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.

Organismi acquatici e ambiente: meccanismi biochimici di interazione, risposta e adattamento

The research is focused on the relationship between some Mg2+-dependent ATPase activities of plasma- and mitochondrial membranes from tissues of cultured marine bivalve molluscs and potentially stressful environmental conditions, such as the exposure to contaminants both of natural origin (ammonia nitrogen, the main contaminant of aquaculture plants) and of anthropic source (alkyltins). The two filter-feeding bivalve species selected colonize different habitats: the common mussel Mytilus galloprovincialis binds to hard substrates and the Philippine clam Tapes philippinarum burrows into sea bottom sandy beds. The choice of typical species of coastal waters, extremely suitable for environmental studies due to their features of poor motility, resistance to transport and great filtering efficiency, may constitute a model to evaluate responses to contaminants of membrane-bound enzyme activities involved in key biochemical mechanisms, namely cell ionic regulation and mitochondrial energy production. In vitro and in vitro approaches have been pursued. In vitro assays were carried out by adding the contaminants (NH4Cl and alkyltins) directly to the ATPase reaction media. In vivo experiments were carried out by exposing mussels to various tributyl tin (TBT) concentrations under controlled conditions in aquaria. ATPase activities were determined spectrophotometrically according to the principles of the method of Fiske and Subbarow (1925). The main results obtained are detailed below. In Tapes philippinarum the interaction of NH4 +, the main form of ammonia nitrogen at physiological and seawater pHs, with the Na,K-ATPase and the ouabaininsensitive Na-ATPase was investigated in vitro on gill and mantle microsomal membranes. The proven replacement by NH4 +of K+ in the activation of the Na,KATPase and of Na+ in the activation of the ouabain-insensitive ATPase displayed similar enzyme affinity for the substituted cation. on the one hand this finding may represent one of the possible mechanisms of ammonia toxicity and, on the other, it supports the hypothesis that NH4 + can be transported across the plasma membrane through the two ATPases. In this case both microsomal ATPases may be involved and co-operate, at least under peculiar circumstances, to nitrogen excretion and ammonia detoxification mechanisms in bivalve molluscs. The two ATPase activities stimulated by NH4 + maintained their typical response to the glycoside ouabain, specific inhibitor of the Na,K-ATPase, being the Na++ NH4 +-activated ATPase even more susceptive to the inhibitor and the ouabain-insensitive ATPase activity activated indifferently by Na+ or NH4 + unaffected by up to 10-2 M ouabain. In vitro assays were carried out to evaluate the response of the two Na-dependent ATPases to organotins in clams and mussels and to investigate the interaction of TBT with mussel mitochondrial oligomycin-sensitive Mg-ATPase. Since no literature data were available, the optimal assay conditions and oligomycin sensitivity of mussel mitochondrial MgATPase were determined. In T. philippinarum the ouabain-insensitive Na-ATPase was found to be refractory to TBT both in the gills and in the mantle, whereas the Na,K-ATPase was progressively inhibited by increasing TBT doses; the enzyme inhibition was more pronounced in the gills than in the mantle. In both tissues of M. galloprovincialis the Na,K-ATPase inhibition by alkyltins decreased in the order TBT>DBT(dibutyltin)>>MBT(monobutyltin)=TeET(tetraethyltin) (no effect). Mussel Na-ATPase confirmed its refractorimess to TBT and derivatives both in the gills and in the mantle. These results indicate that the Na,K-ATPase inhibition decreases as the number of alkyl chains bound to tin decreases; however a certain polarity of the organotin molecule is required to yield Na,K-ATPase inhibition, since no enzyme inhibition occurred in the presence of tetraalkyl-substituted derivatives such as TeET . Assays carried out in the presence of the dithioerythritol (DTE) pointed out that the sulphhydrylic agent is capable to prevent the Na,K-ATPase inhibition by TBT, thus suggesting that the inhibitor may link to -SH groups of the enzyme complex.. Finally, the different effect of alkyltins on the two Na-dependent ATPases may constitute a further tool to differentiate between the two enzyme activities. These results add to the wealth of literature data describing different responses of the two enzyme activities to endogenous and exogenous modulators . Mussel mitochondrial Mg-ATPase was also found to be in vitro inhibited by TBT both in the gills and in the mantle: the enzyme inhibition followed non competitive kinetics. The failed effect of DTE pointed out that in this case the interaction of TBT with the enzyme complex is probably different from that with the Na,K-ATPase. The results are consistent with literature data showing that alkyltin may interact with enzyme structures with different mechanisms. Mussel exposure to different TBT sublethal doses in aquaria was carried out for 120 hours. Two samplings (after 24 and 120 hrs) were performed in order to evaluate a short-term response of gill and mantle Na,K-ATPase, ouabain-insensitive Na-ATPase and Mg-ATPase activities. The in vivo response to the contaminants of the enzyme activities under study was shown to be partially different from that pointed out in the in vitro assays. Mitochondrial Mg-ATPase activity appeared to be activated in TBTexposed mussels with respect to control ones, thus confirming the complexity of evaluating in vivo responses of the enzyme activities to contaminants, due to possible interactions of toxicants with molluscan metabolism. Concluding, the whole of data point out that microsomal and mitochondrial ATPase activities of bivalve molluscs are generally responsive to environmental contaminants and suggest that in some cases membrane-bound enzyme activities may represent the molecular target of their toxicity. Since the Na,K-ATPase, the Na-ATPase and the Mg-ATPase activities are poorly studied in marine bivalves, this research may contribute to enlarge knowledge in this quite unexplored field.

