Eungchun Cho

Grid coverage for surveillance and target location in distributed sensor networks

We present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or three-dimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target at a grid point at any instant in time. We first present an integer linear programming (ILP) solution for minimizing the cost of sensors for complete coverage of the sensor field. We solve the ILP model using a representative public-domain solver and present a divide-and-conquer approach for solving large problem instances. We then use the framework of identifying codes to determine sensor placement for unique target location, We provide coding-theoretic bounds on the number of sensors and present methods for determining their placement in the sensor field. We also show that grid-based sensor placement for single targets provides asymptotically complete (unambiguous) location of multiple targets in the grid.

Coding theory framework for target location in distributed sensor networks

Distributed, real time sensor networks are essential for effective surveillance in the digitized battlefield and for environmental monitoring. We present the first systematic theory that leads to novel sensor deployment strategies for effective surveillance and target location. We represent the sensor field as a grid (two- or three-dimensional) of points (coordinates), and use the term target at a grid point at any instant in time. We use the framework of unidentified codes to determine sensor placement for unique target location. We provide coding-theoretic-bounds on the number of sensors and present methods for determining their placement in the sensor field. We also show that sensor placement for single targets provides asymptotically complete (unambiguous) location of multiple targets.

Application of wavelet analysis to ecological data

Abstract Ecological data are difficult to analyze due to complexity residing in the ecological systems with the variables varying in non-linear fashion. Efficient methods are required to properly extract information out of the complex data. Wavelets have good time–frequency (time-scale) localization, can represent data parsimoniously, and can be implemented with very fast algorithms. Brief backgrounds and computational aspects of wavelets were outlined for implementation to ecological data analysis. Wavelets are well suited for building mathematical models of ecological data and the statistical analysis of combined effects of complex factors in ecological network. Wavelet based analysis and synthesis may lead researchers in ecological studies to new insights and novel theories for understanding complex ecological and environmental phenomena.

De Moivre's formula for quaternions

Abstract Eulers formula and De Moivres formula for complex numbers are generalized for quaternions. De Moivres formula implies that there are uncountably many unit quaternions satisfying x n = 1 for n ≥ 3.

The volume of simplices clipped by a half space

Abstract Formulas for the volume of n-simplices clipped by a half space in Rn are given in terms of the values of a function at the vertices of the simplices.

The volume of a tetrahedron

Abstract A formula for the volume of a tetrahedron in terms of the length of edges is given. It may be viewed as a generalization of Herons formula to the volume of a tetrahedron.