Homology and Robustness of Level and Interlevel Sets

Given a function f: \Xspace \to \Rspace on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of $f$. In addition, we quantify the robustness of the homology classes under perturbations of $f$ using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case \Xspace = \Rspace^3 has ramifications in the fields of medical imaging and scientific visualization

Computational purification of individual tumor gene expression profiles leads to significant improvements in prognostic prediction.

Tumor heterogeneity is a limiting factor in cancer treatment and in the discovery of biomarkers to personalize it. We describe a computational purification tool, ISOpure, to directly address the effects of variable normal tissue contamination in clinical tumor specimens. ISOpure uses a set of tumor expression profiles and a panel of healthy tissue expression profiles to generate a purified cancer profile for each tumor sample and an estimate of the proportion of RNA originating from cancerous cells. Applying ISOpure before identifying gene signatures leads to significant improvements in the prediction of prognosis and other clinical variables in lung and prostate cancer

Design Considerations for Low Power Internet Protocols

Over the past 10 years, low-power wireless networks have transitioned to supporting IPv6 connectivity through 6LoWPAN, a set of standards which specify how to aggressively compress IPv6 packets over low-power wireless links such as 802.15.4. We find that different low-power IPv6 stacks are unable to communicate using 6LoWPAN, and therefore IP, due to design tradeoffs between code size and energy efficiency. We argue that applying traditional protocol design principles to low-power networks is responsible for these failures, in part because receivers must accommodate a wide range of senders. Based on these findings, we propose three design principles for Internet protocols on low-power networks. These principles are based around the importance of providing flexible tradeoffs between code size and energy efficiency. We apply these principles to 6LoWPAN and show that the resulting design of the protocol provides developers a wide range of tradeoff points while allowing implementations with different choices to seamlessly communicate