Stochastic resonance in Gaussian quantum channels

We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a "forbidden interval". We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel, and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case the symmetry between sender and receiver is broken and the "forbidden interval" may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.Comment: 17 pages, 6 figures. Manuscript improved in many ways. New results on private communication adde

Convergence analysis of a multigrid algorithm for the acoustic single layer equation

We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions and we make use of a weak inner product in the multigrid scheme as proposed in \cite{BLP94}. A full error analysis of the algorithm is presented. We also conduct a numerical study of the effect of the weak inner product on the oscillatory behavior of the eigenfunctions for the Laplace single layer operator

Exploring the effectiveness of media in communicating public health messages to people with learning disabilities during the pandemic

The article aims to explore mass and social media’s role in communicating public health messages in Britain during the COVID-19 pandemic. The article presents findings from a realist mixed methods study analysing data collected from 137 participants who have a learning disability and/or autism. Our study discovered that participants reported that social media only led to confusion because of contradictory messages being presented on COVID-19. Although people with learning disabilities and/or autism preferred gaining information from TV news, they also reported that this information was often confusing and inaccessible. Participants drew on family members, and social care professionals, to explain and help them negotiate the complexities of public health messages during the global pandemic. The study concludes by suggesting the need for accessible information and health communications to effectively contend with any future global pandemic or health emergency to reduce the health risks for people with learning disabilities and/or autism

Joint source-channel coding for a quantum multiple access channel

Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal, and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler "separation" strategy where separate codebooks are used for the source coding and the channel coding tasks. In the present paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.Comment: 21 pages, v2: minor changes, accepted into Journal of Physics

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Development of integrated thermionic circuits for high-temperature applications

Integrated thermionic circuits (ITC) capable of extended operation in ambient temperatures up to 500 C are studied. A set of practical design and performance equations is demonstrated. Experimental results are discussed in which both devices and simple circuits were successfully operated in 5000 C environments for extended periods. It is suggested that ITC's may become an important technology for high temperature instrumentation and control systems in geothermal and other high temperature environments

A high frequency hphp boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods

A preliminary investigation of the potential for thermographic images to influence householders' understanding of home energy consumption

This paper explores the potential connections between the thermographic (infrared) imaging of domestic properties and the impact (on energy conservation behaviours) of showing householders infrared images of their homes. Infrared (IR) images, or thermographic imaging, as it has become known has been applied to the investigation of heat losses and other building related phenomena such as moisture penetration of roofs and failures in damp-proofing systems for a number of years. Recently it has been used by a wide range of public and private bodies to demonstrate the heat of a home in a visible format. This suggests a connection between the householder viewing an IR image and engaging in energy conservation behaviour, such as installing insulation. It is hypothesised that information presented in a manner which attracts the attention of the intended audience, being vivid, specific and personal, is more likely to achieve behaviour change (Stern, 1992). In this paper the evidence of the thermal characteristic of the dwelling (as shown within the thermographic image) will be compared with the householder’s reasoning process as prompted by viewing the images. The possible increase in energy saving behaviours and changes in related attitudes leading from this intervention will be investigated. Questions concerning the links between the householder’s reactions to the images and the possibility that this may facilitate a reduction in energy consumption will be discussed

A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page