Competition with Exclusive Contracts in Vertically Related Markets: An Equilibrium Non-Existence Result

I develop a model in the spirit of Ordover, Saloner, and Salop (1990), in which two upstream firms compete to supply a homogeneous input to two downstream firms, who compete in prices with differentiated products in a downstream market. Upstream firms are allowed to offer exclusive two-part tariff contracts to the downstream firms. I show that, under very general conditions, this game does not have a subgame-perfect equilibrium in pure strategies. The intuition is that variable parts in such an equilibrium would have to be pairwise-proof. But when variable parts are pairwise-proof, downstream competitive externalities are not internalized, and there exists a profitable deviation. I contrast this non-existence result with earlier papers that found equilibria in similar models

Gravitational wave sources: An overview

With full-sensitivity operation of the first generation of gravitational wave detectors now just around the corner, and with the LISA space-based detector entering its final design stage, I review the wide variety of predicted sources from the perspective of what further theoretical work may be needed to assist in their detection. Some sources, such as binary black holes, require good theoretical models from which search templates for matched filtering of the data streams can be computed. Others, such as searches for un-modelled bursts, require clever robust search algorithms not tied to detailed waveform models. Still others, such as searches for continuous waves from pulsars, are compute-bound and need improved efficient computer algorithms. The sensitivity of initial ground-based detectors will depend in part on how good we are at searching the data. In the longer term, the amount of information we can extract from the LISA data stream will depend in part on how good we are at removing strong signals so that we can recover the weaker ones as well

Standing in the Dark: Sloth and Stability, Paralysis and Perseverance in Book IV of the Confessio Amantis

In Book IV of the Confessio, things happen in the dark – the dark of night, of dreams, of despair, of secrecy, of treachery, of death. The medieval sin of accidia sets the pace for this beautifully constructed book, whose tales link and cross, as in a dance. Dido, Phyllis, the bad, the forgetful, and the obsessive lovers swing like slowing pendulums back to their starting points, and stop still. On the whole, their dance with Amans is a slow and stately pavane of the dead and desperate. This is Gower’s darkest book, though not the most bloody: Sloth is a sin of failure. Consequently, Book IV is interested in stones, especially statues, an aesthetic harmony between poetry and poetics which cannot be ignored. Statuary – as creation, as punishment, as static, as dynamic – grounds a complex and subtle discussion about stability, and stasis, perseverance and paralysis, beauty and monstrosity. This paper examines the paradoxes and thematic clusters arising out of the suicides and culminating in Araxarathen’s voluntary transformation to stone

The art and science of black hole mergers

The merger of two black holes is one of the most extraordinary events in the natural world. Made of pure gravity, the holes combine to form a single hole, emitting a strong burst of gravitational radiation. Ground-based detectors are currently searching for such bursts from holes formed in the evolution of binary stars, and indeed the very first gravitational wave event detected may well be a black-hole merger. The space-based LISA detector is being designed to search for such bursts from merging massive black holes in the centers of galaxies, events that would emit many thousands of solar masses of pure gravitational wave energy over a period of only a few minutes. To assist gravitational wave astronomers in their searches, and to be in a position to understand the details of what they see, numerical relativists are performing supercomputer simulations of these events. I review here the state of the art of these simulations, what we have learned from them so far, and what challenges remain before we have a full prediction of the waveforms to be expected from these events.Comment: 12 pages, 3 figures, Proceedings of "Growing Black Holes", Garching 21-25 June 200

Introduction to the Analysis of Low-Frequency Gravitational Wave Data

The space-based gravitational wave detector LISA will observe in the low-frequency gravitational-wave band (0.1 mHz up to 1 Hz). LISA will search for a variety of expected signals, and when it detects a signal it will have to determine a number of parameters, such as the location of the source on the sky and the signal's polarisation. This requires pattern-matching, called matched filtering, which uses the best available theoretical predictions about the characteristics of waveforms. All the estimates of the sensitivity of LISA to various sources assume that the data analysis is done in the optimum way. Because these techniques are unfamiliar to many young physicists, I use the first part of this lecture to give a very basic introduction to time-series data analysis, including matched filtering. The second part of the lecture applies these techniques to LISA, showing how estimates of LISA's sensitivity can be made, and briefly commenting on aspects of the signal-analysis problem that are special to LISA.Comment: 20 page

