Assessing the Performance of Simple Contracts Empirically: The Case of Percentage Fees

This paper estimates the cost of using simple percentage fees rather than the broker optimal Bayesian mechanism, using data for real estate transactions in Boston in the mid-1990s. This counterfactual analysis shows that interme- diaries using the best percentage fee mechanisms with fees ranging from 5.4% to 7.4% achieve 85% or more of the maximum profit. With the empirically observed 6% fees intermediaries achieve at least 83% of the maximum profit and with an optimally structured linear fee, they achieve 98% or more of the maximum profit

Complex pattern formation in reaction diffusion systems with spatially-varying parameters

Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer–Meinhardt reaction–diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection

Mode doubling and tripling in reaction-diffusion patterns on growing domains: A piece-wise linear model

Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system

Optimal Feedback Communication via Posterior Matching

In this paper we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback, termed posterior matching. Using this principle, we devise a (simple, sequential) generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions, achieving any rate below the corresponding mutual information. This provides a unified framework for optimal feedback communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that the Horstein scheme indeed attains the BSC capacity, settling a longstanding conjecture. We further provide closed form expressions for the error probability of the scheme over a range of rates, and derive the achievable rates in a mismatch setting where the scheme is designed according to the wrong channel model. Several illustrative examples of the posterior matching scheme for specific channels are given, and the corresponding error probability expressions are evaluated. The proof techniques employed utilize novel relations between information rates and contraction properties of iterated function systems.Comment: IEEE Transactions on Information Theor

Brane inflation and the WMAP data: a Bayesian analysis

The Wilkinson Microwave Anisotropy Probe (WMAP) constraints on string inspired ''brane inflation'' are investigated. Here, the inflaton field is interpreted as the distance between two branes placed in a flux-enriched background geometry and has a Dirac-Born-Infeld (DBI) kinetic term. Our method relies on an exact numerical integration of the inflationary power spectra coupled to a Markov-Chain Monte-Carlo exploration of the parameter space. This analysis is valid for any perturbative value of the string coupling constant and of the string length, and includes a phenomenological modelling of the reheating era to describe the post-inflationary evolution. It is found that the data favour a scenario where inflation stops by violation of the slow-roll conditions well before brane annihilation, rather than by tachyonic instability. Concerning the background geometry, it is established that log(v) > -10 at 95% confidence level (CL), where "v" is the dimensionless ratio of the five-dimensional sub-manifold at the base of the six-dimensional warped conifold geometry to the volume of the unit five-sphere. The reheating energy scale remains poorly constrained, Treh > 20 GeV at 95% CL, for an extreme equation of state (wreh ~ -1/3) only. Assuming the string length is known, the favoured values of the string coupling and of the Ramond-Ramond total background charge appear to be correlated. Finally, the stochastic regime (without and with volume effects) is studied using a perturbative treatment of the Langevin equation. The validity of such an approximate scheme is discussed and shown to be too limited for a full characterisation of the quantum effects.Comment: 65 pages, 15 figures, uses iopart. Shortened version, updated references. Matches publication up to appendix B kept on the arXi