We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical implementations behave very well on some instances of SDP having a large number of constraints. We also show that the "boundary point method" from [PRW06] is an instance of this class.
Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look at tractable approximations and compare with several relaxations from the literature. We show that several of the well-studied models are in fact equivalent. It is still a challenging task to solve the strongest of these models to reasonable accuracy on instances of moderate size.
We are increasingly accumulating molecular data about a cell. The challenge is how to integrate them within a unified conceptual and computational framework enabling new discoveries. Hence, we propose a novel, data-driven concept of an integrated cell, iCell. Also, we introduce a computational prototype of an iCell, which integrates three omics, tissue-specific molecular interaction network types. We construct iCells of four cancers and the corresponding tissue controls and identify the most rewired genes in cancer. Many of them are of unknown function and cannot be identified as different in cancer in any specific molecular network. We biologically validate that they have a role in cancer by knockdown experiments followed by cell viability assays. We find additional support through Kaplan-Meier survival curves of thousands of patients. Finally, we extend this analysis to uncover pan-cancer genes. Our methodology is universal and enables integrative comparisons of diverse omics data over cells and tissues.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.