Related papers: Currents and K-functions for Fiber Point Processes

We propose a novel Bayesian methodology for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). We introduce general models that build upon the RKHS generated by…

We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for…

We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled…

The space of K\"ahler metrics can, on the one hand, be approximated by subspaces of algebraic metrics, while, on the other hand, can be enlarged to finite-energy spaces arising in pluripotential theory. The latter spaces are realized as…

For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of the functional CUSUM process…

The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…

Gavruta introduced $K$-frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K-frames and standard frames, so we study weaving properties of K-frames. Two frames…

We derive a self-consistent hydrodynamic theory of coupled binary-fluid-surfactant systems from the underlying microscopic physics using Rayleigh's variational principle. At the microscopic level, surfactant molecules are modelled as…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

If $q:Y\longrightarrow{B}$ is a fibration and $Z$ is a space, then the free range mapping space $Y!Z$ has a collection of partial maps from $Y$ to $Z$ as underline space, i.e. those such maps whose domains are individual fibre of $q$. It is…

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

We investigate the point spread function of a multimode fiber. The distortion of the focal spot created on the fiber output facet is studied for a variety of the parameters. We develop a theoretical model of wavefront shaping through a…

In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an…

The importance and demands of visual scene understanding have been steadily increasing along with the active development of autonomous systems. Consequently, there has been a large amount of research dedicated to semantic segmentation and…

This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…

During the application of mass-action equation models to the study of amyloid fiber formation, time-consuming numerical calculations constitute a major bottleneck when no analytical solution is available. To conquer this difficulty, here an…

We employ a multi-phase smoothed particle hydrodynamics (SPH) method to study droplet dynamics in shear flow. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet…

We demonstrate the use of spatially encoded magnetic resonance to quantify ensemble dynamics of microscopic particles below the spatial resolution. By evaluating time series of k-space data-points, k-dependent motion patterns can be…