Related papers: Extension and convergence analysis of Iterative Fi…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle…
Slice analysis is a generalization of the theory of holomorphic functions of one complex variable to quaternions. Among the new phenomena which appear in this context, there is the fact that the convergence domain of…
A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
This paper introduces an adaptive filtering process based on shrinking wavelet coefficients from the corresponding signal wavelet representation. The filtering procedure considers a threshold method determined by an iterative algorithm…
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a…
Studying real-world networks such as social networks or web networks is a challenge. These networks often combine a complex, highly connected structure together with a large size. We propose a new approach for large scale networks that is…
The convergence theory for the gradient sampling algorithm is extended to directionally Lipschitz functions. Although directionally Lipschitz functions are not necessarily locally Lipschitz, they are almost everywhere differentiable and…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity…
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the…
This article introduces a spherical latent space model for social network analysis, embedding actors on a hypersphere rather than in Euclidean space as in standard latent space models. The spherical geometry facilitates the representation…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic…
Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the…