Related papers: Currents and K-functions for Fiber Point Processes
On a polarized manifold $(X,L)$, the Bergman iteration $\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the K\"ahler-Ricci flow $\phi_t$ at any time $t \geq…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our…
We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
In this article, we construct the canonical semipositive current or the canonical measure ($=$ the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical…
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with…
This note intends to demonstrate how to discuss scalar curvature functions' admissibility on bundles by directly applying some of the Kazdan--Warner results. Proofs of the concept include determining which functions are realizable as scalar…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
For the task of mobility analysis of 3D shapes, we propose joint analysis for simultaneous motion part segmentation and motion attribute estimation, taking a single 3D model as input. The problem is significantly different from those…
Advances in cellular imaging technologies, especially those based on fluorescence in situ hybridization (FISH) now allow detailed visualization of the spatial organization of human or bacterial cells. Quantifying this spatial organization…
Homodyned K (HK) distribution has been widely used to describe the scattering phenomena arising in various research fields, such as ultrasound imaging or optics. In this work, we propose a machine learning based approach to the estimation…
The motion of an assembly of rigid fibers is investigated for different classes of closed streamline flows, steady or time dependent, two dimensional or three dimensional. In our study, the dynamics of the fiber assembly is fully-coupled to…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis…
Many active particles, both of biological and synthetic origin, can have a light controllable propulsion speed, a property that in biology is commonly referred to as photokinesis. Here we investigate directed transport of photokinetic…
Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over…
There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been appropriately separated and modeled through a domain…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…