14,037 research outputs found
Polynomial bounds for decoupling, with applications
Let f(x) = f(x_1, ..., x_n) = \sum_{|S| <= k} a_S \prod_{i \in S} x_i be an
n-variate real multilinear polynomial of degree at most k, where S \subseteq
[n] = {1, 2, ..., n}. For its "one-block decoupled" version,
f~(y,z) = \sum_{|S| <= k} a_S \sum_{i \in S} y_i \prod_{j \in S\i} z_j,
we show tail-bound comparisons of the form
Pr[|f~(y,z)| > C_k t] t].
Our constants C_k, D_k are significantly better than those known for "full
decoupling". For example, when x, y, z are independent Gaussians we obtain C_k
= D_k = O(k); when x, y, z, Rademacher random variables we obtain C_k = O(k^2),
D_k = k^{O(k)}. By contrast, for full decoupling only C_k = D_k = k^{O(k)} is
known in these settings.
We describe consequences of these results for query complexity (related to
conjectures of Aaronson and Ambainis) and for analysis of Boolean functions
(including an optimal sharpening of the DFKO Inequality).Comment: 19 pages, including bibliograph
DTKI: a new formalized PKI with no trusted parties
The security of public key validation protocols for web-based applications
has recently attracted attention because of weaknesses in the certificate
authority model, and consequent attacks.
Recent proposals using public logs have succeeded in making certificate
management more transparent and verifiable. However, those proposals involve a
fixed set of authorities. This means an oligopoly is created. Another problem
with current log-based system is their heavy reliance on trusted parties that
monitor the logs.
We propose a distributed transparent key infrastructure (DTKI), which greatly
reduces the oligopoly of service providers and allows verification of the
behaviour of trusted parties. In addition, this paper formalises the public log
data structure and provides a formal analysis of the security that DTKI
guarantees.Comment: 19 page
The Electrochemical Oxidation of Substituted Catechols
The oxidation of substituted catechols was studied by cyclic voltammetry, chronoamperometry, rotating ringâdisk electrode, and coulometry. The results showed that the quinones that were formed from the oxidation of substituted catechols reacted with the basic forms of the starting material to yield the dimeric product. These products were generally unstable and rapidly polymerized or underwent some other irreversible reaction to form an electroinactive product. For 3,4âdihydroxyacetophenone and propriophenone, the intermediate was stable long enough to be observed in cyclic voltammetry. The rate of the coupling reaction was found to correlate well with the Hammett ÏâÏ parameters and indicated that there was substantial negative charge in the transition state. Finally, an analysis of the coulometric nâvalues along with the iat1/2/C values indicated that the initial coupling product was a diphenyl ether. Analysis of the coulometry products showed extensive polymerization
The Falling Factorial Basis and Its Statistical Applications
We study a novel spline-like basis, which we name the "falling factorial
basis", bearing many similarities to the classic truncated power basis. The
advantage of the falling factorial basis is that it enables rapid, linear-time
computations in basis matrix multiplication and basis matrix inversion. The
falling factorial functions are not actually splines, but are close enough to
splines that they provably retain some of the favorable properties of the
latter functions. We examine their application in two problems: trend filtering
over arbitrary input points, and a higher-order variant of the two-sample
Kolmogorov-Smirnov test.Comment: Full version for the ICML paper with the same titl
Meta-analysis of functional neuroimaging data using Bayesian nonparametric binary regression
In this work we perform a meta-analysis of neuroimaging data, consisting of
locations of peak activations identified in 162 separate studies on emotion.
Neuroimaging meta-analyses are typically performed using kernel-based methods.
However, these methods require the width of the kernel to be set a priori and
to be constant across the brain. To address these issues, we propose a fully
Bayesian nonparametric binary regression method to perform neuroimaging
meta-analyses. In our method, each location (or voxel) has a probability of
being a peak activation, and the corresponding probability function is based on
a spatially adaptive Gaussian Markov random field (GMRF). We also include
parameters in the model to robustify the procedure against miscoding of the
voxel response. Posterior inference is implemented using efficient MCMC
algorithms extended from those introduced in Holmes and Held [Bayesian Anal. 1
(2006) 145--168]. Our method allows the probability function to be locally
adaptive with respect to the covariates, that is, to be smooth in one region of
the covariate space and wiggly or even discontinuous in another. Posterior
miscoding probabilities for each of the identified voxels can also be obtained,
identifying voxels that may have been falsely classified as being activated.
Simulation studies and application to the emotion neuroimaging data indicate
that our method is superior to standard kernel-based methods.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS523 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Tying Dark Matter to Baryons with Self-interactions
Self-interacting dark matter (SIDM) models have been proposed to solve the
small-scale issues with the collisionless cold dark matter (CDM) paradigm. We
derive equilibrium solutions in these SIDM models for the dark matter halo
density profile including the gravitational potential of both baryons and dark
matter. Self-interactions drive dark matter to be isothermal and this ties the
core sizes and shapes of dark matter halos to the spatial distribution of the
stars, a radical departure from previous expectations and from CDM predictions.
Compared to predictions of SIDM-only simulations, the core sizes are smaller
and the core densities are higher, with the largest effects in baryon-dominated
galaxies. As an example, we find a core size around 0.5 kpc for dark matter in
the Milky Way, more than an order of magnitude smaller than the core size from
SIDM-only simulations, which has important implications for indirect searches
of SIDM candidates.Comment: 5 pages, 2 figures. v2: sections II and III edited heavily for
clarity of presentation, changes to figure 2 (halo shape), conclusions
unchange
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