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Mapping the pathways that give rise to metastasis is one of the key challenges of breast cancer research. Recently, several large-scale studies have shed light on this problem through analysis of gene expression profiles to identify markers correlated with metastasis. Here, we apply a protein-network-based approach that identifies markers not as individual(More)
The advent of microarray technology has made it possible to classify disease states based on gene expression profiles of patients. Typically, marker genes are selected by measuring the power of their expression profiles to discriminate among patients of different disease states. However, expression-based classification can be challenging in complex diseases(More)
  • Gilad D. Evrony, Xuyu Cai, Eunjung Lee, L. Benjamin Hills, Princess C. Elhosary, Hillel S. Lehmann +6 others
  • 2012
A major unanswered question in neuroscience is whether there exists genomic variability between individual neurons of the brain, contributing to functional diversity or to an unexplained burden of neurological disease. To address this question, we developed a method to amplify genomes of single neurons from human brains. Because recent reports suggest(More)
The basic idea of image registration is to find a reasonable transformation of an image so that the resulting difference between it and another image is made small. We derive an optimal control method for determining such a transformation; the approach is based on the grid deformation method and seeks to minimize an objective functional that measures the(More)
DNA copy number variations (CNVs) play an important role in the pathogenesis and progression of cancer and confer susceptibility to a variety of human disorders. Array comparative genomic hybridization has been used widely to identify CNVs genome wide, but the next-generation sequencing technology provides an opportunity to characterize CNVs genome wide(More)
The focus of this paper is on incompressible flows in three dimensions modeled by least-squares finite element methods (LSFEM) and using a novel reformulation of the Navier-Stokes equations. LSFEM are attractive because the resulting discrete equations yield symmetric, positive definite systems of algebraic equations and the functional provides both a local(More)
Least-squares variational methods have several practical and theoretical advantages for solving elliptic partial differential equations, including symmetric positive definite discrete operators and a sharp error measure. One of the potential drawbacks, especially in three dimensions, is that mass conservation is achieved only in a least-squares sense, and(More)
A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods, including least-squares methods, often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges. By minimizing a modified least-squares functional,(More)
In the case that the domain has reentrant edges, the standard finite element method loses its global accuracy because of singularities on the boundary. To overcome this difficulty, FOSLL* is applied in this paper. FOSLL* is a methodology for solving PDEs using the dual operator. Here, a modified FOSLL* method is developed that employs a partially weighted(More)
A weighted-norm least-squares method is considered for the numerical approximation of solutions that have singularities at the boundary. While many methods suffer from a global loss of accuracy due to boundary singularities, the least-squares method can be particularly sensitive to a loss of regularity. The method we describe here requires only a rough(More)