On the classification of binary shifts of finite commutant index

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II1, factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

Extremely sensitive, background-free gene detection using binary probes and beta replicase.

We have developed a specific and sensitive nucleic acid amplification assay that is suitable for routine gene detection. The assay is based on a novel molecular genetic strategy in which two different RNA probes are hybridized to adjacent positions on a target nucleic acid and then ligated to form an amplifiable reporter RNA. The reporter RNA is then replicated up to a hundred billion-fold in a 30-min isothermal reaction that signals the presence of the target. The assay can detect fewer than 100 nucleic acid molecules; it provides quantitative results over a wide range of target concentrations and it employs a universal format that can detect any infectious agent.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1