15,966 research outputs found
Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds
In this paper, we study the efficient numerical integration of functions with
sharp gradients and cusps. An adaptive integration algorithm is presented that
systematically improves the accuracy of the integration of a set of functions.
The algorithm is based on a divide and conquer strategy and is independent of
the location of the sharp gradient or cusp. The error analysis reveals that for
a function (derivative-discontinuity at a point), a rate of convergence
of is obtained in . Two applications of the adaptive integration
scheme are studied. First, we use the adaptive quadratures for the integration
of the regularized Heaviside function---a strongly localized function that is
used for modeling sharp gradients. Then, the adaptive quadratures are employed
in the enriched finite element solution of the all-electron Coulomb problem in
crystalline diamond. The source term and enrichment functions of this problem
have sharp gradients and cusps at the nuclei. We show that the optimal rate of
convergence is obtained with only a marginal increase in the number of
integration points with respect to the pure finite element solution with the
same number of elements. The adaptive integration scheme is simple, robust, and
directly applicable to any generalized finite element method employing
enrichments with sharp local variations or cusps in -dimensional
parallelepiped elements.Comment: 22 page
Minimal surfaces and entanglement entropy in anti-de Sitter space
According to Ryu and Takayanagi, the entanglement entropy in conformal field
theory (CFT) is related through the AdS/CFT correspondence to the area of a
minimal surface in the bulk. We study this holographic geometrical method of
calculating the entanglement entropy in the vacuum case of a CFT which is
holographically dual to empty anti-de Sitter (AdS) spacetime. Namely, we
investigate the minimal surfaces spanned on boundaries of spherical domains at
infinity of hyperbolic space, which represents a time-slice of AdS spacetime.
We consider a generic position of two spherical domains: two disjoint domains,
overlapping domains, and touching domains. In all these cases we find the
explicit expressions for the minimal surfaces and the renormalized expression
for the area. We study also the embedding of the minimal surfaces into full AdS
spacetime and we find that for a proper choice of the static Killing vector we
can model a dynamical situation of "tearing" of the minimal surface when the
domains on which it is spanned are moved away from each other.Comment: 36 pages, 21 figures, for version with high-resolution figures see
http://utf.mff.cuni.cz/~krtous/papers
A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements
International audienceThe first stage in any control system is to be able to accurately estimate the system's state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73% and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems.Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error.Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, the Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), the Markov Chain Monte Carlo approach (MCMC), and the original Box Particle Filter (BPF). The algorithm is demonstrated to outperform existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty.The BRPF yields a computational load reduction of 73% with respect to the SIR-PF and of 90% with respect to MCMC for similar RMSE orders of magnitude. The present work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods
Self-Selective Correlation Ship Tracking Method for Smart Ocean System
In recent years, with the development of the marine industry, navigation
environment becomes more complicated. Some artificial intelligence
technologies, such as computer vision, can recognize, track and count the
sailing ships to ensure the maritime security and facilitates the management
for Smart Ocean System. Aiming at the scaling problem and boundary effect
problem of traditional correlation filtering methods, we propose a
self-selective correlation filtering method based on box regression (BRCF). The
proposed method mainly include: 1) A self-selective model with negative samples
mining method which effectively reduces the boundary effect in strengthening
the classification ability of classifier at the same time; 2) A bounding box
regression method combined with a key points matching method for the scale
prediction, leading to a fast and efficient calculation. The experimental
results show that the proposed method can effectively deal with the problem of
ship size changes and background interference. The success rates and precisions
were higher than Discriminative Scale Space Tracking (DSST) by over 8
percentage points on the marine traffic dataset of our laboratory. In terms of
processing speed, the proposed method is higher than DSST by nearly 22 Frames
Per Second (FPS)
A self-calibration approach for optical long baseline interferometry imaging
Current optical interferometers are affected by unknown turbulent phases on
each telescope. In the field of radio-interferometry, the self-calibration
technique is a powerful tool to process interferometric data with missing phase
information. This paper intends to revisit the application of self-calibration
to Optical Long Baseline Interferometry (OLBI). We cast rigorously the OLBI
data processing problem into the self-calibration framework and demonstrate the
efficiency of the method on real astronomical OLBI dataset
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