A metric map of humans: 23,500 loci in 850 bands

High-resolution maps integrated with the enhanced location data base software (ldb+) give improved estimates of genetic parameters and reveal characteristics of cytogenetic bands. Chiasma interference is intermediate between Kosambi and Carter–Falconer levels, as in Drosophila and the mouse. The autosomal genetic map is 2832 and 4348 centimorgans in males and females, respectively. Telomeric T-bands are strikingly associated with male recombination and gene density. Position and centromeric heterochromatin have large effects, but nontelomeric R-bands are not significantly different from G-bands. Several possible reasons are discussed. These regularities validate the maps, despite their high resolution and inevitable local errors. No other approach has been demonstrated to integrate such a large number of loci, which are increasing at about 45% per year. The maps and the data and software from which they are constructed are available through the Internet (http://cedar.genetics.soton.ac.uk/public_html). Successive versions of this location data base may also be accessed on CD-ROM.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.