Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Transcriptional regulation of human mu-opioid receptor gene: functional characterization of activating and inhibitory transcription factors

The organization of the nervous and immune systems is characterized by obvious differences and striking parallels. Both systems need to relay information across very short and very long distances. The nervous system communicates over both long and short ranges primarily by means of more or less hardwired intercellular connections, consisting of axons, dendrites, and synapses. Longrange communication in the immune system occurs mainly via the ordered and guided migration of immune cells and systemically acting soluble factors such as antibodies, cytokines, and chemokines. Its short-range communication either is mediated by locally acting soluble factors or transpires during direct cell–cell contact across specialized areas called “immunological synapses” (Kirschensteiner et al., 2003). These parallels in intercellular communication are complemented by a complex array of factors that induce cell growth and differentiation: these factors in the immune system are called cytokines; in the nervous system, they are called neurotrophic factors. Neither the cytokines nor the neurotrophic factors appear to be completely exclusive to either system (Neumann et al., 2002). In particular, mounting evidence indicates that some of the most potent members of the neurotrophin family, for example, nerve growth factor (NGF) and brainderived neurotrophic factor (BDNF), act on or are produced by immune cells (Kerschensteiner et al., 1999) There are, however, other neurotrophic factors, for example the insulin-like growth factor-1 (IGF-1), that can behave similarly (Kermer et al., 2000). These factors may allow the two systems to “cross-talk” and eventually may provide a molecular explanation for the reports that inflammation after central nervous system (CNS) injury has beneficial effects (Moalem et al., 1999). In order to shed some more light on such a cross-talk, therefore, transcription factors modulating mu-opioid receptor (MOPr) expression in neurons and immune cells are here investigated. More precisely, I focused my attention on IGF-I modulation of MOPr in neurons and T-cell receptor induction of MOPr expression in T-lymphocytes. Three different opioid receptors [mu (MOPr), delta (DOPr), and kappa (KOPr)] belonging to the G-protein coupled receptor super-family have been cloned. They are activated by structurallyrelated exogenous opioids or endogenous opioid peptides, and contribute to the regulation of several functions including pain transmission, respiration, cardiac and gastrointestinal functions, and immune response (Zollner and Stein 2007). MOPr is expressed mainly in the central nervous system where it regulates morphine-induced analgesia, tolerance and dependence (Mayer and Hollt 2006). Recently, induction of MOPr expression in different immune cells induced by cytokines has been reported (Kraus et al., 2001; Kraus et al., 2003). The human mu-opioid receptor gene (OPRM1) promoter is of the TATA-less type and has clusters of potential binding sites for different transcription factors (Law et al. 2004). Several studies, primarily focused on the upstream region of the OPRM1 promoter, have investigated transcriptional regulation of MOPr expression. Presently, however, it is still not completely clear how positive and negative transcription regulators cooperatively coordinate cellor tissue-specific transcription of the OPRM1 gene, and how specific growth factors influence its expression. IGF-I and its receptors are widely distributed throughout the nervous system during development, and their involvement in neurogenesis has been extensively investigated (Arsenijevic et al. 1998; van Golen and Feldman 2000). As previously mentioned, such neurotrophic factors can be also produced and/or act on immune cells (Kerschenseteiner et al., 2003). Most of the physiologic effects of IGF-I are mediated by the type I IGF surface receptor which, after ligand binding-induced autophosphorylation, associates with specific adaptor proteins and activates different