53,277 research outputs found

    On Integration Methods Based on Scrambled Nets of Arbitrary Size

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    We consider the problem of evaluating I(φ):=[0,1)sφ(x)dxI(\varphi):=\int_{[0,1)^s}\varphi(x) dx for a function φL2[0,1)s\varphi \in L^2[0,1)^{s}. In situations where I(φ)I(\varphi) can be approximated by an estimate of the form N1n=0N1φ(xn)N^{-1}\sum_{n=0}^{N-1}\varphi(x^n), with {xn}n=0N1\{x^n\}_{n=0}^{N-1} a point set in [0,1)s[0,1)^s, it is now well known that the OP(N1/2)O_P(N^{-1/2}) Monte Carlo convergence rate can be improved by taking for {xn}n=0N1\{x^n\}_{n=0}^{N-1} the first N=λbmN=\lambda b^m points, λ{1,,b1}\lambda\in\{1,\dots,b-1\}, of a scrambled (t,s)(t,s)-sequence in base b2b\geq 2. In this paper we derive a bound for the variance of scrambled net quadrature rules which is of order o(N1)o(N^{-1}) without any restriction on NN. As a corollary, this bound allows us to provide simple conditions to get, for any pattern of NN, an integration error of size oP(N1/2)o_P(N^{-1/2}) for functions that depend on the quadrature size NN. Notably, we establish that sequential quasi-Monte Carlo (M. Gerber and N. Chopin, 2015, \emph{J. R. Statist. Soc. B, to appear.}) reaches the oP(N1/2)o_P(N^{-1/2}) convergence rate for any values of NN. In a numerical study, we show that for scrambled net quadrature rules we can relax the constraint on NN without any loss of efficiency when the integrand φ\varphi is a discontinuous function while, for sequential quasi-Monte Carlo, taking N=λbmN=\lambda b^m may only provide moderate gains.Comment: 27 pages, 2 figures (final version, to appear in The Journal of Complexity

    Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A

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    We are interested in the structure of the crystal graph of level ll Fock spaces representations of Uq(sle^)\mathcal{U}_q (\widehat{\mathfrak{sl}_e}). Since the work of Shan [26], we know that this graph encodes the modular branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: - Schensted's classic bumping procedure, - the cyclage isomorphism defined in [13], - a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. We explain how this can be seen as an analogue of the bumping algorithm for affine type AA. Moreover, it yields a combinatorial characterisation of the vertices of any connected component of the crystal of the Fock space

    Cylindric multipartitions and level-rank duality

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    We show that a multipartition is cylindric if and only if its level rank-dual is a source in the corresponding affine type AA 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?

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    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

    Searching for a Modernized Voice: Economics, Institutions, and Predictability in European Competition Law

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    Review of W and Z Production at the Tevatron

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    The CDF and \D0 collaborations have used recent data taken at the Tevatron to perform QCD tests with WW and ZZ bosons decaying leptonically. \D0 measures the production cross section times branching ratio for WW and ZZ bosons. This also gives an indirect measurement of the total width of the WW 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 dσ/dpTd\sigma/dp_T distribution for WW and ZZ bosons decaying to electrons agrees with the combined QCD perturbative and resummation calculations. In addition, the dσ/dpTd\sigma/dp_T distribution for the ZZ boson discriminates between different vector boson production models. Studies of W+JetW+ Jet production at CDF find the NLO QCD prediction for the production rate of W+1JetW+\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

    Corbin and Fuller\u27s Cases on Contracts (1942?): The Casebook that Never Was

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

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    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
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