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.

Identification of stock units of Mullus barbatus (Linnaeus, 1758) in the Italian seas: development of genomic 2b-RAD markers and biological variation analysis.

This thesis is settled within the STOCKMAPPING project, which represents one of the studies that were developed in the framework of RITMARE Flagship project. The main goals of STOCKMAPPING were the creation of a genomic mapping for stocks of demersal target species and the assembling of a database of population genomic, in order to identify stocks and stocks boundaries. The thesis focuses on three main objectives representing the core for the initial assessment of the methodologies and structure that would be applied to the entire STOCKMAPPING project: individuation of an analytical design to identify and locate stocks and stocks boundaries of Mullus barbatus, application of a multidisciplinary approach to validate biological methods and an initial assessment and improvement for the genotyping by sequencing technique utilized (2b-RAD). The first step is the individuation of an analytical design that has to take in to account the biological characteristics of red mullet and being representative for STOCKMAPPING commitments. In this framework a reduction and selection steps was needed due to budget reduction. Sampling areas were ranked according the individuation of four priorities. To guarantee a multidisciplinary approach the biological data associated to the collected samples were used to investigate differences between sampling areas and GSAs. Genomic techniques were applied to red mullet for the first time so an initial assessment of molecular protocols for DNA extraction and 2b-RAD processing were needed. At the end 192 good quality DNAs have been extracted and eight samples have been processed with 2b-RAD. Utilizing the software Stacks for sequences analyses a great number of SNPs markers among the eight samples have been identified. Several tests have been performed changing the main parameter of the Stacks pipeline in order to identify the most explicative and functional sets of parameters.

Stock boundaries of Parapenaeus longirostris (Lucas, 1846) populations in the Italian seas: Development of genomic 2b-RAD markers and biological variation analysis.

This thesis is developed in the contest of Ritmare project WP1, which main objective is the development of a sustainable fishery through the identification of populations boundaries in commercially important species in Italian Seas. Three main objectives are discussed in order to help reach the main purpose of identification of stock boundaries in Parapenaeus longirostris: 1 -Development of a representative sampling design for Italian seas; 2 -Evaluation of 2b-RAD protocol; 3 -Investigation of populations through biological data analysis. First of all we defined and accomplished a sampling design which properly represents all Italian seas. Then we used information and data about nursery areas distribution, abundance of populations and importance of P. longirostris in local fishery, to develop an experimental design that prioritize the most important areas to maximize the results with actual project funds. We introduced for the first time the use of 2b-RAD on this species, a genotyping method based on sequencing the uniform fragments produced by type IIB restriction endonucleases. Thanks to this method we were able to move from genetics to the more complex genomics. In order to proceed with 2b-RAD we performed several tests to identify the best DNA extraction kit and protocol and finally we were able to extract 192 high quality DNA extracts ready to be processed. We tested 2b-RAD with five samples and after high-throughput sequencing of libraries we used the software “Stacks” to analyze the sequences. We obtained positive results identifying a great number of SNP markers among the five samples. To guarantee a multidisciplinary approach we used the biological data associated to the collected samples to investigate differences between geographical samples. Such approach assures continuity with other project, for instance STOCKMED, which utilize a combination of molecular and biological analysis as well.

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.