Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

Ariel - Volume 5 Number 6

Editors J.D. Kanofsky Mark Dembert Entertainment Robert Breckenridge Joe Conti Gary Kaskey Photographer Scot Kastner Overseas Editor Mike Sinason Circulation Jay Amsterdam Humorist Jim McCann Staff Ken Jaffe Bob Sklaroff Janet Welsh Dave Jacoby Phil Nimoityn Frank Chervane

Chemosensory-Mediated Deposit Feeding in the Spionid Polychaete Dipolydora Quadrilobata.

Deposit feeding organisms live and feed in marine soft-sediment habitats. This sediment makes up a majority of the material ingested by deposit feeders and contains a variety of edible material that may constitute their principal nutrient source. However, the specific components that are assimilated by these organisms, and the strategies they employ to efficiently collect those components, remain unclear. Sensory interactions between an organism and its surrounding environment typically play an important role in helping the organism detect and locate potential food. Accordingly, chemical sensing by deposit feeders is most likely involved in feeding, yet few specifics about this role and its ecological implications are known. This study, a multi-disciplined investigation of chemoreception, focuses on putative chemosensory structures located on the palps of the deposit-feeding spionid polychaete Diplydora quadrilobata. Using behavioral studies, neurophysiological methods, and molecular biological techniques, this study examines the sensory capabilities of this deposit feeder and their potential role as a mediator of selective feeding. A series of behavioral assays tested for feeding responses to a selected number of potential cues that might be used to indicate food availability or quality. Two sets of glass beads, one with and one without covalently bound compounds such as single amino acids, mixtures of amino acids, and single simple sugars, were separately presented to an organism. The differences in observed responses were used to identify these compounds as stimulatory, inhibitory, or inactive. Stirnulatory cues identified in the behavioral studies were then used to label, in an activity-dependent manner, putative receptor neurons in the palps. Stimulatory cues were perfused over the palp in the presence of the cationic molecule agmatine. Agmatine can enter into stimulated receptor neurons via activated non-selective cation channels. Those cells containing agmatine are then stained using an anti-agmatine antibody followed by silver intensification. Four putative sensory cell types located in the palps were identified by comparing cell labeling in response to the perfusion of a mixture of amino acids in the presence of agmatine to controls of agmatine in the absence of stimuli. Two of these cells types appear to be mechanosensory in function, and two appear to be chemosensory in function. Finally, molecular biological techniques were employed in attempts at isolating gene sequences that code for chemoreceptor proteins. Using RNA isolated fiom two tissues, D. quadrilobata palps and tails, single-stranded complementary DNA was constructed and amplified via the polymerase chain reaction. Gene expression patterns in the two tissues were compared (i.e. differential display) in order to isolate genes differentially expressed in the palps with the goal of finding receptor gene sequences. These studies indicate that chemoreception is an important influence in particle selection by this organism, and similarly suggest that this influence is at least partially mediated via chemoreceptor structures of the palp

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $\beta>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $\beta pn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,\lambda)$-graphs with $\lambda\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.Comment: 30 pages, 1 figur

Coupling models of cattle and farms with models of badgers for predicting the dynamics of bovine tuberculosis (TB)

Bovine TB is a major problem for the agricultural industry in several countries. TB can be contracted and spread by species other than cattle and this can cause a problem for disease control. In the UK and Ireland, badgers are a recognised reservoir of infection and there has been substantial discussion about potential control strategies. We present a coupling of individual based models of bovine TB in badgers and cattle, which aims to capture the key details of the natural history of the disease and of both species at approximately county scale. The model is spatially explicit it follows a very large number of cattle and badgers on a different grid size for each species and includes also winter housing. We show that the model can replicate the reported dynamics of both cattle and badger populations as well as the increasing prevalence of the disease in cattle. Parameter space used as input in simulations was swept out using Latin hypercube sampling and sensitivity analysis to model outputs was conducted using mixed effect models. By exploring a large and computationally intensive parameter space we show that of the available control strategies it is the frequency of TB testing and whether or not winter housing is practised that have the most significant effects on the number of infected cattle, with the effect of winter housing becoming stronger as farm size increases. Whether badgers were culled or not explained about 5%, while the accuracy of the test employed to detect infected cattle explained less than 3% of the variance in the number of infected cattle

