Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

Neural progenitor number is regulated by nuclear factor-kappa B p65 and p50 subunit-dependent proliferation rather than cell survival

The number of cells generated by a proliferating stem or precursor cell can be influenced both by proliferation and by the degree of cell death/survival of the progeny generated. In this study, the extent to which cell survival controls progenitor number was examined by comparing the growth characteristics of neurosphere cultures derived from mice lacking genes for the death inducing Bcl-2 homologue Hara Kiri (Hrk), apoptosis-associated protein 1 (Apaf1), or the prosurvival nuclear factor-kappa B (NF kappa B) subunits p65, p50, or c-rel. We found no evidence that Hrk or Apaf1, and by inference the mitochondrial cell death pathway, are involved in regulating the number of neurosphere-derived progeny. However, we identified the p65p50 NF kappa B dimer as being required for the normal growth and expansion of neurosphere cultures. Genetic loss of both p65 and p50 NF kappa B subunits resulted in a reduced number of progeny but an increased proportion of neurons. No effect on cell survival was observed. This suggests that the number and fate of neural progenitor cells are more strongly regulated by cell cycle control than survival. (c) 2005 Wiley-Liss, Inc.