What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory

Spacetime and the Holographic Renormalization Group

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.Comment: 12 page

Asymptotic Analysis of Generative Semi-Supervised Learning

Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP.Comment: 12 pages, 9 figure

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

The Library of Babel

We show that heavy pure states of gravity can appear to be mixed states to almost all probes. Our arguments are made for $\rm{AdS}_5$ Schwarzschild black holes using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For certain supersymmetric states of the theory, our account is exact: the microstates are described in gravity by a spacetime ``foam'', the precise details of which are invisible to almost all probes.Comment: 7 pages, 1 figure, Essay receiving honorable mention in the 2005 Gravity Research Foundation essay competitio

Typicality versus thermality: An analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure

Deconstruction and Holography

It was recently pointed out that the physics of a single discrete gravitational extra dimension exhibits a peculiar UV/IR connection relating the UV scale to the radius of the effective extra dimension. Here we note that this non-locality is a manifestation of holography, encoding the correct scaling of the number of fundamental degrees of freedom of the UV theory. This in turn relates the Wilsonian RG flow in the UV theory to the effective gravitational dynamics in the extra dimension. The relevant holographic c-function is determined by the expression for the holographic bound. Holography in this context is a result of the requirements of unitarity and diffeomorphism invariance. We comment on the relevance of this observation for the cosmological constant problem.Comment: 11 pages, LaTe

Dependability of body area wireless sensor networks in assistive care loop framework

University of Technology, Sydney. Faculty of Engineering and Information Technology.The exponential growth in wireless communication and micro-electro-mechanical systems gave birth to low power, low cost, multifunctional and miniature wireless sensors. Wireless sensor networks (WSNs) are finding applications in many areas, particularly in healthcare, a WSN can be used highly effectively in the form of a Body Area Wireless Sensor Network (BAWSN), to enhance the quality of the contemporary healthcare services. This tendency triggered the in-house healthcare monitoring application (HMA) with the BAWSN as their monitoring component. The quality of life of the patients can be improved with the deployment of a BAWSN because the patients and the care staff would be able to monitor the health condition, to access the electronic medical records and communicate with each other by using a Personal Digital Assistant (PDA) or smart phone in their hands, regardless of where they are located or what their duties might be. This remote monitoring and consultations might reduce the traditional stressful and costly exercise of frequent hospitalisation. The rising costs of healthcare in many developed countries have influenced the introduction of the HMA into existing health care practices. However, the successful deployment of the civilian and commercial HMA is still in its infancy stages for some of the following reasons: (a) a generic framework for building the HMA is needed for the application developer to materialise the concepts, (b) an effective set of measurable properties is required for the users to evaluate the performance of the BAWSN used in the HMA, (c) the method used for measuring the performance of a monitoring application is not suitable for the BAWSN used in the HMA, (d) any unauthorized modifications to health data may induce a false diagnosis and put a life in danger; this must be considered together with the privacy of the users in the application, without any compromise and, (e) the body sensors operate in close proximity to the human body, therefore it is imperative to ensure the operational safety of BAWSN. Our research shows that the dependable properties of an application encompass most of the essential demands for the actual realization of the HMA. It also shows that the dependable system can deliver services that can be justifiably trusted. The focus of this work is on the BAWSN, because the service ability of the HMA depends heavily on its monitoring component, the BAWSN. Therefore, in this thesis, we define and investigate six fundamental effective properties, maintainability, reliability, availability, confidentiality, integrity and safety, based on BAWSN requirements under the dependability framework. We built an Assistive Care Loop Framework (ACLF), a maintainable BAWSN-based HMA, for monitoring pregnant women based on an event-driven architecture that follows layered functionalities. A novel critical time parameter is introduced to satisfy the needs of the medical diagnoses that require the BA WSN to rely on the collection of data within a critical time from all of the source sensor nodes. The process and issues involved in the medical diagnoses are also explored; these influenced the characterization of the BAWSN as a time critical application. Based on the critical time, we derived non-device-centric time-specific parameters with which we formulated a novel empirical measure model for the transmission reliability and availability in the BAWSN. To compare the empirical measure model, analogous theoretical models are also derived for the BAWSN's reliability and availability. To safeguard the patient's health data and also to ensure their privacy in the BAWSN, we proposed a secure adaptive triple-key scheme (aTKS) in such a way that it incurs minimal overheads while meeting the stringent time requirements of the BAWSN. The deployed ACLF exemplifies the concept of the HMA being used not only for alerting the care staff in case of emergency, but also for analysing a patient's progress over a period of time to forecast any emergency situation. The performance of the proposed measure models and the implemented aTKS from our real-time test-bed would enable the application developer to measure the performance of the BAWSN-based application because, to the best of our knowledge, no measure exists in the literature as such for a BAWSN-based application. The formulated minimal set of dependable properties might serve as a benchmark for evaluating the performance of a BAWSN, and in turn, the HMA