Computing the associatied cycles of certain Harish-Chandra modules

Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm rank}(K_\mathbb{R})$. In \cite{MPVZ} we proved that for any representation $X$ of Gelfand-Kirillov dimension $\frac{1}{2}\dim(G_{\mathbb{R}}/K_{\mathbb{R}})$, the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing $X$ is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In this paper we compute these coefficients explicitly

IMPACT OF BREXIT ON UK-EU TRADE RELATIONSHIP

This research analyses the different scenarios for the trade relationship between the UK and the EU after Brexit. It analyses three possible models and covers ten years after Brexit. The first one, using the comparative methodology, examines the possibility and consequences of reaching a deal under existing arrangements that the EU has with non-EU countries. The second model will be presented in case of „no-deal” and trade relations under WTO rules. The third model will be analyzed by the computable general equilibrium (CGE) model. All these models suggest that Brexit will change the future trade relationship between UK and EU economy, and consequently will have a significant impact on the UK economy. This is because researches in this context suggest that the EU will impose several restrictions on the British economy after Brexit, which will ultimately have a significant negative impact on its trade within the European market

Reasoning with Defeasible Reasons

The information age is marked by a tremendous amount of incoming information. Even so, we are almost always dealing with information that is only incomplete or even conflicting. This thesis investigates the logical principles behind our abilities to find out the right answers and recover from errors that we make in drawing hasty conclusions. Consider, for example, the following headline: "NASA warns of an asteroid capable of ending human civilization approaching''. The headline gives you a reason to conclude that the Earth is on a collision course. However, were you to read below the headline that although the asteroid is approaching closer, it will pass by the Earth at a distance over sixteen times farther than our Moon, you would doubt your reasons to conclude that the collision is about to happen. This commonsense ability to question old reasons in the wake of new information is known as "defeasibility'' of reasons. Defeasible reasons came to the attention of AI researchers who realized that the design of intelligent computer programs requires principled understanding of our commonsense abilities. The relevance of commonsense reasoning is nowadays emphasized by the need to increase the transparency of AI systems, but also by the fact that AI systems still underperform in commonsense reasoning tasks.This thesis investigates the role of logic in commonsense reasoning. Firstly, it develops logical systems that are successful in modeling defeasible and commonsense reasoning. Secondly, the thesis shows why commonsense reasoners are bound to reason logically, despite being prone to errors