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**11 - 17**of**17**### Identification of Multiple Hypoxia Signatures in Neuroblastoma

"... Copyright © 2010 Paolo Fardin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hypoxia is a condition of low oxygen tension occ ..."

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Copyright © 2010 Paolo Fardin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hypoxia is a condition of low oxygen tension occurring in the tumor and negatively correlated with the progression of the disease. We studied the gene expression profiles of nine neuroblastoma cell lines grown under hypoxic conditions to define gene signatures that characterize hypoxic neuroblastoma. The l1-l2 regularization applied to the entire transcriptome identified a single signature of 11 probesets discriminating the hypoxic state. We demonstrate that new hypoxia signatures, with similar discriminatory power, can be generated by a prior knowledge-based filtering in which a much smaller number of probesets, characterizing hypoxia-related biochemical pathways, are analyzed. l1-l2 regularization identified novel and robust hypoxia signatures within apoptosis, glycolysis, and oxidative phosphorylation Gene Ontology classes. We conclude that the filtering approach overcomes the noisy nature of the microarray data and allows generating robust signatures suitable for biomarker discovery and patients risk assessment in a fraction of computer time. 1. Background Neuroblastoma is the most common pediatric solid tumor, deriving from immature or precursor cells of the ganglionic lineage of the sympathetic nervous system [1, 2] endowed

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, 2013

"... We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vect ..."

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We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, the consistency of the discrepancy principle as well as convergence rate are established, and an a posteriori error estimate for the balancing principle is established. Also two fixed point algorithms are proposed for computing the regularization parameter by the latter rule. Numerical results for several nonsmooth multi-parameter models are presented, which show clearly their superior performance over their single-parameter counterparts.

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"... We consider the problem of learning a set from random samples. We show how relevant geometric and topo-logical properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays ..."

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We consider the problem of learning a set from random samples. We show how relevant geometric and topo-logical properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our study and is analyzed in detail. We prove a new analytic characterization of the support of a distribution, that naturally leads to a family of provably consistent regularized learning algorithms and we discuss the stability of these methods with respect to random sampling. Numerical experiments show that the approach is competitive, and often better, than other state of the art techniques. 1 ar X iv

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"... family of interpretable multivariate models for regression and classification ..."

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family of interpretable multivariate models for regression and classification