Importance sampling the union of rare events with an application to power systems analysis

We consider importance sampling to estimate the probability $\mu$ of a union of $J$ rare events $H_j$ defined by a random variable $\boldsymbol{x}$. The sampler we study has been used in spatial statistics, genomics and combinatorics going back at least to Karp and Luby (1983). It works by sampling one event at random, then sampling $\boldsymbol{x}$ conditionally on that event happening and it constructs an unbiased estimate of $\mu$ by multiplying an inverse moment of the number of occuring events by the union bound. We prove some variance bounds for this sampler. For a sample size of $n$, it has a variance no larger than $\mu(\bar\mu-\mu)/n$ where $\bar\mu$ is the union bound. It also has a coefficient of variation no larger than $\sqrt{(J+J^{-1}-2)/(4n)}$ regardless of the overlap pattern among the $J$ events. Our motivating problem comes from power system reliability, where the phase differences between connected nodes have a joint Gaussian distribution and the $J$ rare events arise from unacceptably large phase differences. In the grid reliability problems even some events defined by $5772$ constraints in $326$ dimensions, with probability below $10^{-22}$, are estimated with a coefficient of variation of about $0.0024$ with only $n=10{,}000$ sample values

Cathodoluminescence of shocked quartz at the Cretaceous-Tertiary boundary

Empirical studies have documented an association between rock type and the cathodoluminescence color of constituent quartz grains. Quartz from extrusive igneous sources luminesces uniform pale blue. Quartz from intrusive igneous and high-grade metamorphic rocks generally luminesces darker purple-blue, whereas quartz recrystallized under low-grade metamorphic conditions luminesces reddish-brown. Quartz grains in most sandstones luminesce a heterogeneous mixture of these colors because the grains were derived from a variety of ultimate source rocks. If shocked quartz found at the Cretaceous-Tertiary (K-T) boundary is volcanic in origin, its cathodoluminescence should be predominantly pale blue. Alternatively, quartz grains derived from bolide impact upon, and ejection of, mixed igneous, metamorphic, and sedimentary rocks should luminesce a variety of colors. Grain mounts of sand collected at the K-T boundary horizon from the Clear Creek North site in the Raton Basin, Colorado were examined. Shocked quartz luminesced a variety of colors and very few grains luminesced the pale blue color that is typical of volcanic quartz. It was concluded that the shocked quartz was derived from a petrologically diverse source region without substantial volcanic contribution. Most shocked grains apparently were derived from low-grade metamorphic rocks, with a slightly smaller contribution from high-grade metamorphic and intrusive igneous rocks. Rare quartz grains with brown-luminescing rims reflect a minor addition from detrital sedimentary sources. The apparent relative abundances of intrusive (and rare extrusive) igneous, metamorphic, and sedimentary ultimate source rocks suggested by CL colors of shock-deformed quartz at the K-T boundary is consistent with a crustal/supracrustal origin for the grains

Implementing Carbon Tariffs: A Fool's Errand?

Some governments are considering taxes on imports based on carbon content from countries that have not introduced climate change policies. Such carbon border taxes appeal to domestic industries facing higher charges for their own carbon emissions. This research demonstrates that there are enormous practical difficulties surrounding such plans. Various policies are evaluated according to World Trade Organization compliance, administrative plausibility, help in meeting environmental goals, and ability to deal with domestic pressures. The steel industry is used as a case study in this analysis. All considered policies arguably fail to meet at least one of these constraints, bringing into question the plausibility that a carbon border tax can be practical policy.carbon tariffs, climate change, environmental policy

CRKSPH - A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme

We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric. Here, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity. Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH. CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zeroth-order inaccuracy. We compare CRKSPH to two different modern SPH formulations (pressure based SPH and compatibly differenced SPH), demonstrating the advantages of our new formulation when modeling fluid mixing, strong shock, and adiabatic phenomena

Location Decisions of Heterogeneous Multinational Firms

We examine how multinational Örms with heterogeneous total factor productivity (TFP) self-select into different host countries. Both aggregate- and Örm-level estimates suggest that more productive French Örms are more likely than their less efficient competitors to invest in relatively tough host countries. Countries with a smaller market potential, higher Öxed costs of investment or lower import tariffs tend to have higher cutoff productivities and attract a greater proportion of productive multinationals. This self-selection mechanism remains largely robust when we control for unobserved Örm and country heterogeneity and address the potential TFP endogeneity.multinational firm, location decision, firm heterogeneity, productivity

