Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 2X 2X algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms

A divide-and-conquer approach to analyze underdetermined biochemical models

Motivation: To obtain meaningful predictions from dynamic computational models, their uncertain parameter values need to be estimated from experimental data. Due to the usually large number of parameters compared to the available measurement data, these estimation problems are often underdetermined meaning that the solution is a multidimensional space. In this case, the challenge is yet to obtain a sound system understanding despite non-identifiable parameter values, e.g. through identifying those parameters that most sensitively determine the model’s behavior. Results: Here, we present the so-called divide-and-conquer approach—a strategy to analyze underdetermined biochemical models. The approach draws on steady state omics measurement data and exploits a decomposition of the global estimation problem into independent subproblems. The solutions to these subproblems are joined to the complete space of global optima, which can be easily analyzed. We derive the conditions at which the decomposition occurs, outline strategies to fulfill these conditions and—using an example model—illustrate how the approach uncovers the most important parameters and suggests targeted experiments without knowing the exact parameter values.

Large-Scale Sensor Network Localization via Rigid Subnetwork Registration

In this paper, we describe an algorithm for sensor network localization (SNL) that proceeds by dividing the whole network into smaller subnetworks, then localizes them in parallel using some fast and accurate algorithm, and finally registers the localized subnetworks in a global coordinate system. We demonstrate that this divide-and-conquer algorithm can be used to leverage existing high-precision SNL algorithms to large-scale networks, which could otherwise only be applied to small-to-medium sized networks. The main contribution of this paper concerns the final registration phase. In particular, we consider a least-squares formulation of the registration problem (both with and without anchor constraints) and demonstrate how this otherwise non-convex problem can be relaxed into a tractable convex program. We provide some preliminary simulation results for large-scale SNL demonstrating that the proposed registration algorithm (together with an accurate localization scheme) offers a good tradeoff between run time and accuracy.Comment: 5 pages, 8 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201