A generalization of Szebehely's inverse problem of dynamics in dimension three

Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the problem is to find a potential V such that the Lagrangian L = T - V, where T is the standard Euclidean kinetic energy function, generates integral curves which include the given family of curves. Our more general way of posing the problem makes use of ideas of the inverse problem of the calculus of variations and essentially consists of allowing more general kinetic energy functions, with a metric which is still constant, but need not be the standard Euclidean one. In developing our generalization, we review and clarify different aspects of the existing literature on the problem and illustrate the relevance of the newly introduced additional freedom with many examples.Comment: 23 pages, to appear in Rep. Math. Phy

Detection of variable frequency signals using a fast chirp transform

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a Fast Chirp Transform (FCT) analogous to the Fast Fourier Transform (FFT). Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest

A generalization of Szebehely's inverse problem of dynamics

The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify different aspects of the current state of the art of the problem (mainly restricted to the case of planar curves), and then develop our more general approach.Comment: 21 pages, to appear in Rep. Math. Phy

Does Service Bundling Reduce Churn?

We examine whether bundling in telecommunications services reduces churn using a series of large, independent cross sections of household decisions. To identify the effect of bundling, we construct a pseudo-panel dataset and utilize a linear, dynamic panel-data model, supplemented by nearest-neighbor matching. We find bundling does reduce churn for all three "triple-play" services. However, the effect is only "visible" during times of turbulent demand. We also find evidence that broadband was substituting for pay television in 2009. This analysis highlights that bundling helps with customer retention in service industries, and may play an important role in preserving contracting markets.Bundle, Service, Churn, Triple Play, Telecommunications, Cable, Broadband, Telephone, Screen

Do Incumbents Improve Service Quality in Response to Entry? Evidence from Airlines’ On-Time Performance

We examine if and how incumbent firms respond to entry, and entry threats, using non-price modes of competition. Our analysis focuses on service quality within the airline industry. We find that incumbent on-time performance actually worsens in response to entry, and even entry threats, by Southwest Airlines. Given Southwest’s general superiority in on-time performance, this result is consistent with equilibria of theoretical models of quality and price competition, which generally predict differentiation along quality. We corroborate this intuition with further analysis, showing there is no notable response by incumbents when an airline with average on-time performance (Continental) threatens to enter or enters a route.

Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type

We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system

The Welfare Impact of Reducing Choice in Medicare Part D: A Comparison of Two Regulation Strategies

Medicare’s prescription drug benefit (Part D) has been its largest expansion of benefits since 1965. Since the implementation of Part D, many regulatory proposals have been advanced in order to improve this government-created market. Among the most debated are proposals to limit the number of options, in response to concerns that there are “too many” plans. In this paper we study the welfare impact of two feasible approaches (of similar magnitude) toward limiting the number of Part D plans: reducing the maximum number of plans each firm can offer per region and removing plans that provide doughnut hole coverage. To this end, we propose and estimate a model of market equilibrium, which we later use to evaluate the impact of regulating down the number of Part D plans. Our counterfactuals provide an important assessment of the losses to consumers (and producers) resulting from government limitations on choice. These losses must be weighed against the widely discussed expected gains due to reduced search costs from limiting options. We find that the annual search costs should be at least two thirds of the average monthly premium in order to justify a regulation that allows only two plans per firm. However, this number would be substantially lower if the limitation in the number of plans is coupled with a decrease in product differentiation (e.g., by removing plans that cover the doughnut hole). For validation purposes, we also assess the impact of a recent major merger, and find that our model performs very well out of sample.Medicare Part D, regulation, number of plans, product differentiation, discrete choice

Racial Bias in Expert Quality Assessment: A Study of Newspaper Movie Reviews

Newspaper critics' movie reviews are often used by potential movie viewers as signals of expert quality assessment. In this paper, we assess if there is any racial bias in these critics' reviews, and if so, what impact these biases have on viewer demand. To do this, we develop a dataset that tracks ratings from 68 popular movie critics for 566 movies released in the U.S. between 2003 and 2007. The data also include measures of movie production costs, marketing expenditures, type of movie (i.e. genre, MPAA rating, etc.), actor and director quality measures, audience tastes and critics' gender, experience and race. Despite inclusion of all these controls for movie quality and other drivers of critic ratings, we find that ratings for movies with a black lead actor and all white supporting cast are approximately 6% lower than for other racial compositions. These results appear consistent with implicit discrimination. Using estimates of the impact of critics' ratings on movie revenues, we find that lower critic ratings for black lead-white support movies translate into lost revenues of up to 4% or about $2.57 million on average. In sum, prejudice concerning race roles (e.g., the race of the leader versus supporters/followers) can have a direct impact on critic quality assessment, and thereby alter market outcomes.racial bias, quality assessment, expert ratings, movies