Stochastic switching in infinite dimensions with applications to random parabolic PDEs

We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.Comment: 30 pages. Published version containing some minor corrections and improvement

Smooth invariant densities for random switching on the torus

We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.Comment: 19 page

Thurstonian Scaling of Compositional Questionnaire Data

To prevent response biases, personality questionnaires may use comparative response formats. These include forced choice, where respondents choose among a number of items, and quantitative comparisons, where respondents indicate the extent to which items are preferred to each other. The present article extends Thurstonian modeling of binary choice data (Brown & Maydeu-Olivares, 2011a) to “proportion-of-total” (compositional) formats. Following Aitchison (1982), compositional item data are transformed into log-ratios, conceptualized as differences of latent item utilities. The mean and covariance structure of the log-ratios is modelled using Confirmatory Factor Analysis (CFA), where the item utilities are first-order factors, and personal attributes measured by a questionnaire are second-order factors. A simulation study with two sample sizes, N=300 and N=1000, shows that the method provides very good recovery of true parameters and near-nominal rejection rates. The approach is illustrated with empirical data from N=317 students, comparing model parameters obtained with compositional and Likert scale versions of a Big Five measure. The results show that the proposed model successfully captures the latent structures and person scores on the measured traits

User guide for 'BGS Civils' : a suite of engineering properties datasets

This report is the user’s guide for the national assessment of a suite of seven Engineering Properties datasets. These complimentary datasets provide information and advice on Excavatability, Strength, Discontinuities, Bulking of soils and rocks, Sulfate and sulfide potential, Corrosivity (ferrous) and Use for fill. The purpose of this user guide is to provide the background, overview of the methodology developed by the British Geological Survey, and the potential applications and limitations of this GIS information

Coherence of a room-temperature CW GaAs/GaAlAs injection laser

The temporal coherence of a stripe-geometry double-heterojunction GaAs/GaAlAs laser operating CW at room temperature was determined. A heterodyne detection scheme was used involving the mixing of the laser field with a frequency-shifted and time-delayed image of itself in an interferometer. Because the laser device oscillated in several longitudinal modes, the autocorrelation function of its output exhibited resonances for specific time delays. The rate at which the amplitude of these resonances decreased with increasing time delays provided a measure of an apparent coherence length associated with individual longitudinal modes. The coherence length, so defined, was found to increase linearly with drive current in excess of threshold. This observation is interpreted as evidence that the intrinsic linewidth of a longitudinal mode is inversely proportional to the coherent optical power in that mode. Apparent coherence lengths were a few centimeters for a few milliwatts of total optical power emitted per facet. For a perfectly balanced interferometer, a sharp heterodyne beat signal was also observed when the laser device was operated considerably below threshold, i.e., in the LED mode

Drivers and barriers to seafood consumption in Australia.

Purpose: This paper aims to explore the drivers and barriers to seafood consumption in Australia and to investigate attitudes toward pre-packaged fresh chilled seafood products. Design/methodology/approach: A two-stage study of seafood consumption in Australia was conducted comprising ten focus groups across six states (n=60) and a national online consumer survey (n=1,815). Findings: The main drivers for seafood consumption in Australia are health, taste, convenience, and a desire for diet variety. The main barriers to seafood consumption are price, concerns regarding origin, concerns about freshness, difficulty in evaluating seafood quality, and not liking the taste or texture of fish. The main appeals of pre-packaged fresh chilled seafood products are convenience and ease of preparation, while barriers include price and concerns about origin and freshness. Research limitations/implications: The survey focussed on the main or joint grocery buyers in households and thus may not be representative of the entire Australian population. Practical implications: The findings provide important insights for the Australian seafood industry in developing and delivering seafood offerings that will appeal to Australian consumers and thus stimulate seafood consumption. This knowledge will also assist the Australian Government and health educators to more effectively campaign to encourage increased seafood consumption. Originality/value: While research on antecedents to seafood consumption in Europe has been extensive, research into the drivers and barriers to seafood consumption in Western countries such as Australia and strategies for increasing seafood consumption is less evident

User guide for the BGS Geology : 50k dataset (V8)

The British Geological Survey provides nationwide digital geological maps at a range of scales. These digital products are known by the name ‘BGS Geology’ (formerly DiGMapGB). This guide is written for users of the 1:50 000 scale digital geological map data (BGS Geology: 50k) version 8, released in 2016. It describes the basic layout and content of the dataset and provides background information as to how this version of the dataset has changed compared with previous versions. A basic appreciation of Geographical Information System (GIS) terminology is needed to understand some of the information outlined here. Users should also familiarise themselves with some of the basic principles behind geological description of our landscape; further information about how BGS has made the geological map of Great Britain can be found on the BGS website at: http://www.bgs.ac.uk/products/digitalmaps/digmapgb.htm