Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion

A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce an iterative hard thresholding (IHT) algorithm and a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that $O(r^2\log^2(n))$ number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for IHT and FIHT. In particular, numerical simulations on $3$D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data

HDAC6 Mediates Macrophage iNOS Expression and Excessive Nitric Oxide Production in the Blood During Endotoxemia

Excessive nitric oxide (NO) production and NO-mediated nitrative stress contribute to vascular dysfunction, inflammation, and tissue injury in septic shock. New therapeutic targets are urgently needed to provide better control of NO level during septic shock. In the present study, we investigated the role of HDAC6 in the regulation of NO production and nitrative stress in a mouse model of endotoxin-induced septic shock. HDAC6 deficient mice and a specific HDAC6 inhibitor were utilized in our studies. Our data clearly indicate that HDAC6 is an important mediator of NO production in macrophages. HDAC6 mediates NO production through the regulation of iNOS expression in macrophages. HDAC6 up-regulates iNOS expression in macrophages by modulating STAT1 activation and IRF-1 expression. HDAC6 inhibition potently blocked endotoxin-induced STAT1 activation and iNOS expression in macrophages. Furthermore, HDAC6 contributes to excessive NO production and nitrotyrosine level in the blood and promotes iNOS expression in the lung tissues during septic shock. Our data reveal a novel HDAC6/STAT1/iNOS pathway that mediates excessive NO production and nitrative stress in septic shock