相关论文: Optimal Data-based Kernel Estimation of Evolutiona…
In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding a regression function that takes a delay embedded…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function -- or smoothing kernel -- w(\theta). We show…
Consistent in-focus input imagery is an essential precondition for machine vision systems to perceive the dynamic environment. A defocus blur severely degrades the performance of vision systems. To tackle this problem, we propose a…
We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes at the right hand side of the first accumulation point of…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
Spectral data is routinely broadened in order to improve appearance, approximate a higher sampling level or model experimental measurement effects. While there has been extensive work in the signal processing field to develop efficient…
Sleep is crucial for human health, and EEG signals play a significant role in sleep research. Due to the high-dimensional nature of EEG signal data sequences, data visualization and clustering of different sleep stages have been challenges.…
Reconstruction of the sky brightness measured by radio interferometers is typically achieved through gridding techniques, or histograms in spatial Fourier space. For Epoch of Reionisation (EoR) 21 cm power spectrum measurements, extreme…
The Eilers-Whittaker method for data smoothing effectiveness depends on the choice of the regularisation parameter, and automatic selection is a necessity for large datasets. Common methods, such as leave-one-out cross-validation, can…
Recent progress in image deblurring techniques focuses mainly on operating in both frequency and spatial domains using the Fourier transform (FT) properties. However, their performance is limited due to the dependency of FT on stationary…
We propose a two-stage procedure for estimating the location $\bolds{\mu}$ and size M of the maximum of a smooth d-variate regression function f. In the first stage, a preliminary estimator of $\bolds{\mu}$ obtained from a standard…
In this article, we explore the use of contour deformation for the numerical evaluation of Feynman integrals after sector decomposition. In existing codes, the contour of integration is determined heuristically for each phase-space point by…
The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to…
We present a general analysis for determining the optimal modulation parameters for the modulation transfer spectroscopy scheme. The results are universally valid and can be applied to spectroscopy of any atomic species requiring only the…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are…