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In this paper we show that if the restricted isometry constant δ k of the compressed sensing matrix satisfies δ k < 0.307, then k-sparse signals are guaranteed to be recovered exactly via ℓ 1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantively improved.(More)
—In this paper, we present a concise and coherent analysis of the constrained`1 minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary , while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved(More)
—This paper considers constrained`1 minimization methods in a unified framework for the recovery of high-dimensional sparse signals in three settings: noiseless, bounded error, and Gaussian noise. Both`1 minimization with an`1 constraint (Dantzig selector) and`1 minimization under an`2 constraint are considered. The results of this paper improve the(More)
—This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is(More)
CD8(+) T cell responses focus on a small fraction of pathogen- or vaccine-encoded peptides, and for some pathogens, these restricted recognition hierarchies limit the effectiveness of antipathogen immunity. We found that simian immunodeficiency virus (SIV) protein-expressing rhesus cytomegalovirus (RhCMV) vectors elicit SIV-specific CD8(+) T cells that(More)
In this paper we propose three refinements to Miller's algorithm for computing Weil/Tate Pairing. The first one is an overall improvement and achieves its optimal behavior if the binary expansion of the involved integer has more zeros. If more ones are presented in the binary expansion, second improvement is suggested. The third one is especially efficient(More)
Established infections with the human and simian immunodeficiency viruses (HIV and SIV, respectively) are thought to be permanent with even the most effective immune responses and antiretroviral therapies only able to control, but not clear, these infections. Whether the residual virus that maintains these infections is vulnerable to clearance is a question(More)
This article considers constrained ℓ 1 minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaus-sian noise. A unified and elementary treatment is given in these noise settings for two ℓ 1 minimization methods: the Dantzig selector and ℓ 1 minimization with an ℓ 2 constraint. The results of(More)
The RNA-binding protein AUF1 binds AU-rich elements in 3'-untranslated regions to regulate mRNA degradation and/or translation. Many of these mRNAs are predicted microRNA targets as well. An emerging theme in post-transcriptional control of gene expression is that RNA-binding proteins and microRNAs co-regulate mRNAs. Recent experiments and bioinformatic(More)