From the 2 of 13 linked papers with an AI index.
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Contour Hankel dynamics and indicator fields for the Riemann -function
Zhiliang Deng, Xiaomei Yang, Huazhong Lü
We develop a moving-contour Hankel framework for encoding local zero configurations of the Riemann -function. Weighted contour integrals of the logarithmic derivative , ex…
Contour-count indicator fields for visible pole clusters in meromorphic continuation
Zhiliang Deng, Xiaomei Yang
The paper introduces a contour-count indicator method that uses determinant characteristics from Fourier coefficients to image and certify clusters of visible poles in outward mero…
Determinant Characteristics and Argument-Principle Certification for Visible Poles in Meromorphic Continuation
Xiaomei Yang, Zhiliang Deng
We study outward meromorphic continuation from circular boundary data in the unit disk. The unknown function is holomorphic in the unit disk and admits a meromorphic continuation t…
Hamiltonian Monte Carlo from -deformed phase-space mechanics
Xiaomei Yang, Zhiliang Deng
Hamiltonian Monte Carlo (HMC) generates efficient Markov transitions by combining Hamiltonian dynamics with a Metropolis correction. This paper develops a geometric \(q\)-analogue…
Fourier--Hankel Moment Imaging of Components, Phase Centers, and Detectable Cavities in Acoustic Scattering
Zhiliang Deng, Xiaofei Guan, Xiaomei Yang
We develop a Fourier--Hankel moment framework for recovering component counts, phase-center locations, and detectable cavity information from full-aperture acoustic far-field data.…
A persistent-homology-Gaussian prior for solving infinite-dimensional Bayesian inverse scattering problems
Zhiyuan Wang, Hang Qi, Xiaofei Guan +2
Bayesian inference methods have been developed to address inverse problems in function spaces where the unknown parameters are of infinite dimension. However, conventional Gaussian…