Taylor formula for Kolmogorov equations

After briefly discuss the natural homogeneous Lie group structure induced by Kolmogorov equations in chapter one, we define an intrinsic version of Taylor polynomials and Holder spaces in chapter two. We also compare our definition with others yet known in literature. In chapter three we prove an analogue of Taylor formula, that is an estimate of the remainder in terms of the homogeneous metric.

First assessment on genetic structure and phylogeography of Mediterranean blue shark (prionace glauca, L. 1758) population using mitochondrial gene variation: a comparison with the Atlantic.

The blue shark, Prionace glauca, is one of the most vagile shark species worldwide distributed. The particular body shape allows blue sharks make transoceanic movements, leading to a circumglobal distribution. Due to its reproductive cycle, an extraordinarily high number of specimens is globally registered but, even if it is still a major bycatch of longline fishery rather than a commercial target, it is characterized by a high vulnerability. In this perspective it is important to increase the amount of informations regarding its population extent in the different worldwide areas, evaluating the possible phylogeographic patterns between different locations. This study, included in the "MedBlueSGen" European project, aims exactly at filling a gap in knowledges regarding the genetic population structure of the Mediterranean blue sharks, which has never been investigated before, with a comparison with the North-Eastern Atlantic blue shark population. To reach this objective, we used a dataset of samples from different Mediterranean areas implementing it with some samples from North-Eastern Atlantic. Analyzing the variability of the two mitochondrial markers control region and cytochrome b, with the design of new species-specific primer pairs, we assessed the mitochondrial genetic structure of Mediterranean and North-Eastern Atlantic samples, focusing on the analysis of their possible connectivity, and we tried to reconstruct their demographic history and population size. Data analyses highlighted the absence of a genetic structuring within the Mediterranean and among it and North-Eastern Atlantic, suggesting that the Strait of Gibraltar doesn't represent a phylogeographic barrier. These results are coherent to what has been found in similar investigations on other worldwide blue shark populations. Analysis of the historical demographic trend revealed a general stable pattern for the cytochrome-b and a slightly population expansion for the control region marker.

Quality and Aspect based Argument Generation

Natural Language Processing has always been one of the most popular topics in Artificial Intelligence. Argument-related research in NLP, such as argument detection, argument mining and argument generation, has been popular, especially in recent years. In our daily lives, we use arguments to express ourselves. The quality of arguments heavily impacts the effectiveness of our communications with others. In professional fields, such as legislation and academic areas, arguments of good quality play an even more critical role. Therefore, argument generation with good quality is a challenging research task that is also of great importance in NLP. The aim of this work is to investigate the automatic generation of arguments with good quality, according to the given topic, stance and aspect (control codes). To achieve this goal, a module based on BERT [17] which could judge an argument's quality is constructed. This module is used to assess the quality of the generated arguments. Another module based on GPT-2 [19] is implemented to generate arguments. Stances and aspects are also used as guidance when generating arguments. After combining all these models and techniques, the ranks of the generated arguments could be acquired to evaluate the final performance. This dissertation describes the architecture and experimental setup, analyzes the results of our experimentation, and discusses future directions.