In this paper, we propose some recent works on data analysis and synthesis based on Empirical Mode Decomposition (EMD). Firstly, a direct 2D extension of original Huang EMD algorithm with application to texture analysis, and fractional Brownian motion synthesis. Secondly, an analytical version of EMD based on PDE in 1D-space is presented. We proposed an extension in 2D-case of the so-called “si...

A common motif in the expositions of spline-based methods in statistical smoothing or numerical interpolation is an allusion to mechanical analogies—motivated perhaps by a desire to provide some explanation why the resulting shapes ought to be regarded as “natural”. The univariate case has its Oxford English Dictionary reference to draftsman spline as “a flexible strip of wood or hard rubber us...

We address the problem of reconstructing scalar and vector functions from non-uniform data. The reconstruction problem is formulated as a minimization problem where the cost is a weighted sum of two terms. The first data term is the quadratic measure of goodness of fit, whereas the second regularization term is a smoothness functional. We concentrate on the case where the later is a semi-norm i...

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve seamless integration between the design and analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines allow multiple extraordinary points within same face. This generalization drastically increases flexibility build geometries using AST-splines; e.g., much coarser meshes can b...

In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation with boundary data by solving the corresponding inverse problems for 2D elasticity, and vice versa. For example, we can derive bounds on the volume fraction...

BACKGROUND Income, air pollution, obesity, and smoking are primary factors associated with human health and longevity in population-based studies. These four factors may have countervailing impacts on longevity. This analysis investigates longevity trade-offs between air pollution and income, and explores how relative effects of income and air pollution on human longevity are potentially influe...

In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...

It has been documented that AE signals propagate in thin plates as extensional and flexural plate modes. This was demonstrated using simulated AE sources (pencil lead breaks) by Gorman [1] on thin aluminum and gr/ep composite plates and by Gorman and Prosser [2] on thin aluminum plates. A typical signal from a pencil lead break source which identifies these two modes is shown in Figure 1. AE si...

Rainfall is one of the most important climatic variables in the hydrology cycle. In flood estimation as well as environmental pollution studies in medium to large watersheds not only mus temporal pattern of rainfall t be known, but also the knowledge of its spatial distribution is required. Estimation of daily rainfall distribution without comparison and selection of suitable methods may lead...