Extending partial representations of circle graphs

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph and a partial representation giving some predrawn chords that represent an induced subgraph of . The question is whether one can extend to a representation of the entire graph , that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of . Our main result is an time algorithm for partial representation extension of circle graphs, where is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.     

Complete genome sequence of Bacillus megaterium JX285 isolated from Camellia oleifera rhizosphere

Bacillus megaterium strain JX285, isolated from rhizosphere red soil sample, can solubilize inorganic phosphorus, which increases the amount of available phosphorus and promotes plant growth. To investigate the mechanisms underlying phosphate solubilization, we sequenced the entire genome of B. megaterium strain JX285 (CGMCC 1.1621), which comprises a circular chromosome of 5,066,463 bp and seven plasmids of 167,030, 128,297, 60,905, 134,795, 9,598, 37,455, and 6332 bp, respectively. The whole genome sequence includes 5948 protein-coding genes, 124 tRNAs, and 29 rRNAs, and has been deposited at Genbank/EMBL/DDBJ with accession numbers CP018874–CP018881. We detected genes associated with organic acid production, which may be vital for phosphate conversion. Furthermore, phosphatase-encoding genes were also detected. The information embedded in the genome will assist in studying the mechanisms of phosphate solubilization. In conclusion, analysis of the JX285 genome will further our knowledge regarding this strain and may contribute to its biotechnological application.     

Another proof of the almost purity theorem for perfectoid valuation rings

The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation ring. We give a new proof by exploiting the behavior of Faltings' normalized length under the Frobenius map.     

Methods of Split Reporter Reconstitution for the Analysis of Biomolecules

Intracellular signaling inside living cells is controlled by the specific localization of biomolecules, including proteins, with timescales ranging from milliseconds to several hours. To elucidate the related spatial and temporal signal processes, development of optical probes for cellular events is a challenging task in present studies. Herein, we describe recent advances in the basic design of the optical probes, which have been inspired by luminescent creatures, and their practical application to visualize intracellular events in living cells and animals. A discussion of different probe designs reveals their benefits and shortcomings.     

Diastereoselective synthesis of dihydroindolizin-3(2H)-one derivatives via catalytic sulfur-Michael addition triggered intramolecular tandem sequence

A diastereoselective synthesis of functionalized dihydroindolizidine derivatives bearing sulfur moiety was reported with high stereoselectivity via a catalytic sulfur-Michael addition triggered intramolecular aldol-type tandem sequence. This protocol allowed to readily access trans- and cis-dihydroindolizidine products in high yields with moderate to excellent diastereoselectivities under the optimized mild reaction conditions, which also can be easily transformed into various substituted functionalized pyridines incorporating β-quaternary carbon centers.