qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

Population Genetic Structuring in Opisthorchis viverrini over Various Spatial Scales in Thailand and Lao PDR

Khon Kaen Province in northeast Thailand is known as a hot spot for opisthorchiasis in Southeast Asia. Preliminary allozyme and mitochondrial DNA haplotype data from within one endemic district in this Province (Ban Phai), indicated substantial genetic variability within Opisthorchis viverrini. Here, we used microsatellite DNA analyses to examine the genetic diversity and population structure of O. viverrini from four geographically close localities in Khon Kaen Province. Genotyping based on 12 microsatellite loci yielded a mean number of alleles per locus that ranged from 2.83 to 3.7 with an expected heterozygosity in Hardy-Weinberg equilibrium of 0.44-0.56. Assessment of population structure by pairwise F(ST) analysis showed inter-population differentiation (P<0.05) which indicates population substructuring between these localities. Unique alleles were found in three of four localities with the highest number observed per locality being three. Our results highlight the existence of genetic diversity and population substructuring in O. viverrini over a small spatial scale which is similar to that found at a larger scale. This provides the basis for the investigation of the role of parasite genetic diversity and differentiation in transmission dynamics and control of O. viverrini

Changing Bases: Multistage Optimization for Matroids and Matchings

This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems, without creating too much churn in the solution itself. We model this as a multistage combinatorial optimization problem where the input is a sequence of cost functions (one for each time step); while we can change the solution from step to step, we incur an additional cost for every such change. We study the multistage matroid maintenance problem, where we need to maintain a base of a matroid in each time step under the changing cost functions and acquisition costs for adding new elements. The online version of this problem generalizes online paging. E.g., given a graph, we need to maintain a spanning tree $T_t$ at each step: we pay $c_t(T_t)$ for the cost of the tree at time $t$, and also $| T_t\setminus T_{t-1} |$ for the number of edges changed at this step. Our main result is an $O(\log m \log r)$-approximation, where $m$ is the number of elements/edges and $r$ is the rank of the matroid. We also give an $O(\log m)$ approximation for the offline version of the problem. These bounds hold when the acquisition costs are non-uniform, in which caseboth these results are the best possible unless P=NP. We also study the perfect matching version of the problem, where we must maintain a perfect matching at each step under changing cost functions and costs for adding new elements. Surprisingly, the hardness drastically increases: for any constant $\epsilon>0$, there is no $O(n^{1-\epsilon})$-approximation to the multistage matching maintenance problem, even in the offline case

Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page

Integer Partitions and Exclusion Statistics

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.Comment: 16 pages, 4 .eps figures include

Thermal Radiation Hazards from Gas Pipeline Rupture Fireballs

Increasing world-wide demand for gas is resulting in an increased network of gas piping which poses potential hazards to the natural and man-made environment in proximity to the pipelines. In this work we report experimental measurements of the thermal radiation levels generated by fireballs from two fullscale, below-ground, natural-gas pipeline ruptures. The tests were carried out at the DNV GL’s Spadeadam Test Site simulating the rupture of a 1219 mm diameter pipe carrying high pressure natural gas (at 13.4 MPa -nominal gauge pressure). The duration of the fireball and the maximum heat fluxes (as high as 70 kW/m2 at 200 m downwind) were well predicted by current simple mathematical models when a reasonable radiative fraction of the total energy release was assumed. The empirical radiant fraction equation adopted by OGP was shown to overpredict the incident heat flux in these tests. In the second test the grass surrounding the test location was ignited and other vegetation showed significant thermal damage. To interpret such data correctly and to evaluate the hazards, to natural and man-made environments, more information is needed on the effects of short exposure times (of the order of a few seconds) to high transient heat fluxes