Sources of radiation from neutron stars

I give a brief introduction to the problem of detecting gravitational radiation from neutron stars. After a review of the mechanisms by which such stars may produce radiation, I consider the different search strategies appropriate to the different kinds of sources: isolated known pulsars, neutron stars in binaries, and unseen neutron stars. The problem of an all-sky survey for unseen stars is the most taxing one that we face in analysing data from interferometers. I describe the kinds of hierarchical methods that are now being investigated to reach the maximal sensitivity, and I suggest a replacement for standard Fourier-transform search methods that requires fewer floating-point operations for Fourier-based searches over large parameter spaces, and in addition is highly parallelizable, working just as well on a loosely coupled network of workstations as on a tightly coupled parallel computer.Comment: 11 pages, no figure

Getting Ready for GEO600 Data

Data of good quality is expected from a number of gravitational wave detectors within the next two years. One of these, GEO600, has special capabilities, such as narrow-band operation. I describe here the preparations that are currently being made for the analysis of GEO600 data.Comment: 17 pages, 7 figures, proceedings of Yukawa International Seminar 199

Low-Frequency Sources of Gravitational Waves: A Tutorial

Gravitational wave detectors in space, particularly the LISA project, can study a rich variety of astronomical systems whose gravitational radiation is not detectable from the ground, because it is emitted in the low-frequency gravitational wave band (0.1 mHz to 1 Hz) that is inaccessible to ground-based detectors. Sources include binary systems in our Galaxy and massive black holes in distant galaxies. The radiation from many of these sources will be so strong that it will be possible to make remarkably detailed studies of the physics of the systems. These studies will have importance both for astrophysics (most notably in binary evolution theory and models for active galaxies) and for fundamental physics. In particular, it should be possible to make decisive measurements to confirm the existence of black holes and to test, with accuracies better than 1%, general relativity's description of them. Other observations can have fundamental implications for cosmology and for physical theories of the unification of forces. In order to understand these conclusions, one must know how to estimate the gravitational radiation produced by different sources. In the first part of this lecture I review the dynamics of gravitational wave sources, and I derive simple formulas for estimating wave amplitudes and the reaction effects on sources of producing this radiation. With these formulas one can estimate, usually to much better than an order of magnitude, the physics of most of the interesting low-frequency sources. In the second part of the lecture I use these estimates to discuss, in the context of the expected sensitivity of LISA, what we can learn by from observations of binary systems, massive black holes, and the early Universe itself.Comment: 12 pages, 2 figure

Binary neutron star inspiral, LIGO, and cosmology

Recent work on the expected event rate of neutron star inspiral signals in the LIGO detector is summarized. The observed signals will be from inspirals at cosmological distances, and the important cosmological effects on the event rate and spectrum are discussed. This paper is a contribution to the proceedings of the 17th Texas Symposium held in Munich, 12-17 December 1994.Comment: 4 pages, REVTeX3.x, no figure

Gravitational Wave Astronomy: Delivering on the Promises

Now that LIGO and Virgo have begun to detect gravitational wave events with regularity, the field of gravitational wave astronomy is beginning to realise its promise. Binary black holes and, very recently, binary neutron stars have been observed, and we are already learning much from them. The future, with improved sensitivity, more detectors, and detectors like LISA in different frequency bands, has even more promise to open a completely hidden side of the Universe to our exploration.Comment: 12 pages, 1 figure, presented at a discussion meeting "Promises of gravitational wave astronomy" held at the Royal Society London, 11 September 201