Cosmological Equations for a Thick Brane

Generalized Friedmann equations governing the cosmological evolution inside a thick brane embedded in a five-dimensional Anti-de Sitter spacetime are derived. These equations are written in terms of four-dimensional effective brane quantities obtained by integrating, along the fifth dimension, over the brane thickness. In the case of a Randall-Sundrum type cosmology, different limits of these effective quantities are considered yielding cosmological equations which interpolate between the thin brane limit (governed by unconventional brane cosmology), and the opposite limit of an ``infinite'' brane thickness corresponding to the familiar Kaluza-Klein approach. In the more restrictive case of a Minkowski bulk, it is shown that no effective four-dimensional reduction is possible in the regimes where the brane thickness is not small enough.Comment: 23 pages, Latex, 2 figure

Can Lightcone Fluctuations be Probed with Cosmological Backgrounds?

Finding signatures of quantum gravity in cosmological observations is now actively pursued both from the theoretical and the experimental side. Recent work has concentrated on finding signatures of light-cone fluctuations in the CMB. Because in inflationary scenarios a Gravitational Wave Background (GWB) is always emitted much before the CMB, we can ask, in the hypothesis where this GWB could be observed, what is the imprint of light cone fluctuations on this GWB. We show that due to the flat nature of the GWB spectrum, the effect of lightcone fluctuations are negligible.Comment: 10 pages, references adde

Finite-State Dimension and Lossy Decompressors

This paper examines information-theoretic questions regarding the difficulty of compressing data versus the difficulty of decompressing data and the role that information loss plays in this interaction. Finite-state compression and decompression are shown to be of equivalent difficulty, even when the decompressors are allowed to be lossy. Inspired by Kolmogorov complexity, this paper defines the optimal *decompression *ratio achievable on an infinite sequence by finite-state decompressors (that is, finite-state transducers outputting the sequence in question). It is shown that the optimal compression ratio achievable on a sequence S by any *information lossless* finite state compressor, known as the finite-state dimension of S, is equal to the optimal decompression ratio achievable on S by any finite-state decompressor. This result implies a new decompression characterization of finite-state dimension in terms of lossy finite-state transducers.Comment: We found that Theorem 3.11, which was basically the motive for this paper, was already proven by Sheinwald, Ziv, and Lempel in 1991 and 1995 paper

Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters

Precision Lattice Calculation of SU(2) 't Hooft loops

The [dual] string tension of a spatial 't Hooft loop in the deconfined phase of Yang-Mills theory can be formulated as the tension of an interface separating different Z_N deconfined vacua. We review the 1-loop perturbative calculation of this interface tension in the continuum and extend it to the lattice. The lattice corrections are large. Taking these corrections into account, we compare Monte Carlo measurements of the dual string tension with perturbation theory, for SU(2). Agreement is observed at the 2% level, down to temperatures O(10) T_c.Comment: 17 pages, 7 figures; reference added, typos correcte

Revisiting two strong approximation results of Dudley and Philipp

We demonstrate the strength of a coupling derived from a Gaussian approximation of Zaitsev (1987a) by revisiting two strong approximation results for the empirical process of Dudley and Philipp (1983), and using the coupling to derive extended and refined versions of them.Comment: Published at http://dx.doi.org/10.1214/074921706000000824 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Towards a theory of deception

This paper proposes an equilibrium approach to deception where deception is defined to be the process by which actions are chosen to induce erroneous inferences so as to take advantage of them. Specifically, we introduce a framework with boundedly rational players in which agents make inferences based on a coarse information about others' behaviors: Agents are assumed to know only the average reaction function of other agents over groups of situations. Equilibrium requires that the coarse information available to agents is correct, and that inferences and optimizations are made based on the simplest theories compatible with the available information. We illustrate the phenomenon of deception and how reputation concerns may arise even in zero-sum games in which there is no value to commitment. We further illustrate how the possibility of deception affects standard economic insights through a number of stylized applications including a monitoring game and two simple bargaining games. The approach can be viewed as formalizing into a game theoretic setting a well documented bias in social psychology, the Fundamental Attribution Error.deception ; game theory ; fundamental attribution error