Wordline approach to higher spin fields

The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Organocatalytic asymmetric mannich-type reactions: an easy approach to optically active amine derivatives

The topics I came across during the period I spent as a Ph.D. student are mainly two. The first concerns new organocatalytic protocols for Mannich-type reactions mediated by Cinchona alkaloids derivatives (Scheme I, left); the second topic, instead, regards the study of a new approach towards the enantioselective total synthesis of Aspirochlorine, a potent gliotoxin that recent studies indicate as a highly selective and active agent against fungi (Scheme I, right). At the beginning of 2005 I had the chance to join the group of Prof. Alfredo Ricci at the Department of Organic Chemistry of the University of Bologna, starting my PhD studies. During the first period I started to study a new homogeneous organocatalytic aza-Henry reaction by means of Cinchona alkaloid derivatives as chiral base catalysts with good results. Soon after we introduced a new protocol which allowed the in situ synthesis of N-carbamoyl imines, scarcely stable, moisture sensitive compounds. For this purpose we used α-amido sulfones, bench stable white crystalline solids, as imine precursors (Scheme II). In particular we were able to obtain the aza-Henry adducts, by using chiral phase transfer catalysis, with a broad range of substituents as R-group and excellent results, unprecedented for Mannich-type transformations (Scheme II). With the optimised protocol in hand we have extended the methodology to the other Mannich-type reactions. We applied the new method to the Mannich, Strecker and Pudovik (hydrophosphonylation of imines) reactions with very good results in terms of enantioselections and yields, broadening the usefulness of this novel protocol. The Mannich reaction was certainly the most extensively studied work in this thesis (Scheme III). Initially we developed the reaction with α-amido sulfones as imine precursors and non-commercially available malonates with excellent results in terms of yields and enantioselections.3 In this particular case we recorded 1 mol% of catalyst loading, very low for organocatalytic processes. Then we thought to develop a new Mannich reaction by using simpler malonates, such as dimethyl malonate.4 With new optimised condition the reaction provided slightly lower enantioselections than the previous protocol, but the Mannich adducts were very versatile for the obtainment of β3-amino acids. Furthermore we performed the first addition of cyclic β-ketoester to α-amido sulfones obtaining the corresponding products in good yield with high level of diastereomeric and enantiomeric excess (Scheme III). Further studies were done about the Strecker reaction mediated by Cinchona alkaloid phase-transfer quaternary ammonium salt derivatives, using acetone cyanohydrin, a relatively harmless cyanide source (Scheme IV). The reaction proceeded very well providing the corresponding α-amino nitriles in good yields and enantiomeric excesses. Finally, we developed two new complementary methodologies for the hydrophosphonylation of imines (Scheme V). As a result of the low stability of the products derived from aromatic imines, we performed the reactions in mild homogeneous basic condition by using quinine as a chiral base catalyst giving the α-aryl-α-amido phosphonic acid esters as products (Scheme V, top).6 On the other hand, we performed the addition of dialkyl phosphite to aliphatic imines by using chiral Cinchona alkaloid phase transfer quaternary ammonium salt derivatives using our methodology based on α-amido sulfones (Scheme V, bottom). The results were good for both procedures covering a broad range of α-amino phosphonic acid ester. During the second year Ph.D. studies, I spent six months in the group of Prof. Steven V. Ley, at the Department of Chemistry of the University of Cambridge, in United Kingdom. During this fruitful period I have been involved in a project concerning the enantioselective synthesis of Aspirochlorine. We provided a new route for the synthesis of a key intermediate, reducing the number of steps and increasing the overall yield. Then we introduced a new enantioselective spirocyclisation for the synthesis of a chiral building block for the completion of the synthesis (Scheme VI).

A Unitary Approach to Information and Estimation Theory in Digital Communication Systems

This thesis presents the outcomes of a Ph.D. course in telecommunications engineering. It is focused on the optimization of the physical layer of digital communication systems and it provides innovations for both multi- and single-carrier systems. For the former type we have first addressed the problem of the capacity in presence of several nuisances. Moreover, we have extended the concept of Single Frequency Network to the satellite scenario, and then we have introduced a novel concept in subcarrier data mapping, resulting in a very low PAPR of the OFDM signal. For single carrier systems we have proposed a method to optimize constellation design in presence of a strong distortion, such as the non linear distortion provided by satellites' on board high power amplifier, then we developed a method to calculate the bit/symbol error rate related to a given constellation, achieving an improved accuracy with respect to the traditional Union Bound with no additional complexity. Finally we have designed a low complexity SNR estimator, which saves one-half of multiplication with respect to the ML estimator, and it has similar estimation accuracy.

Enhancing predictive capability of models for solubility and permeability in polymers and composites

The interpretation of phase equilibrium and mass transport phenomena in gas/solvent - polymer system at molten or glassy state is relevant in many industrial applications. Among tools available for the prediction of thermodynamics properties in these systems, at molten/rubbery state, is the group contribution lattice-fluid equation of state (GCLF-EoS), developed by Lee and Danner and ultimately based on Panayiotou and Vera LF theory. On the other side, a thermodynamic approach namely non-equilibrium lattice-fluid (NELF) was proposed by Doghieri and Sarti to consistently extend the description of thermodynamic properties of solute polymer systems obtained through a suitable equilibrium model to the case of non-equilibrium conditions below the glass transition temperature. The first objective of this work is to investigate the phase behaviour in solvent/polymer at glassy state by using NELF model and to develop a predictive tool for gas or vapor solubility that could be applied in several different applications: membrane gas separation, barrier materials for food packaging, polymer-based gas sensors and drug delivery devices. Within the efforts to develop a predictive tool of this kind, a revision of the group contribution method developed by High and Danner for the application of LF model by Panayiotou and Vera is considered, with reference to possible alternatives for the mixing rule for characteristic interaction energy between segments. The work also devotes efforts to the analysis of gas permeability in polymer composite materials as formed by a polymer matrix in which domains are dispersed of a second phase and attention is focused on relation for deviation from Maxwell law as function of arrangement, shape of dispersed domains and loading.