Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and ...

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling with tractable reference variables. This paper generalises functional tensor-train approximation inverse Rosenblatt recently developed Dolgov et al. (...

A theoretical relation is presented between the seismological Fourier amplitude spectrumand the mean squared value of the elastic response, which is defined by Gaussian distribution. Byshifting a general process to its mean value, spectrum of the mean squared value of the displacementis computed from the Fourier amplitude spectrum and the real part of the relative displacementtransfer function ...

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inver...

Spatially explicit capture-recapture methods, used widely to estimate the abundance of large carnivores, allow for movement within home ranges during sampling. Probability of detection is a decreasing function of distance from the home range center, with one parameter for magnitude and another for spatial scale. Sex-based and other differences in home range size potentially cause heterogeneity ...

INTRODUCTION The Theory of Distance Geometry [1] allows coordinate-free formulations for most position analysis problems. Using such formulations, the inverse kinematics of a serial robot can be performed by using a distance matrix, one whose entries are squared distances between pairs of points selected on the axes of the robot. While some of these distances are known (such as the distances be...