Representations of a class of lattice type vertex algebras

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these vertex algebras are related to the representation theory of some associative algebras.Comment: latex 24 page

Connectivity-guaranteed and obstacle-adaptive deployment schemes for mobile sensor networks

Mobile sensors can relocate and self-deploy into a network. While focusing on the problems of coverage, existing deployment schemes largely over-simplify the conditions for network connectivity: they either assume that the communication range is large enough for sensors in geometric neighborhoods to obtain location information through local communication, or they assume a dense network that remains connected. In addition, an obstacle-free field or full knowledge of the field layout is often assumed. We present new schemes that are not governed by these assumptions, and thus adapt to a wider range of application scenarios. The schemes are designed to maximize sensing coverage and also guarantee connectivity for a network with arbitrary sensor communication/sensing ranges or node densities, at the cost of a small moving distance. The schemes do not need any knowledge of the field layout, which can be irregular and have obstacles/holes of arbitrary shape. Our first scheme is an enhanced form of the traditional virtual-force-based method, which we term the Connectivity-Preserved Virtual Force (CPVF) scheme. We show that the localized communication, which is the very reason for its simplicity, results in poor coverage in certain cases. We then describe a Floor-based scheme which overcomes the difficulties of CPVF and, as a result, significantly outperforms it and other state-of-the-art approaches. Throughout the paper our conclusions are corroborated by the results from extensive simulations

A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations

Retrodictive states and two-photon quantum imaging

We use retrodictive quantum theory to analyse two-photon quantum imaging systems. The formalism is particularly suitable for calculating conditional probability distributions.Comment: 5 pages, 3 figure

Much Ado about Something: The First Amendment and Mandatory Labeling of Genetically Engineered Foods

This Article evaluates the free speech implications of laws requiring that GE foods be labeled and concludes that such regulations would meet all First Amendment requirements for compelled commercial speech. Part I traces the history of food labeling in the United States, the advent of genetic engineering, and the application of that technology in agriculture and the food industry. Part II evaluates the scope of commercial free speech and the appropriate test to be applied in determining whether a GE food labeling law would violate the First Amendment. Part III examines the impacts of an agricultural and food system increasingly dominated by GE crops. It explains how controversy over a single issue, whether GE foods pose a potential risk to human health, has stunted the debate over whether mandatory labeling serves a useful purpose by diverting attention from other material impacts. It concludes that greater consumer and public awareness of the adverse environmental, economic, cultural, and social impacts of GE foods would serve a substantial government interest