On reconstructing n-point configurations from the distribution of distances or areas

One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this distribution. After giving some counterexamples, we prove that this is the case for the vast majority of configurations. In the second part of the paper, the distribution of areas of sub-triangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.Comment: 21 pages, late

Lossless Representation of Graphs using Distributions

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their sub-triangles. In the second part, we propose graph representations in terms of one-dimensional distributions (e.g., distribution of the node weights, sum of adjacent weights, etc.). For the case when the weights of the graph are real-valued vectors, we show that all graphs, except for a set of measure zero, are uniquely determined, up to isomorphism, from these distributions. The motivating application for this paper is the problem of browsing through large sets of graphs.Comment: 19 page

Are Prices Really Affected by Mergers?

During the 80s, several empirical studies have shown a positive correlation between concentration, prices and profits. It is well known that these estimates all suffer from simultaneity bias: market structure and prices are affected by common factors, some of which are not observable, which rules out any causal interpretation of cross-sectional correlations. Mergers are an interesting instrument to identify the (static) impact of concentration on prices, since they induce breaks in strategic interactions between actors. The few ex post studies on mergers that are currently available are difficult to generalize, because they pertain to specific markets. This study looks more systematically to selling prices in 63 sectors observed between 1989 and 2002. The approach that has been chosen is a difference in differences approach, applied to price movements around mergers. The rate of inflation in a sector where a merger has occurred is compared to a counterfactual. In a simple framework, in line with previous studies (McCabe 2002), this counterfactual would be built as the mean of inflation rates in other sectors. This paper focuses on more relevant estimates, provided by a factor model. This methodology allows tracking the profile of prices around mergers. We separate mergers between French firms and mergers between other European firms controlled by European authorities (and thus assumed to have affected the common market). We also distinguish mergers having led to an in-depth inquiry by competition authorities (« phase 2 ») and those benefiting from a shorter procedure (« phase 1 »). We observe an acceleration of price movements around the most important of French mergers, but not for the ones authorized under phase 1. We also observe a break in price movements for mergers between foreign firms examined by the European Commission, generally in the other direction.mergers, prices, factor models