Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistenby of the estimates. The results are generalized to obtain a simple mean-shift estimate that can be extended in a k-nearestneighbor approach. Applications of gradient estimation to pa...

Franz G. Mertens Physikalisches Institut, Universität Bayreuth, D–95440 Bayreuth, Germany (Dated: November 11, 2002) Abstract The Levinson theorem for two–dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m–th partial wave is related to the phase shift and the singularity strength of the potential. For ...

Mean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on a surface constructed with a “shadow” kernel. For Gaussian kernels, mean shift is a gradient...

General multivariate periodic wavelets are an efficient tool for the approximation of multidimensional functions, which feature dominant directions of the periodicity. One-dimensional shift invariant spaces and tensor-product wavelets are generalized to multivariate shift invariant spaces on non-tensor-product patterns. In particular, the algebraic properties of the automorphism group are inves...

In this paper, based on the shift splitting of coefficient matrix, a generalized two-sweep (GTSS) method is introduced to solve non-Hermitian positive definite linear systems. Theoretical analysis shows that GTSS convergent unique solution systems under loose restriction iteration parameter. Numerical experiments are reported efficiency method.

Generalized quantum measurements identifying nonorthogonal states without ambiguity often play an indispensable role in various applications. For such unambiguous state-discrimination scenario, we have a finite probability of obtaining inconclusive results and minimizing the is particular importance. In this paper, experimentally demonstrate adaptive generalized measurement that can unambiguous...

Abstract A common task in computational text analyses is to quantify how two corpora differ according a measurement like word frequency, sentiment, or information content. However, collapsing the texts’ rich stories into single number often conceptually perilous, and it difficult confidently interpret interesting unexpected textual patterns without looming concerns about data artifacts validity...