Information Surfaces in Systems Biology and Applications to Engineering Sustainable Agriculture

Systems biology of plants offers myriad opportunities and many challenges in modeling. A number of technical challenges stem from paucity of computational methods for discovery of the most fundamental properties of complex dynamical systems. In systems engineering, eigen-mode analysis have proved to be a powerful approach. Following this philosophy, we introduce a new theory that has the benefits of eigen-mode analysis, while it allows investigation of complex dynamics prior to estimation of optimal scales and resolutions. Information Surfaces organizes the many intricate relationships among "eigen-modes" of gene networks at multiple scales and via an adaptable multi-resolution analytic approach that permits discovery of the appropriate scale and resolution for discovery of functions of genes in the model plant Arabidopsis. Applications are many, and some pertain developments of crops that sustainable agriculture requires.Comment: 24 Pages, DoCEIS 1

Coxeter Groups and Wavelet Sets

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead of by translations along a lattice. Although both theories look different at their onset, there exist connections and communalities which are exhibited in this semi-expository paper. In particular, there is a natural notion of a dilation-reflection wavelet set. We prove that dilation-reflection wavelet sets exist for arbitrary expansive matrix dilations, paralleling the traditional dilation-translation wavelet theory. There are certain measurable sets which can serve simultaneously as dilation-translation wavelet sets and dilation-reflection wavelet sets, although the orthonormal structures generated in the two theories are considerably different

Local Reconstruction and Visualization of Point-Based Surfaces Using Subdivision Surfaces

Extended version of our Shape Modeling 2005 paper.International audiencePoint-Based Surfaces, i.e. surfaces represented by discrete point sets which are either directly obtained by current 3D acquisition devices or converted from other surface representations, are well designed for multiresolution storage and transmission of complex objects. Unfortunately, visualization of point-based surfaces requires to develop specific rendering techniques (e.g. splatting) since point sets are not well adapted to existing graphics hardware which is optimized for polygonal meshes. In this paper, we propose an efficient reconstruction and visualization technique of point-based surfaces that takes full benefit from the entire optimized pipeline implemented in graphics hardware. The basic idea is to generate a set of independent meshes using a local 2D Delaunay triangulation of the point set. These meshes are then glued together to get a visual continuity by using a subdivision process