Effondrement de quotients aléatoires de groupes hyperboliques avec torsion

We show that random quotients of hyperbolic groups with ‘harmful’ torsion collapse at densities smaller than expected. To cite this article: Y. Ollivier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

The Relationship Between Stock Markets Of Major Developed Countries And Asian Emerging Markets

With the emergence of new capital markets and liberalization of stock markets in recent years, there has been an increase in investors' interest in international diversification. This is so because international diversification allows investors to have a larger basket of foreign securities to choose from as part of their portfolio assets, so as to enhance the reward-to-volatility ratio. This benefit would be limited if national equity markets tend to move together in the long run. This paper thus studies the issue of co-movement between stock markets in major developed countries and those in Asian emerging markets using the concept of cointegration. We find that there is co-movement between some of the developed and emerging markets, but some emerging markets do differ from the developed markets with which they share a long-run equilibrium relationship. Furthermore, it has been observed that there has been increasing interdependence between most of the developed and emerging markets since the 1987 Stock Market Crash. This interdependence intensified after the 1997 Asian Financial Crisis. With this phenomenon of increasing co-movement between developed and emerging stock markets, the benefits of international diversification become limited.     

An integrable example of gradient flow based on optimal transport of differential forms

Optimal transport theory has been a powerful tool for the analysis of parabolic equations viewed as gradient flows of volume forms (or, in other words, 0-currents) according to suitable transportation metrics. In this paper, we present an example of gradient flow for closed \((d-1)\)-differential forms, or, more appropriately, to closed 1-currents, which can be identified to divergence-free vector fields, in the Euclidean space \(\mathbb {R}^d\). In spite of its apparent complexity, the resulting very degenerate parabolic system is fully integrable and can be viewed, in a suitable sense, as an Eulerian version of the heat equation for loops in the Euclidean space. We analyze this system in terms of “relative entropy” and “dissipative solutions” and provide global existence and weak–strong uniqueness results.     

Exploring the latent segmentation space for the assessment of multiple change-point models

This paper addresses the retrospective or off-line multiple change-point detection problem. Multiple change-point models are here viewed as latent structure models and the focus is on inference concerning the latent segmentation space. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a dynamic programming algorithm for computing the top $N$ most probable segmentations is derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the segmentation space for successive numbers of change points and provide a set of assessment tools for multiple change-point models that can be applied both in a non-Bayesian and a Bayesian framework. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the position of change points.     

X-ray absorption study of Cu,Zn SOD under high pressure

Abstract

We have investigated Cu, Zn Superoxide Dismutase (Cu, Zn SOD) metal sites at high pressure using X-ray absorption. XAS (X-ray Absorption Spectroscopy) gives information on local structure and it is particularly suited to metal site investigation. To the best of our knowledge, this is the first time that protein conformational states have been investigated using the high pressure XAS technique. Cu, Zn SOD catalyses the dismutation of toxic oxygen radicals produced in cells; this reaction occurs at the copper metal site. Structural changes around the copper, induced by pressure, can be directly related to protein substates. Their characterisation is thus important in the understanding of protein activity.

The high-pressure device was a Paris-Edinburgh large volume cell.

Experiments were performed on lyophilised Cu, Zn SOD between 0 and 48 kbar at the copper and zinc K-edges. The two metal local atomic environments have a different behaviour as pressure increases: copper exhibits a more flexible environment; on the contrary, zinc shows small structural modifications. We have identified a state, formed between 3 and 8 kbar, which is stable up to 48 kbar.     

Approximation by Algebraic Integers and Hausdorff Dimension

The paper computes the Hausdorff dimension of sets of real numberswhich are close to infinitely many real algebraic integers ofbounded degree. It also investigates the distribution of realalgebraic integers of bounded degree, which are proved to beevenly spaced.     

Sharp phase transition theorems for hyperbolicity of random groups

We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability, whereas above this critical value a random quotient is very probably trivial. We give explicit characterizations of these critical densities for the various models.     

