Characterization and modeling of the barrier properties in nanostructured systems

The object of the present study is the process of gas transport in nano-sized materials, i.e. systems having structural elements of the order of nanometers. The aim of this work is to advance the understanding of the gas transport mechanism in such materials, for which traditional models are not often suitable, by providing a correct interpretation of the relationship between diffusive phenomena and structural features. This result would allow the development new materials with permeation properties tailored on the specific application, especially in packaging systems. The methods used to achieve this goal were a detailed experimental characterization and different simulation methods. The experimental campaign regarded the determination of oxygen permeability and diffusivity in different sets of organic-inorganic hybrid coatings prepared via sol-gel technique. The polymeric samples coated with these hybrid layers experienced a remarkable enhancement of the barrier properties, which was explained by the strong interconnection at the nano-scale between the organic moiety and silica domains. An analogous characterization was performed on microfibrillated cellulose films, which presented remarkable barrier effect toward oxygen when it is dry, while in the presence of water the performance significantly drops. The very low value of water diffusivity at low activities is also an interesting characteristic which deals with its structural properties. Two different approaches of simulation were then considered: the diffusion of oxygen through polymer-layered silicates was modeled on a continuum scale with a CFD software, while the properties of n-alkanthiolate self assembled monolayers on gold were analyzed from a molecular point of view by means of a molecular dynamics algorithm. Modeling transport properties in layered nanocomposites, resulting from the ordered dispersion of impermeable flakes in a 2-D matrix, allowed the calculation of the enhancement of barrier effect in relation with platelets structural parameters leading to derive a new expression. On this basis, randomly distributed systems were simulated and the results were analyzed to evaluate the different contributions to the overall effect. The study of more realistic three-dimensional geometries revealed a prefect correspondence with the 2-D approximation. A completely different approach was applied to simulate the effect of temperature on the oxygen transport through self assembled monolayers; the structural information obtained from equilibrium MD simulations showed that raising the temperature, makes the monolayer less ordered and consequently less crystalline. This disorder produces a decrease in the barrier free energy and it lowers the overall resistance to oxygen diffusion, making the monolayer more permeable to small molecules.

Hybrid Methods for Resource Allocation and Scheduling Problems in Deterministic and Stochastic Environments

This work presents exact, hybrid algorithms for mixed resource Allocation and Scheduling problems; in general terms, those consist into assigning over time finite capacity resources to a set of precedence connected activities. The proposed methods have broad applicability, but are mainly motivated by applications in the field of Embedded System Design. In particular, high-performance embedded computing recently witnessed the shift from single CPU platforms with application-specific accelerators to programmable Multi Processor Systems-on-Chip (MPSoCs). Those allow higher flexibility, real time performance and low energy consumption, but the programmer must be able to effectively exploit the platform parallelism. This raises interest in the development of algorithmic techniques to be embedded in CAD tools; in particular, given a specific application and platform, the objective if to perform optimal allocation of hardware resources and to compute an execution schedule. On this regard, since embedded systems tend to run the same set of applications for their entire lifetime, off-line, exact optimization approaches are particularly appealing. Quite surprisingly, the use of exact algorithms has not been well investigated so far; this is in part motivated by the complexity of integrated allocation and scheduling, setting tough challenges for ``pure'' combinatorial methods. The use of hybrid CP/OR approaches presents the opportunity to exploit mutual advantages of different methods, while compensating for their weaknesses. In this work, we consider in first instance an Allocation and Scheduling problem over the Cell BE processor by Sony, IBM and Toshiba; we propose three different solution methods, leveraging decomposition, cut generation and heuristic guided search. Next, we face Allocation and Scheduling of so-called Conditional Task Graphs, explicitly accounting for branches with outcome not known at design time; we extend the CP scheduling framework to effectively deal with the introduced stochastic elements. Finally, we address Allocation and Scheduling with uncertain, bounded execution times, via conflict based tree search; we introduce a simple and flexible time model to take into account duration variability and provide an efficient conflict detection method. The proposed approaches achieve good results on practical size problem, thus demonstrating the use of exact approaches for system design is feasible. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.

