A Random Difference Equation with Dufresne Variables revisited

The Dufresne laws (laws of product of independent random variables with gamma and beta distributions) occur as stationary distribution of certain Markov chains $X_n$ on $R$ defined by: \begin{equation} X_n = A_n ( X_{n-1} + B_n ) \end{equation} where $X_0 , (A_1,B_1),...,(A_n,B_n)$ are independent and the $(A_i,B_i)'$s are identically distributed. This paper generalizes an explicit example where $A$ is the product of two independent $\beta_{a,1} , \beta_{b,1}$ and $B \sim \gamma_1$ or $\gamma_2$. Keywords: beta, gamma and Dufresne distributions,Markov chains, stationary distributions, hypergeometric differential equations, Poisson process.Comment: 11 pages, 2 tables, 1 figur

Masticatory biomechanics in the rabbit : a multi-body dynamics analysis

Acknowledgement We thank Sue Taft (University of Hull) for the µCT-scanning of the rabbit specimen used in this study. We also thank Raphaël Cornette, Jacques Bonnin, Laurent Dufresne, and l'Amicale des Chasseurs Trappistes (ACT) for providing permission and helping us capture the rabbits used for the in vivo bite force measurements at la Réserve Naturelle Nationale de St Quentin en Yvelines, France.Peer reviewedPublisher PD

Separating algebras and finite reflection groups

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.Comment: 12 pages, corrected yet another typ

Method of evaporation

Liquids, such as juices, milk, molten metal and the like are concentrated by forming uniformly-sized, small droplets in a precision droplet forming assembly and deploying the droplets in free fall downwardly as a central column within an evacuated column with cool walls. A portion of the solvent evaporates. The vapor flows to the wall, condenses, and usually flows down the wall as a film to condensate collector and drain. The vertical column of freely falling droplets enters the splash guard. The condensate can be collected, sent to other towers or recycled

SLIDES: ACTS: Anadarko Completion Transport System

Presenter: Jeff Dufresne, Completions Manager, Anadarko Corporation 18 slide

A flexible matrix Libor model with smiles

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numerical exercise illustrates the flexibility of Wishart Libor model in describing the movements of the implied volatility surface

Unraveling the genomic mosaic of a ubiquitous genus of marine cyanobacteria

Background: The picocyanobacterial genus Synechococcus occurs over wide oceanic expanses, having colonized most available niches in the photic zone. Large scale distribution patterns of the different Synechococcus clades (based on 16S rRNA gene markers) suggest the occurrence of two major lifestyles ('opportunists'/'specialists'), corresponding to two distinct broad habitats ('coastal'/'open ocean'). Yet, the genetic basis of niche partitioning is still poorly understood in this ecologically important group. Results: Here, we compare the genomes of 11 marine Synechococcus isolates, representing 10 distinct lineages. Phylogenies inferred from the core genome allowed us to refine the taxonomic relationships between clades by revealing a clear dichotomy within the main subcluster, reminiscent of the two aforementioned lifestyles. Genome size is strongly correlated with the cumulative lengths of hypervariable regions (or 'islands'). One of these, encompassing most genes encoding the light-harvesting phycobilisome rod complexes, is involved in adaptation to changes in light quality and has clearly been transferred between members of different Synechococcus lineages. Furthermore, we observed that two strains (RS9917 and WH5701) that have similar pigmentation and physiology have an unusually high number of genes in common, given their phylogenetic distance. Conclusion: We propose that while members of a given marine Synechococcus lineage may have the same broad geographical distribution, local niche occupancy is facilitated by lateral gene transfers, a process in which genomic islands play a key role as a repository for transferred genes. Our work also highlights the need for developing picocyanobacterial systematics based on genome-derived parameters combined with ecological and physiological data