Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case error. A general algorithm is presented and explicit expressions for base~2 are given. To obtain an efficient component-by-component construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte Carlo rules based on higher order digital nets

Does Consciousness Collapse the Wave Function

A conceptual replication of the Hall-experiment to test the 'subjective reduction' interpretation of the measurement problem in Quantum Physics is reported. Two improvements are introduced. First the delay between pre-observation and final observation of the same quantum event is increased from a few microseconds in the original experiment to 1 second in this replication. Second, rather than using the observers conscious response as the dependent variable, we use the early brain responses as measured by EEG. These early responses cover a period where the observer is not yet conscious of the quantum event. Results support the 'subjective reduction' hypothesis because significant differences between the brain responses of the final observer are found dependent upon the pre-observer looking or not looking at the quantum event (exact binomial p < 0.02). Alternative 'normal' explanations are discussed and rejected. It is concluded that the present results do justify further research along these lines.Comment: 11 pages, 4 figures, 1 tabl

Measurement and analysis of cryogenic sapphire dielectric resonators and DROs

Presented are the experimental and computational results of a study on a new kind of dielectric resonator oscillator (DRO). It consists of a cooled, cylindrically symmetric sapphire resonator surrounded by a metallic shield and is capable of higher Q's than any other dielectric resonator. Isolation of fields to the sapphire by the special nature of the electromagnetic mode allows the very low loss of the sapphire itself to be expressed. Calculations show that the plethora of modes in such resonators can be effectively reduced through the use of a ring resonator with appropriate dimensions. Experimental results show Q's ranging from 3 x 10 to the 8th at 77 K to 10 to the 9th at 4.2 K. Performance is estimated for several types of DROs incorporating these resonators. Phase noise reductions in X-band sources are indicated at values substantially lower than those previously available

Microwave oscillator with reduced phase noise by negative feedback incorporating microwave signals with suppressed carrier

Oscillator configurations which reduce the effect of 1/f noise sources for both direct feedback and stabilized local oscillator (STALO) circuits are developed and analyzed. By appropriate use of carrier suppression, a small signal is generated which suffers no loss of loop phase information or signal-to-noise ratio. This small signal can be amplified without degradation by multiplicative amplifier noise, and can be detected without saturation of the detector. Together with recent advances in microwave resonator Qs, these circuit improvements will make possible lower phase noise than can be presently achieved without the use of cryogenic devices

Landscape influence on small-scale water temperature variations in a moorland catchment

Acknowledgements Iain Malcolm and staff at Marine Scotland (Pitlochry) are thanked for the provision of data from the AWS. Finally, the two anonymous reviewers are greatly acknowledged for their constructive comments.Peer reviewedPostprin

U.S. International Trade: Trends and Forecasts

[Excerpt] This report provides an overview of the current status, trends, and forecasts for U.S. import and export flows as well as certain balances. The purpose of this report is to provide current data and brief explanations for the various types of trade flows along with a brief discussion of trends that may require attention or point to the need for policy changes. The use of trade policy as an economic or strategic tool is beyond the scope of this report but can be found in various other CRS reports. Further detail on trade in specific commodities, with particular countries or regions, or for different time periods, can be obtained from the Department of Commerce, U.S. International Trade Commission, or by contacting the authors of this report

Modelling landscape controls on dissolved organic carbon sources and fluxes to streams

Acknowledgments We thank the Natural Environment Research Council NERC (project NE/K000268/1) for funding. Iain Malcolm and staff at Marine Scotland (Pitlochry) are also thanked for the provision of data from the AWS as are the Scottish Environmental Protection Agency and British Atmospheric Data Centre for the provision of meteorological data.Peer reviewedPublisher PD

Consistency of Markov chain quasi-Monte Carlo on continuous state spaces

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than i.i.d. U(0,1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Appropriate Economic Space for Transnational Infrastructural Projects: Gateways, Multimodal Corridors, and Special Economic Zones

This study addresses three questions that arise in Asia when formulating, financing, implementing, and maintaining transnational linkages versus purely domestic connections. Firstly, how is optimal economic space to be defined as a useful starting point? Secondly, how can relevant criteria be developed to define the emerging spatial economy and identify efficient transnational transport networks? Thirdly, what are the main investment opportunities in physical infrastructure that would result in more efficient and effective regional cooperation and integration (making special reference to the potential role of cross-border special economic zones (SEZs) or their equivalents)?asia transnational infrastructure; asia regional cooperation

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661