Permutation-based stochastic ordering using pairwise comparisons

The topic of this work concerns nonparametric permutation-based methods aiming to find a ranking (stochastic ordering) of a given set of groups (populations), gathering together information from multiple variables under more than one experimental designs. The problem of ranking populations arises in several fields of science from the need of comparing G>2 given groups or treatments when the main goal is to find an order while taking into account several aspects. As it can be imagined, this problem is not only of theoretical interest but it also has a recognised relevance in several fields, such as industrial experiments or behavioural sciences, and this is reflected by the vast literature on the topic, although sometimes the problem is associated with different keywords such as: "stochastic ordering", "ranking", "construction of composite indices" etc., or even "ranking probabilities" outside of the strictly-speaking statistical literature. The properties of the proposed method are empirically evaluated by means of an extensive simulation study, where several aspects of interest are let to vary within a reasonable practical range. These aspects comprise: sample size, number of variables, number of groups, and distribution of noise/error. The flexibility of the approach lies mainly in the several available choices for the test-statistic and in the different types of experimental design that can be analysed. This render the method able to be tailored to the specific problem and the to nature of the data at hand. To perform the analyses an R package called SOUP (Stochastic Ordering Using Permutations) has been written and it is available on CRAN.

Simulation of Smart Materials

The aim of this thesis is the elucidation of structure-properties relationship of molecular semiconductors for electronic devices. This involves the use of a comprehensive set of simulation techniques, ranging from quantum-mechanical to numerical stochastic methods, and also the development of ad-hoc computational tools. In more detail, the research activity regarded two main topics: the study of electronic properties and structural behaviour of liquid crystalline (LC) materials based on functionalised oligo(p-phenyleneethynylene) (OPE), and the investigation on the electric field effect associated to OFET operation on pentacene thin film stability. In this dissertation, a novel family of substituted OPE liquid crystals with applications in stimuli-responsive materials is presented. In more detail, simulations can not only provide evidence for the characterization of the liquid crystalline phases of different OPEs, but elucidate the role of charge transfer states in donor-acceptor LCs containing an endohedral metallofullerene moiety. Such systems can be regarded as promising candidates for organic photovoltaics. Furthermore, exciton dynamics simulations are performed as a way to obtain additional information about the degree of order in OPE columnar phases. Finally, ab initio and molecular mechanics simulations are used to investigate the influence of an applied electric field on pentacene reactivity and stability. The reaction path of pentacene thermal dimerization in the presence of an external electric field is investigated; the results can be related to the fatigue effect observed in OFETs, that show significant performance degradation even in the absence of external agents. In addition to this, the effect of the gate voltage on a pentacene monolayer are simulated, and the results are then compared to X-ray diffraction measurements performed for the first time on operating OFETs.

Tools and methods for the quality assurance of force platforms in human movement analysis

