Reducibility of polynomials f(x,y)f(x,y) modulo pp

We consider absolutely irreducible polynomials $f \in Z[x,y]$ with $\deg_x(f)=m$, $\deg_y(f)=n$ and height $H$. We show that for any prime $p$ with $p>c_{mn} H^{2mn+n-1}$ the reduction $f \bmod p$ is also absolutely irreducible. Furthermore if the Bouniakowsky conjecture is true we show that there are infinitely many absolutely irreducible polynomials $f \in Z[x,y]$ which are reducible mod $p$ where $p$ is a prime with $p>H^{2m}$.Comment: Latex, 7 page

TRPV4-A Missing Link Between Mechanosensation and Immunity

Transient receptor potential vanilloid-type 4 (TRPV4) cation channel is widely expressed in all tissues as well as in immune cells and its function as mechanosensitive Ca2+ channel seems to be conserved throughout all mammalian species. Of late, emerging evidence has implicated TRPV4 in the activation and differentiation of innate immune cells, especially in neutrophils, monocytes, and macrophages. As such, TRPV4 has been shown to mediate neutrophil adhesion and chemotaxis, as well as production of reactive oxygen species in response to pro-inflammatory stimuli. In macrophages, TRPV4 mediates formation of both reactive oxygen and nitrogen species, and regulates phagocytosis, thus facilitating bacterial clearance and resolution of infection. Importantly, TRPV4 may present a missing link between mechanical forces and immune responses. This connection has been exemplary highlighted by the demonstrated role of TRPV4 in macrophage activation and subsequent induction of lung injury following mechanical overventilation. Mechanosensation via TRPV4 is also expected to activate innate immune cells and establish a pro-inflammatory loop in fibrotic diseases with increased deposition of extracellular matrix (ECM) and substrate stiffness. Likewise, TRPV4 may be activated by cell migration through the endothelium or the extracellular matrix, or even by circulating immune cells squeezing through the narrow passages of the pulmonary or systemic capillary bed, a process that has recently been linked to neutrophil priming and depriming. Here, we provide an overview over the emerging role of TRPV4 in innate immune responses and highlight two distinct modes for the activation of TRPV4 by either mechanical forces (“mechanoTRPV4”) or by pathogens (“immunoTRPV4”)

Default swaps and hedging credit baskets

We investigate the pricing of basket credit derivatives and their hedging with single name credit default swaps (CDS) based on a model for the joint dynamics of the fair CDS spreads. In the situation of the market flow of information being a pure jump filtration, we present an extremely efficient approach to pricing and study explicit hedging strategies. --credit default swap,credit basket,hedging

Introduction to Library Trends 23 (3) Winter 1975: Music and Fine Arts in the General Library

published or submitted for publicatio

The marginated pool

The pulmonary circulation harbors a large intravascular reservoir of leukocytes refered to as the Marginated Pool. This marginated pool is balanced by propeling and retaining forces acting on leukocytes during their passage through the pulmonary circulation. The present paper discusses these factors and their underlying mechanisms. Copyright (C) 2002 S. Karger AG, Basel

Latin hypercube sampling with dependence and applications in finance

In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random variables. The resulting estimator is shown to be consistent and asymptotically unbiased. For the bivariate case and under some conditions on the joint distribution, a central limit theorem together with a closed formula for the limit variance are derived. It is shown that for a class of estimators satisfying some monotonicity condition, the LHSD limit variance is never greater than the corresponding Monte Carlo limit variance. In some valuation examples of financial payoffs, when compared to standard Monte Carlo simulation, a variance reduction of factors up to 200 is achieved. LHSD is suited for problems with rare events and for high-dimensional problems, and it may be combined with Quasi-Monte Carlo methods. --Monte Carlo simulation,variance reduction,Latin hypercube sampling,stratified sampling