Computing the Volume of n-Dimensional Copulas

Abstract

A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put–call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance.     

Rocking ratchets in two-dimensional Josephson networks: collective effects and current reversal

A detailed numerical study on the directed motion of ac-driven vortices and antivortices in 2D Josephson junction arrays with an asymmetric periodic pinning potential is reported. dc-voltage rectification shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with ac amplitude for a wide range of vortex density around f = 1/2 (f = Ha(2)/Phi(0)), in good agreement with recent experiments by Shalóm and Pastoriza [Phys. Rev. Lett. 94, 177001 (2005)10.1103/PhysRevLett.94.177001]. The study of vortex structures, spatial and temporal correlations, and vortex-antivortex pairs formation gives insight into a purely collective mechanism behind the current reversal effect.     

Electrospray ionization ion trap multiple-stage mass spectrometric fragmentation pathways of leucine and isoleucine: an ab initio computational study

We recently demonstrated the possibility to distinguish between leucine and isoleucine in several tryptic peptides by means of consecutive tandem mass steps (Armirotti et al. J. Am. Soc. Mass Spectrom. 2007; 18: 57), exploiting a gas-phase rearrangement of the immonium ion of Ile. In the present paper we explore the tandem mass spectrometric behaviour of the two amino acids. We propose a plausible structure for the diagnostic m/z 69 ion of Ile, that was reported for the first time in 1996 (Hulst and Kientz J. Mass. Spectrom. 1996; 31: 1188), and we explain why its formation is favoured with respect to Leu. Our conclusions are supported by ab initio quantum chemistry calcultations and isotope-labelled standards experiments.     

Phase-space approach to dynamical density functional theory

The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.     

Efficient resolution of racemic N-benzyl beta3-amino acids by iterative liquid-liquid extraction with a chiral (salen)cobalt(III) complex as enantioselective selector

The efficient (up to 93% ee) resolution of racemic N-benzyl beta(3)-amino acids has been achieved by an iterative (two cycle) liquid-liquid extraction process using a lipophilic chiral (salen)cobalt(III) complex [Co(III)(1)(OAc)]. As a result of the resolution by extraction, one enantiomer of the N-benzyl beta(3)-amino acid predominated in the aqueous phase, while the other enantiomer was driven into the organic phase by complexation to cobalt. The complexed amino acid was then quantitatively released into an aqueous phase, by a reductive (Co(III)--> Co(II)) counter-extraction using l-ascorbic acid. The reductive cleavage allowed for the recovery of the cobalt(II) selector in up to 90% yield (easily re-oxidable to Co(III) with air/AcOH).     

Stereocontrolled synthesis of substituted N-arenesulfonyl azetidines from gamma-(phenylseleno)alkyl arylsulfonamides

Different synthetic methodologies for the stereocontrolled synthesis of substituted azetidines are reported. The approach utilizes an optimized oxidation reaction of gamma-(phenylseleno)alkyl arylsulfonamides, followed by the intramolecular substitution of the resulting phenylselenonyl group by the nitrogen atom.     

Temperature dependant polycrystal model application to bainitic steel behavior under tri-axial loading in the ductile–brittle transition

A polycrystal finite element (FE) model describing the temperature evolution of low carbon steel is proposed in order to forecast the local mechanical fields as a function of temperature, for bainitic microstructure submitted to tri-axial loading. The model is designed for finite strains, large lattice rotations and temperatures ranging into the brittle–ductile transition domain. The dislocation densities are the internal variables. At low temperature in Body Centred Cubic (BCC) materials, plasticity is governed by double kink nucleation of screw dislocations, whereas at high temperature, plasticity depends on interactions between mobile dislocations and the forest dislocations. In this paper, the constitutive law and the evolution of the dislocation densities are written as a function of temperature and describe low and high temperature mechanisms. The studied aggregates are built from Electron Back Scattering Diffraction (EBSD) images of real bainitic steel. The aggregate is submitted to a tri-axial loading in order to describe the material at a crack tip. Mechanical parameters are deduced from mechanical tests. The local strain and stress fields, computed for different applied loadings, present local variations which depend on temperature and on tri-axial ratio. The distribution curves of the maximal principal stresses show that heterogeneities respectively increase with temperature and decrease with tri-axial ratio. A direct application of this model provides the evaluation of the rupture probability within the aggregate, which is treated as the elementary volume in the weak link theory. A comparison with the Beremin criterion calibrated on experimental data, shows that the computed fracture probability dispersion induced by the stress heterogeneities is of the same order than the measured dispersion. Temperature and stress tri-axiality ratio effects are also investigated. It is shown that these two parameters have a strong effect on fracture owing to their influence on the heterogeneous plastic strain. These inhomogeneities can initiate cleavage fracture.     

Varieties of interlaced bilattices

The paper contains some algebraic results on several varieties of algebras having an (interlaced) bilattice reduct. Some of these algebras have already been studied in the literature (for instance bilattices with conflation, introduced by M. Fitting), while others arose from the algebraic study of O. Arieli and A. Avron??s bilattice logics developed in the third author??s PhD dissertation. We extend the representation theorem for bounded interlaced bilattices (proved, among others, by A. Avron) to unbounded bilattices and prove analogous representation theorems for the other classes of bilattices considered. We use these results to establish categorical equivalences between these structures and well-known varieties of lattices.     

Surface supramolecular organization of a terbium(III) double-decker complex on graphite and its single molecule magnet behavior

The two-dimensional self-assembly of a terbium(III) double-decker phthalocyanine on highly oriented pyrolitic graphite (HOPG) was studied by atomic force microscopy (AFM), and it was shown that it forms highly regular rectangular two-dimensional nanocrystals on the surface, that are aligned with the graphite symmetry axes, in which the molecules are organized in a rectangular lattice as shown by scanning tunneling microscopy. Molecular dynamics simulations were run in order to model the behavior of a collection of the double-decker complexes on HOPG. The results were in excellent agreement with the experiment, showing that-after diffusion on the graphite surface-the molecules self-assemble into nanoscopic islands which align preferentially along the three main graphite axes. These low dimension assemblies of independent magnetic centers are only one molecule thick (as shown by AFM) and are therefore very interesting nanoscopic magnetic objects, in which all of the molecules are in interaction with the graphite substrate and might therefore be affected by it. The magnetic properties of these self-assembled bar-shaped islands on HOPG were studied by X-ray magnetic circular dichroism, confirming that the compounds maintain their properties as single-molecule magnets when they are in close interaction with the graphite surface.