Color/kinematic duality, double copies and scalar matrix models

In questa tesi presentiamo una descrizione autoconsistente della dualità Colore/Cinematica nelle teorie di gauge e al processo di Double Copy. Particolare attenzione viene data all'approccio alla dualità con il formalismo di cono-luce, in quanto semplifica notevolmente sia il calcolo sia l'interpretazione fisica: vengono indagati i settori duale e self-duale per poi passare al modello di Chalmers e Siegel per l'estensione alla teoria generale. Proponiamo quindi uno Scalar Matrix Model, che può essere un buon modello per generare ampiezze ottenibili da una Double Copy `inversa', e ne studiamo un'eventuale dualità a la Colore/Cinematica. Vengono illustrati alcuni casi particolari di rottura spontanea di simmetria. In appendice riportiamo un notebook di Mathematica per il calcolo di ampiezze tree level di puro gauge, utile per i calcoli necessari allo studio della dualità.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

Multicelled Behaviour in E. coli: Design and experimental characterization of an engineered library of hybrid promoters.

Synthetic biology has recently had a great development, many papers have been published and many applications have been presented, spanning from the production of biopharmacheuticals to the synthesis of bioenergetic substrates or industrial catalysts. But, despite these advances, most of the applications are quite simple and don’t fully exploit the potential of this discipline. This limitation in complexity has many causes, like the incomplete characterization of some components, or the intrinsic variability of the biological systems, but one of the most important reasons is the incapability of the cell to sustain the additional metabolic burden introduced by a complex circuit. The objective of the project, of which this work is part, is trying to solve this problem through the engineering of a multicellular behaviour in prokaryotic cells. This system will introduce a cooperative behaviour that will allow to implement complex functionalities, that can’t be obtained with a single cell. In particular the goal is to implement the Leader Election, this procedure has been firstly devised in the field of distributed computing, to identify the process that allow to identify a single process as organizer and coordinator of a series of tasks assigned to the whole population. The election of the Leader greatly simplifies the computation providing a centralized control. Further- more this system may even be useful to evolutionary studies that aims to explain how complex organisms evolved from unicellular systems. The work presented here describes, in particular, the design and the experimental characterization of a component of the circuit that solves the Leader Election problem. This module, composed of an hybrid promoter and a gene, is activated in the non-leader cells after receiving the signal that a leader is present in the colony. The most important element, in this case, is the hybrid promoter, it has been realized in different versions, applying the heuristic rules stated in [22], and their activity has been experimentally tested. The objective of the experimental characterization was to test the response of the genetic circuit to the introduction, in the cellular environment, of particular molecules, inducers, that can be considered inputs of the system. The desired behaviour is similar to the one of a logic AND gate in which the exit, represented by the luminous signal produced by a fluorescent protein, is one only in presence of both inducers. The robustness and the stability of this behaviour have been tested by changing the concentration of the input signals and building dose response curves. From these data it is possible to conclude that the analysed constructs have an AND-like behaviour over a wide range of inducers’ concentrations, even if it is possible to identify many differences in the expression profiles of the different constructs. This variability accounts for the fact that the input and the output signals are continuous, and so their binary representation isn’t able to capture the complexity of the behaviour. The module of the circuit that has been considered in this analysis has a fundamental role in the realization of the intercellular communication system that is necessary for the cooperative behaviour to take place. For this reason, the second phase of the characterization has been focused on the analysis of the signal transmission. In particular, the interaction between this element and the one that is responsible for emitting the chemical signal has been tested. The desired behaviour is still similar to a logic AND, since, even in this case, the exit signal is determined by the hybrid promoter activity. The experimental results have demonstrated that the systems behave correctly, even if there is still a substantial variability between them. The dose response curves highlighted that stricter constrains on the inducers concentrations need to be imposed in order to obtain a clear separation between the two levels of expression. In the conclusive chapter the DNA sequences of the hybrid promoters are analysed, trying to identify the regulatory elements that are most important for the determination of the gene expression. Given the available data it wasn’t possible to draw definitive conclusions. In the end, few considerations on promoter engineering and complex circuits realization are presented. This section aims to briefly recall some of the problems outlined in the introduction and provide a few possible solutions.

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.