Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student's copula, cannot be rejected if it has sufficiently many ``degrees of freedom''. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the correlation coefficient between the pair of asset is too high as the tail dependence neglected by the Gaussian copula can be as large as 0.6, i.e., three out five extreme events which occur in unison are missed.Comment: Latex document of 43 pages including 14 eps figure

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Modelling stochastic bivariate mortality

Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining increasing reputation as a way to represent mortality risk. This paper represents a first attempt to model the mortality risk of couples of individuals, according to the stochastic intensity approach. On the theoretical side, we extend to couples the Cox processes set up, i.e. the idea that mortality is driven by a jump process whose intensity is itself a stochastic process, proper of a particular generation within each gender. Dependence between the survival times of the members of a couple is captured by an Archimedean copula. On the calibration side, we fit the joint survival function by calibrating separately the (analytical) copula and the (analytical) margins. First, we select the best fit copula according to the methodology of Wang and Wells (2000) for censored data. Then, we provide a sample-based calibration for the intensity, using a time-homogeneous, non mean-reverting, affine process: this gives the analytical marginal survival functions. Coupling the best fit copula with the calibrated margins we obtain, on a sample generation, a joint survival function which incorporates the stochastic nature of mortality improvements and is far from representing independency.On the contrary, since the best fit copula turns out to be a Nelsen one, dependency is increasing with age and long-term dependence exists

SosA inhibits cell division in Staphylococcus aureus in response to DNA damage.

Inhibition of cell division is critical for viability under DNA-damaging conditions. DNA damage induces the SOS response that in bacteria inhibits cell division while repairs are being made. In coccoids, such as the human pathogen, Staphylococcus aureus, this process remains poorly studied. Here, we identify SosA as the staphylococcal SOS-induced cell division inhibitor. Overproduction of SosA inhibits cell division, while sosA inactivation sensitizes cells to genotoxic stress. SosA is a small, predicted membrane protein with an extracellular C-terminal domain in which point mutation of residues that are conserved in staphylococci and major truncations abolished the inhibitory activity. In contrast, a minor truncation led to SosA accumulation and a strong cell division inhibitory activity, phenotypically similar to expression of wild-type SosA in a CtpA membrane protease mutant. This suggests that the extracellular C-terminus of SosA is required both for cell division inhibition and for turnover of the protein. Microscopy analysis revealed that SosA halts cell division and synchronizes the cell population at a point where division proteins such as FtsZ and EzrA are localized at midcell, and the septum formation is initiated but unable to progress to closure. Thus, our findings show that SosA is central in cell division regulation in staphylococci

The Chaperone ClpX Stimulates Expression of Staphylococcus aureus Protein A by Rot Dependent and Independent Pathways

The Clp ATPases (Hsp100) constitute a family of closely related proteins that have protein reactivating and remodelling activities typical of molecular chaperones. In Staphylococcus aureus the ClpX chaperone is essential for virulence and for transcription of spa encoding Protein A. The present study was undertaken to elucidate the mechanism by which ClpX stimulates expression of Protein A. For this purpose, we prepared antibodies directed against Rot, an activator of spa transcription, and demonstrated that cells devoid of ClpX contain three-fold less Rot than wild-type cells. By varying Rot expression from an inducible promoter we showed that expression of Protein A requires a threshold level of Rot. In the absence of ClpX the Rot content is reduced below this threshold level, hence, explaining the substantially reduced Protein A expression in the clpX mutant. Experiments addressed at pinpointing the role of ClpX in Rot synthesis revealed that ClpX is required for translation of Rot. Interestingly, translation of the spa mRNA was, like the rot mRNA, enhanced by ClpX. These data demonstrate that ClpX performs dual roles in regulating Protein A expression, as ClpX stimulates transcription of spa by enhancing translation of Rot, and that ClpX additionally is required for full translation of the spa mRNA. The current findings emphasize that ClpX has a central role in fine-tuning virulence regulation in S. aureus

The ClpX chaperone controls autolytic splitting of Staphylococcus aureus daughter cells, but is bypassed by β-lactam antibiotics or inhibitors of WTA biosynthesis.

β-lactam antibiotics interfere with cross-linking of the bacterial cell wall, but the killing mechanism of this important class of antibiotics is not fully understood. Serendipitously we found that sub-lethal doses of β-lactams rescue growth and prevent spontaneous lysis of Staphylococcus aureus mutants lacking the widely conserved chaperone ClpX, and we reasoned that a better understanding of the clpX phenotypes could provide novel insights into the downstream effects of β-lactam binding to the PBP targets. Super-resolution imaging revealed that clpX cells display aberrant septum synthesis, and initiate daughter cell separation prior to septum completion at 30°C, but not at 37°C, demonstrating that ClpX becomes critical for coordinating the S. aureus cell cycle as the temperature decreases. FtsZ localization and dynamics were not affected in the absence of ClpX, suggesting that ClpX affects septum formation and autolytic activation downstream of Z-ring formation. Interestingly, oxacillin antagonized the septum progression defects of clpX cells and prevented lysis of prematurely splitting clpX cells. Strikingly, inhibitors of wall teichoic acid (WTA) biosynthesis that work synergistically with β-lactams to kill MRSA synthesis also rescued growth of the clpX mutant, as did genetic inactivation of the gene encoding the septal autolysin, Sle1. Taken together, our data support a model in which Sle1 causes premature splitting and lysis of clpX daughter cells unless Sle1-dependent lysis is antagonized by β-lactams or by inhibiting an early step in WTA biosynthesis. The finding that β-lactams and inhibitors of WTA biosynthesis specifically prevent lysis of a mutant with dysregulated autolytic activity lends support to the idea that PBPs and WTA biosynthesis play an important role in coordinating cell division with autolytic splitting of daughter cells, and that β-lactams do not kill S. aureus simply by weakening the cell wall

Comparative genomics of isolates of a pseudomonas aeruginosa epidemic strain associated with chronic lung infections of cystic fibrosis patients

Pseudomonas aeruginosa is the main cause of fatal chronic lung infections among individuals suffering from cystic fibrosis (CF). During the past 15 years, particularly aggressive strains transmitted among CF patients have been identified, initially in Europe and more recently in Canada. The aim of this study was to generate high-quality genome sequences for 7 isolates of the Liverpool epidemic strain (LES) from the United Kingdom and Canada representing different virulence characteristics in order to: (1) associate comparative genomics results with virulence factor variability and (2) identify genomic and/or phenotypic divergence between the two geographical locations. We performed phenotypic characterization of pyoverdine, pyocyanin, motility, biofilm formation, and proteolytic activity. We also assessed the degree of virulence using the Dictyostelium discoideum amoeba model. Comparative genomics analysis revealed at least one large deletion (40-50 kb) in 6 out of the 7 isolates compared to the reference genome of LESB58. These deletions correspond to prophages, which are known to increase the competitiveness of LESB58 in chronic lung infection. We also identified 308 non-synonymous polymorphisms, of which 28 were associated with virulence determinants and 52 with regulatory proteins. At the phenotypic level, isolates showed extensive variability in production of pyocyanin, pyoverdine, proteases and biofilm as well as in swimming motility, while being predominantly avirulent in the amoeba model. Isolates from the two continents were phylogenetically and phenotypically undistinguishable. Most regulatory mutations were isolate-specific and 29% of them were predicted to have high functional impact. Therefore, polymorphism in regulatory genes is likely to be an important basis for phenotypic diversity among LES isolates, which in turn might contribute to this strain's adaptability to varying conditions in the CF lung

Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java