On Integration Methods Based on Scrambled Nets of Arbitrary Size

We consider the problem of evaluating $I(\varphi):=\int_{[0,1)^s}\varphi(x) dx$ for a function $\varphi \in L^2[0,1)^{s}$. In situations where $I(\varphi)$ can be approximated by an estimate of the form $N^{-1}\sum_{n=0}^{N-1}\varphi(x^n)$, with $\{x^n\}_{n=0}^{N-1}$ a point set in $[0,1)^s$, it is now well known that the $O_P(N^{-1/2})$ Monte Carlo convergence rate can be improved by taking for $\{x^n\}_{n=0}^{N-1}$ the first $N=\lambda b^m$ points, $\lambda\in\{1,\dots,b-1\}$, of a scrambled $(t,s)$-sequence in base $b\geq 2$. In this paper we derive a bound for the variance of scrambled net quadrature rules which is of order $o(N^{-1})$ without any restriction on $N$. As a corollary, this bound allows us to provide simple conditions to get, for any pattern of $N$, an integration error of size $o_P(N^{-1/2})$ for functions that depend on the quadrature size $N$. Notably, we establish that sequential quasi-Monte Carlo (M. Gerber and N. Chopin, 2015, \emph{J. R. Statist. Soc. B, to appear.}) reaches the $o_P(N^{-1/2})$ convergence rate for any values of $N$. In a numerical study, we show that for scrambled net quadrature rules we can relax the constraint on $N$ without any loss of efficiency when the integrand $\varphi$ is a discontinuous function while, for sequential quasi-Monte Carlo, taking $N=\lambda b^m$ may only provide moderate gains.Comment: 27 pages, 2 figures (final version, to appear in The Journal of Complexity

Cylindric multipartitions and level-rank duality

We show that a multipartition is cylindric if and only if its level rank-dual is a source in the corresponding affine type $A$ crystal. This provides an algebraic interpretation of cylindricity, and completes a similar result for FLOTW multipartitions.Comment: 7 pages, 7 figure

When Does Government Limit the Impact of Voter Initiatives?

Citizens use the initiative process to make new laws. Many winning initiatives, however, are altered or ignored after Election Day. We examine why this is, paying particular attention to several widely-ignored properties of the post-election phase of the initiative process. One such property is the fact that initiative implementation can require numerous governmental actors to comply with an initiative’s policy instructions. Knowing such properties, the question then becomes: When do governmental actors comply with winning initiatives? We clarify when compliance is full, partial, or not at all. Our findings provide a template for scholars and observers to better distinguish cases where governmental actors\u27 policy preferences replace initiative content as a determinant of a winning initiative\u27s policy impact from cases where an initiative’s content affects policy despite powerful opponents’ objections. Our work implies that the consequences of this form of democracy are more predictable, but less direct, than often presumed

National Policies and the Limits of International Integration

In spite of the rapid growth of merchandise trade since the end of World War II, the world economy is far from integrated. Services trade, capital flows, population migration, and price differences demonstrate far more scope for international economic integration. Even among nations with preferential trade agreements, networks of merchandise trade relations are far denser intra-nationally than internationally. The absence of goods trade predicted by trade models when nations have few policy barriers implies that crossing national boundaries is a significant indicator of increased transaction costs. These patterns have caused the world trade agenda to examine some unintended trade restrictions which make up a part of national domestic policies. This focus is apparent in current negotiations such as the Free Trade of the Americas Agreement. New items for negotiation include product standards, competition policies, services, and investment policies. Most contentious are labor and environmental standards, where the potential for protectionist capture is greater and the mutual recognition versus harmonization debate is obscured.deeper integration, free trade, Heckscher-Ohlin model, integration, trade barriers, WTO, International Relations/Trade,

Review of W and Z Production at the Tevatron

The CDF and \D0 collaborations have used recent data taken at the Tevatron to perform QCD tests with $W$ and $Z$ bosons decaying leptonically. \D0 measures the production cross section times branching ratio for $W$ and $Z$ bosons. This also gives an indirect measurement of the total width of the $W$ boson: \gw=2.126\pm0.092 GeV. CDF reports on a direct measurement of \gw=2.19\pm0.19 GeV, in good agreement with the indirect determination and Standard Model predictions. \D0's measurement of the differential $d\sigma/dp_T$ distribution for $W$ and $Z$ bosons decaying to electrons agrees with the combined QCD perturbative and resummation calculations. In addition, the $d\sigma/dp_T$ distribution for the $Z$ boson discriminates between different vector boson production models. Studies of $W+ Jet$ production at CDF find the NLO QCD prediction for the production rate of $W+\ge1 Jet$ events to be in good agreement with the data.Comment: 8 pages, 6 figures, presented at XXXIIIrd Recontres de Moriond, QCD AND HIGH ENERGY HADRONIC INTERACTIONS,Les Arcs, Savoie, France, 199

Supersaturation, droplet spectra, and turbulent mixing in clouds

Much effort has recently gone into explaining the observed broad precoalescence size distribution of droplets in cloud and fogs, because this differs from the results of condensational growth calculations which lead to much narrower distributions. A good example of droplet size-distribution broadening was observed on flight 17 (25 July) of the NRL tethered balloon during the 1987 FIRE San Nicolas Island IFO. These observations caused the interactions between cloud microphysics and turbulent mixing to be re-examined. The findings of Broadwell and Breidenthal (1982) who conducted laboratory and theoretical studies of mixing in shear flow, and those of Baker et al. (1984) who applied the earlier work to mixing in clouds, were used. Rather than looking at the 25 July case at SNI, earlier fog observations made at SUNY (6 Oct. 1982) which also indicated that shear-induced mixing was taking place, and which had a better collection of microphysical measurements including more precise supersaturation measurements and detailed vertical profiles of meteorological parameters were chosen instead