53,277 research outputs found

### 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

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

We are interested in the structure of the crystal graph of level $l$ Fock
spaces representations of $\mathcal{U}_q (\widehat{\mathfrak{sl}_e})$. 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 $A$. 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

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 initiativeâ€™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 initiativeâ€™s content affects policy despite powerful opponentsâ€™ 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

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