In the past, full-service stock brokerage firms had a strategic advantage over discount brokers because of the control full-service brokers had over the information provided to the customer. Full-service stockbrokers acted as information intermediaries in that they were able to capture residual value from the transfer of information to make a profit. Strategic vulnerability occurs, in this case...

One goal of genome projects is to systematically identify genes (1,2). The best current knowledge indicates that humans carry approximately 35000 genes. This number is an estimate that varies from expert to expert and range up to 100,000 (3-5). To anyone who has taken an elementary biology class, this ambiguity must seem strange. How hard can it be to count genes? After all, don't cells transla...

The braid group Bn is the mapping class group of an n-punctured disk. An n-braid is reducible if it has an invariant essential curve system in the punctured disk. We show that for some class of reducible braids (including split braids), finding a reduction system is as easy as finding one element in the ultra summit set.