Synthesis and Supramolecular Architectures of Lipophilic Derivatives of Guanine

Self-assembly relies on the association of pre-programmed building blocks through non-covalent interactions to give complex supramolecular architectures. Previous studies provided evidence for the unique self-assembly properties of semi-synthetic lipophilic guanosine derivatives which can sequestrate ions from an aqueous phase, carry them into an organic phase where they promote the generation of well-defined supramolecular assemblies. In the presence of cations lipophilic guanosines form columnar aggregates while in their absence they generate supramolecular ribbons. The aim of this thesis has been the synthesis of guanine derivatives, in particular N9-alkylated guanines and a guanosine functionalized as a perchlorotriphenylmetil moiety (Gace-a-HPTM) in order to observe their supramolecular behaviour in the absence of sugar (ribose or deoxyribose) and in the presence of a bulky and chiral substituent respectively. By using guanine instead of guanosine, while maintaining all the hydrogen bond acceptor and donor groups required for supramolecular aggregation, the steric hindrance to supramolecular aggregation is notably reduced because (i.e. guanines with groups in N9 different from sugar are expected to have a greatest conformational freedom even in presence of bulky groups in C8). Supramolecular self-assembly of these derivatives has been accomplished in solutions by NMR and CD spectroscopy and on surface by STM technique. In analogy with other guanosine derivatives, also N9-substituted guanines and GAceHPTM form either ribbon-like aggregates or cation-templated G-quartet based columnar structures.

Chemical Production and Microelectronic Applications of Graphene and Nano-Graphene Derivatives

Graphene and graphenic derivatives have rapidly emerged as an extremely promising system for electronic, optical, thermal, and electromechanical applications. Several approaches have been developed to produce these materials (i.e. scotch tape, CVD, chemical and solvent exfoliation). In this work we report a chemical approach to produce graphene by reducing graphene oxide (GO) via thermal or electrical methods. A morphological and electrical characterization of these systems has been performed using different techniques such as SPM, SEM, TEM, Raman and XPS. Moreover, we studied the interaction between graphene derivates and organic molecules focusing on the following aspects: - improvement of optical contrast of graphene on different substrates for rapid monolayer identification1 - supramolecular interaction with organic molecules (i.e. thiophene, pyrene etc.)4 - covalent functionalization with optically active molecules2 - preparation and characterization of organic/graphene Field Effect Transistors3-5 Graphene chemistry can potentially allow seamless integration of graphene technology in organic electronics devices to improve device performance and develop new applications for graphene-based materials. [1] E. Treossi, M. Melucci, A. Liscio, M. Gazzano, P. Samorì, and V. Palermo, J. Am. Chem. Soc., 2009, 131, 15576. [2] M. Melucci, E. Treossi, L. Ortolani, G. Giambastiani, V. Morandi, P. Klar, C. Casiraghi, P. Samorì, and V. Palermo, J. Mater. Chem., 2010, 20, 9052. [3] J.M. Mativetsky, E. Treossi, E. Orgiu, M. Melucci, G.P. Veronese, P. Samorì, and V. Palermo, J. Am. Chem. Soc., 2010, 132, 14130. [4] A. Liscio, G.P. Veronese, E. Treossi, F. Suriano, F. Rossella, V. Bellani, R. Rizzoli, P. Samorì and V. Palermo, J. Mater. Chem., 2011, 21, 2924. [5] J.M. Mativetsky, A. Liscio, E. Treossi, E. Orgiu, A. Zanelli, P. Samorì , V. Palermo, J. Am. Chem. Soc., 2011, 133, 14320

