Wong-Rosay Theorem in almost complex manifolds

We study the compactness of sequences of diffeomorphisms in almost complex manifolds in terms of the direct images of the standard integrable structure.Comment: date de redaction: 2003-6-1

Riemann maps in almost complex manifolds

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.Comment: 2003.6.1

Estimates of the Kobayashi metric on almost complex manifolds

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in $M$ and to give a sufficient condition for the complete hyperbolicity of a domain in $(M,J)$. Finally we obtain the regularity up to the bounday of $J$-holomorphic discs attached to a totally real submanifold in $M$.Comment: date de redaction: 2003-4-

Obstructions to embeddability into hyperquadrics and explicit examples

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further study the embeddability problem for real-analytic submanifolds of higher codimension and answer a question by Forstneri\v{c}.Comment: Revised version, appendix and references adde

A robot trace maker: modeling the fossil evidence of early invertebrate behavior.

The study of trace fossils, the fossilized remains of animal behavior, reveals interesting parallels with recent research in behavior-based robotics. This article reports robot simulations of the meandering foraging trails left by early invertebrates that demonstrate that such trails can be generated by mechanisms similar to those used for robot wall-following. We conclude with the suggestion that the capacity for intelligent behavior shown by many behavior-based robots is similar to that of animals of the late Precambrian and early Cambrian periods approximately 530 to 565 million years ago

Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variables

In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), to the Newtonian free particle equation Y_XX = 0. This result, preliminary to the deep group-theoretic classification of second order analytic ordinary differential equations, was parachieved later in 1896 by Arthur Tresse, a French student of S. Lie. In the present paper, following closely the original strategy of proof of S. Lie, which we firstly expose and restitute in length, we generalize this explicit characterization to the case of several second order ordinary differential equations. Let K=R or C, or more generally any field of characteristic zero equipped with a valuation, so that K-analytic functions make sense. Let x in K, let m > 1, let y := (y^1, ..., y^m) in K^m and let y_xx^j = F^j(x,y,y_x^l), j = 1,...,m be a collection of m analytic second order ordinary differential equations, in general nonlinear. We provide an explicit necessary and sufficient condition in order that this system is equivalent, under a point transformation (x, y^1, ..., y^m) --> (X(x,y), Y^1(x,y),..., Y^m(x, y)), to the Newtonian free particle system Y_XX^1 = ... = Y_XX^m = 0. Strikingly, the (complicated) differential system that we obtain is of first order in the case m > 1, whereas it is of second order in S. Lie's original case m = 1.Comment: 76 pages, no figur

The Defective Prophage Pool of Escherichia coli O157: Prophage–Prophage Interactions Potentiate Horizontal Transfer of Virulence Determinants

Bacteriophages are major genetic factors promoting horizontal gene transfer (HGT) between bacteria. Their roles in dynamic bacterial genome evolution have been increasingly highlighted by the fact that many sequenced bacterial genomes contain multiple prophages carrying a wide range of genes. Enterohemorrhagic Escherichia coli O157 is the most striking case. A sequenced strain (O157 Sakai) possesses 18 prophages (Sp1–Sp18) that encode numerous genes related to O157 virulence, including those for two potent cytotoxins, Shiga toxins (Stx) 1 and 2. However, most of these prophages appeared to contain multiple genetic defects. To understand whether these defective prophages have the potential to act as mobile genetic elements to spread virulence determinants, we looked closely at the Sp1–Sp18 sequences, defined the genetic defects of each Sp, and then systematically analyzed all Sps for their biological activities. We show that many of the defective prophages, including the Stx1 phage, are inducible and released from O157 cells as particulate DNA. In fact, some prophages can even be transferred to other E. coli strains. We also show that new Stx1 phages are generated by recombination between the Stx1 and Stx2 phage genomes. The results indicate that these defective prophages are not simply genetic remnants generated in the course of O157 evolution, but rather genetic elements with a high potential for disseminating virulence-related genes and other genetic traits to other bacteria. We speculate that recombination and various other types of inter-prophage interactions in the O157 prophage pool potentiate such activities. Our data provide new insights into the potential activities of the defective prophages embedded in bacterial genomes and lead to the formulation of a novel concept of inter-prophage interactions in defective prophage communities

Tuning chelation by the surfactant-like peptide A6H using predetermined pH values

We examine the self-assembly of a peptide A6H comprising a hexa-alanine sequence A6 with a histidine (H) “head group”, which chelates Zn2+ cations. We study the self assembly of A6H and binding of Zn2+ ions in ZnCl2 solutions, under acidic and neutral conditions. A6H self-assembles into nanotapes held together by a β-sheet structure in acidic aqueous solutions. By dissolving A6H in acidic ZnCl2 solutions, the carbonyl oxygen atoms in A6H chelate the Zn2+ ions and allow for β-sheet formation at lower concentrations, consequently reducing the onset concentration for nanotape formation. A6H mixed with water or ZnCl2 solutions under neutral conditions produces short sheets or pseudocrystalline tapes, respectively. The imidazole ring of A6H chelates Zn2+ ions in neutral solutions. The internal structure of nanosheets and pseudocrystalline sheets in neutral solutions is similar to the internal structure of A6H nanotapes in acidic solutions. Our results show that it is possible to induce dramatic changes in the self-assembly and chelation sites of A6H by changing the pH of the solution. However, it is likely that the amphiphilic nature of A6H determines the internal structure of the self-assembled aggregates independent from changes in chelation

Self-assembly and anti-amyloid cytotoxicity activity of amyloid beta peptide derivatives

The self-assembly of two derivatives of KLVFF, a fragment Abeta(16-20) of the amyloid beta (Abeta) peptide, is investigated and recovery of viability of neuroblastoma cells exposed to Abeta is observed at sub-stoichiometric peptide concentrations. Fluorescence assays show that NH2-KLVFF-CONH2 undergoes hydrophobic collapse and amyloid formation at the same critical aggregation concentration (cac). In contrast, NH2-K(Boc)LVFF-CONH2 undergoes hydrophobic collapse at a low concentration, followed by amyloid formation at a higher cac. These findings are supported by the beta-sheet features observed by FTIR. Electrospray ionization mass spectrometry indicates that NH2-K(Boc)LVFF-CONH2 forms a significant population of oligomeric species above the cac. Cryo-TEM, used together with SAXS to determine fibril dimensions, shows that the length and degree of twisting of peptide fibrils seem to be influenced by the net peptide charge. Grazing incidence X-ray scattering from thin peptide films shows features of beta-sheet ordering for both peptides, along with evidence for lamellar ordering of NH2-KLVFF-CONH2. This work provides a comprehensive picture of the aggregation properties of these two KLVFF derivatives and show their utility, in unaggregated form, in restoring the viability of neuroblastoma cells against Abeta-induced toxicity