43,976 research outputs found
Exact Asymptotic Behavior of Singular Positive Solutions of Fractional Semi-Linear Elliptic Equations
In this paper, we prove the exact asymptotic behavior of singular positive
solutions of fractional semi-linear equations with an isolated singularity, where
and .Comment: 11 page
Qualitative analysis for an elliptic system in the punctured space
In this paper, we investigate the qualitative properties of positive
solutions for the following two-coupled elliptic system in the punctured space:
where and are all positive
constants, . We establish a monotonicity formula that completely
characterizes the singularity of positive solutions. We prove a sharp global
estimate for both components of positive solutions. We also prove the
nonexistence of positive semi-singular solutions, which means that one
component is bounded near the singularity and the other component is unbounded
near the singularity.Comment: 27 page
Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds
In this paper, we extend the GKZ-system method to the more general case:
compact Complete Intersection Calabi-Yau manifolds (CICY). For several
one-deformation modulus compact CICYs with D-branes, the on-shell
superpotentials in this paper from the extended GKZ-system method are exactly
consistent with published results obtained from other methods. We further
compute the off-shell superpotentials of these models. Then we obtain both the
on-shell and off-shell superpotentials for sev- eral two-deformation moduli
compact CICYs with D-branes by using the extended GKZ-system method. The
discrete symmetrical groups, Z2, Z3 and Z4, of the holo- morphic curves wrapped
by D-branes play the important roles in computing the superpotentials, in some
sense, they are the quantum symmetries of these models. Furthermore, through
the mirror symmetry, the Ooguri-Vafa invariants are extracted from the A-model
instanton expansion
Flexible Expectile Regression in Reproducing Kernel Hilbert Space
Expectile, first introduced by Newey and Powell (1987) in the econometrics
literature, has recently become increasingly popular in risk management and
capital allocation for financial institutions due to its desirable properties
such as coherence and elicitability. The current standard tool for expectile
regression analysis is the multiple linear expectile regression proposed by
Newey and Powell in 1987. The growing applications of expectile regression
motivate us to develop a much more flexible nonparametric multiple expectile
regression in a reproducing kernel Hilbert space. The resulting estimator is
called KERE which has multiple advantages over the classical multiple linear
expectile regression by incorporating non-linearity, non-additivity and complex
interactions in the final estimator. The kernel learning theory of KERE is
established. We develop an efficient algorithm inspired by
majorization-minimization principle for solving the entire solution path of
KERE. It is shown that the algorithm converges at least at a linear rate.
Extensive simulations are conducted to show the very competitive finite sample
performance of KERE. We further demonstrate the application of KERE by using
personal computer price data
Chiral Symmetry Breaking in Micro-Ring Optical Cavity By Engineered Dissipation
We propose a method to break the chiral symmetry of light in traveling wave
resonators by coupling the optical modes to a lossy channel. Through the
engineered dissipation, an indirect dissipative coupling between two oppositely
propagating modes can be realized. Combining with reactive coupling, it can
break the chiral symmetry of the resonator, allowing light propagating only in
one direction. The chiral symmetry breaking is numerically verified by the
simulation of an electromagnetic field in a micro-ring cavity, with proper
refractive index distributions. This work provokes us to emphasize the
dissipation engineering in photonics, and the generalized idea can also be
applied to other systems.Comment: 6 pages, 3 figure
Sliced Wasserstein Kernels for Probability Distributions
Optimal transport distances, otherwise known as Wasserstein distances, have
recently drawn ample attention in computer vision and machine learning as a
powerful discrepancy measure for probability distributions. The recent
developments on alternative formulations of the optimal transport have allowed
for faster solutions to the problem and has revamped its practical applications
in machine learning. In this paper, we exploit the widely used kernel methods
and provide a family of provably positive definite kernels based on the Sliced
Wasserstein distance and demonstrate the benefits of these kernels in a variety
of learning tasks. Our work provides a new perspective on the application of
optimal transport flavored distances through kernel methods in machine learning
tasks
Edge Detection Methods Based on Differential Phase Congruency of Monogenic Image
Edge Detection Methods Based on Differential Phase Congruency of Monogenic
Image Abstract: Edge detection has been widely used in medical image processing
and automatic diagnosis. Some novel edge detection algorithms,based on the
monogenic scale-space, are proposed by detecting points of local extrema in
local amplitude, the local attenuation and modified differential phase
congruency methods. The monogenic scale-space is obtained from a known image by
Poisson and conjugate Poisson filtering. In mathematics, it is the Hardy space
in the upper half-space. The boundary value of the monogenic scale-space
representation is a monogenic image. In the monogenic scale-space, the
definitions involving scale, such as local amplitude,local attenuation, local
phase angle, local phase vector and local frequency (phase derivatives) are
proposed. Using Clifford analysis, the relations between the local attenuation
and the local phase vector are obtained. These study will be improved the
understanding of image analysis in higher dimensional spaces. Experimental
results are shown by using some typical images.Comment: 18 pages, 2 figure
Security of Medical Cyber-physical Systems: An Empirical Study on Imaging Devices
Recent years have witnessed a boom of connected medical devices, which brings
security issues in the meantime. Medical imaging devices, an essential part of
medical cyber-physical systems, play a vital role in modern hospitals and are
often life-critical. However, security and privacy issues in these medical
cyber-physical systems are sometimes ignored.
In this paper, we perform an empirical study on imaging devices to analyse
the security of medical cyber-physical systems. To be precise, we design a
threat model and propose prospective attack techniques for medical imaging
devices. To tackle potential cyber threats, we introduce protection mechanisms,
evaluate the effectiveness and efficiency of protection mechanisms as well as
its interplay with attack techniques. To scoring security, we design a
hierarchical system that provides actionable suggestions for imaging devices in
different scenarios. We investigate 15 devices from 9 manufacturers to
demonstrate empirical comprehension and real-world security issues
Fast and Accurate Graph Stream Summarization
A graph stream is a continuous sequence of data items, in which each item
indicates an edge, including its two endpoints and edge weight. It forms a
dynamic graph that changes with every item in the stream. Graph streams play
important roles in cyber security, social networks, cloud troubleshooting
systems and other fields. Due to the vast volume and high update speed of graph
streams, traditional data structures for graph storage such as the adjacency
matrix and the adjacency list are no longer sufficient. However, prior art of
graph stream summarization, like CM sketches, gSketches, TCM and gMatrix,
either supports limited kinds of queries or suffers from poor accuracy of query
results. In this paper, we propose a novel Graph Stream Sketch (GSS for short)
to summarize the graph streams, which has the linear space cost (O(|E|), E is
the edge set of the graph) and the constant update time complexity (O(1)) and
supports all kinds of queries over graph streams with the controllable errors.
Both theoretical analysis and experiment results confirm the superiority of our
solution with regard to the time/space complexity and query results' precision
compared with the state-of-the-art
Interference control of nonlinear excitation in a multiatom cavity QED system
We show that by manipulating quantum interference in a multi-atom cavity QED
system, the nonlinear excitation of the cavity-atom polariton can be resonantly
enhanced while the linear excitation is suppressed. Under appropriate
conditions, it is possible to selectively enhance or suppress the polariton
excitation with two free-pace laser fields. We report an experiment with cold
Rb atoms in an optical cavity and present experimental results that demonstrate
such interference control of the cavity QED excitation and its direct
applications for studies of all-optical switching and cross-phase modulation of
the cavity transmitted light.Comment: 4 pages, 5 figure
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