Split Sampling: Expectations, Normalisation and Rare Events

In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling

Sharp Threshold Asymptotics for the Emergence of Additive Bases

A subset A of {0,1,...,n} is said to be a 2-additive basis for {1,2,...,n} if each j in {1,2,...,n} can be written as j=x+y, x,y in A, x<=y. If we pick each integer in {0,1,...,n} independently with probability p=p_n tending to 0, thus getting a random set A, what is the probability that we have obtained a 2-additive basis? We address this question when the target sum-set is [(1-alpha)n,(1+alpha)n] (or equivalently [alpha n, (2-alpha) n]) for some 0<alpha<1. Under either model, the Stein-Chen method of Poisson approximation is used, in conjunction with Janson's inequalities, to tease out a very sharp threshold for the emergence of a 2-additive basis. Generalizations to k-additive bases are then given.Comment: 22 page

Demand for Wine in Australia: Systems Versus Single Equation Approach

The objective of the study is to estimate demand for wine in Australia, based on both the systems approach and the single equation approach. Both approaches consider demand for three categories of alcoholic drinks (beer, wine and spirits) in a seemingly unrelated regression framework to take account of cross-equation correlations. Time series data on retail price indexes and apparent per capita consumption of alcoholic beverages for Australia for the period 1975/76 to 1998/99 are used for econometric estimation. The results show that over the short run, beer and wine are necessities; however, over the long run, wine becomes a luxury good. Beer and wine are complements. Demand for all three beverages is price inelastic. The study also found that the behaviour of wine consumers reflect past consumption patterns, indicating that wine is more addictive than either beer or spirits. A structural change in consumer preferences away from cheaper cask wines to more expensive bottled table wines has a significant impact on the volume of wine consumption. Finally, wine consumption has increased over time. The study re-confirms the importance of developing a model that considers the impacts of both economic and non-economic variables on wine consumption.wine demand, demand analysis, almst ideal demand system, Demand and Price Analysis,

Brain awareness week and beyond: encouraging the next generation.

The field of neuroscience is generating increased public appetite for information about exciting brain research and discoveries. As stewards of the discipline, together with FUN and others, the Society for Neuroscience (SfN) embraces public outreach and education as essential to its mission of promoting understanding of the brain and nervous system. The Society looks to its members, particularly the younger generation of neuroscientists, to inspire, inform and engage citizens of all ages, and most importantly our youth, in this important endeavor. Here we review SfN programs and resources that support public outreach efforts to inform, educate and tell the story of neuroscience. We describe the important role the Brain Awareness campaign has played in achieving this goal and highlight opportunities for FUN members and students to contribute to this growing effort. We discuss specific programs that provide additional opportunities for neuroscientists to get involved with K-12 teachers and students in ways that inspire youth to pursue further studies and possible careers in science. We draw attention to SfN resources that support outreach to broader audiences. Through ongoing partnerships such as that between SfN and FUN, the neuroscience community is well positioned to pursue novel approaches and resources, including harnessing the power of the Internet. These efforts will increase science literacy among our citizens and garner more robust support for scientific research

Improving Natural Language Inference Using External Knowledge in the Science Questions Domain

Natural Language Inference (NLI) is fundamental to many Natural Language Processing (NLP) applications including semantic search and question answering. The NLI problem has gained significant attention thanks to the release of large scale, challenging datasets. Present approaches to the problem largely focus on learning-based methods that use only textual information in order to classify whether a given premise entails, contradicts, or is neutral with respect to a given hypothesis. Surprisingly, the use of methods based on structured knowledge -- a central topic in artificial intelligence -- has not received much attention vis-a-vis the NLI problem. While there are many open knowledge bases that contain various types of reasoning information, their use for NLI has not been well explored. To address this, we present a combination of techniques that harness knowledge graphs to improve performance on the NLI problem in the science questions domain. We present the results of applying our techniques on text, graph, and text-to-graph based models, and discuss implications for the use of external knowledge in solving the NLI problem. Our model achieves the new state-of-the-art performance on the NLI problem over the SciTail science questions dataset.Comment: 9 pages, 3 figures, 5 table

Constructing “Designer Atoms” via Resonant Graphene-Induced Lamb Shifts

The properties of an electron in an atom or molecule are not fixed; rather they are a function of the optical environment of the emitter. Not only is the spontaneous emission a function of the optical environment, but also the underlying wave functions and energy levels, which are modified by the potential induced by quantum fluctuations of the electromagnetic field. In free space, this modification of atomic levels and wave functions is very weak and generally hard to observe due to the prevalence of other perturbations like fine structure. Here, we explore the possibility of highly tailorable electronic structure by exploiting large Lamb shifts in tunable electromagnetic environments such as graphene, whose optical properties are dynamically controlled via doping. The Fermi energy can be chosen so that the Lamb shift is very weak, but it can also be chosen so that the shifts become more prominent than the fine structure of the atom and even potentially the Coulomb interaction with the nucleus. Potential implications of this idea include being able to electronically shift an unfavorable emitter structure into a favorable one, a new approach to probe near-field physics in fluorescence, and a way to access regimes of physics where vacuum fluctuations are not a weak perturbation but rather the dominant physics. Keywords: graphene plasmonics; Lamb shift; light-matter interactions; quantum electrodynamicsUnited States. Army Research Office (Grant W911NF-13-D-0001)United States. Department of Energy (Award DE-FG02-97ER25308