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

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

Atom Scattering from Disordered Surfaces in the Sudden Approximation: Double Collisions Effects and Quantum Liquids

The Sudden Approximation (SA) for scattering of atoms from surfaces is generalized to allow for double collision events and scattering from time-dependent quantum liquid surfaces. The resulting new schemes retain the simplicity of the original SA, while requiring little extra computational effort. The results suggest that inert atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 15 pages, 1 figure. Related papers available at http://neon.cchem.berkeley.edu/~dan