The human movement analysis (HMA) aims to measure the abilities of a subject to stand or to walk. In the field of HMA, tests are daily performed in research laboratories, hospitals and clinics, aiming to diagnose a disease, distinguish between disease entities, monitor the progress of a treatment and predict the outcome of an intervention [Brand and Crowninshield, 1981; Brand, 1987; Baker, 2006]. To achieve these purposes, clinicians and researchers use measurement devices, like force platforms, stereophotogrammetric systems, accelerometers, baropodometric insoles, etc. This thesis focus on the force platform (FP) and in particular on the quality assessment of the FP data. The principal objective of our work was the design and the experimental validation of a portable system for the in situ calibration of FPs. The thesis is structured as follows: Chapter 1. Description of the physical principles used for the functioning of a FP: how these principles are used to create force transducers, such as strain gauges and piezoelectrics transducers. Then, description of the two category of FPs, three- and six-component, the signals acquisition (hardware structure), and the signals calibration. Finally, a brief description of the use of FPs in HMA, for balance or gait analysis. Chapter 2. Description of the inverse dynamics, the most common method used in the field of HMA. This method uses the signals measured by a FP to estimate kinetic quantities, such as joint forces and moments. The measures of these variables can not be taken directly, unless very invasive techniques; consequently these variables can only be estimated using indirect techniques, as the inverse dynamics. Finally, a brief description of the sources of error, present in the gait analysis. Chapter 3. State of the art in the FP calibration. The selected literature is divided in sections, each section describes: systems for the periodic control of the FP accuracy; systems for the error reduction in the FP signals; systems and procedures for the construction of a FP. In particular is detailed described a calibration system designed by our group, based on the theoretical method proposed by ?. This system was the “starting point” for the new system presented in this thesis. Chapter 4. Description of the new system, divided in its parts: 1) the algorithm; 2) the device; and 3) the calibration procedure, for the correct performing of the calibration process. The algorithm characteristics were optimized by a simulation approach, the results are here presented. In addiction, the different versions of the device are described. Chapter 5. Experimental validation of the new system, achieved by testing it on 4 commercial FPs. The effectiveness of the calibration was verified by measuring, before and after calibration, the accuracy of the FPs in measuring the center of pressure of an applied force. The new system can estimate local and global calibration matrices; by local and global calibration matrices, the non–linearity of the FPs was quantified and locally compensated. Further, a non–linear calibration is proposed. This calibration compensates the non– linear effect in the FP functioning, due to the bending of its upper plate. The experimental results are presented. Chapter 6. Influence of the FP calibration on the estimation of kinetic quantities, with the inverse dynamics approach. Chapter 7. The conclusions of this thesis are presented: need of a calibration of FPs and consequential enhancement in the kinetic data quality. Appendix: Calibration of the LC used in the presented system. Different calibration set–up of a 3D force transducer are presented, and is proposed the optimal set–up, with particular attention to the compensation of non–linearities. The optimal set–up is verified by experimental results.

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.

Evolutionary methods for self-organizing cooperation in peer-to-peer networks

The Peer-to-Peer network paradigm is drawing the attention of both final users and researchers for its features. P2P networks shift from the classic client-server approach to a high level of decentralization where there is no central control and all the nodes should be able not only to require services, but to provide them to other peers as well. While on one hand such high level of decentralization might lead to interesting properties like scalability and fault tolerance, on the other hand it implies many new problems to deal with. A key feature of many P2P systems is openness, meaning that everybody is potentially able to join a network with no need for subscription or payment systems. The combination of openness and lack of central control makes it feasible for a user to free-ride, that is to increase its own benefit by using services without allocating resources to satisfy other peers’ requests. One of the main goals when designing a P2P system is therefore to achieve cooperation between users. Given the nature of P2P systems based on simple local interactions of many peers having partial knowledge of the whole system, an interesting way to achieve desired properties on a system scale might consist in obtaining them as emergent properties of the many interactions occurring at local node level. Two methods are typically used to face the problem of cooperation in P2P networks: 1) engineering emergent properties when designing the protocol; 2) study the system as a game and apply Game Theory techniques, especially to find Nash Equilibria in the game and to reach them making the system stable against possible deviant behaviors. In this work we present an evolutionary framework to enforce cooperative behaviour in P2P networks that is alternative to both the methods mentioned above. Our approach is based on an evolutionary algorithm inspired by computational sociology and evolutionary game theory, consisting in having each peer periodically trying to copy another peer which is performing better. The proposed algorithms, called SLAC and SLACER, draw inspiration from tag systems originated in computational sociology, the main idea behind the algorithm consists in having low performance nodes copying high performance ones. The algorithm is run locally by every node and leads to an evolution of the network both from the topology and from the nodes’ strategy point of view. Initial tests with a simple Prisoners’ Dilemma application show how SLAC is able to bring the network to a state of high cooperation independently from the initial network conditions. Interesting results are obtained when studying the effect of cheating nodes on SLAC algorithm. In fact in some cases selfish nodes rationally exploiting the system for their own benefit can actually improve system performance from the cooperation formation point of view. The final step is to apply our results to more realistic scenarios. We put our efforts in studying and improving the BitTorrent protocol. BitTorrent was chosen not only for its popularity but because it has many points in common with SLAC and SLACER algorithms, ranging from the game theoretical inspiration (tit-for-tat-like mechanism) to the swarms topology. We discovered fairness, meant as ratio between uploaded and downloaded data, to be a weakness of the original BitTorrent protocol and we drew inspiration from the knowledge of cooperation formation and maintenance mechanism derived from the development and analysis of SLAC and SLACER, to improve fairness and tackle freeriding and cheating in BitTorrent. We produced an extension of BitTorrent called BitFair that has been evaluated through simulation and has shown the abilities of enforcing fairness and tackling free-riding and cheating nodes.

