ultivated peanut or groundnut (A. hypogaea L.) is among the most important oil and food legumes, grown on 25 million ha between latitudes 40° N and 40° S with annual production of ~46 million tons (http://www.fao.org/faostat/en/#home). It presumably was domesticated in South America ~6,000 years ago and then was widely distributed in post-Columbian times 1. Combining richness in seed oil (~46-58%) and protein (~22-32%), peanut is important in fighting malnutrition and ensuring food security.

Water lilies belong to the angiosperm order Nymphaeales. Amborellales, Nymphaeales and Austrobaileyales together form the so-called ANA-grade of angiosperms, which are extant representatives of lineages that diverged the earliest from the lineage leading to the extant mesangiosperms 1-3. Here we report the 409-megabase genome sequence of the blue-petal water lily (Nymphaea colorata). Our phylogenomic analyses support Amborellales and Nymphaeales as successive sister lineages to all other extant angiosperms. The N. colorata genome and 19 other water lily transcriptomes reveal a Nymphaealean whole-genome duplication event, which is shared by Nymphaeaceae and possibly Cabombaceae. Among the genes retained from this whole-genome duplication are homologues of genes that regulate flowering transition and flower development. The broad expression of homologues of floral ABCE genes in N. colorata might support a similarly broadly active ancestral ABCE model of floral organ determination in early angiosperms. Water lilies have evolved attractive floral scents and colours, which are features shared with mesangiosperms, and we identified their putative biosynthetic genes in N. colorata. The chemical compounds and biosynthetic genes behind floral scents suggest that they have evolved in parallel to those in mesangiosperms. Because of its unique phylogenetic position, the N. colorata genome sheds light on the early evolution of angiosperms. Many water lily species, particularly from Nymphaea (Nymphaeaceae), have large and showy flowers and belong to the angiosperms (also called flowering plants). Their aesthetic beauty has captivated notable artists such as the French impressionist Claude Monet. Water lily flowers have limited differentiation in perianths (outer floral organs), but they possess both male and female organs and have diverse scents and colours, similar to many mesangiosperms (core angiosperms, including eudicots, monocots, and magnoliids) (Supplementary Note 1). In addition, some water lilies have short life cycles and enormous numbers of seeds 4 , which increase their potential as a model plant to represent the ANA-grade of angiosperms and to study early evolutionary events within the angiosperms. In particular, N. colorata Peter has a relatively small genome size (2n = 28 and approximately 400 Mb) and blue petals that make it popular in breeding programs (Supplementary Note 1). We report here the genome sequence of N. colorata, obtained using PacBio RSII single-molecule real-time (SMRT) sequencing technology. The genome was assembled into 1,429 contigs (with a contig N50 of 2.1 Mb) and total length of 409 Mb with 804 scaffolds, 770 of which were anchored onto 14 pseudo-chromosomes (Extended Data Fig. 1 and Extended Data Table 1). Genome completeness was estimated to be 94.4% (Supplementary Note 2). We annotated 31,580 protein-coding genes and predicted repetitive elements with a collective length of 160.4 Mb, accounting for 39.2% of the genome (Supplementary Note 3). The N. colorata genome provides an opportuni...

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We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.