Soil application of Meliaceae derivatives: effect on carbon and nitrogen dynamics in the soil-plant system

The effect of soil incorporation of 7 Meliaceae derivatives (6 commercial neem cakes and leaves of Melia azedarach L.) on C and N dynamics and on nutrient availability to micropropagated GF677 rootstock was investigated. In a first laboratory incubation experiment the derivatives showed different N mineralization dynamics, generally well predicted by their C:N ratio and only partly by their initial N concentration. All derivatives increased microbial biomass C, thus representing a source of C for the soil microbial population. Soil addition of all neem cakes (8 g kg-1) and melia leaves (16 g kg-1) had a positive effect on plant growth and increased root N uptake and leaf green colour of micropropagated plants of GF677. In addition, the neem cakes characterized by higher nutrient concentration increased P and K concentration in shoot and leaves 68 days after the amendment. In another experiment, soil incorporation of 15N labeled melia leaves (16 g kg-1) had no effect on the total amount of plant N, however the percentage of melia derived-N of treated plants ranged between 0.8% and 34% during the experiment. At the end of the growing season, about 7% of N added as melia leaves was recovered in plant, while 70% of it was still present in soil. Real C mineralization and the priming effect induced by the addition of the derivatives were quantified by a natural 13C abundance method. The real C mineralization of the derivatives ranged between 22% and 40% of added-C. All the derivatives studied induced a positive priming effect and, 144 days after the amendment, the amount of C primed corresponded to 26% of added-C, for all the derivatives. Despite this substantial priming effect, the C balance of the soil, 144 days after the amendment, always resulted positive.

Regiocontrolled Synthesis of Pyrazole Derivatives Through 1,3-Dipolar Cycloaddition Reaction And Synthesis of Helicene-Thiourea based and Polymer Supported Soos's Catalyst for Asymmetric Synthesis

In first part we have developed a simple regiocontrolled protocol of 1,3-DC to get ring fused pyrazole derivatives. These pyrazole derivatives were synthesized using 1,3-DC between nitrile imine and various dipolarophiles such as alkynes, cyclic α,β-ketones, lactones, thiocatones and lactums. The reactions were found to be highly regiospecific. In second part we have discussed about helicene, its properties, synthesis and applications as asymmetric catalyst.Due to inherent chirality, herein we have made an attempt to synthesize the helicene-thiourea based catalyst for asymmetric catalysis. The synthesis involved formation of two key intermediates viz, bromo-phenanthrene 5 and a vinyl-naphthalene 10. The coupling of these two intermediates leads to formation of hexahelicene.

Activity and mechanisms of action of novel organosulfur derivatives of the HDAC inhibitor Valproic Acid in human experimental models of non-small-cell lung cancer

