Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Synthesis of thioenol ether functionalized cyclooctyne and its orthogonal cycloaddition sequence

In this work, the synthesis of a new bifunctionalized cyclooctyne for a possible layer by layer surface functionalization is presented. The main objective is to find a more stable molecule than the literature known methyl enol ether substituted cyclooctyne. Accordingly, the two target functionalities are an internal alkyne group and a vinyl methyl sulfide group. The synthesis was achieved in 9 steps and consists first of all in the preparation of an aldehyde starting from 1,5-cyclooctadiene with a cyclopropanation reaction followed by a reduction and the SWERN oxidation to an aldehyde. The new functionality was introduced by exploiting the WITTIG reaction. For the alkyne group a bromination followed by a double elimination gave good results. The reactivity of the new molecule was tested using a sequential application of SPAAC and iEDDA reactions, comparing it with the cyclooctyne functionalized with a methyl enol ether. Concerning the comparison of both compounds the sulfur ether is significantly slower and therefore more stable. It will be tested in the future for surface functionalization from the KOERT group.

Orthogonal chirp division multiplexing: performance evaluation in the presence of phase noise

In Beyond 5G technologies, Terahertz communications will be used: frequency bands between 100 GHz and 10 THz will be exploited in order to have higher throughput and lower latency. Those frequency bands suffer from several impairments, and it is thought that phase noise is one of the most significant. Orthogonal Chirp Division Multiplexing (OCDM) might be used in Beyond 5G communications, thanks to its robustness to multipath fading: it outperforms Orthogonal Frequency Division Multiplexing (OFDM) systems. The aim of this thesis is to find a suitable model for describing phase noise in Terahertz communications, and to study the performance of an OCDM system affected by this impairment. After this, a simple compensation scheme is introduced, and the improvement that it provides is analysed. The thesis is organized as follow: in the first chapter Terahertz communications and Beyond 5G are introduced, in the second chapter phase noise is studied, in the third chapter OCDM is analysed, and in the fourth chapter numerical results are presented.

A novel approach to Non-Orthogonal Random Access with application to NB-IoT NTN systems

In the Massive IoT vision, millions of devices need to be connected to the Internet through a wireless access technology. However, current IoT-focused standards are not fully prepared for this future. In this thesis, a novel approach to Non-Orthogonal techniques for Random Access, which is the main bottleneck in high density systems, is proposed. First, the most popular wireless access standards are presented, with a focus on Narrowband-IoT. Then, the Random Access procedure as implemented in NB-IoT is analyzed. The Non-Orthogonal Random Access technique is presented next, along with two potential algorithms for the detection of non-orthogonal preambles. Finally, the performance of the proposed solutions are obtained through numerical simulations.

Fabrication of 2D and 3D microelectrode arrays for amperometric dopamine sensing: towards a metal free approach to bioelectronics

Dopamine is a neurotransmitter which has a role in several psychiatric and neurological disorders. In-vivo detection of its concentration at the microscopic scale would benefit the study of these conditions and help in the development of therapies. The ideal sensor would be biocompatible, able to probe concentrations in microscopic volumes and sensitive to the small physiological concentrations of this molecule (10 nM - 1 μM). The ease of oxidation of dopamine makes it possible to detect it by electrochemical methods. An additional requirement in this kind of experiments when run in water, though, is to have a large potential window inside which no redox reactions with water take place. A promising class of materials which are being explored is the one of pyrolyzed photoresists. Photoresists can be lithographically patterned with micrometric resolution and after pyrolysis leave a glassy carbon material which is conductive, biocompatible and has a large electrochemical water window. In this work I developed a fabrication procedure for microelectrode arrays with three dimensional electrodes, making the whole device using just a negative photoresist called SU8. Making 3D electrodes could be a way to enhance the sensitivity of the electrodes without occupying a bigger footprint on the device. I characterized the electrical, morphological, and electrochemical properties of these electrodes, in particular their sensitivity to dopamine. I also fabricated and tested a two dimensional device for comparison. The three dimensional devices fabricated showed inferior properties to their two dimensional counter parts. I found a possible explanation and suggested some ways in which the fabrication could be improved.

Neural Network based Non Orthogonal Random Access for 6G NTN-IoT

Pervasive and distributed Internet of Things (IoT) devices demand ubiquitous coverage beyond No-man’s land. To satisfy plethora of IoT devices with resilient connectivity, Non-Terrestrial Networks (NTN) will be pivotal to assist and complement terrestrial systems. In a massiveMTC scenario over NTN, characterized by sporadic uplink data reports, all the terminals within a satellite beam shall be served during the short visibility window of the flying platform, thus generating congestion due to simultaneous access attempts of IoT devices on the same radio resource. The more terminals collide, the more average-time it takes to complete an access which is due to the decreased number of successful attempts caused by Back-off commands of legacy methods. A possible countermeasure is represented by Non-Orthogonal Multiple Access scheme, which requires the knowledge of the number of superimposed NPRACH preambles. This work addresses this problem by proposing a Neural Network (NN) algorithm to cope with the uncoordinated random access performed by a prodigious number of Narrowband-IoT devices. Our proposed method classifies the number of colliding users, and for each estimates the Time of Arrival (ToA). The performance assessment, under Line of Sight (LoS) and Non-LoS conditions in sub-urban environments with two different satellite configurations, shows significant benefits of the proposed NN algorithm with respect to traditional methods for the ToA estimation.