second messengers (Bondy and Cheng 2004). These include: phosphatidylinositol 3-kinase, mitogen-activated protein kinase (Vincent and Feldman 2002; Di Toro et al. 2005) and members of the Janus kinase (JAK)/STAT3 signalling pathway (Zong et al. 2000; Yadav et al. 2005). REST plays a complex role in neuronal cells by differentially repressing target gene expression (Lunyak et al. 2004; Coulson 2005; Ballas and Mandel 2005). REST expression decreases during neurogenesis, but has been detected in the adult rat brain (Palm et al. 1998) and is up-regulated in response to global ischemia (Calderone et al. 2003) and induction of epilepsy (Spencer et al. 2006). Thus, the REST concentration seems to influence its function and the expression of neuronal genes, and may have different effects in embryonic and differentiated neurons (Su et al. 2004; Sun et al. 2005). In a previous study, REST was elevated during the early stages of neural induction by IGF-I in neuroblastoma cells. REST may contribute to the down-regulation of genes not yet required by the differentiation program, but its expression decreases after five days of treatment to allow for the acquisition of neural phenotypes. Di Toro et al. proposed a model in which the extent of neurite outgrowth in differentiating neuroblastoma cells was affected by the disappearance of REST (Di Toro et al. 2005). The human mu-opioid receptor gene (OPRM1) promoter contains a DNA sequence binding the repressor element 1 silencing transcription factor (REST) that is implicated in transcriptional repression. Therefore, in the fist part of this thesis, I investigated whether insulin-like growth factor I (IGF-I), which affects various aspects of neuronal induction and maturation, regulates OPRM1 transcription in neuronal cells in the context of the potential influence of REST. A series of OPRM1-luciferase promoter/reporter constructs were transfected into two neuronal cell models, neuroblastoma-derived SH-SY5Y cells and PC12 cells. In the former, endogenous levels of human mu-opioid receptor (hMOPr) mRNA were evaluated by real-time PCR. IGF-I upregulated OPRM1 transcription in: PC12 cells lacking REST, in SH-SY5Y cells transfected with constructs deficient in the REST DNA binding element, or when REST was down-regulated in retinoic acid-differentiated cells. IGF-I activates the signal transducer and activator of transcription-3 (STAT3) signaling pathway and this transcription factor, binding to the STAT1/3 DNA element located in the promoter, increases OPRM1 transcription. T-cell receptor (TCR) recognizes peptide antigens displayed in the context of the major histocompatibility complex (MHC) and gives rise to a potent as well as branched intracellular signalling that convert naïve T-cells in mature effectors, thus significantly contributing to the genesis of a specific immune response. In the second part of my work I exposed wild type Jurkat CD4+ T-cells to a mixture of CD3 and CD28 antigens in order to fully activate TCR and study whether its signalling influence OPRM1 expression. Results were that TCR engagement determined a significant induction of OPRM1 expression through the activation of transcription factors AP-1, NF-kB and NFAT. Eventually, I investigated MOPr turnover once it has been expressed on T-cells outer membrane. It turned out that DAMGO induced MOPr internalisation and recycling, whereas morphine did not. Overall, from the data collected in this thesis we can conclude that that a reduction in REST is a critical switch enabling IGF-I to up-regulate human MOPr, helping these findings clarify how human MOPr expression is regulated in neuronal cells, and that TCR engagement up-regulates OPRM1 transcription in T-cells. My results that neurotrophic factors a and TCR engagement, as well as it is reported for cytokines, seem to up-regulate OPRM1 in both neurons and immune cells suggest an important role for MOPr as a molecular bridge between neurons and immune cells; therefore, MOPr could play a key role in the cross-talk between immune system and nervous system and in particular in the balance between pro-inflammatory and pro-nociceptive stimuli and analgesic and neuroprotective effects.

