Extended Systems with Deterministic Local Dynamics and Random Jumps

We consider particle systems on lattices with internal dynamics at each site and random jumps between sites. Models with simple chaotic local dynamics, namely expanding circle maps, are considered. Results on mean drift rates, central limit theorems and dependences on jump parameters are proved. A version of most of the results in this paper is contained in this author’s Ph.D. thesis [K]. This research is partially supported by a grant from the NSF.     

Constructing spherical CR manifolds by gluing tetrahedra

We propose a general method of constructing spherical CR manifolds by gluing tetrahedra adapted to CR geometry. We obtain spherical CR structures on the complement of the figure eight knot and the Whitehead link complement with holonomy in $\mathrm{PU}(2,1,\mathbb{Z}[\omega ])$ and $\mathrm{PU}(2,1,\mathbb{Z}[\mathrm{i}])$ respectively (the same integer rings appearing in real hyperbolic geometry). To cite this article: E. Falbel, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Formation of [b3 - 1 + cat]+ ions from metal-cationized tetrapeptides containing beta-alanine, gamma-aminobutyric acid or epsilon-aminocaproic acid residues

The presence and position of a single beta-alanine (betaA), gamma-aminobutyric acid (gammaABu) or epsilon-aminocaproic acid (Cap) residue has been shown to have a significant influence on the formation of b(n)+ and y(n)+ product ions from a series of model, protonated peptides. In this study, we examined the effect of the same residues on the formation of analogous [b3 - 1 + cat]+ products from metal (Li+, Na+ and Ag+)-cationized peptides. The larger amino acids suppress formation of b3+ from protonated peptides with general sequence AAXG (where X = beta-alanine, gamma-aminobutyric acid or epsilon-aminocaproic acid), presumably because of the prohibitive effect of larger cyclic intermediates in the 'oxazolone' pathway. However, abundant [b3 - 1 + cat]+ products are generated from metal-cationized versions of AAXG. Using a group of deuterium-labeled and exchanged peptides, we found that formation of [b3 - 1 + cat]+ involves transfer of either amide or alpha-carbon position H atoms, and the tendency to transfer the atom from the alpha-carbon position increases with the size of the amino acid in position X. To account for the transfer of the H atom, a mechanism involving formation of a ketene product as [b3 - 1 + cat]+ is proposed.     

Eigenvalues of products of unitary matrices and Lagrangian involutions

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.     

The PU(2,1) configuration space of four points in <Emphasis Type="Italic">S</Emphasis><Superscript>3</Superscript> and the cross-ratio variety

The configuration space of four points on the standard CR 3-sphere up to CR-automorphisms is a real four dimensional variety. We prove the existence of natural complex and CR structures on this space. I. D. Platis was supported by a Marie Curie Reintegration Grant fellowship (contract no. MEIF-CT-2005-028371) within the 6th Community Framework Programme.     

Barriers to rotation in substituted O-aryl-hydroxylamines.

The effect of substituents on rotational barriers in O-arylhydroxylamines was studied. The results do not support any of the proposed mechanisms for substituent effects in the analogues sulfenamide series.     

Percolation in living neural networks

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with an exponent beta approximately or = 0.65. Beta is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is Gaussian rather than scale free.     

Photoexcited nitrobenzene for benzylic hydroxylation: the synthesis of 17β-acetoxy-9α-hydroxy-3-methoxy-estra-1,3,5(10)-triene

A novel method for benzylic hydroxylation is introduced based on the use of photo-excited nitrobenzene. Applying this method 17β-acetoxy-3-methoxy-estra-1,3,5(10)-triene (I) is efficiently converted to 17β-acetoxy-9α-hydroxy-3-methoxy-estra-1,3,5(10)-triene (IIIa).