Distribution of interstitial stem cells in Hydra

The distribution of interstitial stem cells along the Hydra body column was determined using a simplified cloning assay. The assay measures stem cells as clone-forming units (CFU) in aggregates of nitrogen mustard inactivated Hydra tissue. The concentration of stem cells in the gastric region was uniform at about 0.02 CFU/epithelial cell. In both the hypostome and basal disk the concentration was 20-fold lower. A decrease in the ratio of stem cells to committed nerve and nematocyte precursors was correlated with the decrease in stem cell concentration in both hypostome and basal disk. The ratio of stem cells to committed precursors is a sensitive indicator of the rate of self-renewal in the stem cell population. From the ratio it can be estimated that <10% of stem cells self-renew in the hypostome and basal disk compared to 60% in the gastric region. Thus, the results provide an explanation for the observed depletion of stem cells in these regions. The results also suggest that differentiation and self-renewal compete for the same stem cell population

Monopole clusters and critical dynamics in four-dimensional U(1)

We investigate monopoles in four-dimensional compact U(1) with Wilson action. We focus our attention on monopole clusters as they can be identified unambiguously contrary to monopole loops. We locate the clusters and determine their properties near the U(1) phase transition. The Coulomb phase is characterized by several small clusters, whereas in the confined phase the small clusters coalesce to one large cluster filling up the whole system. We find that clusters winding around the periodic lattice are absent within both phases and during the transition. However, within the confined phase, we observe periodically closed monopole loops if cooling is applied.Comment: 3 pages, Wuppertal preprint WUB 93-3

Completed tensor products and a global approach to pp-adic analytic differential operators

Ardakov-Wadsley defined the sheaf D-cap of $p$-adic analytic differential operators on a smooth rigid analytic variety $X$ by restricting to the case where $X$ is affinoid and the tangent sheaf admits a smooth Lie lattice. We generalize their results by dropping the assumption of a smooth Lie lattice throughout, which allows us to describe the sections of D-cap for arbitrary affinoid subdomains and not just on a suitable base of the topology. The structural results concerning D-cap and coadmissible D-cap-modules can then be generalized in a natural way. The main ingredient for our proofs is a study of completed tensor products over normed $K$-algebras, for $K$ a discretely valued field of mixed characteristic. Given a normed right module $U$ over a normed $K$-algebra $A$, we provide several exactness criteria for the functor $U\widehat{\otimes}_A-$ applied to complexes of strict morphisms, including a necessary and sufficient condition in the case of short exact sequences.Comment: 29 page

Reading (in/and) Miranda

"Australian fiction, like that of all nations, is written, published, received and read in the context of a literary canon, both national and transnational. In regards to women's fiction in Australia, this canon is predominantly composed of writers from two particular eras: authors of the nineteenth and early twentieth centuries (like Henry Handel Richardson, Miles Franklin, Katharine Susannah Prichard and Christina Stead) and women writers who came to prominence during the 1980s (like Helen Garner, Kate Grenville, Elizabeth Jolley, Barbara Hanrahan, Jessica Anderson and Beverley Farmer ... The second-wave feminist movement was responsible for the creation of this dual canon: in the first case, due to a desire to recover and reclaim women writers of the past, and in the second, due to a desire to celebrate and explore contemporary Australian women's fiction. Indeed, it is the preoccupation of second-wave feminism with uncovering and celebrating women's occluded stories that underlies the current critical focus on realist and experiential aspects of Australian women's fiction ... Among those whose work has been occluded by the critical attention given to the canonical figures of Australian women's writing, Wendy Scarfe is indicative in various ways.

Crossing numbers of composite knots and spatial graphs

We study the minimal crossing number $c(K_{1}\# K_{2})$ of composite knots $K_{1}\# K_{2}$, where $K_1$ and $K_2$ are prime, by relating it to the minimal crossing number of spatial graphs, in particular the $2n$-theta curve $\theta_{K_{1},K_{2}}^n$ that results from tying $n$ of the edges of the planar embedding of the $2n$-theta graph into $K_1$ and the remaining $n$ edges into $K_2$. We prove that for large enough $n$ we have $c(\theta_{K_1,K_2}^n)=n(c(K_1)+c(K_2))$. We also formulate additional relations between the crossing numbers of certain spatial graphs that, if satisfied, imply the additivity of the crossing number or at least give a lower bound for $c(K_1\# K_2)$.Comment: 20 pages, 11 figures, changes from version1: added Lemma 5.2 and corrected mistake in Proposition 5.3, improved quality of figure