Dynamics for holographic codes

We describe how to introduce dynamics for the holographic states and codes introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the definition of a continuous limit of the kinematical Hilbert space which we argue may be achieved via the semicontinuous limit of Jones. Dynamics is then introduced by building a unitary representation of a group known as Thompson's group T, which is closely related to the conformal group in 1+1 dimensions. The bulk Hilbert space is realised as a special subspace of the semicontinuous limit Hilbert space spanned by a class of distinguished states which can be assigned a discrete bulk geometry. The analogue of the group of large bulk diffeomorphisms is given by a unitary representation of the Ptolemy group Pt, on the bulk Hilbert space thus realising a toy model of the AdS/CFT correspondence which we call the Pt/T correspondence.Comment: 40 pages (revised version submitted to journal). See video of related talk: https://www.youtube.com/watch?v=xc2KIa2LDF

Lossy Source Transmission over the Relay Channel

Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 200

Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators

The ability to tune resonant frequency in optical microcavities is an essential feature for many applications. Integration of electrical-based tuning as part of the fabrication process has been a key advantage of planar microresonant devices. Until recently, the combination of these features has not been available in devices that operate in the ultrahigh-Q regime where device quality factors (Q) can exceed 100 million. In this letter, we demonstrate an electrically tunable resonator on a chip with ultrahigh-quality factors. Futhermore, the devices have demonstrated tuning rates in excess of 85 GHz/V2 and are capable of tuning more than 300 GHz

Covariant Symplectic Structure and Conserved Charges of New Massive Gravity

We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a Poincare invariant 2-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory. Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for spacetimes with non-constant curvature backgrounds, by using the diffeomorphism invariance of the symplectic 2-form. As an example, we calculate the conserved charges of some solutions of New Massive Gravity (NMG) and compare the results with the previous works.Comment: 18 pages, No figures, RevTEX4.1; ver 2: minor corrections, version accepted for publication in Physical Review

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: To appear in the proceedings of the 2007 IEEE International Symposium on Information Theory, Nice, France, June 24-29, 200

BAYESIAN ANALYSIS OF THE COMPOUND COLLECTIVE MODEL: THE NET PREMIUM PRINCIPLE WITH EXPONENTIAL POISSON AND GAMMA–GAMMA DISTRIBUTIONS

This article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior distributions. The robustness of the posterior premium was analyzed with respect to the prior distribution specification of the severity of the accident/event, utilizing contamination classes, these being the class of all the distributions and that of all the unimodal distributions with the same mode. Numerical applications of the results obtained were performed.Compound collective model; Bayesian analysis; Robustness analysis.