Related papers: Smooth maps from clumpy data: generalizations
A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…
The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…
Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
The two-point correlation function has been the standard statistic for quantifying how galaxies are clustered. The statistic uses the positions of galaxies, but not their properties. Clustering as a function of galaxy property, be it type,…
We are using computer models to explore the observational sensitivity to changes in atmospheric and surface properties, and the detectability of biosignatures, in the globally averaged spectra and light-curves of the Earth. Using AIRS…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
In Astronomy, Survival Analysis and Epidemiology, among many other fields, doubly truncated data often appear. Double truncation generally induces a sampling bias, so ordinary estimators may be inconsistent. In this paper, smoothing spline…
The sea level observations from satellite altimetry are characterised by a sparse spatial and temporal coverage. For this reason, along-track data are routinely interpolated into daily grids. The latter are strongly smoothed in time and…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…
In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…
Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
Despite the fact that the physics of the cosmic microwave background anisotropies is most naturally expressed in Fourier space, pixelised maps are almost always used in the analysis and simulation of microwave data. A complementary approach…
In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…
We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…
We present methods for approximating the mapping that defines the invariant manifold for two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If…