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here, we describe two algorithmic methods for evenly distributing points on surfaces, that when paired can be used to build 3D spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary, radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such as planets with core-mantle boundaries.Comment: 7 pages, 8 figures, ApJ accepte

A 20cm VLA Survey of Abell Clusters of Galaxies VI. Radio/Optical Luminosity Functions

From a statistically complete sample of 188 radio galaxies in Abell clusters, we examine the radio/optical correlations, the FR I/II division, and the univariate and bivariate luminosity functions. As suggested by Owen (1993), the FR I/II division is shown to be a strong function of the optical luminosity of the host galaxy (proportional to L_opt^2). This dependence is also seen in the bivariate luminosity function, which suggests that the evolutionary tracks of radio sources and/or the initial conditions in the source are governed by the host galaxy properties. The probability for detecting radio emission increases with optical luminosity. The optical dependence is clearly separated in the integral luminosity functions which can be used as a constraint to models of FR I radio power evolution. Additionally, the source counts from the integrated univariate radio luminosity function (RLF) are consistent with our suggestion in paper V that radio sources may be a transient phenomenon which occurs in all elliptical galaxies at some time (or several times) over their lifetime. We find no statistically significant differences in the luminosity functions between rich cluster samples and radio sources not selected to reside in clusters. These results suggest that all radio galaxies live in similar environments in that the optical luminosity and the properties of the host galaxy are the most important parameters which affect radio source formation and evolution.Comment: 21 pages LaTeX, 3 tables, 12 figures. To appear in July 1996 A

Autism-associated SNPs in the clock genes _npas2_, _per1_ and the homeobox gene _en2_ alter DNA sequences that show characteristics of microRNA genes.

Intronic single nucleotide polymorphisms (SNPs) in the clock genes _npas2_ and _per1_ and the homeobox gene _en2_ are reported to be associated with autism. This bioinformatics analysis of the intronic regions which contain the autism-associated SNPs rs1861972 and rs1861973 in _en2_, rs1811399 in _npas2_, and rs885747 in _per1_, shows that these regions encode RNA transcripts with predicted structural characteristics of microRNAs. These microRNA-like structures are disrupted _in silico_ by the presence of the autism enriched alleles of rs1861972, rs1861973, rs1811399 and rs885747 specifically, as compared with the minor alleles of these SNPs. The predicted gene targets of these microRNA-like structures include genes reported to be implicated in autism (_gabrb3_, _shank3_) and genes causative of diseases co-morbid with autism (_mecp2_ and _rai1_). The inheritance of the AC haplotype of rs1861972 - rs1861973 in _en2_, the C allele of rs1811399 in _npas2_, and the C allele of rs1234747 in _per1_ may contribute to the causes of autism by affecting microRNA genes that are co-expressed along with the homeobox gene _en2_ and the circadian genes _npas2_ and _per1_

Monitoring of nitrogen leaching on a dairy farm during four drainage seasons

peer-reviewedThe authors acknowledge funding from the Environmental Protection Agency and Teagasc under the 2000–2006 RTDI programme.The effect of four commonly used dairy farm management systems (treatments), on nitrogen leaching to 1 m was studied over a 4-year period from October 2001 to April 2005. The treatments were (i) grazed plots receiving dirty water, (ii) 2-cut silage plots receiving slurry, (iii) grazed plots and (iv) 1-cut silage plots receiving slurry. All plots had fertiliser N applied; the soil was free-draining overlying fissured limestone. Mean 4-year N input (kg/ha) was 319 and mean annual stocking density was ~2.38 LU/ha. The annual average and weekly NO3-N and NH4-N concentrations in drainage water were analysed for all years, using a repeated measures analysis. For the annual NO3-N data, there was an interaction between treatment and year (P < 0.001). There were significant differences (P < 0.05) in NO3-N concentrations between the treatments in all years except the third. For the NH4-N data there was no interaction between treatment and year or main effect of treatment but there were differences between years (P < 0.01). Mean weekly concentrations were analysed separately for each year. For NO3-N, in all years but the third, there was an interaction between treatment and week (P < 0.001); this occurred with NH4-N, in all 4 years. Dirty water was significantly higher than grazed-fertiliser only and 1-cut silage in NO3-N concentrations in 2001–02; in 2002–03, dirty water and 2-cut silage were significantly higher than the other treatments; while in 2004–05, dirty water and grazed-fertiliser only were significantly higher than the other two treatments. The overall 4-year mean NO3-N and NH4-N concentrations were 8.2 and 0.297 mg/L, respectively.Environmental Protection Agenc