Non-small-cell lung cancer (NSCLC) represents the leading cause of cancer death worldwide, and 5-year survival is about 16% for patients diagnosed with advanced lung cancer and about 70-90% when the disease is diagnosed and treated at earlier stages. Treatment of NSCLC is changed in the last years with the introduction of targeted agents, such as gefitinib and erlotinib, that have dramatically changed the natural history of NSCLC patients carrying specific mutations in the EGFR gene, or crizotinib, for patients with the EML4-ALK translocation. However, such patients represent only about 15-20% of all NSCLC patients, and for the remaining individuals conventional chemotherapy represents the standard choice yet, but response rate to thise type of treatment is only about 20%. Development of new drugs and new therapeutic approaches are so needed to improve patients outcome. In this project we aimed to analyse the antitumoral activity of two compounds with the ability to inhibit histone deacethylases (ACS 2 and ACS 33), derived from Valproic Acid and conjugated with H2S, in human cancer cell lines derived from NSCLC tissues. We showed that ACS 2 represents the more promising agent. It showed strong antitumoral and pro-apoptotic activities, by inducing membrane depolarization, cytocrome-c release and caspase 3 and 9 activation. It was able to reduce the invasive capacity of cells, through inhibition of metalloproteinases expression, and to induce a reduced chromatin condensation. This last characteristic is probably responsible for the observed high synergistic activity in combination with cisplatin. In conclusion our results highlight the potential role of the ACS 2 compound as new therapeutic option for NSCLC patients, especially in combination with cisplatin. If validated in in vivo models, this compound should be worthy for phase I clinical trials.

Cinchona alkaloids and BINOL derivatives as privileged catalysts or ligands in asymmetric synthesis

During the last fifteen years organocatalysis emerged as a powerful tool for the enantioselective functionalization of the most different organic molecules. Both C-C and C-heteroatom bonds can be formed in an enantioselective fashion using many types of catalyst and the field is always growing. Many kind of chiral catalysts have emerged as privileged, but among them Proline, cinchona alkaloids, BINOL, and their derivatives showed to be particularly useful chiral scaffolds. This thesis, after a short presentation of many organocatalysts and activation modes, focuses mainly on cinchona alkaloid derived primary amines and BINOL derived chiral Brønsted acids, describing their properties and applications. Then, in the experimental part, these compounds are used for the catalysis of new transformations. The enantioselective Friedel-Crafts alkylation of cyclic enones with naphthols using cinchona alkaloid derived primary amines as catalysts is presented and discussed. The results of this work were very good and this resulted also in a publication. The same catalysts are then used to accomplish the enantioselective addition of indoles to cyclic enones. Many catalysts in combination with many acids as co-catalysts were tried and the reaction was fully studied. Selective N-alkylation was obtained in many cases, in combination with quite good to good enantioselectivities. Also other kind of catalysis were tried for this reaction, with interesting results. Another aza-Michael reaction between OH-free hydroxylamines and nitrostyrene using cinchona alkaloid derived thioureas is briefly discussed. Then our attention focused on Brønsted acid catalyzed transformations. With this regard, the Prins cyclization, a reaction never accomplished in an enantioselective fashion until now, is presented and developed. The results obtained are promising. In the last part of this thesis the work carried out abroad is presented. In Prof. Rueping laboratories, an enantioselective Nazarov cyclization using cooperative catalysis and the enantioselective desymmetrization of meso-hydrobenzoin catalyzed by Brønsted acid were studied.

Structure, Dynamics and Reactivity in the Organic Solid State: Anthracene Derivatives and Charge Transfer Crystals

The work presented in this thesis tackles some important points concerning the collective properties of two typical categories of molecular crystals, i.e., anthracene derivatives and charge transfer crystals. Anthracene derivatives have constituted the class of materials from which systematical investigations of crystal-to-crystal photodimerization reactions started, developed and have been the subject of a new awakening in the recent years. In this work some of these compounds, namely, 9-cyanoanthacene, 9-anthacenecarboxylic acid and 9-methylanthracene, have been selected as model systems for a phenomenological approach to some key properties of the solid state, investigated by spectroscopic methods. The present results show that, on the basis of the solid state organization and the chemical nature of each compound, photo-reaction dynamics and kinetics display distinctive behaviors, which allows for a classification of the various processes in topochemical, non topochemical, reversible or topophysical. The second part of the thesis was focused on charge transfer crystals, binary systems formed by stoichiometric combinations of the charge donating perylene (D) and the charge accepting tetracyano-quinodimethane (A), this latter also in its fluorinated derivatives. The work was focused on the growth of single crystals, some of which not yet reported in the literature, by PVT technique. Structural and spectroscopic characterizations have been performed, with the aim of determining the degree of charge transfer between donor and acceptor in the co-crystals. An interesting outcome of the systematic search performed in this work is the definition of the experimental conditions which drive the crystal growth of the binary systems either towards the low (1:1) or the high ratio (3:1 or 3:2) stoichiometries.