Related papers: Quantifying the uncertainty of contour maps
Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse…
Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
Since the prediction of climate is mainly considered as a prediction of second kind, it is indispensable to assess the accuracy with which these boundary conditions can be determined so that we can find a reasonable answer, whether climate…
Data integration is a notoriously difficult and heuristic-driven process, especially when ground-truth data are not readily available. This paper presents a measure of uncertainty by providing maximal and minimal ranges of a query outcome…
Marching squares (MS) and marching cubes (MC) are widely used algorithms for level-set visualization of scientific data. In this paper, we address the challenge of uncertainty visualization of the topology cases of the MS and MC algorithms…
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…
In this paper, we investigate the problem of assessing statistical methods and effectively summarizing results from simulations. Specifically, we consider problems of the type where multiple methods are compared on a reasonably large test…
Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Data science and informatics tools have been proliferating recently within the computational materials science and catalysis fields. This proliferation has spurned the creation of various frameworks for automated materials screening,…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
In this paper we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify…
As the world increasingly relies on mathematical models for forecasts in different areas, effective communication of uncertainty in time series predictions is important for informed decision making. This study explores how users estimate…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…