Iterative Soft/Hard Thresholding with Homotopy Continuation for Sparse Recovery

In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal $x^\dag$ from noisy data of a noise level $\epsilon$. Under suitable regularity and sparsity conditions, we design a path along which the algorithm can find a solution $x^*$ which admits a sharp reconstruction error $\|x^* - x^\dag\|_{\ell^\infty} = O(\epsilon)$ with an iteration complexity $O(\frac{\ln \epsilon}{\ln \gamma} np)$, where $n$ and $p$ are problem dimensionality and $\gamma\in (0,1)$ controls the length of the path. Numerical examples are given to illustrate its performance.Comment: 5 pages, 4 figure

Triticeae crop genome biology: an endless frontier

Triticeae, the wheatgrass tribe, includes several major cereal crops and their wild relatives. Major crops within the Triticeae are wheat, barley, rye, and oat, which are important for human consumption, animal feed, and rangeland protection. Species within this tribe are known for their large genomes and complex genetic histories. Powered by recent advances in sequencing technology, researchers worldwide have made progress in elucidating the genomes of Triticeae crops. In addition to assemblies of high-quality reference genomes, pan-genome studies have just started to capture the genomic diversities of these species, shedding light on our understanding of the genetic basis of domestication and environmental adaptation of Triticeae crops. In this review, we focus on recent signs of progress in genome sequencing, pan-genome analyses, and resequencing analysis of Triticeae crops. We also propose future research avenues in Triticeae crop genomes, including identifying genome structure variations, the association of genomic regions with desired traits, mining functions of the non-coding area, introgression of high-quality genes from wild Triticeae resources, genome editing, and integration of genomic resources

A genome-wide transcriptional activity survey of rice transposable element-related genes

BACKGROUND: Transposable element (TE)-related genes comprise a significant portion of the gene catalog of grasses, although their functions are insufficiently characterized. The recent availability of TE-related gene annotation from the complete genome sequence of rice (Oryza sativa) has created an opportunity to conduct a comprehensive evaluation of the transcriptional activities of these potentially mobile elements and their related genes. RESULTS: We conducted a genome-wide survey of the transcriptional activity of TE-related genes associated with 15 developmental stages and stress conditions. This dataset was obtained using a microarray encompassing 2,191 unique TE-related rice genes, which were represented by oligonucleotide probes that were free from cross-hybridization. We found that TE-related genes exhibit much lower transcriptional activities than do non-TE-related genes, although representative transcripts were detected from all superfamilies of both type I and II TE-related genes. The strongest transcriptional activities were detected in TE-related genes from among the MULE and CACTA superfamilies. Phylogenetic analyses suggest that domesticated TE-related genes tend to form clades with active transcription. In addition, chromatin-level regulations through histone and DNA modifications, as well as enrichment of certain cis elements in the promoters, appear to contribute to the transcriptional activation of representative TE-related genes. CONCLUSION: Our findings reveal clear, albeit low, general transcription of TE-related genes. In combination with phylogenetic analysis, transcriptional analysis has the potential to lead to the identification of domesticated TEs with adapted host functions