 geographic samples from Atlantic and Mediterranean. Genome-scan approaches were applied to identify polymorphisms on genes potentially under divergent selection (outlier SNPs), showing higher genetic differentiation among populations respect to the average observed across loci. Comparative analysis on population structure were carried out on putative neutral and outlier loci at wide (Atlantic and Mediterranean samples) and regional (samples within each basin) spatial scales, to disentangle the effects of demographic and adaptive evolutionary forces on European hake populations genetic structure. Results demonstrated the potential of outlier loci to unveil fine scale genetic structure, possibly identifying locally adapted populations, despite the weak signal showed from putative neutral SNPs. The application of outlier SNPs within the framework of fishery resources management was also explored. A minimum panel of SNP markers showing maximum discriminatory power was selected and applied to a traceability scenario aiming at identifying the basin (and hence the stock) of origin, Atlantic or Mediterranean, of individual fish. This case study illustrates how molecular analytical technologies have operational potential in real-world contexts, and more specifically, potential to support fisheries control and enforcement and fish and fish product traceability.

Institutional Processes and Discursive Strategies: Rhetoric and Vocabulary Analysis of CSR and Sustainability

The candidate tackled an important issue in contemporary management: the role of CSR and Sustainability. The research proposal focused on a longitudinal and inductive research, directed to specify the evolution of CSR and contribute to the new institutional theory, in particular institutional work framework, and to the relation between institutions and discourse analysis. The documental analysis covers all the evolution of CSR, focusing also on a number of important networks and associations. Some of the methodologies employed in the thesis have been employed as a consequence of data analysis, in a truly inductive research process. The thesis is composed by two section. The first section mainly describes the research process and the analyses results. The candidates employed several research methods: a longitudinal content analysis of documents, a vocabulary research with statistical metrics as cluster analysis and factor analysis, a rhetorical analysis of justifications. The second section puts in relation the analysis results with theoretical frameworks and contributions. The candidate confronted with several frameworks: Actor-Network-Theory, Institutional work and Boundary Work, Institutional Logic. Chapters are focused on different issues: a historical reconstruction of CSR; a reflection about symbolic adoption of recurrent labels; two case studies of Italian networks, in order to confront institutional and boundary works; a theoretical model of institutional change based on contradiction and institutional complexity; the application of the model to CSR and Sustainability, proposing Sustainability as a possible institutional logic.

Development and applications of hollow fiber flow field-flow fractionation in the bioanalytical field. Studies of aggregation phenomena in complex protein samples

Recent advances in the fast growing area of therapeutic/diagnostic proteins and antibodies - novel and highly specific drugs - as well as the progress in the field of functional proteomics regarding the correlation between the aggregation of damaged proteins and (immuno) senescence or aging-related pathologies, underline the need for adequate analytical methods for the detection, separation, characterization and quantification of protein aggregates, regardless of the their origin or formation mechanism. Hollow fiber flow field-flow fractionation (HF5), the miniaturized version of FlowFFF and integral part of the Eclipse DUALTEC FFF separation system, was the focus of this research; this flow-based separation technique proved to be uniquely suited for the hydrodynamic size-based separation of proteins and protein aggregates in a very broad size and molecular weight (MW) range, often present at trace levels. HF5 has shown to be (a) highly selective in terms of protein diffusion coefficients, (b) versatile in terms of bio-compatible carrier solution choice, (c) able to preserve the biophysical properties/molecular conformation of the proteins/protein aggregates and (d) able to discriminate between different types of protein aggregates. Thanks to the miniaturization advantages and the online coupling with highly sensitive detection techniques (UV/Vis, intrinsic fluorescence and multi-angle light scattering), HF5 had very low detection/quantification limits for protein aggregates. Compared to size-exclusion chromatography (SEC), HF5 demonstrated superior selectivity and potential as orthogonal analytical method in the extended characterization assays, often required by therapeutic protein formulations. In addition, the developed HF5 methods have proven to be rapid, highly selective, sensitive and repeatable. HF5 was ideally suitable as first dimension of separation of aging-related protein aggregates from whole cell lysates (proteome pre-fractionation method) and, by HF5-(UV)-MALS online coupling, important biophysical information on the fractionated proteins and protein aggregates was gathered: size (rms radius and hydrodynamic radius), absolute MW and conformation.