Symbolic dynamics and relatively hyperbolic groups

We study the action of a relatively hyperbolic group on its boundary, by methods of symbolic dynamics. Under a condition on the parabolic subgroups, we show that this dynamical system is finitely presented. We give examples where this condition is satisfied, including geometrically finite kleinian groups.Comment: Revision, 16 pages, 1 figur

A Product Shape Congruity Measure via Entropy in Shape Scale Space

Product shape is one of the factors that trigger preference decisions of customers. Congruity of shape elements and deformation of shape from the prototype are two factors that are found to influence aesthetic response, hence preference. We propose a measure to indirectly quantify congruity of different parts of the shape and the degree to which the parts deviate from a sphere, i.e. our choice of the prototype, without explicitly defining parts and their relations. The basic signals and systems concept that we use is the entropy. Our measure attains its lowest value for a volume enclosed by a sphere. On one hand, deformations from the prototype cause an increase in the measure. On the other hand, as deformations create congruent parts, our measure decreases due to the attained harmony. Our preliminary experimental results are consistent with our expectations.Comment: Proceedings of EUSIPCO 2017 Satellite Workshops, Corresponding Workshop: Creative Design and Advanced Manufacturing: An emerging application area for Signals and System

"A Regime Switching Analysis of Exchange Rate Pass-through"

We investigate changes in the pricing policies of exporters, including changes in the exchange rate pass-through elasticity, and changes in the elasticities of variables that affect the firm’s markup. We set up a theoretical model of optimal export pricing in order to illustrate how changes in the pass-through elasticity can emerge together with changes in other elasticities in the pricing policy. Based on our theoretical formulation, we empirically study changes in all the elasticities that define the pricing policy as opposed to focusing only on the exchange rate pass-through. In the empirical model, we assume that in every period exporters get to set prices by following either a “high pass-through” or a “low passthrough” pricing policy. The transition from one policy to the other is governed by a Markov process whose transition probabilities depend on economic fundamentals. We estimate the model using data we have collected on 35 lines of imported cars to the US, from seven exporting countries, for the 1980-2004 period. We find that the “low pass-through” regime is characterized by: a low exchange rate pass-through; a low response to misalignments in the firm’s relative price; a low volatility of technology and preference shocks; and a higher duration than the high pass-through regime. Monetary stability and the market structure are significant factors behind the switching of pricing policies. Ceteris paribus, monetary stability measured as the cross-country inflation differential explains abut 22% of the year-to-year variation in the exchange rate pass-through coefficient; when measured by the volatility of the exchange rate, it explains 37%. Market concentration measured by the Herfindahl index explains about 40%.Exchange Rate Pass-through; Markov Regime Switching; Export Pricing