Nonuniform tubular neighborhoods of curves in Rn are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtained for nonuniform thickness. All singularities within almost injectivity radius are classifie...

The dynamic time warping (DTW) distance has been used as a misfit function for wave-equation inversion to mitigate the local minima issue. However, original DTW is not smooth; therefore it can yield strong discontinuity in adjoint source. Such weakness does help nonlinear inverse problems converge plausible minimum by any means. We introduce first geophysics smooth distance, which demonstrated ...

We propose optimal dimensionality reduction techniques for the solution of goal–oriented linear–Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covari...

This paper examines statistical approaches for interpolating climatic data over large regions, providing a brief introduction to interpolation techniques for climate variables of use in agricultural research, as well as general recommendations for future research to assess interpolation techniques. Three approaches—1) inverse distance weighted averaging (IDWA), 2) thin plate smoothing splines a...

Given a network G(V,A,c), the eccentric node of a node v ∈ V is the furthest node from v with respect to the edge length vector c. The inverse eccentric problem consists of modifying the edge length vector c minimally so that a specific node t becomes the eccentric node of another specific node s. The length modifications can be measured by different distances. In this paper, the problem under ...

NonGaussian Markov image models are e ective in the preservation of edge detail in Bayesian formulations of restoration and reconstruction problems. Included in these models are coe cients quantifying the statistical links among pixels in local cliques, which are typically assumed to have an inverse dependence on distance among the corresponding neighboring pixels. Estimation of these coe cient...

Spatial dataset representing the nutrient distribution in Karayar reservoir during pre and post-monsoon season is presented. Random sampling method was used for data collection and the sample location were fixed using a handheld global positioning system (Garmin GPSMAP-76). The nutrients were estimated using the standard techniques as described in the American Public Health Association (APHA) m...