Models and methods for power monolithic microwave integrated circuits

Computer aided design of Monolithic Microwave Integrated Circuits (MMICs) depends critically on active device models that are accurate, computationally efficient, and easily extracted from measurements or device simulators. Empirical models of active electron devices, which are based on actual device measurements, do not provide a detailed description of the electron device physics. However they are numerically efficient and quite accurate. These characteristics make them very suitable for MMIC design in the framework of commercially available CAD tools. In the empirical model formulation it is very important to separate linear memory effects (parasitic effects) from the nonlinear effects (intrinsic effects). Thus an empirical active device model is generally described by an extrinsic linear part which accounts for the parasitic passive structures connecting the nonlinear intrinsic electron device to the external world. An important task circuit designers deal with is evaluating the ultimate potential of a device for specific applications. In fact once the technology has been selected, the designer would choose the best device for the particular application and the best device for the different blocks composing the overall MMIC. Thus in order to accurately reproducing the behaviour of different-in-size devices, good scalability properties of the model are necessarily required. Another important aspect of empirical modelling of electron devices is the mathematical (or equivalent circuit) description of the nonlinearities inherently associated with the intrinsic device. Once the model has been defined, the proper measurements for the characterization of the device are performed in order to identify the model. Hence, the correct measurement of the device nonlinear characteristics (in the device characterization phase) and their reconstruction (in the identification or even simulation phase) are two of the more important aspects of empirical modelling. This thesis presents an original contribution to nonlinear electron device empirical modelling treating the issues of model scalability and reconstruction of the device nonlinear characteristics. The scalability of an empirical model strictly depends on the scalability of the linear extrinsic parasitic network, which should possibly maintain the link between technological process parameters and the corresponding device electrical response. Since lumped parasitic networks, together with simple linear scaling rules, cannot provide accurate scalable models, either complicate technology-dependent scaling rules or computationally inefficient distributed models are available in literature. This thesis shows how the above mentioned problems can be avoided through the use of commercially available electromagnetic (EM) simulators. They enable the actual device geometry and material stratification, as well as losses in the dielectrics and electrodes, to be taken into account for any given device structure and size, providing an accurate description of the parasitic effects which occur in the device passive structure. It is shown how the electron device behaviour can be described as an equivalent two-port intrinsic nonlinear block connected to a linear distributed four-port passive parasitic network, which is identified by means of the EM simulation of the device layout, allowing for better frequency extrapolation and scalability properties than conventional empirical models. Concerning the issue of the reconstruction of the nonlinear electron device characteristics, a data approximation algorithm has been developed for the exploitation in the framework of empirical table look-up nonlinear models. Such an approach is based on the strong analogy between timedomain signal reconstruction from a set of samples and the continuous approximation of device nonlinear characteristics on the basis of a finite grid of measurements. According to this criterion, nonlinear empirical device modelling can be carried out by using, in the sampled voltage domain, typical methods of the time-domain sampling theory.