Fiber-Optic Technologies for Wireline and Wireless In-building Networks

This doctoral dissertation aims to establish fiber-optic technologies overcoming the limiting issues of data communications in indoor environments. Specific applications are broadband mobile distribution in different in-building scenarios and high-speed digital transmission over short-range wired optical systems. Two key enabling technologies are considered: Radio over Fiber (RoF) techniques over standard silica fibers for distributed antenna systems (DAS) and plastic optical fibers (POFs) for short-range communications. Hence, the objectives and achievements of this thesis are related to the application of RoF and POF technologies in different in-building scenarios. On one hand, a theoretical and experimental analysis combined with demonstration activities has been performed on cost-effective RoF systems. An extensive modeling on modal noise impact both on linear and non-linear characteristics of RoF link over silica multimode fiber has been performed to achieve link design rules for an optimum choice of the transmitter, receiver and launching technique. A successful transmission of Long Term Evolution (LTE) mobile signals on the resulting optimized RoF system over silica multimode fiber employing a Fabry-Perot LD, central launch technique and a photodiode with a built-in ball lens was demonstrated up to 525m with performances well compliant with standard requirements. On the other hand, digital signal processing techniques to overcome the bandwidth limitation of POF have been investigated. An uncoded net bit-rate of 5.15Gbit/s was obtained on a 50m long POF link employing an eye-safe transmitter, a silicon photodiode, and DMT modulation with bit and power loading algorithm. With the insertion of 3x2N quadrature amplitude modulation constellation formats, an uncoded net-bit-rate of 5.4Gbit/s was obtained on a 50 m long POF link employing an eye-safe transmitter and a silicon avalanche photodiode. Moreover, simultaneous transmission of baseband 2Gbit/s with DMT and 200Mbit/s with an ultra-wideband radio signal has been validated over a 50m long POF link.

Genome characterization through a mathematical model of the genetic code: an analysis of the whole chromosome 1 of A. thaliana

The objective of this work is to characterize the genome of the chromosome 1 of A.thaliana, a small flowering plants used as a model organism in studies of biology and genetics, on the basis of a recent mathematical model of the genetic code. I analyze and compare different portions of the genome: genes, exons, coding sequences (CDS), introns, long introns, intergenes, untranslated regions (UTR) and regulatory sequences. In order to accomplish the task, I transformed nucleotide sequences into binary sequences based on the definition of the three different dichotomic classes. The descriptive analysis of binary strings indicate the presence of regularities in each portion of the genome considered. In particular, there are remarkable differences between coding sequences (CDS and exons) and non-coding sequences, suggesting that the frame is important only for coding sequences and that dichotomic classes can be useful to recognize them. Then, I assessed the existence of short-range dependence between binary sequences computed on the basis of the different dichotomic classes. I used three different measures of dependence: the well-known chi-squared test and two indices derived from the concept of entropy i.e. Mutual Information (MI) and Sρ, a normalized version of the “Bhattacharya Hellinger Matusita distance”. The results show that there is a significant short-range dependence structure only for the coding sequences whose existence is a clue of an underlying error detection and correction mechanism. No doubt, further studies are needed in order to assess how the information carried by dichotomic classes could discriminate between coding and noncoding sequence and, therefore, contribute to unveil the role of the mathematical structure in error detection and correction mechanisms. Still, I have shown the potential of the approach presented for understanding the management of genetic information.

Engineering Complex Computational Ecosystems

Self-organising pervasive ecosystems of devices are set to become a major vehicle for delivering infrastructure and end-user services. The inherent complexity of such systems poses new challenges to those who want to dominate it by applying the principles of engineering. The recent growth in number and distribution of devices with decent computational and communicational abilities, that suddenly accelerated with the massive diffusion of smartphones and tablets, is delivering a world with a much higher density of devices in space. Also, communication technologies seem to be focussing on short-range device-to-device (P2P) interactions, with technologies such as Bluetooth and Near-Field Communication gaining greater adoption. Locality and situatedness become key to providing the best possible experience to users, and the classic model of a centralised, enormously powerful server gathering and processing data becomes less and less efficient with device density. Accomplishing complex global tasks without a centralised controller responsible of aggregating data, however, is a challenging task. In particular, there is a local-to-global issue that makes the application of engineering principles challenging at least: designing device-local programs that, through interaction, guarantee a certain global service level. In this thesis, we first analyse the state of the art in coordination systems, then motivate the work by describing the main issues of pre-existing tools and practices and identifying the improvements that would benefit the design of such complex software ecosystems. The contribution can be divided in three main branches. First, we introduce a novel simulation toolchain for pervasive ecosystems, designed for allowing good expressiveness still retaining high performance. Second, we leverage existing coordination models and patterns in order to create new spatial structures. Third, we introduce a novel language, based on the existing ``Field Calculus'' and integrated with the aforementioned toolchain, designed to be usable for practical aggregate programming.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.