Discrete Physics and the Dirac Equation

We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over lattice paths. The rational, real form can also be interpreted in terms of bit-strings.Comment: LaTex 16 pages, 10 figures. To obtain a copy, send e-mail to [email protected]

Using Echo State Networks for Cryptography

Echo state networks are simple recurrent neural networks that are easy to implement and train. Despite their simplicity, they show a form of memory and can predict or regenerate sequences of data. We make use of this property to realize a novel neural cryptography scheme. The key idea is to assume that Alice and Bob share a copy of an echo state network. If Alice trains her copy to memorize a message, she can communicate the trained part of the network to Bob who plugs it into his copy to regenerate the message. Considering a byte-level representation of in- and output, the technique applies to arbitrary types of data (texts, images, audio files, etc.) and practical experiments reveal it to satisfy the fundamental cryptographic properties of diffusion and confusion.Comment: 8 pages, ICANN 201

Instructions for schools on saving a copy of their SEF or SIEF: guidance for maintained, non-maintained and independent schools for summer term 2011

This guidance is for use by maintained, non-maintained and independent day, boarding and residential special schools, during the summer term 2011. It provides instructions for schools on saving a copy of the information they have entered into their online self-evaluation form for maintained schools (SEF) or school information and self-evaluation form for independent schools (SIEF). Schools may wish to take this action during the summer term, before Ofsted’s online SEF and SIEF are discontinued

The classical double copy in maximally symmetric spacetimes

The classical double copy procedure relates classical asymptotically-flat gravitational field solutions to Yang-Mills and scalar field solutions living in Minkowski space. In this paper we extend this correspondence to maximally symmetric curved spacetimes. We consider asymptotically (A)dS spacetimes in Kerr-Schild form and construct the corresponding single and zeroth copies. In order to clarify the interpretation of these copies, we study several examples including (A)dS-Schwarzschild, (A)dS-Kerr, black strings, black branes, and waves, paying particular attention to the source terms. We find that the single and zeroth copies of stationary solutions satisfy different equations than those of wave solutions. We also consider how to obtain Einstein-Maxwell solutions using this procedure. Finally, we derive the classical single and zeroth copy of the BTZ black hole.Comment: matches published versio

Seiberg-Witten invariants and pseudo-holomorphic subvarieties for self-dual, harmonic 2-forms

A smooth, compact 4-manifold with a Riemannian metric and b^(2+) > 0 has a non-trivial, closed, self-dual 2-form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set, the symplectic form and the metric define an almost complex structure; and the latter can be used to define pseudo-holomorphic submanifolds and subvarieties. The main theorem in this paper asserts that if the 4-manifold has a non zero Seiberg-Witten invariant, then the zero set of any given self-dual harmonic 2-form is the boundary of a pseudo-holomorphic subvariety in its complement.Comment: 44 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper8.abs.htm

Application of the no-signaling principle to obtain quantum cloners for any allowed value of fidelity

Special relativity forbids superluminal influences. Using only the no-signaling principle and an assumption about the form of the Schmidt decomposition, we show that for "any" allowed fidelity there is a "unique" approximate qubit cloner which can be written explicitly. We introduce the prime cloners whose fidelities have multiplicative property and show that the fidelity of the prime cloners for the infinite copy limit is 1/2.Comment: 8 pages, no figure

Advertising Research Issues from FTC Versus Stouffer Foods Corporation

Extrinsic evidence is frequently offered in Federal Trade Commission advertising deception cases, most often in the form of advertising research, such as copy tests. Although generally accepted principles exist for copy test evidence presented before the Commission, how these principles are operationalized can provide fertile ground for challenges. Thus, the authors review six copy testing and ad interpretation issues from the recent Stouffer Foods case. The authors discuss difficult tradeoffs inherent in relative versus absolute claims, multiple claims, control ad groups, control questions, and disclosure information. The careful consideration of such trade-offs in advertising research decisions will help in the preparation of extrinsic evidence before the Commission