41,517 research outputs found
The Cardy-Verlinde Formula and Charged Topological AdS Black Holes
We consider the brane universe in the bulk background of the charged
topological AdS black holes. The evolution of the brane universe is described
by the Friedmann equations for a flat or an open FRW-universe containing
radiation and stiff matter. We find that the temperature and entropy of the
dual CFT are simply expressed in terms of the Hubble parameter and its time
derivative, and the Friedmann equations coincide with thermodynamic formulas of
the dual CFT at the moment when the brane crosses the black hole horizon. We
obtain the generalized Cardy-Verlinde formula for the CFT with an R-charge, for
any values of the curvature parameter k in the Friedmann equations.Comment: 10 pages, LaTeX, references adde
Improved Compressive Sensing Of Natural Scenes Using Localized Random Sampling
Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging
Efficient Image Processing Via Compressive Sensing Of Integrate-And-Fire Neuronal Network Dynamics
Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an I&F network. In this paper, we present a new framework for recovering sparse inputs of nonlinear neuronal networks via compressive sensing. By recovering both one-dimensional inputs and two-dimensional images, resembling natural stimuli, we demonstrate that input information can be well-preserved through nonlinear I&F network dynamics even when the number of network-output measurements is significantly smaller than the number of input-signal components. This work suggests an important extension of CS theory potentially useful in improving the processing of medical or natural images through I&F network dynamics and understanding the transmission of stimulus information across the visual system
Quantum probe and design for a chemical compass with magnetic nanostructures
Magnetic fields as weak as Earth's may affect the outcome of certain
photochemical reactions that go through a radical pair intermediate. When the
reaction environment is anisotropic, this phenomenon can form the basis of a
chemical compass and has been proposed as a mechanism for animal
magnetoreception. Here, we demonstrate how to optimize the design of a chemical
compass with a much better directional sensitivity simply by a gradient field,
e.g. from a magnetic nanostructure. We propose an experimental test of these
predictions, and suggest design principles for a hybrid metallic-organic
chemical compass. In addition to the practical interest in designing a
biomimetic weak magnetic field sensor, our result shows that gradient fields
can server as powerful tools to probe spin correlations in radical pair
reactions.Comment: 8 pages, 6 figures, comments are welcom
Microscopic origin of light emission in Al_yGa_{1-y}N/GaN superlattice: Band profile and active site
We present first-principles calculations of AlGaN/GaN superlattice,
clarifying the microscopic origin of the light emission and revealing the
effect of local polarization within the quantum well. Profile of energy band
and distributions of electrons and holes demonstrate the existence of a main
active site in the well responsible for the main band-edge light emission. This
site appears at the position where the local polarization becomes zero. With
charge injection, the calculated optical spectra show that the broadening of
the band gap at the active site leads to the blueshift of emission wavelength
Chiron: A Robust Recommendation System with Graph Regularizer
Recommendation systems have been widely used by commercial service providers
for giving suggestions to users. Collaborative filtering (CF) systems, one of
the most popular recommendation systems, utilize the history of behaviors of
the aggregate user-base to provide individual recommendations and are effective
when almost all users faithfully express their opinions. However, they are
vulnerable to malicious users biasing their inputs in order to change the
overall ratings of a specific group of items. CF systems largely fall into two
categories - neighborhood-based and (matrix) factorization-based - and the
presence of adversarial input can influence recommendations in both categories,
leading to instabilities in estimation and prediction. Although the robustness
of different collaborative filtering algorithms has been extensively studied,
designing an efficient system that is immune to manipulation remains a
significant challenge. In this work we propose a novel "hybrid" recommendation
system with an adaptive graph-based user/item similarity-regularization -
"Chiron". Chiron ties the performance benefits of dimensionality reduction
(through factorization) with the advantage of neighborhood clustering (through
regularization). We demonstrate, using extensive comparative experiments, that
Chiron is resistant to manipulation by large and lethal attacks
FPTAS for Weighted Fibonacci Gates and Its Applications
Fibonacci gate problems have severed as computation primitives to solve other
problems by holographic algorithm and play an important role in the dichotomy
of exact counting for Holant and CSP frameworks. We generalize them to weighted
cases and allow each vertex function to have different parameters, which is a
much boarder family and #P-hard for exactly counting. We design a fully
polynomial-time approximation scheme (FPTAS) for this generalization by
correlation decay technique. This is the first deterministic FPTAS for
approximate counting in the general Holant framework without a degree bound. We
also formally introduce holographic reduction in the study of approximate
counting and these weighted Fibonacci gate problems serve as computation
primitives for approximate counting. Under holographic reduction, we obtain
FPTAS for other Holant problems and spin problems. One important application is
developing an FPTAS for a large range of ferromagnetic two-state spin systems.
This is the first deterministic FPTAS in the ferromagnetic range for two-state
spin systems without a degree bound. Besides these algorithms, we also develop
several new tools and techniques to establish the correlation decay property,
which are applicable in other problems
A Tight Karp-Lipton Collapse Result in Bounded Arithmetic
Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems
A semiparametric additive rate model for recurrent events with an informative terminal event
We propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event. The dependence between recurrent events and terminal event is nonparametric. A general transformation model is used to model the terminal event. We construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings. Application to a medical study is presented
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