Estimation of the Rate-Distortion Function

Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is the behavior of the so-called "plug-in" estimator, which is simply the rate-distortion function of the empirical distribution of the observed data. Sufficient conditions are given for its consistency, and examples are provided to demonstrate that in certain cases it fails to converge to the true rate-distortion function. The analysis of its performance is complicated by the fact that the rate-distortion function is not continuous in the source distribution; the underlying mathematical problem is closely related to the classical problem of establishing the consistency of maximum likelihood estimators. General consistency results are given for the plug-in estimator applied to a broad class of sources, including all stationary and ergodic ones. A more general class of estimation problems is also considered, arising in the context of lossy data compression when the allowed class of coding distributions is restricted; analogous results are developed for the plug-in estimator in that case. Finally, consistency theorems are formulated for modified (e.g., penalized) versions of the plug-in, and for estimating the optimal reproduction distribution.Comment: 18 pages, no figures [v2: removed an example with an error; corrected typos; a shortened version will appear in IEEE Trans. Inform. Theory

Manufacturing flexible light-emitting polymer displays with conductive lithographic film technology

We report on a new low-cost manufacturing process for flexible displays that has the potential to rapidly expand the market into areas that have traditionally been outside the scope of such technology. In this paper we consider the feasibility of using offset-lithography to deposit contacts for polymer light-emitting displays. We compare and contrast manufacturing criteria and present a case study detailing our initial results. It is expected that these developments will stimulate further progress in multilayer device fabrication. Cheap, flexible conductive interconnects have the potential to find applications in a wide variety of device structures. For the more challenging exploitation areas in multilayer devices, such as displays, it was found that the properties of conductive lithographic films were not optimal in their current form. Three parameters (conductivity, surface roughness and surface work function) were identified as critical to device fabrication. Calendering and electroless plating were investigated as methods to improve these properties. Both methods aimed to modify the surface roughness and conductivity, with the plating study also modifying the work function

Gap opening in graphene by simple periodic inhomogeneous strain

Using ab-initio methods, we show that the uniform deformation either leaves graphene (semi)metallic or opens up a small gap yet only beyond the mechanical breaking point of the graphene, contrary to claims in the literature based on tight-binding (TB) calculations. It is possible, however, to open up a global gap by a sine-like one-dimensional inhomogeneous deformation applied along any direction but the armchair one, with the largest gap for the corrugation along the zigzag direction (~0.5 eV) without any electrostatic gating. The gap opening has a threshold character with very sharp rise when the ratio of the amplitude A and the period of the sine wave deformation lambda exceeds (A/lambda)_c ~0.1 and the inversion symmetry is preserved, while it is threshold-less when the symmetry is broken, in contrast with TB-derived pseudo-magnetic field models.Comment: 6 pages, 6 figures; (v2) added figures illustrating opening gap in Graphene mesh on BN, expanded analysis illustrating absence of pseudo-magnetic fields in deformed Graphen

Lie point symmetries and the geodesic approximation for the Schr\"odinger-Newton equations

We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to widely separated lumps of probability. The lumps are found to move like point particles under a mutual inverse-square law of attraction

Quantum box energies as a route to the ground state levels of self-assembled InAs pyramidal dots

A theoretical investigation of the ground state electronic structure of InAs/GaAs quantum confined structures is presented. Energy levels of cuboids and pyramidal shaped dots are calculated using a single-band, constant-confining-potential model that in former applications has proved to reproduce well both the predictions of very sophisticated treatments and several features of many experimental photoluminescence spectra. A connection rule between their ground state energies is found which allows the calculation of the energy levels of pyramidal dots using those of cuboids of suitably chosen dimensions, whose solution requires considerably less computational effort. The purpose of this work is to provide experimentalists with a versatile and simple method to analyze their spectra. As an example, this rule is then applied to successfully reproduce the position of the ground state transition peaks of some experimental photoluminescence spectra of self-assembled pyramidal dots. Furthermore the rule is used to predict the dimensions of a pyramidal dot, starting from the knowledge of the ground state transition energy and an estimate for the aspect ratio Q. © 2000 American Institute of Physics

A linear acoustic model for multi-cylinder IC engine intake manifolds including the effects of the intake throttle

This paper presents a linear acoustic model of a multi-cylinder intake manifold that can be used as part of a hybrid time/frequency domain method to calculate the intake wave dynamics of practical naturally aspirated engines. The method allows the user to construct a model of almost any manifold of complex geometry. The model is constructed as an assemblage of sub-models: (i) A model for a straight pipe with both ends open and through-flow. (ii) A model for an expansion chamber consisting of three lengths of pipe laid end-to-end: a narrow bore pipe expanding into a wide bore pipe contracting into a narrower bore pipe once more. (iii) A model of a side-branch, which includes a model for a straight pipe with one end closed and a model for the three way junction that joins the side-branch to a length of flow pipe. (iv) A model for an expansion with two (or more) side-branches, which combines the sub-models (i, ii, iii) into a multi-way (n-way) junction model. (v) A model for an intake throttle. Good agreement with measurement has been found for each sub-model when bench-tested in isolation and encouraging agreement has been found when many sub-models are used together to model a complex intake manifold on a running engine

Stable, inflatable life raft for high seas rescue operations

Raft is easily deployed and highly maneuverable in water. It has false bottom of water ballast containers attached to underside, making it exceptionally stable platform from which swimmers can operate. Raft is attachable to external moorings

Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors

We consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $\xi^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced by $\xi^a$. It is proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation we argue that it is enough to solve merely Einstein's equation for these electrovac spacetimes because the relevant equations of motion will be satisfied automatically. It is also shown that for the exceptional case of functionally related potentials \n^aT_{ab}=0 implies along with one of the relevant equations of motion that the complementary equation concerning the electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+