Optimal Regular Expressions for Permutations

The permutation language P_n consists of all words that are permutations of a fixed alphabet of size n. Using divide-and-conquer, we construct a regular expression R_n that specifies P_n. We then give explicit bounds for the length of R_n, which we find to be 4^{n}n^{-(lg n)/4+Theta(1)}, and use these bounds to show that R_n has minimum size over all regular expressions specifying P_n

A Simple Algorithm for Minimum Cuts in Near-Linear Time

We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the complicated subroutine given in Karger's near-linear time minimum cut algorithm (J. ACM, 2000). We give a self-contained version of Karger's algorithm with the new procedure, which is easy to state and relatively simple to implement. It produces a minimum cut on an $m$-edge, $n$-vertex graph in $O(m \log^3 n)$ time with high probability, matching the complexity of Karger's approach.Comment: To appear in SWAT 202

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

A randomized trial of planned cesarean or vaginal delivery for twin pregnancy

Background: Twin birth is associated with a higher risk of adverse perinatal outcomes than singleton birth. It is unclear whether planned cesarean section results in a lower risk of adverse outcomes than planned vaginal delivery in twin pregnancy.\ud \ud Methods: We randomly assigned women between 32 weeks 0 days and 38 weeks 6 days of gestation with twin pregnancy and with the first twin in the cephalic presentation to planned cesarean section or planned vaginal delivery with cesarean only if indicated. Elective delivery was planned between 37 weeks 5 days and 38 weeks 6 days of gestation. The primary outcome was a composite of fetal or neonatal death or serious neonatal morbidity, with the fetus or infant as the unit of analysis for the statistical comparison.\ud \ud Results: A total of 1398 women (2795 fetuses) were randomly assigned to planned cesarean delivery and 1406 women (2812 fetuses) to planned vaginal delivery. The rate of cesarean delivery was 90.7% in the planned-cesarean-delivery group and 43.8% in the planned-vaginal-delivery group. Women in the planned-cesarean-delivery group delivered earlier than did those in the planned-vaginal-delivery group (mean number of days from randomization to delivery, 12.4 vs. 13.3; P = 0.04). There was no significant difference in the composite primary outcome between the planned-cesarean-delivery group and the planned-vaginal-delivery group (2.2% and 1.9%, respectively; odds ratio with planned cesarean delivery, 1.16; 95% confidence interval, 0.77 to 1.74; P = 0.49).\ud \ud Conclusion: In twin pregnancy between 32 weeks 0 days and 38 weeks 6 days of gestation, with the first twin in the cephalic presentation, planned cesarean delivery did not significantly decrease or increase the risk of fetal or neonatal death or serious neonatal morbidity, as compared with planned vaginal delivery