Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

O(N) Models with Topological Lattice Actions

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss “weird” lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear σ-models). Amazingly, such “weird” lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

Detection and functional portrayal of a novel class of dihydrotestosterone derived selective progesterone receptor modulators (SPRM).

In early pregnancy, abortion can be induced by blocking the actions of progesterone receptors (PR). However, the PR antagonist, mifepristone (RU38486), is rather unselective in clinical use because it also cross-reacts with other nuclear receptors. Since the ligand-binding domain of human progesterone receptor (hPR) and androgen receptor (hAR) share 54% identity, we hypothesized that derivatives of dihydrotestosterone (DHT), the cognate ligand for hAR, might also regulate the hPR. Compounds designed and synthesized in our laboratory were investigated for their affinities for hPRB, hAR, glucocorticoid receptor (hGRα) and mineralocorticoid receptor (hMR), using whole cell receptor competitive binding assays. Agonistic and antagonistic activities were characterized by reporter assays. Nuclear translocation was monitored using cherry-hPRB and GFP-hAR chimeric receptors. Cytostatic properties and apoptosis were tested on breast cancer cells (MCF7, T-47D). One compound presented a favorable profile with an apparent neutral hPRB antagonistic function, a selective cherry-hPRB nuclear translocation and a cytostatic effect. 3D models of human PR and AR with this ligand were constructed to investigate the molecular basis of selectivity. Our data suggest that these novel DHT-derivatives provide suitable templates for the development of new selective steroidal hPR antagonists.