Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Quantum Riemannian geometry on graphs for gauge field theory

In questo lavoro estendiamo concetti classici della geometria Riemanniana al fine di risolvere le equazioni di Maxwell sul gruppo delle permutazioni $S_3$. Cominciamo dando la strutture algebriche di base e la definizione di calcolo differenziale quantico con le principali proprietà. Generalizziamo poi concetti della geometria Riemanniana, quali la metrica e l'algebra esterna, al caso quantico. Tutto ciò viene poi applicato ai grafi dando la forma esplicita del calcolo differenziale quantico su $\mathbb{K}(V)$, della metrica e Laplaciano del secondo ordine e infine dell'algebra esterna. A questo punto, riscriviamo le equazioni di Maxwell in forma geometrica compatta usando gli operatori e concetti della geometria differenziale su varietà che abbiamo generalizzato in precedenza. In questo modo, considerando l'elettromagnetismo come teoria di gauge, possiamo risolvere le equazioni di Maxwell su gruppi finiti oltre che su varietà differenziabili. In particolare, noi le risolviamo su $S_3$.

Robotics and neurodevelopmental disorder: design and implementation of a system of engagement metrics in human-robot interactions.

In the recent decades, robotics has become firmly embedded in areas such as education, teaching, medicine, psychology and many others. We focus here on social robotics; social robots are designed to interact with people in a natural and interpersonal way, often to achieve positive results in different applications. To interact and cooperate with humans in their daily-life activities, robots should exhibit human-like intelligence. The rapid expansion of social robotics and the existence of various kinds of robots on the market have allowed research groups to carry out multiple experiments. The experiments carried out have led to the collections of various kinds of data, which can be used or processed for psychological studies, and studies in other fields. However, there are no tools available in which data can be stored, processed and shared with other research groups. This thesis proposes the design and implementation of visual tool for organizing dataflows in Human Robot Interaction (HRI).

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.

Evaluation Metrics and Transfer Learning for Sales Prediction

Sales prediction plays a huge role in modern business strategies. One of it's many use cases revolves around estimating the effects of promotions. While promotions generally have a positive effect on sales of the promoted product, they can also have a negative effect on those of other products. This phenomenon is calles sales cannibalisation. Sales cannibalisation can pose a big problem to sales forcasting algorithms. A lot of times, these algorithms focus on sales over time of a single product in a single store (a couple). This research focusses on using knowledge of a product across multiple different stores. To achieve this, we applied transfer learning on a neural model developed by Kantar Consulting to demo an approach to estimating the effect of cannibalisation. Our results show a performance increase of between 10 and 14 percent. This is a very good and desired result, and Kantar will use the approach when integrating this test method into their actual systems.