Knot theory and its applications

Nella tesi verranno presi in considerazione tre aspetti: si descriverà come la teoria dei nodi si sia sviluppata nel corso degli anni in relazione alle diverse scoperte scientifiche avvenute. Si potrà quindi subito avere una idea di come questa teoria sia estremamente connessa a diverse altre. Nel secondo capitolo ci si occuperà degli aspetti più formali di questa teoria. Si introdurrà il concetto di nodi equivalenti e di invariante dei nodi. Si definiranno diversi invarianti, dai più elementari, le mosse di Reidemeister, il numero di incroci e la tricolorabilità, fino ai polinomi invarianti, tra cui il polinomio di Alexander, il polinomio di Jones e quello di Kaufman. Infine si spiegheranno alcune applicazioni della teoria dei nodi in chimica, fisica e biologia. Sulla chimica, si definirà la chiralità molecolare e si mostrerà come la chiralità dei nodi possa essere utile nel determinare quella molecolare. In campo fisico, si mostrerà la relazione che esiste tra l'equazione di Yang-Baxter e i nodi. E in conclusione si mostrerà come modellare un importante processo biologico, la recombinazione del DNA, grazie alla teoria dei nodi.

Fractal sets and their applications in medicine

La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.

State of the art and future perspectives on security metrics and their applications

In modern society, security issues of IT Systems are intertwined with interdisciplinary aspects, from social life to sustainability, and threats endanger many aspects of every- one’s daily life. To address the problem, it’s important that the systems that we use guarantee a certain degree of security, but to achieve this, it is necessary to be able to give a measure to the amount of security. Measuring security is not an easy task, but many initiatives, including European regulations, want to make this possible. One method of measuring security is based on the use of security metrics: those are a way of assessing, from various aspects, vulnera- bilities, methods of defense, risks and impacts of successful attacks then also efficacy of reactions, giving precise results using mathematical and statistical techniques. I have done literature research to provide an overview on the meaning, the effects, the problems, the applications and the overall current situation over security metrics, with particular emphasis in giving practical examples. This thesis starts with a summary of the state of the art in the field of security met- rics and application examples to outline the gaps in current literature, the difficulties found in the change of application context, to then advance research questions aimed at fostering the discussion towards the definition of a more complete and applicable view of the subject. Finally, it stresses the lack of security metrics that consider interdisciplinary aspects, giving some potential starting point to develop security metrics that cover all as- pects involved, taking the field to a new level of formal soundness and practical usability.

Biopolyester fibers for sustainable and biocompatible applications

The rising of concerns around the scarcity of non-renewable resources has raised curiosity around new frontiers in the polymer science field. Biopolymers is a general term describing different kind of polymers that are linked with the biological world because of either monomer derivation, end of life degradation or both. The current work is aimed at studying one example of both biopolymers types. Polyhydroxibutyrate (P3HB) is a biodegradable microbial-produced polymer which holds massive potentiality as a substitute of polyolefins such as polypropylene. Though, its highly crystalline nature and stereoregularity of structure make it difficult to work with. The project P3HB-Mono take advantage of polarized Raman spectroscopy to see how annealing of chains with different weights influence the crystallinity and molecular structure of the polymer, eventually reflecting on its mechanical properties. The technique employed is also optimal in order to see how mesophase, a particular conformation of chains different from crystalline and amorphous phase, develops in the polymer structure and changes depending on temperature and mechanical stress applied to the fiber. Polycaprolactone (PCL) on the other hand is a biodegradable fossil-fuel polymer which has biocompatibility and bio-resorbability features. As a consequence this material is very appealing for medical industry and can be used for different applications in this field. One interesting option is to produce narrow and long liquid filled fibers for drug delivery inside human body, using a traditional technique in an innovative way. The project BioLiCoF investigates the feasability of producing liquid filled fibers using melt-spinning techniques and will examine the role that melt-spinning parameters and liquids employed as a core solution have on the final fiber. The physical analysis of the fibers is also interpreted and idea on future developments of the trials are suggested.

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.

Authoring tools and management information systems: study of a generalizable architecture

The need to effectively manage the documentation covering the entire production process, from the concept phase right through to market realise, constitutes a key issue in the creation of a successful and highly competitive product. For almost forty years the most commonly used strategies to achieve this have followed Product Lifecycle Management (PLM) guidelines. Translated into information management systems at the end of the '90s, this methodology is now widely used by companies operating all over the world in many different sectors. PLM systems and editor programs are the two principal types of software applications used by companies for their process aotomation. Editor programs allow to store in documents the information related to the production chain, while the PLM system stores and shares this information so that it can be used within the company and made it available to partners. Different software tools, which capture and store documents and information automatically in the PLM system, have been developed in recent years. One of them is the ''DirectPLM'' application, which has been developed by the Italian company ''Focus PLM''. It is designed to ensure interoperability between many editors and the Aras Innovator PLM system. In this dissertation we present ''DirectPLM2'', a new version of the previous software application DirectPLM. It has been designed and developed as prototype during the internship by Focus PLM. Its new implementation separates the abstract logic of business from the real commands implementation, previously strongly dependent on Aras Innovator. Thanks to its new design, Focus PLM can easily develop different versions of DirectPLM2, each one devised for a specific PLM system. In fact, the company can focus the development effort only on a specific set of software components which provides specialized functions interacting with that particular PLM system. This allows shorter Time-To-Market and gives the company a significant competitive advantage.

The road to augmented reality: a comprehensive study of hardware and applications over the last ten years

Augmented reality has been growing extensively over the years in all aspects and multiple fields. My aim in this paper is to present a comprehensive study on augmented reality(AR) hardware and its applications from early developments to the possible future trends. Particularly my research is more focused on last 11 years(2012-2022), where I systematically reviewed 30 research papers per year to get a clear knowledge on trends of AR. A total of 330 publications were reviewed and grouped according to their application. The review's main contribution is to show the entire landscape of AR research and to provide a broad view of how it has evolved. Along with various AR glasses history and specifications are presented in detail. In the penultimate chapter I explained my methodology of research following my analysis from the past to the present along with my thoughts for the future. To conclude my study, In the final chapter I made some statements about possible future with AR, VR and XR(extended reality).