Central factorials under the Kontorovich-Lebedev transform of polynomials

We show that slight modifications of the Kontorovich-Lebedev transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of monomials to central factorial polynomials. A special attention is driven to the polynomial sequences whose KL-transform is the canonical sequence, which will be fully characterized. Finally, new identities between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August 201

Summation and transformation formulas for elliptic hypergeometric series

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.Comment: 21 pages, AMS-LaTe

Absolute ozone densities in a radio-frequency driven atmospheric pressure plasma using two-beam UV-LED absorption spectroscopy and numerical simulations

International audienceThe efficient generation of reactive oxygen species (ROS) in cold atmospheric pressure plasma jets (APPJs) is an increasingly important topic, e.g. for the treatment of temperature sensitive biological samples in the field of plasma medicine. A 13.56 MHz radio-frequency (rf) driven APPJ device operated with helium feed gas and small admixtures of oxygen (up to 1%), generating a homogeneous glow-mode plasma at low gas temperatures, was investigated. Absolute densities of ozone, one of the most prominent ROS, were measured across the 11 mm wide discharge channel by means of broadband absorption spectroscopy using the Hartley band centred at lambda = 255 nm. A two-beam setup with a reference beam in Mach--Zehnder configuration is employed for improved signal-to-noise ratio allowing high-sensitivity measurements in the investigated single-pass weak-absorbance regime. The results are correlated to gas temperature measurements, deduced from the rotational temperature of the N2 (C 3 {{{\Pi }}}u \to B 3 {{{\Pi }}}g , upsilo = 0 \to 2) optical emission from introduced air impurities. The observed opposing trends of both quantities as a function of rf power input and oxygen admixture are analysed and explained in terms of a zero-dimensional plasma-chemical kinetics simulation. It is found that the gas temperature as well as the densities of O and O2(b{}1{{{Sigma }}}g ) influence the absolute O3 densities when the rf power is varied

The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovasz local lemma -- which provides a sufficient condition for this to occur -- corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer and explicitly by Dobrushin. We also present some refinements and extensions of both arguments, including a generalization of the Lovasz local lemma that allows for "soft" dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity. To be published in J. Stat. Phy

Early indicators of exposure to biological threat agents using host gene profiles in peripheral blood mononuclear cells

<p>Abstract</p> <p>Background</p> <p>Effective prophylaxis and treatment for infections caused by biological threat agents (BTA) rely upon early diagnosis and rapid initiation of therapy. Most methods for identifying pathogens in body fluids and tissues require that the pathogen proliferate to detectable and dangerous levels, thereby delaying diagnosis and treatment, especially during the prelatent stages when symptoms for most BTA are indistinguishable flu-like signs.</p> <p>Methods</p> <p>To detect exposures to the various pathogens more rapidly, especially during these early stages, we evaluated a suite of host responses to biological threat agents using global gene expression profiling on complementary DNA arrays.</p> <p>Results</p> <p>We found that certain gene expression patterns were unique to each pathogen and that other gene changes occurred in response to multiple agents, perhaps relating to the eventual course of illness. Nonhuman primates were exposed to some pathogens and the <it>in vitro</it> and <it>in vivo</it> findings were compared. We found major gene expression changes at the earliest times tested post exposure to aerosolized <it>B. anthracis </it>spores and 30 min post exposure to a bacterial toxin.</p> <p>Conclusion</p> <p>Host gene expression patterns have the potential to serve as diagnostic markers or predict the course of impending illness and may lead to new stage-appropriate therapeutic strategies to ameliorate the devastating effects of exposure to biothreat agents.</p

Plasma–liquid interactions: a review and roadmap

Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, fluid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identifies the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on non-equilibrium plasmas