12,413 research outputs found
A Photonic Crystal Slab Laplace Differentiator
We introduce an implementation of a Laplace differentiator based on a
photonic crystal slab that operates at transmission mode. We show that the
Laplace differentiator can be implemented provided that the guided resonances
near the point exhibit an isotropic band structure. Such a device may
facilitate nanophotonics-based optical analog computing for image processing.Comment: Primary text 6 pages, 5 figures; Supplementary material 5 pages, 3
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Thank God That Regressing Y on X is Not the Same as Regressing X on Y: Direct and Indirect Residual Augmentations
What does regressing Y on X versus regressing X on Y have to do with MCMC? It turns out that many strategies for speeding up data-augmentation type algorithms can be understood as fostering independence or “de-correlation” between a regression function and the corresponding residual, thereby reducing or even eliminating dependence among MCMC iterates. There are two general classes of algorithms, those corresponding to regressing parameters on augmented data/auxiliary variables and those that operate the other way around. The interweaving strategy (Yu and Meng, 2011, JCGS) provides a general recipe to automatically take advantage of both, and it is the existence of two different types of residuals that makes the interweaving strategy seemingly magical in some cases and promising in general. The concept of residuals—which depends on actual data—also highlights the potential for substantial improvements when data augmentation schemes are allowed to depend on the observed data. At the same time, there is an intriguing phase transition type of phenomenon regarding choosing (partially) residual augmentation schemes, reminding us once more of the prevailing issue of trade-off between robustness and efficiency. This article reports on these latest theoretical investigations (using a class of normal/independence models) and empirical findings (using a posterior sampling for a Probit regression) in the search for effective residual augmentations—and ultimately more MCMC algorithms—that meet the 3-S criterion: simple, stable, and speedy.Statistic
Photon regions, shadow observables and constraints from M87* of a charged rotating black hole
Inspired by the observations of supermassive black hole M87* in \emph{Event
Horizon Telescope }(EHT) experiment, a remarkable surge in black hole physics
is to use the black hole shadow's observables to distinguish general relativity
(GR) and modified theories of gravity (MoG), which could also help to disclose
the astrophysical nature of the center black hole in EHT observation. In this
paper, we shall extensively carry out the study of a charged rotating black
hole in conformal gravity, in which the term related with the charge has
different falloffs from the usual Kerr-Newman (KN) black hole. We investigate
the spacetime properties including the horizons, ergospheres and the photon
regions; afterward, we show the boundary of black hole shadow and investigate
its characterized observables. The features closely depend on the spin and
charge parameters, which are compared with those in Kerr and KN black holes.
Then presupposing the M87* a charged rotating black hole in conformal gravity,
we also constrain the black hole parameters via the observation constraints
from EHT experiment. We find that the constraints on the inferred circularity
deviation, , and on the shadow axial ratio, , for the M87* black hole are satisfied for the entire parameter
space of the charged rotating black hole in conformal gravity. However, the
shadow angular diameter will give upper bound on
the parameter space. Our findings indicate that the current charged rotating
black hole in conformal gravity could be a candidate for astrophysical black
holes. Moreover, the EHT observation on the axial ratio may help us to
distinguish Kerr black hole and the current charged rotating black hole in
conformal gravity in some parameter space.Comment: references adde
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