Large deviations of a modified Jackson network: stability and rough asymptotics

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the unmodified Jackson network which spends a nonzero proportion of time on this boundary.Comment: Published at http://dx.doi.org/10.1214/105051604000000666 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mean field convergence of a model of multiple TCP connections through a buffer implementing RED

RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows by dropping or marking packets with a probability that increases with the queue length. The objectives are reduced packet loss, higher throughput, reduced delay and reduced delay variation achieved through an equitable distribution of packet loss and reduced synchronization. Baccelli, McDonald and Reynier [Performance Evaluation 11 (2002) 77--97] have proposed a fluid model for multiple TCP connections in the congestion avoidance regime multiplexed through a bottleneck buffer implementing RED. The window sizes of each TCP session evolve like independent dynamical systems coupled by the queue length at the buffer. The key idea in [Performance Evaluation 11 (2002) 77--97] is to consider the histogram of window sizes as a random measure coupled with the queue. Here we prove the conjecture made in [Performance Evaluation 11 (2002) 77--97] that, as the number of connections tends to infinity, this system converges to a deterministic mean-field limit comprising the window size density coupled with a deterministic queue.Comment: Published at http://dx.doi.org/10.1214/105051605000000700 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluation of the onset time and intubation conditions of rocuronium bromide in children

Publisher's copy made available with the permission of the publisher © 1997 Australian Society of AnaesthetistsWe have assessed, in children aged three to eight years, the intubating conditions after administration of rocuronium 0.6 mg/kg at 50 or 60 seconds, in groups of 15 patients. Intubating conditions were excellent in 11, good in 3 and fair in 1 patient at 50 seconds and excellent in 12 and good in 3 patients at 60 seconds. The mean onset time, for all patients, to when the first twitch of the train of four (T1), measured at the adductor pollicis, was depressed to less than 30% and 5% of control was 50 (SD 11.4) seconds and 94 (SD 31.7) seconds respectively. Depression of T1 to less than 30% of control, measured at the adductor pollicis in children, appears to indicate that intubating conditions will be clinically acceptable when using rocuronium.P.F. McDonald, D.A. Sainsbury, R.J. Lain

Evolutionary associations between sand seatrout (Cynoscion arenarius) and silver seatrout (C. nothus) inferred from morphological characters, mitochondrial DNA, and microsatellite markers

The evolutionary associations between closely related fish species, both contemporary and historical, are frequently assessed by using molecular markers, such as microsatellites. Here, the presence and variability of microsatellite loci in two closely related species of marine fishes, sand seatrout (Cynoscion arenarius) and silver seatrout (C. nothus), are explored by using heterologous primers from red drum (Sciaenops ocellatus). Data from these loci are used in conjunction with morphological characters and mitochondrial DNA haplotypes to explore the extent of genetic exchange between species offshore of Galveston Bay, TX. Despite seasonal overlap in distribution, low genetic divergence at microsatellite loci, and similar life history parameters of C. arenarius and C. nothus, all three data sets indicated that hybridization between these species does not occur or occurs only rarely and that historical admixture in Galveston Bay after divergence between these species was unlikely. These results shed light upon the evolutionary history of these fishes and highlight the genetic properties of each species that are influenced by their life history and ecology

Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

Enhanced Fermi surface nesting in superconducting BaFe2_2(As1−x_{1-x}Px_x)2_2 revealed by de Haas-van Alphen effect

The three-dimensional Fermi surface morphology of superconducting BaFe_2(As_0.37}P_0.63)_2 with T_c=9K, is determined using the de Haas-van Alphen effect (dHvA). The inner electron pocket has a similar area and k_z interplane warping to the observed hole pocket, revealing that the Fermi surfaces are geometrically well nested in the (\pi,\pi) direction. These results are in stark contrast to the Fermiology of the non-superconducting phosphides (x=1), and therefore suggests an important role for nesting in pnictide superconductivity.Comment: 5 pages, 4 figure