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.

Enzimi, acidi organici ed altri metaboliti coinvolti nella patogenesi di Penicillium spp

Blue mould caused by Penicillium expansum Link is one of the most destructive rot of pome fruit in all growing areas (Snowdon, 1990; Jones and Aldwinckle, 1991; Tonini,1996) In the past, Penicillium rot has been controlled by fungicide postharvest treatment mainly by thiabendazole (TBZ) and benomyl (Hardenburg and Spalding, 1972), but their intense use produced the appearance of resistant strains with a great reduction of their activity The aims of the present study were to characterize the isolates of Pencillium sp causing blue mold on pear in Italy by physiological and biochemical parameters. In particular differencing also the behavior of isolates to relationship with sensitivity or resistance to TBZ treatments. We have examined the early stage of infection in relation to enzyme activity, local modulation of pH, production of organic acids, and to secondary metabolism of pathogen. The results described here confirm that the majority of P. expansum isolates from pears packing houses are resistant to TBZ, Among the TBZ-resistant isolates scored in this work, different isolates (RR) showed higher percentage of conidial germination on TBZ-amended medium compared to non amended medium. This may indicate a stimulatory effect of TBZ on conidial germination. Therefore TBZ treatments are not only ineffective for controlling P. expansum, but they may also increase the severity of blue mould on fruits. In the absence of fungicide, isolates showed a significant difference for infection severity, R and RR isolates are characterized by higher pathogenic fitness on fruits, producing larger lesions than S isolates. These data are supported by the study with laboratory-induced resistant isolates, which shows the lack of correlation between TBZ resistance and osmotic sensitivity, and highlights the association between TBZ resistance and infection severity (Baraldi et al 2003). Enzymatic screening gave a positive reaction to esterase, urease, pectinase activity, in addition, the pathogen is able to synthesize a complex enzyme act to degrade the main components of the cell wall especially pectin and cellulose. Isolated sensitive and resistant are characterized by a good activity of pectinase, especially from poligactoronase, which, as already reported by several studies (D'hallewin et al, 2004; Prusky et al, 2004), are the basis of degradative process of cell wall. Also, although the measure was minor also highlighted some activities of cellulase, but even note in the production of this kind of cellulase and hemicellulase P. Expansum were not targeted, studies have found no other source of information in this regard. Twenty isolates of Penicillium expansum, were tested in vitro ad in vivo for acid production ability and pH drop. We have found that modulation of pH and the organic acids extrusion were influence to various parameter:  Initial pH: in general, the greatest reduction of pH was observed in isolates grown at pH 7, except for four isolates that maintained the pH of the medium close to 7, the others significantly decreased the pH, ranging from 5.5 to 4.1.. In extreme acid condition (pH 3,0) growth and modulation of pH is most lower respect optimal condition (pH 5,0). Also isolates R and RR have showed a greater adaptation to environmental condition more than isolates S.  Time: although the acidification continues for some days, PH modulation is strongest in early hours (48-72 hours)of inoculation process. Time also affects the quality of organic acids, for example in vitro results showed an initial abundant production of succinc acid, followed to important production of galacturoinc acid.  Substrates: there are many differences for the type of acids produced in vitro and in vivo. Results showed in vivo an abundant production of galacturonic, malic, and citric acids and some unknown organic acids in smaller concentrations. Secondary metabolite analysis revealed intra-specific differences, and patulin was found in all isolates, but most significant reduction was observed between in vitro and in vivo samples. There was no correlation between the concentration of patulin, and the percentage of infected fruits, but sample with a lower infection severity of rotten area than the others, showed a significantly lower mycotoxin concentration than samples with a higher lesion diameter of rotten area. Beyond of patulin was detected the presence of another secondary metabolite, penitrem A.

