Computing Large-scale Distance Matrices on GPU

Abstract-A distance matrix is simply an n×n two-dimensional array that contains pairwise distances of a set of n points in a metric space. It has a wide range of usage in several fields of scientific research e.g., data clustering, machine learning, pattern recognition, image analysis, information retrieval, signal processing, bioinformatics etc. However, as the size of n increases, the computation of distance matrix becomes very slow or incomputable on traditional general purpose computers. In this paper, we propose an inexpensive and scalable data-parallel solution to this problem by dividing the computational tasks and data on GPUs. We demonstrate the performance of our method on a set of real-world biological networks constructed from a renowned breast cancer study

Coupled cell networks: Boolean perspective

During the 1980s and early 1990s, Martin Golubitsky and Ian Stewart  formulated and developed a theory of "coupled cell networks" (CCNs). Their research was primarily focused onquadrupeds' gaits and they applied the framework of differential equations. Golubitsky and Stewart were particularly interested in change of synchrony between $4$ legs of an animal. For example what happens when the animal speeds up from walk to gallop.  The most important concept of their theory is a {\it cell}. The cell captures the dynamics of one unit and a dynamical system consists of many identical (governed by the same principles) cells influencing (coupling to) each other. Models based on identical cooperating units are fairly common in many areas, especially in biology, ecology and sociology.  The goal of investigation in Coupled Cell Networks theory  is understanding the dependencies and interplay between dynamics of an individual cell, graph of connections between cells, and the nature of couplings. \vspace*{0.2em} In this paper, I redefine Coupled Cell Networks using framework of Boolean functions. This moves the entire theory to a new setting. Some phenomena proved to be very similar as for continuous networks and some are completely different. Also, for discrete networks we ask questions differently and study different phenomena. The paper presents two examples: networks that bring 2-cell bidirectional ring as a quotient and networks that bring 3-cell bidirectional ring as a quotient

Clustering nodes in large-scale biological networks using external memory algorithms

Novel analytical techniques have dramatically enhanced our understanding of many application domains including biological networks inferred from gene expression studies. However, there are clear computational challenges associated to the large datasets generated from these studies. The algorithmic solution of some NP-hard combinatorial optimization problems that naturally arise on the analysis of large networks is difficult without specialized computer facilities (i.e. supercomputers). In this work, we address the data clustering problem of large-scale biological networks with a polynomial-time algorithm that uses reasonable computing resources and is limited by the available memory. We have adapted and improved the MSTkNN graph partitioning algorithm and redesigned it to take advantage of external memory (EM) algorithms. We evaluate the scalability and performance of our proposed algorithm on a well-known breast cancer microarray study and its associated dataset. © 2011 Springer-Verlag