Multi-Country Event Study Methods

Which event study methods are best in non-U.S. multi-country samples? Nonparametric tests, especially the rank and generalized sign, are better specified and more powerful than common parametric tests, especially in multi-day windows. The generalized sign test is the best statistic but must be applied to buy-and-hold abnormal returns for correct specification. Market-adjusted and market-model methods with local market indexes, without conversion to a common currency, work well. The results are robust to limiting the samples to situations expected to be problematic for test specification or power. Applying the tests that perform best in simulation to merger announcements produces reasonable results.

Statistical methods for biomedical signal analysis and processing

Statistical modelling and statistical learning theory are two powerful analytical frameworks for analyzing signals and developing efficient processing and classification algorithms. In this thesis, these frameworks are applied for modelling and processing biomedical signals in two different contexts: ultrasound medical imaging systems and primate neural activity analysis and modelling. In the context of ultrasound medical imaging, two main applications are explored: deconvolution of signals measured from a ultrasonic transducer and automatic image segmentation and classification of prostate ultrasound scans. In the former application a stochastic model of the radio frequency signal measured from a ultrasonic transducer is derived. This model is then employed for developing in a statistical framework a regularized deconvolution procedure, for enhancing signal resolution. In the latter application, different statistical models are used to characterize images of prostate tissues, extracting different features. These features are then uses to segment the images in region of interests by means of an automatic procedure based on a statistical model of the extracted features. Finally, machine learning techniques are used for automatic classification of the different region of interests. In the context of neural activity signals, an example of bio-inspired dynamical network was developed to help in studies of motor-related processes in the brain of primate monkeys. The presented model aims to mimic the abstract functionality of a cell population in 7a parietal region of primate monkeys, during the execution of learned behavioural tasks.

Metodi di ottimizzazione morfologica nel progetto preliminare di propulsori aeronautici avanzati

The aim of this Doctoral Thesis is to develop a genetic algorithm based optimization methods to find the best conceptual design architecture of an aero-piston-engine, for given design specifications. Nowadays, the conceptual design of turbine airplanes starts with the aircraft specifications, then the most suited turbofan or turbo propeller for the specific application is chosen. In the aeronautical piston engines field, which has been dormant for several decades, as interest shifted towards turboaircraft, new materials with increased performance and properties have opened new possibilities for development. Moreover, the engine’s modularity given by the cylinder unit, makes it possible to design a specific engine for a given application. In many real engineering problems the amount of design variables may be very high, characterized by several non-linearities needed to describe the behaviour of the phenomena. In this case the objective function has many local extremes, but the designer is usually interested in the global one. The stochastic and the evolutionary optimization techniques, such as the genetic algorithms method, may offer reliable solutions to the design problems, within acceptable computational time. The optimization algorithm developed here can be employed in the first phase of the preliminary project of an aeronautical piston engine design. It’s a mono-objective genetic algorithm, which, starting from the given design specifications, finds the engine propulsive system configuration which possesses minimum mass while satisfying the geometrical, structural and performance constraints. The algorithm reads the project specifications as input data, namely the maximum values of crankshaft and propeller shaft speed and the maximal pressure value in the combustion chamber. The design variables bounds, that describe the solution domain from the geometrical point of view, are introduced too. In the Matlab® Optimization environment the objective function to be minimized is defined as the sum of the masses of the engine propulsive components. Each individual that is generated by the genetic algorithm is the assembly of the flywheel, the vibration damper and so many pistons, connecting rods, cranks, as the number of the cylinders. The fitness is evaluated for each individual of the population, then the rules of the genetic operators are applied, such as reproduction, mutation, selection, crossover. In the reproduction step the elitist method is applied, in order to save the fittest individuals from a contingent mutation and recombination disruption, making it undamaged survive until the next generation. Finally, as the best individual is found, the optimal dimensions values of the components are saved to an Excel® file, in order to build a CAD-automatic-3D-model for each component of the propulsive system, having a direct pre-visualization of the final product, still in the engine’s preliminary project design phase. With the purpose of showing the performance of the algorithm and validating this optimization method, an actual engine is taken, as a case study: it’s the 1900 JTD Fiat Avio, 4 cylinders, 4T, Diesel. Many verifications are made on the mechanical components of the engine, in order to test their feasibility and to decide their survival through generations. A system of inequalities is used to describe the non-linear relations between the design variables, and is used for components checking for static and dynamic loads configurations. The design variables geometrical boundaries are taken from actual engines data and similar design cases. Among the many simulations run for algorithm testing, twelve of them have been chosen as representative of the distribution of the individuals. Then, as an example, for each simulation, the corresponding 3D models of the crankshaft and the connecting rod, have been automatically built. In spite of morphological differences among the component the mass is almost the same. The results show a significant mass reduction (almost 20% for the crankshaft) in comparison to the original configuration, and an acceptable robustness of the method have been shown. The algorithm here developed is shown to be a valid method for an aeronautical-piston-engine preliminary project design optimization. In particular the procedure is able to analyze quite a wide range of design solutions, rejecting the ones that cannot fulfill the feasibility design specifications. This optimization algorithm could increase the aeronautical-piston-engine development, speeding up the production rate and joining modern computation performances and technological awareness to the long lasting traditional design experiences.

