12,989 research outputs found
Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets"
Discussion of "Frequentist coverage of adaptive nonparametric Bayesian
credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].Comment: Published at http://dx.doi.org/10.1214/15-AOS1270D in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Strong transmission and reflection of edge modes in bounded photonic graphene
The propagation of linear and nonlinear edge modes in bounded photonic
honeycomb lattices formed by an array of rapidly varying helical waveguides is
studied. These edge modes are found to exhibit strong transmission (reflection)
around sharp corners when the dispersion relation is topologically nontrivial
(trivial), and can also remain stationary. An asymptotic theory is developed
that establishes the presence (absence) of edge states on all four sides,
including in particular armchair edge states, in the topologically nontrivial
(trivial) case. In the presence of topological protection, nonlinear edge
solitons can persist over very long distances.Comment: 5 pages, 4 figures. Minor updates on the presentation and
interpretation of results. The movies showing transmission and reflection of
linear edge modes are available at
https://www.youtube.com/watch?v=XhaZZlkMadQ and
https://www.youtube.com/watch?v=R8NOw0NvRu
A universal asymptotic regime in the hyperbolic nonlinear Schr\"odinger equation
The appearance of a fundamental long-time asymptotic regime in the two space
one time dimensional hyperbolic nonlinear Schr\"odinger (HNLS) equation is
discussed. Based on analytical and extensive numerical simulations an
approximate self-similar solution is found for a wide range of initial
conditions -- essentially for initial lumps of small to moderate energy. Even
relatively large initial amplitudes, which imply strong nonlinear effects,
eventually lead to local structures resembling those of the self-similar
solution, with appropriate small modifications. These modifications are
important in order to properly capture the behavior of the phase of the
solution. This solution has aspects that suggest it is a universal attractor
emanating from wide ranges of initial data.Comment: 36 pages, 26 pages text + 20 figure
Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and
two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic
front initial data. Employing a front tracking type ansatz exactly reduces the
study of DSWs in two space one time (2+1) dimensions to finding DSW solutions
of (1+1) dimensional equations. With this ansatz, the KP and 2DBO equations can
be exactly reduced to cylindrical Korteweg-de Vries (cKdV) and cylindrical
Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which
describe DSW evolution in the cKdV and cBO equations are derived in general and
Riemann type variables are introduced. DSWs obtained from the numerical
solutions of the corresponding Whitham systems and direct numerical simulations
of the cKdV and cBO equations are compared with excellent agreement obtained.
In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO
equations are compared with the cKdV and cBO equations, again with remarkable
agreement. It is concluded that the (2+1) DSW behavior along parabolic fronts
can be effectively described by the DSW solutions of the reduced (1+1)
dimensional equations.Comment: 25 Pages, 16 Figures. The movies showing dispersive shock wave
propagation in Kadomtsev-Petviashvili II and Two Dimensional Benjamin-Ono
equations are available at https://youtu.be/AExAQHRS_vE and
https://youtu.be/aXUNYKFlke
Lensed Arcs and Inner Structure of Abell 697
We present new optical observations of the z=0.282 cluster Abell 697 from the
Keck II telescope. Images show an unusual disturbed structure in the cD halo
and a previously unknown faint gravitational lens arc. A spectrum of the arc
did not yield a redshift, but its spectrum and colors suggest it lies at z>1.3.
We construct models to reproduce the arc that show the potential is likely to
be highly elliptical. We suggest that this cluster may have undergone a recent
merger and is in the process of forming its cD galaxy. Analysis of X-ray data
from ROSAT and ASCA suggests that the merging process is sufficiently advanced
that the gas in the cluster has relaxed, and A697 lies near the L_x-T_x
relation for normal clusters.Comment: LaTeX; 12 pages, 3 figures, submitted to ApJ Letter
Investigation of Programming Languages for an Automated Manufacturing System
This paper is an investigation of alternative programming languages for use in manufacturing control applications. After reviewing several types of languages, two alternative languages for programming the flexible manufacturing cell in Miami University's Manufacturing Engineering Department are investigated. One language, called Cell Programming Language (CPL), is an object-like high level language developed at Miami
University. The other is Relay Ladder Logic (RLL) which is the
predominant language used in industry to program programmable logic controllers. An RLL program that is equivalent to an existing CPL program was developed for this purpose
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Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption
An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,...,B_n) of square matrices over F_q and a function Eval: F_q → {0,1}, and evaluated on x \in {0,1}^n by computing Eval(det(A + sum_{i \in [n]} x_i B_i)).
In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation.
As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (iO) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation
Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality
We study the tradeoff between the statistical error and communication cost of
distributed statistical estimation problems in high dimensions. In the
distributed sparse Gaussian mean estimation problem, each of the machines
receives data points from a -dimensional Gaussian distribution with
unknown mean which is promised to be -sparse. The machines
communicate by message passing and aim to estimate the mean . We
provide a tight (up to logarithmic factors) tradeoff between the estimation
error and the number of bits communicated between the machines. This directly
leads to a lower bound for the distributed \textit{sparse linear regression}
problem: to achieve the statistical minimax error, the total communication is
at least , where is the number of observations that
each machine receives and is the ambient dimension. These lower results
improve upon [Sha14,SD'14] by allowing multi-round iterative communication
model. We also give the first optimal simultaneous protocol in the dense case
for mean estimation.
As our main technique, we prove a \textit{distributed data processing
inequality}, as a generalization of usual data processing inequalities, which
might be of independent interest and useful for other problems.Comment: To appear at STOC 2016. Fixed typos in theorem 4.5 and incorporated
reviewers' suggestion
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