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Book Reviews

Reviews of the following books: Was Baseball Really Invented in Maine? by Will Anderson; Acadian Hard Times: The Farm Security Administration in Maine\u27s St. John Valley, 1940-1943 by C. Stewart Doty; The Latchstring Was Always Out: A History of Lodging Hospitality and Tourism in Bartlett, New Hampshire by Aileen M. Carroll; A Fair Field and No Favor: A Concise History of the Maine State Grange by Stanley Russell Howe; Dell Turner: The Stories of His Life by John T. Meader; Hail Britannia: Maine Pewter and Silverplate: An Exhibition of Maine Britannia Ware and Silverplate, 1829-1941, in the Collections of the Maine State Museum, May 15, 1992-May 15, 1993 by Edwin A. Churchil

Role of Interaction and Nucleoside Diphosphate Kinase B in Regulation of the Cystic Fibrosis Transmembrane Conductance Regulator Function by cAMP-Dependent Protein Kinase A

Cystic fibrosis results from mutations in the cystic fibrosis transmembrane conductance regulator (CFTR), a cAMP-dependent protein kinase A (PKA) and ATP-regulated chloride channel. Here, we demonstrate that nucleoside diphosphate kinase B (NDPK-B, NM23-H2) forms a functional complex with CFTR. In airway epithelia forskolin/IBMX significantly increases NDPK-B co-localisation with CFTR whereas PKA inhibitors attenuate complex formation. Furthermore, an NDPK-B derived peptide (but not its NDPK-A equivalent) disrupts the NDPK-B/CFTR complex in vitro (19-mers comprising amino acids 36-54 from NDPK-B or NDPK-A). Overlay (Far-Western) and Surface Plasmon Resonance (SPR) analysis both demonstrate that NDPK-B binds CFTR within its first nucleotide binding domain (NBD1, CFTR amino acids 351-727). Analysis of chloride currents reflective of CFTR or outwardly rectifying chloride channels (ORCC, DIDS-sensitive) showed that the 19-mer NDPK-B peptide (but not its NDPK-A equivalent) reduced both chloride conductances. Additionally, the NDPK-B (but not NDPK-A) peptide also attenuated acetylcholine-induced intestinal short circuit currents. In silico analysis of the NBD1/NDPK-B complex reveals an extended interaction surface between the two proteins. This binding zone is also target of the 19-mer NDPK-B peptide, thus confirming its capability to disrupt NDPK-B/CFTR complex. We propose that NDPK-B forms part of the complex that controls chloride currents in epithelia

SiRNA delivery of ENAC mediated by targeted nanocomplex: a therapeutic strategy for cystic fibrosis

The inhibition of ENaC may have therapeutic potential in CF airways by reducing sodium hyperabsorption, restoring lung epithelial surface fluid levels, airway hydration and mucociliary function. The challenge has been to deliver siRNA to the lung with sufficient efficacy for a sustained therapeutic effect. We have developed a self-assembling nanocomplex formulation for siRNA delivery to the airways that consists of a liposome (DOTMA/DOPE; L), an epithelial targeting peptide (P) and siRNA (R). LPR formulations were assessed for their ability to silence expression of the transcript of the gene encoding the α-subunit of the sodium channel ENaC in cell lines and primary epithelial cells, in submerged cultures or grown in air-liquid interface conditions. LPRs, containing 50 nM or 100 nM siRNA, showed high levels of silencing, particularly in primary airway epithelial cells. When nebulised these nanocomplexes still retained their biophysical properties and transfection efficiencies. The silencing ability was determined at protein level by confocal microscopy and western blotting. In vivo data demonstrated that these nanoparticles had the ability to silence expression of the α-ENaC subunit gene. In conclusion, these findings show that LPRs can modulate the activity of ENaC and this approach might be promising as co-adjuvant therapy for cystic fibrosis

Method for Quantitative Study of Airway Functional Microanatomy Using Micro-Optical Coherence Tomography

We demonstrate the use of a high resolution form of optical coherence tomography, termed micro-OCT (μOCT), for investigating the functional microanatomy of airway epithelia. μOCT captures several key parameters governing the function of the airway surface (airway surface liquid depth, periciliary liquid depth, ciliary function including beat frequency, and mucociliary transport rate) from the same series of images and without exogenous particles or labels, enabling non-invasive study of dynamic phenomena. Additionally, the high resolution of μOCT reveals distinguishable phases of the ciliary stroke pattern and glandular extrusion. Images and functional measurements from primary human bronchial epithelial cell cultures and excised tissue are presented and compared with measurements using existing gold standard methods. Active secretion from mucus glands in tissue, a key parameter of epithelial function, was also observed and quantified