Estimation of conditional laws given an extreme component

Let (X,Y) be a bivariate random vector. The estimation of a probability of the form P(Y ≤ y |X > t) is challenging when t is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector (X,Y), suitably normalized, given that X is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations. Some real data are analysed.     

Shear-induced permeation and fusion of lipid vesicles

This paper introduces a novel approach to controlling membrane permeability in free unilamellar vesicles using shearing in the presence of a detergent with a large head-group to tune pore formation. Such shear-induced permeation could offer a simple means of postencapsulating bioactive molecules to prepare vesicle vectors for drug delivery. Using UV absorption, fluorescence emission, dynamic light scattering, and electron microscopy, we investigated the membrane permeability and the morphology of unilamellar lipid vesicles (diameter in the range 50-400 nm) subjected to a shear stress in the presence of a small amount of nonionic surfactant (Brij 76). Shear-induced leakage and fusion events were observed. We analyzed the significance of the vesicle size, the shear rate, and the surfactant-to-lipid ratio for the observed phenomena. The present approach is evaluated for postloading of preformed vesicles.     

Is the axial zero-field splitting parameter of tetragonally elongated high-spin manganese(III) complexes always negative?

The positive axial zero-field splitting parameter D relevant for the S = 2 ground state of [Mn(cyclam)I2]I (cyclam = 1,4,8,11-tetraazacyclotetradecane) is interpreted using the valence bond configuration interaction model which explicitly considers the covalency of the manganese-iodide bond.     

Quadrupolar interaction study of various cations confined in porous charged polymer film of sPI ionomers

The structure of a sulfonated polyimide (sPI) ionomer membranes was investigated via the transport properties of various confined cations (7Li+, 23Na+, 87Rb+, 133Cs+). Their NMR spectra show large residual quadrupolar splitting depending on the orientation of the film in the static magnetic field B0. This behavior is the fingerprint of a macroscopic nematic ordering of charged interfaces. This is also confirmed by the anisotropy of the self-diffusion tensor measured by 1H and 7Li PGSE experiments on N(CH3)4+ and Li+ cations, respectively.     

Ferromagnetic and antiferromagnetic intermolecular interactions in a new family of Mn4 complexes with an energy barrier to magnetization reversal

A new family of tetranuclear Mn complexes [Mn4X4L4] (H2L = salicylidene-2-ethanolamine; X = Cl (1) or Br (2)) and [Mn4Cl4(L')4] (H2L' = 4-tert-butyl-salicylidene-2-ethanolamine, (3)) has been synthesized and studied. Complexes 1-3 possess a square-shaped core with ferromagnetic exchange interactions between the four Mn(III) centers resulting in an S = 8 spin ground state. Magnetochemical studies and high-frequency EPR spectroscopy reveal an axial magnetoanisotropy with D values in the range -0.10 to -0.20 cm(-1) for complexes 2 and 3 and for differently solvated forms of 1. As a result, these species possess an anisotropy-induced energy barrier to magnetization reversal and display slow relaxation of the magnetization, which is observed as hysteresis for 1 and 3 and frequency-dependent peaks in out-of-phase AC susceptibility measurements for 3. The effective energy barrier was determined to be 7.7 and 7.9 K for 1 and 3, respectively, and evidence for quantum tunneling of the magnetization was observed. Detailed magnetochemical studies, including measurements at ultralow temperatures, have revealed that complexes 1 and 2 possess solvation-dependent antiferromagnetic intermolecular interactions. Complex 3 displays ferromagnetic intermolecular interactions and approaches a ferromagnetic phase transition with a critical temperature of approximately 1 K, which is coincident with the onset of slow relaxation of the magnetization due to the molecular anisotropy barrier to magnetization reversal. It was found that the intermolecular interactions have a significant effect on the manifestation of slow relaxation of the magnetization, and thereby, these complexes represent a new family of "exchange-biased single-molecule magnets", where the exchange bias is controlled by chemical and structural modifications.     

Bayesian model averaging for multivariate extremes

The main framework of multivariate extreme value theory is well-known in terms of probability, but inference and model choice remain an active research field. Theoretically, an angular measure on the positive quadrant of the unit sphere can describe the dependence among very high values, but no parametric form can entirely capture it. The practitioner often makes an assertive choice and arbitrarily fits a specific parametric angular measure on the data. Another statistician could come up with another model and a completely different estimate. This leads to the problem of how to merge the two different fitted angular measures. One natural way around this issue is to weigh them according to the marginal model likelihoods. This strategy, the so-called Bayesian Model Averaging (BMA), has been extensively studied in various context, but (to our knowledge) it has never been adapted to angular measures. The main goal of this article is to determine if the BMA approach can offer an added value when analyzing extreme values.     

Glycoligands tuning the magnetic anisotropy of Ni(II) complexes

Two organic ligands based on a sugar-scaffold derived from galactose and possessing three O-CH(2)-pyridine pendant arms at the 3-, 4-, and 5-positions of the galactopyranose that act as chelates afford mononuclear complexes when reacted with a Ni(II) salt. The magnetization behavior in the form of M=f(H/T) plots suggests the presence of appreciable magnetic anisotropy within the two complexes. The analysis of the EPR spectra performed at two different temperatures (7 and 17 K) and at three frequencies (190, 285, and 380 GHz) leads to the conclusion that the anisotropy has a high degree of axiality (E/D=0.17 for the two complexes), but with a different sign of the D parameter. The spin hamiltonian parameters D and E were reproduced for the two complexes by using calculations based on the angular overlap model (AOM). The structural difference between the two complexes responsible of the sign of the D parameters was also determined using AOM calculations. A thorough analysis of the structures showed that the structural differences in the coordination sphere of the two complexes responsible of the different D parameter sign result from the nature of the sugar scaffolds. In complex 1, the sugar scaffold imposes an intramolecular hydrogen bond with one of the atoms linked to Ni(II); this arrangement leads to a distorted coordination sphere and positive D value, while the absence of such a hydrogen bond in complex 2 leads to a less distorted environment around the Ni center and to a negative D value.     

Local structure of Mn4+ and Fe3+ spin probes in layered LiAlO2 oxide by modelling of zero-field splitting parameters

The zero-field splitting parameters (ZFS) of Mn(4+) and Fe(3+) ions in LiAlO(2) with a layered structure are analyzed experimentally and theoretically by using high-frequency electron paramagnetic resonance spectroscopy, Neuman superposition model (NSM), DFT and multiconfigurational calculations. The interpretation of ZFS is based on the comparison of the experimentally determined values with the calculated ones. This approach allows assessing the performance of different methods for computation of ZFS of Fe(3+) and Mn(4+) in layered oxide matrices. DFT and multiconfigurational calculations are used to analyze the effect of oxygen, aluminium, and lithium neighbours on ZFS of Fe(3+) and Mn(4+). These calculations are based on a cluster comprising Fe(3+) or Mn(4+) ions in a trigonally compressed octahedron with 6 metal ions (Al(3+) or Co(3+)) as first metal neighbours and 6 O(2-) and 2 Li(+) (above and below the layer) as second neighbours. A satisfactory agreement with the experimental data is achieved when the local structure of Mn(4+) and Fe(3+) deviates from the trigonal host-site geometry. The local structure of Fe(3+) comprises an axial distortion, while trigonal environment with reduced extent of distortion appears around Mn(4+).     

Effective boundary condition at a rough surface starting from a slip condition

We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ?. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ε=0 is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in Basson and Gérard-Varet (2008) [6] and Gerard-Varet and Masmoudi (2010) [13], in which the special case of a Dirichlet condition at the rough boundary was examined.