463 research outputs found
Generalized iterated wreath products of cyclic groups and rooted trees correspondence
Consider the generalized iterated wreath product where . We
prove that the irreducible representations for this class of groups are indexed
by a certain type of rooted trees. This provides a Bratteli diagram for the
generalized iterated wreath product, a simple recursion formula for the number
of irreducible representations, and a strategy to calculate the dimension of
each irreducible representation. We calculate explicitly fast Fourier
transforms (FFT) for this class of groups, giving literature's fastest FFT
upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science
Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
We introduce an efficient method for computing the Stekloff eigenvalues
associated with the Helmholtz equation. In general, this eigenvalue problem
requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary
condition repeatedly. We propose solving the related constant coefficient
Helmholtz equation with Fast Fourier Transform (FFT) based on carefully
designed extensions and restrictions of the equation. The proposed Fourier
method, combined with proper eigensolver, results in an efficient and clear
approach for computing the Stekloff eigenvalues.Comment: 12 pages, 4 figure
Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence
Consider the generalized iterated wreath product of symmetric groups. We give a complete description of the traversal
for the generalized iterated wreath product. We also prove an existence of a
bijection between the equivalence classes of ordinary irreducible
representations of the generalized iterated wreath product and orbits of labels
on certain rooted trees. We find a recursion for the number of these labels and
the degrees of irreducible representations of the generalized iterated wreath
product. Finally, we give rough upper bound estimates for fast Fourier
transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv
admin note: text overlap with arXiv:1409.060
ALBATROSS: Publicly AttestabLe BATched Randomness Based On Secret Sharing
In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption.
We also address the important issue of constructing Universally Composable randomness beacons, showing two UC versions of Albatross: one based on simple UC NIZKs and another one based on novel efficient ``designated verifier\u27\u27 homomorphic commitments. Interestingly this latter version can be instantiated from a global random oracle under the weaker Computational Diffie-Hellman (CDH) assumption.
An execution of ALBATROSS with parties, out of which up to are corrupt for a constant , generates uniformly random values,
requiring in the worst case
an amortized cost per party of exponentiations per random value.
We significantly improve on the SCRAPE protocol (Cascudo and David, ACNS 17), which
required exponentiations per party to generate one uniformly random value. This is mainly achieved via two techniques: first, the use of packed Shamir secret sharing for the PVSS; second, the use of linear -resilient functions (computed via a Fast Fourier Transform-based algorithm) to improve the randomness extraction
Fast Algorithms for Join Operations on Tree Decompositions
Treewidth is a measure of how tree-like a graph is. It has many important
algorithmic applications because many NP-hard problems on general graphs become
tractable when restricted to graphs of bounded treewidth. Algorithms for
problems on graphs of bounded treewidth mostly are dynamic programming
algorithms using the structure of a tree decomposition of the graph. The
bottleneck in the worst-case run time of these algorithms often is the
computations for the so called join nodes in the associated nice tree
decomposition.
In this paper, we review two different approaches that have appeared in the
literature about computations for the join nodes: one using fast zeta and
M\"obius transforms and one using fast Fourier transforms. We combine these
approaches to obtain new, faster algorithms for a broad class of vertex subset
problems known as the [\sigma,\rho]-domination problems. Our main result is
that we show how to solve [\sigma,\rho]-domination problems in arithmetic operations. Here, t is the treewidth, s is the
(fixed) number of states required to represent partial solutions of the
specific [\sigma,\rho]-domination problem, and n is the number of vertices in
the graph. This reduces the polynomial factors involved compared to the
previously best time bound (van Rooij, Bodlaender, Rossmanith, ESA 2009) of arithmetic operations. In particular, this removes
the dependence of the degree of the polynomial on the fixed number of
states~.Comment: An earlier version appeared in "Treewidth, Kernels, and Algorithms.
Essays Dedicated to Hans L. Bodlaender on the Occasion of His 60th Birthday"
LNCS 1216
Having a lot of a good thing: multiple important group memberships as a source of self-esteem.
Copyright: © 2015 Jetten et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedMembership in important social groups can promote a positive identity. We propose and test an identity resource model in which personal self-esteem is boosted by membership in additional important social groups. Belonging to multiple important group memberships predicts personal self-esteem in children (Study 1a), older adults (Study 1b), and former residents of a homeless shelter (Study 1c). Study 2 shows that the effects of multiple important group memberships on personal self-esteem are not reducible to number of interpersonal ties. Studies 3a and 3b provide longitudinal evidence that multiple important group memberships predict personal self-esteem over time. Studies 4 and 5 show that collective self-esteem mediates this effect, suggesting that membership in multiple important groups boosts personal self-esteem because people take pride in, and derive meaning from, important group memberships. Discussion focuses on when and why important group memberships act as a social resource that fuels personal self-esteem.This study was supported by 1. Australian Research Council Future Fellowship (FT110100238) awarded to Jolanda Jetten (see http://www.arc.gov.au) 2. Australian Research Council Linkage Grant (LP110200437) to Jolanda Jetten and Genevieve Dingle (see http://www.arc.gov.au) 3. support from the Canadian Institute for Advanced Research Social Interactions, Identity and Well-Being Program to Nyla Branscombe, S. Alexander Haslam, and Catherine Haslam (see http://www.cifar.ca)
A meta-analytic review of stand-alone interventions to improve body image
Objective
Numerous stand-alone interventions to improve body image have been developed. The
present review used meta-analysis to estimate the effectiveness of such interventions, and
to identify the specific change techniques that lead to improvement in body image.
Methods
The inclusion criteria were that (a) the intervention was stand-alone (i.e., solely focused on
improving body image), (b) a control group was used, (c) participants were randomly
assigned to conditions, and (d) at least one pretest and one posttest measure of body
image was taken. Effect sizes were meta-analysed and moderator analyses were conducted.
A taxonomy of 48 change techniques used in interventions targeted at body image
was developed; all interventions were coded using this taxonomy.
Results
The literature search identified 62 tests of interventions (N = 3,846). Interventions produced
a small-to-medium improvement in body image (d+ = 0.38), a small-to-medium reduction in
beauty ideal internalisation (d+ = -0.37), and a large reduction in social comparison tendencies
(d+ = -0.72). However, the effect size for body image was inflated by bias both within
and across studies, and was reliable but of small magnitude once corrections for bias were
applied. Effect sizes for the other outcomes were no longer reliable once corrections for
bias were applied. Several features of the sample, intervention, and methodology moderated
intervention effects. Twelve change techniques were associated with improvements in
body image, and three techniques were contra-indicated.
Conclusions
The findings show that interventions engender only small improvements in body image, and
underline the need for large-scale, high-quality trials in this area. The review identifies effective
techniques that could be deployed in future interventions
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