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We show the existence of two and three finger grasps in the presence of arbitrarily small friction for two and three dimensional smooth objects using a simple new technique. No con-vexity of the objects is assumed. We also prove the existence of finger gaits for rotating a planar object using three and four fingers. Additional results for smooth convex(More)
The current standard correlation coefficient used in the analysis of microarray data was introduced by M. B. Eisen, P. T. Spellman, P. O. Brown, and D. Botstein [(1998) Proc. Natl. Acad. Sci. USA 95, 14863-14868]. Its formulation is rather arbitrary. We give a mathematically rigorous correlation coefficient of two data vectors based on James-Stein shrinkage(More)
The whole-genome sequence assembly (WGSA) problem is among one of the most studied problems in computational biology. Despite the availability of a plethora of tools (i.e., assemblers), all claiming to have solved the WGSA problem, little has been done to systematically compare their accuracy and power. Traditional methods rely on standard metrics and read(More)
1 Prologue Presently, there is no clear way to determine if the current body of biological facts is sufficient to explain phenomenology. In the biological community, it is not uncommon to assume certain biological problems to have achieved a cog-nitive finality without rigorous justification. In these particular cases, rigorous mathematical models with(More)
A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to(More)
In this work, we explore the use of representations in conjunction with DNA microarray technology to measure gene copy number changes in cancer. We demonstrate that arrays of DNA probes derived from low-complexity representations can be used to detect amplifications, deletions, and polymorphic differences when hybridized to representations of genomic DNA.(More)
In just the last decade, a multitude of bio-technologies and software pipelines have emerged to revolutionize genomics. To further their central goal, they aim to accelerate and improve the quality of de novo whole-genome assembly starting from short DNA sequences/reads. However, the performance of each of these tools is contingent on the length and quality(More)
M ajor advances in genome science and molecular technologies provide new opportunities at the interface between basic biological research and medical practice. The unprecedented completeness, accuracy, and volume of genomic and molecular data necessitate a new kind of computational biology for translational research. Key challenges are standardization of(More)