Evaluation of capillary isoelectric focusing in glycerol-water media with a view to hydrophobic protein applications

Capillary isoelectric focusing (CIEF) separations are usually performed with neutral coated fused-silica capillaries in aqueous anticonvective media. Glycerol, a very viscous solvent (eta = 945 mPa x s at 25 degrees C), known to help stabilize any kind of proteins and solubilize hydrophobic ones, was tested as an alternative to using commercial gels. Viscosity and electroosmotic mobility were measured as a function of gel or glycerol content in water, and a 30:70 v/v glycerol-water medium appeared as a good compromise for performing CIEF in a bare fused-silica capillary without imposing too high a viscosity. To demonstrate the feasibility of this new CIEF system, a standard mixture of nine model proteins was separated according to their pI with a good agreement between experimental and literature aqueous pIs. Moreover, better resolution was achieved with this system than with the conventional aqueous CIEF system, as two of the model proteins could not be separated in the latter system. Glycerol-water CIEF in bare silica capillary was next applied to the separation of horse radish peroxidase, a complex mixture of protein isoforms. The good concordance with the separation obtained by the conventional CIEF system indicated the adequacy of this new system. Finally, as anticipated from the results obtained for the separation of bacteriorhodopsin, a membrane protein, glycerol-water CIEF performed in bare silica capillary appears to be a promising alternative to conventional aqueous CIEF for hydrophobic protein characterization, under their native form.     

KINETICS AND MECHANISM OF THE REACTION BETWEEN OLIGOSILOXANES AND P-TRICHLORO-N-DICHLOROPHOSPHORYL MONOPHOSPHAZENE (Cl3P[dbnd]N-POCl2)

Abstract

³¹P NMR investigation has been made of the action of Cl₃P[dbnd]N-POCl₂(I) first on hexamethyldisiloxane (Me₃Si)₂O and then on oligosiloxanes Me₃Si-(OSiMe₂)_n-OSiMe₃ n = 2 and n=3. The reactions were carried out in bulk or in solution with molar ratios siloxane/(I) varying from I to 5. It was demonstrated that only the monosubstitution of a chlorine atom by the -(OSiMe₂)_n,-OSiMe₃ species n = 0, 2, 3 with elimination of trimethylchlorosilane occurred leading to the derivatives Cl₂OP-N[dbnd]PCl₂O(SiMe₂-O)_nSiMe₃ (II). For n=2, 3 the siloxane redistribution reactions were observed by ²⁹Si NMR analysis. A two steps mechanism is proposed. consisting in a nucleophilic substitution, involving a tricoordinate phosphazenium intermediate, followed by the formation of an active ionic centre probably an oxonium ion, arising from the solvatation by the siloxane of this phosphazeniurn ion and /or of (II) leading to the redistribution reactions. The influences of the solvent, of trimethylchlorosilane, of the temperature, and of the addition of a protonated species (MDH) were investigated.     

Photoinduced electron transfer in Zn(II)porphyrin-bridge-Pt(II)acetylide complexes: variation in rate with anchoring group and position of the bridge

The synthesis and photophysical characterization of two sets of zinc porphyrin platinum acetylide complexes are reported. The two sets of molecules differ in the way the bridging phenyl-ethynyl unit is attached to the porphyrin ring. One set is attached via an ethynyl unit on the β position, while the other set is attached via a phenyl unit on the meso position of the porphyrin. These were compared with previously studied complexes where attachment was made via an ethynyl unit on the meso position. Femtosecond transient absorption measurements showed in all systems a rapid quenching of the porphyrin singlet state. Electron transfer is suggested as the quenching mechanism, followed by an even faster recombination to form both the porphyrin ground and triplet excited states. This is supported by the variation in quenching rate and porphyrin triplet yield with solvent polarity, and the observation of an intermediate state in the meso-phenyl linked systems. The different linking motifs between the dyads resulted in significant variations in electron transfer rates.