Numerical simulation of ion transport through ion channels and solid-state nanopores

Ion channels are pore-forming proteins that regulate the flow of ions across biological cell membranes. Ion channels are fundamental in generating and regulating the electrical activity of cells in the nervous system and the contraction of muscolar cells. Solid-state nanopores are nanometer-scale pores located in electrically insulating membranes. They can be adopted as detectors of specific molecules in electrolytic solutions. Permeation of ions from one electrolytic solution to another, through a protein channel or a synthetic pore is a process of considerable importance and realistic analysis of the main dependencies of ion current on the geometrical and compositional characteristics of these structures are highly required. The project described by this thesis is an effort to improve the understanding of ion channels by devising methods for computer simulation that can predict channel conductance from channel structure. This project describes theory, algorithms and implementation techniques used to develop a novel 3-D numerical simulator of ion channels and synthetic nanopores based on the Brownian Dynamics technique. This numerical simulator could represent a valid tool for the study of protein ion channel and synthetic nanopores, allowing to investigate at the atomic-level the complex electrostatic interactions that determine channel conductance and ion selectivity. Moreover it will provide insights on how parameters like temperature, applied voltage, and pore shape could influence ion translocation dynamics. Furthermore it will help making predictions of conductance of given channel structures and it will add information like electrostatic potential or ionic concentrations throughout the simulation domain helping the understanding of ion flow through membrane pores.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Local Trigonometric Methods for Time Series Smoothing.

The thesis is concerned with local trigonometric regression methods. The aim was to develop a method for extraction of cyclical components in time series. The main results of the thesis are the following. First, a generalization of the filter proposed by Christiano and Fitzgerald is furnished for the smoothing of ARIMA(p,d,q) process. Second, a local trigonometric filter is built, with its statistical properties. Third, they are discussed the convergence properties of trigonometric estimators, and the problem of choosing the order of the model. A large scale simulation experiment has been designed in order to assess the performance of the proposed models and methods. The results show that local trigonometric regression may be a useful tool for periodic time series analysis.

Simulation Guided Navigation in cranio-maxillo-facial surgery: a new approach to improve intraoperative three-dimensional accuracy and reproducibility during surgery.

The aim of this PhD thesis " Simulation Guided Navigation in cranio- maxillo- facial surgery : a new approach to Improve intraoperative three-dimensional accuracy and reproducibility during surgery ." was at the center of its attention the various applications of a method introduced by our School in 2010 and has as its theme the increase of interest of reproducibility of surgical programs through methods that in whole or in part are using intraoperative navigation. It was introduced in Orthognathic Surgery Validation a new method for the interventions carried out according to the method Simulation Guided Navigation in facial deformities ; was then analyzed the method of three-dimensional control of the osteotomies through the use of templates and cutting of plates using the method precontoured CAD -CAM and laser sintering . It was finally proceeded to introduce the method of piezonavigated surgery in the various branches of maxillofacial surgery . These studies have been subjected to validation processes and the results are presented .