The minimal free resolution of the coordinate ring a complete intersection in projective space is Koszul complex on regular sequence. In product spaces P1×P1, we investigate which sets points have virtual that This paper provides conditions points; some guarantee this property, and do not property.

paris polyphylla smith var. yunnanensis (liliaceae) is an important traditional medicinal plant of the yunnan province in china. however, the genomic information regarding this plant is limited. to further understand its molecular background, we conducted illumina hiseq 2000 second-generation sequencing of this plant species. approximately 30,198,679 reads with an average length of 202 bases we...

bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. many computational algorithms have been applied for solving the sequence alignment problem. dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods applied t...

For non-negative integers~$k$, we consider graphs in which every vertex has exactly $k$ vertices at distance~$2$, i.e., whose distance-$2$ are $k$-regular. We call such $k$-metamour-regular motivated by the terminology polyamory. While constructing is relatively easy -- provide a generic construction for arbitrary~$k$ finding all much more challenging. show that only with certain property canno...