Multi-scalar critical theories: first steps for a non perturbative functional renormalization group analysis

In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.

Work environments implementation for genomic reporting and analytics

A global italian pharmaceutical company has to provide two work environments that favor different needs. The environments will allow to develop solutions in a controlled, secure and at the same time in an independent manner on a state-of-the-art enterprise cloud platform. The need of developing two different environments is dictated by the needs of the working units. Indeed, the first environment is designed to facilitate the creation of application related to genomics, therefore, designed more for data-scientists. This environment is capable of consuming, producing, retrieving and incorporating data, furthermore, will support the most used programming languages for genomic applications (e.g., Python, R). The proposal was to obtain a pool of ready-togo Virtual Machines with different architectures to provide best performance based on the job that needs to be carried out. The second environment has more of a traditional trait, to obtain, via ETL (Extract-Transform-Load) process, a global datamodel, resembling a classical relational structure. It will provide major BI operations (e.g., analytics, performance measure, reports, etc.) that can be leveraged both for application analysis or for internal usage. Since, both architectures will maintain large amounts of data regarding not only pharmaceutical informations but also internal company informations, it would be possible to digest the data by reporting/ analytics tools and also apply data-mining, machine learning technologies to exploit intrinsic informations. The thesis work will introduce, proposals, implementations, descriptions of used technologies/platforms and future works of the above discussed environments.