A two weight local Tb theorem for the Hilbert transform

We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform and in a sense improves on the T1 theorem by the authors and M. Lacey.Comment: 121 pages, 3 figures, 50 pages of appendices. We correct three gaps in the treatment of the stopping form in v12: the proof of Lemma 9.3 there requires a larger size functional, a collection of pairs is missing from the decomposition at the bottom of page 149, and an error was made in the definition of restricted norm of a stopping form. Main results unchange

ROC curve of the classification of patients in METABRIC validation data.

<p>ROC curve of the classification of patients in METABRIC validation data.</p

Functional enrichment of genes identified from the discovery dataset in signaling pathways and associated p-values.

<p>Functional enrichment of genes identified from the discovery dataset in signaling pathways and associated p-values.</p

CyNetSVM: A Cytoscape App for Cancer Biomarker Identification Using Network Constrained Support Vector Machines

<div><p>One of the important tasks in cancer research is to identify biomarkers and build classification models for clinical outcome prediction. In this paper, we develop a CyNetSVM software package, implemented in Java and integrated with Cytoscape as an app, to identify network biomarkers using network-constrained support vector machines (NetSVM). The Cytoscape app of NetSVM is specifically designed to improve the usability of NetSVM with the following enhancements: (1) user-friendly graphical user interface (GUI), (2) computationally efficient core program and (3) convenient network visualization capability. The CyNetSVM app has been used to analyze breast cancer data to identify network genes associated with breast cancer recurrence. The biological function of these network genes is enriched in signaling pathways associated with breast cancer progression, showing the effectiveness of CyNetSVM for cancer biomarker identification. The CyNetSVM package is available at Cytoscape App Store and <a href="http://sourceforge.net/projects/netsvmjava" target="_blank">http://sourceforge.net/projects/netsvmjava</a>; a sample data set is also provided at sourceforge.net.</p></div

ROC curve of the classification of patients in Loi <i>et al</i>. data.

<p>ROC curve of the classification of patients in Loi <i>et al</i>. data.</p

Network identified from METABRIC discovery data.

<p>Network identified from METABRIC discovery data.</p

Screenshot of the CyNetSVM app.

<p>Screenshot of the CyNetSVM app.</p

Network identified from Loi <i>et al</i>. data.

<p>Network identified from Loi <i>et al</i>. data.</p

Means and standard deviations of accuracy for phenotype prediction and AUC for network identification on simulation data with different SNR.

<p>Means and standard deviations of accuracy for phenotype prediction and AUC for network identification on simulation data with different SNR.</p

An overview of the CyNetSVM app.

<p>An overview of the CyNetSVM app.</p