Studies on biotic and abiotic elicitors inducing defense responses in tomato

Tomato (Lycopersicon esculentum Mill., Solanum lycopersicon L.) is one of the most popular vegetable throughout the world, and the importance of its cultivation is threatened by a wide array of pathogens. In the last twenty years this plant has been successfully used as a model plant to investigate the induction of defense pathways after exposure to fungal, bacterial and abiotic molecules, showing triggering of different mechanisms of resistance. Understanding these mechanisms in order to improve crop protection is a main goal for Plant Pathology. The aim of this study was to search for general or race-specific molecules able to determine in Solanum lycopersicon immune responses attributable to the main systems of plant defense: non-host, host-specific and induced resistance. Exopolysaccharides extracted by three fungal species (Aureobasidium pullulans, Cryphonectria parasitica and Epicoccum purpurascens), were able to induce transcription of pathogenesis-related (PR) proteins and accumulation of enzymes related to defense in tomato plants cv Money Maker,using the chemical inducer Bion® as a positive control. During the thesis, several Pseudomonas spp. strains were also isolated and tested for their antimicrobial activity and ability to produce antibiotics. Using as a positive control jasmonic acid, one of the selected strain was shown to induce a form of systemic resistance in tomato. Transcription of PRs and reduction of disease severity against the leaf pathogen Pseduomonas syringae pv. tomato was determined in tomato plants cv Money Maker and cv Perfect Peel, ensuring no direct contact between the selected rhizobacteria and the aerial part of the plant. To conclude this work, race-specific resistance of tomato against the leaf mold Cladosporium fulvum is also deepened, describing the project followed at the Phytopathology Laboratory of Wageningen (NL) in 2007, dealing with localization of a specific R-Avr interaction in transfected tomato protoplast cultures through fluorescence microscopy.

Osteogenesi imperfetta e Dentinogenesi imperfetta Tipo I: correlazioni cliniche e istologiche

Osteogenesis imperffecta (OI) is a heterogeneous group of heritable connetive tissue diseases, quantity and/or qualitative defect in type 1 collagen syntesis; sometimes and in some types it can be associated to dentinogenesis imperfecta (DI), a hereditary disorder in dentin formation that comprises a group of autosomal dominant genetic conditions characterized by abnormal dentine structure affecting either the primary or both the primary and secondary dentitions. Aim: the aim of this study was to assess the correlation between OI and DI from both a clinical and histological point of view, clarifying the structural and ultrastructural changes. Eighteen children (&-15 years aged) with diagnosis of OI were examined for dental alterations referable to DI; for each patient, the OI type (I, III, IV) was recorded. Extracted or normally exfolied teeth were subjected to a histological examination.Results: a total of eleven patients had abnormal discolourations referable to DI: five patients were affected by OI type I, three by OI III, and three patients by OI type IV. The discolourations, yellow/brown or oplaescent grey, could not be related to the different types of OI. Histological exam of primary teeth showed severe pathological change in dentin, structured into four diffeent layers. A collagen defect due to odontoblast dysfunction was theorized to be on the base of the histological changes. Conclusions: there is no correlation between the type of OI and the type of discolouration. The underlying dentinal defect seems to be related to an odontoblast dysfunction.

Analisi sperimentale dell'influenza dei parametri di processo sulla resistenza di contatto tra polimero e stampo durante la formatura

Con gli strumenti informatici disponibili oggi per le industrie, in particolar modo coi software CAE, le possibile simulare in maniera più che soddisfacente i fenomeni fisici presenti in natura. Anche il raffreddamento di un manufatto in polimero può venire simulato, a patto che si conoscano tutti i dati dei materiali e delle condizioni al contorno. Per quanto riguarda i dati dei materiali, i produttori di polimeri sono molto spesso in grado di fornirli, mentre le condizioni al contorno devono essere padroneggiate dal detentore della tecnologia. Nella pratica, tale conoscenza è al più incompleta, quindi si fanno ipotesi per colmare le lacune. Una tra le ipotesi più forti fatte è quella di una perfetta conduzione all'interfaccia tra due corpi. Questo è un vincolo troppo forte, se paragonato alla precisione di tutti gli altri dati necessari alla simulazione, e quindi si è deciso di eseguire una campagna sperimentale per stimare la resistenza al passaggio flusso termico all'interfaccia polimero-stampo ovvero determinare la conduttanza termica di contatto. L'attività svolta in questa tesi di dottorato ha come scopo quello di fornire un contributo significativo allo sviluppo e al miglioramento dell'efficienza termica degli stampi di formatura dei polimeri termoplastici con tecnologia a compressione.