Italian texts as networks: Topological measurements, Zipf and Heaps' laws

In questa tesi si è studiato un corpus di importanti testi della letteratura Italiana utilizzando la teoria dei network. Le misure topologiche tipiche dei network sono state calcolate sui testi letterari, poi sono state studiate le loro distribuzioni e i loro valori medi, per capire quali di esse possono distinguere un testo reale da sue modificazioni. Inoltre si è osservato come tutti i testi presentino due importanti leggi statistiche: la legge di Zipf e quella di Heaps.

Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups

The main task of this work is to present a concise survey on the theory of certain function spaces in the contexts of Hörmander vector fields and Carnot Groups, and to discuss briefly an application to some polyharmonic boundary value problems on Carnot Groups of step 2.

Fibered knots and links in lens spaces

La tesi propone alcuni esempi di link fibrati in spazi lenticolari. Sfruttando la compatibilità fra le mosse di chirurgia intera e la nozione di open book decomposition, si ricava un esempio di link fibrato prima in L(p,1), per poi generalizzarlo a L(p,q). Si conclude determinando una struttura di contatto equivalente alla open book relativa agli spazi del tipo L(p,1).

Recycling the city: a sustainable planning framework to reduce, reuse and recycle urban residual spaces

Cities are key locations where Sustainability needs to be addressed at all levels, as land is a finite resource. However, not all urban spaces are exploited at best, and land developers often evaluate unused, misused, or poorly-designed urban portions as impracticable constraints. Further, public authorities lose the challenge to enable and turn these urban spaces into valuable opportunities where Sustainable Urban Development may flourish. Arguing that these spatial elements are at the centre of SUD, the paper elaborates a prototype in the form of a conceptual strategic planning framework, committed to an effective recycling of the city spaces using a flexible and multidisciplinary approach. Firstly, the research focuses upon a broad review of Sustainability literature, highlighting established principles and guidelines, building a sound theoretical base for the new concept. Hence, it investigates origins, identifies and congruently suggests a definition, characterisation and classification for urban “R-Spaces”. Secondly, formal, informal and temporary fitting functions are analysed and inserted into a portfolio meant to enhance adaptability and enlarge the choices for the on-site interventions. Thirdly, the study outlines ideal quality requirements for a sustainable planning process. Then, findings are condensed in the proposal, which is articulated in the individuation of tools, actors, plans, processes and strategies. Afterwards, the prototype is tested upon case studies: Solar Community (Casalecchio di Reno, Bologna) and Hyllie Sustainable City Project, the latter developed via an international workshop (ACSI-Camp, Malmö, Sweden). Besides, the qualitative results suggest, inter alia, the need to right-size spatial interventions, separate structural and operative actors, involve synergies’ multipliers and intermediaries (e.g. entrepreneurial HUBs, innovation agencies, cluster organisations…), maintain stakeholders’ diversity and create a circular process open for new participants. Finally, the paper speculates upon a transfer of the Swedish case study to Italy, and then indicates desirable future researches to favour the prototype implementation.

Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.