Endogenous Growth in an Open Economy and the Real Exchange Rate

This paper is a step in the direction of a larger research project aimed at determining the long run equilibrium value of the euro/dollar real exchange rate. Given this value, one could then give a precise meaning to the notion of undervaluation or overvaluation of the euro, and calculate its misalignment. The problem however arises of how to assess the reliability of such misalignment calculations. In our opinion, we must have a benchmark (namely a period in which we exactly know from outside sources the misalignment itself), against which we can test the validity of the model underlying our calculations. This of course is not (yet) possible for the euro, so that all the calculations of the misalignment of the euro that have been made can only be compared with one another, without knowing which is the good one. Hence, before building a model to be applied to the euro/dollar, we tested our ideas incorporating them in a basic model to be applied to the lira/dollar in a period in which we do exactly know the actual misalignment of the lira from outside sources.NATREX, equilibrium exchange rates, international capital flows, misalignment

A manifold of pure Gibbs states of the Ising model on a Cayley tree

We study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited

The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?

The aim of this paper is to develop a continuous time exchange rate model that allows for heterogeneity of the agents’ beliefs, in order to explore non-linearities and possible chaotic behaviour. The theoretical model contains an intrinsic non-linearity that gives rise to a jerk differential equation, which is in principle capable of generating chaos. The model is econometrically estimated in continuous time with Euro/Dollar data and examined for the possible presence of chaotic motion. Our results indicate that the possibility of chaotic dynamics has to be rejected.exchange rate, chaos, jerk equation, continuous time econometrics

A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane

In this paper we construct many `new' Gibbs states of the Ising model on the Lobachevsky plane, the millefeuilles. Unlike the usual states on the integer lattices, our foliated states have infinitely many interfaces. The interfaces are rigid and fill the Lobachevsky plane with positive density.Comment: 25 pages, 7 figure

RLE Plots: Visualising Unwanted Variation in High Dimensional Data

Unwanted variation can be highly problematic and so its detection is often crucial. Relative log expression (RLE) plots are a powerful tool for visualising such variation in high dimensional data. We provide a detailed examination of these plots, with the aid of examples and simulation, explaining what they are and what they can reveal. RLE plots are particularly useful for assessing whether a procedure aimed at removing unwanted variation, i.e. a normalisation procedure, has been successful. These plots, while originally devised for gene expression data from microarrays, can also be used to reveal unwanted variation in many other kinds of high dimensional data, where such variation can be problematic.Comment: 9 pages, 3 figure

Glassy states: the free Ising model on a tree

We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards-Anderson parameter, measuring the variance of the (random) magnetization obtained from drawing boundary conditions from the free state