Topological entropy in totally disconnected locally compact groups

Let $G$ be a topological group, let $\phi$ be a continuous endomorphism of $G$ and let $H$ be a closed $\phi$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is, $$h_{top}(\phi)=h_{top}(\phi\restriction_H)+h_{top}(\bar\phi)\,,$$ where $\bar\phi:G/H\to G/H$ is the map induced by $\phi$. We concentrate on the case when $G$ is locally compact totally disconnected and $H$ is either compact or normal. Under these hypotheses, we show that the above additivity property holds true whenever $\phi H=H$ and $\ker(\phi)\leq H$. As an application we give a dynamical interpretation of the scale $s(\phi)$, by showing that $\log s(\phi)$ is the topological entropy of a suitable map induced by $\phi$. Finally, we give necessary and sufficient conditions for the equality $\log s(\phi)=h_{top}(\phi)$ to hold.Comment: 18 page

Algebraic Yuzvinski Formula

In 1965 Adler, Konheim and McAndrew defined the topological entropy for continuous self-maps of compact spaces. Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is the so-called Yuzvinski Formula, showing that the value of the topological entropy of a full solenoidal automorphism coincides with the Mahler measure of its characteristic polynomial. In two papers of 1979 and 1981 Peters gave a different definition of entropy for automorphisms of locally compact Abelian groups. This notion has been appropriately modified forendomorphisms in two recent papers, where it is called algebraic entropy. The goal of this paper is to prove a perfect analog of the Yuzvinski Formula for the algebraic entropy, namely, the Algebraic Yuzvinski Formula, giving the value of the algebraic entropy of an endomorphism of a finite-dimensional rational vector space as the Mahler measure of its characteristic polynomial. Finally, several applications of the Algebraic Yuzvinski Formula and related open problems are discussed.Comment: 32 page

A Hybrid Drift Diffusion Model: Derivation, Weak Steady State Solutions and Simulations

In this paper we derive a new hybrid model for drift di usion equations. This model provides a description of the quantum phenomena in the parts of the device where they are relevant, and degenerates to a semiclassical model where quantum e ects are negligible, so that the system can be considered classically. The study of quantum correction to the equation of state of an electron gas in a semiconductor with the assumption of localized quantum e ects leads to a further condition on the classical-quantum interface. Moreover, we prove the existence of weak solutions for our hybrid model. Finally, we present numerical results for di erent devices, by means of Colsys software

Measuring comovements by regression quantiles

This paper develops a rigorous econometric framework to investigate the structure of codependence between random variables and to test whether it changes over time. Our approach is based on the computation - over both a test and a benchmark period - of the conditional probability that a random variable yt is lower than a given quantile, when the other random variable xt is also lower than its corresponding quantile, for any set of prespecified quantiles. Time-varying conditional quantiles are modeled via regression quantiles. The conditional probability is estimated through a simple OLS regression. We illustrate the methodology by investigating the impact of the crises of the 1990s on the major Latin American equity markets returns. Our results document significant increases in equity return co-movements during crises consistent with the presence of financial contagion. JEL Classification: C14, C22, G15codependence, conditional quantiles, semi-parametric

The Contagion Box: Measuring Co-Movements in Financial Markets by Regression Quantiles

We propose a semi-parametric approach to investigate whether co-dependence across markets increase in periods of extreme returns. Given that returns on one market fall in the extreme tail of their own distribution, we compute the conditional probability that returns on another market will also take on extreme values. An application to the “tequila†crisis is performedcontagion, conditional probabilities, CAViaR

Financial integration of new EU Member States

This study assesses the degree of financial integration for a selected number of new EU member states between themselves and with the euro zone. Within the framework of a factor model for market returns, we measure integration as the amount of variance explained by the common factor relative to the local components. We show that this measure of integration coincides with return correlation. Correlations are proxied by comovements, estimated via a regression quantile-based methodology. We find that the largest new member states, the Czech Republic, Hungary and Poland, exhibit strong comovements both between themselves and with the euro area. As for smaller countries, only Estonia and to a less extent Cyprus show increased integration both with the euro zone and the block of large economies. In the bond markets, we document an increase in integration only for the Czech Republic versus Germany and Poland. JEL Classification: C32, F30, G12integration, new EU member states, regression quantile

Smart Specialisation Strategies for Supporting Europe 2020 Vision. Looking at the American Experience: the Case of the Boston Area

These reflections aim to highlight the crucial challenge that European Regions are called to face applying the ‘Research and Innovation Strategies for Smart Specialization’ policy for pursuing the virtuous implementation of EU Cohesion Policy and ‘Europe 2020’ Agenda. The original cultural style of the ‘US Smart Specialization model’, supported by the ‘cluster theory’ and the ‘innovation paradigm’, represents a significant lesson in Boston area

The logical consistency of time inconsistency: A theory of forward-looking behavior

This paper argues that, to be forward-looking in a logically consistent sense, a decision maker must take account of his overall well-being, not just his instantaneous utility, in all future periods. However, such a decision-maker is necessarily time inconsistent. The paper explores the relationship between how a decision-maker discounts well-being and how he discounts instantaneous utility. It also provides simple axiomatizations of preferences that exhibit forward-looking behavior, including quasi-hyperbolic discounting (Phelps and Pollack (1968) [18]; Laibson (1997) [12]). Finally, the paper provides a rigorous way to think about welfare criteria in models with time inconsistent agents