The Queue-Number of Posets of Bounded Width or Height

Heath and Pemmaraju conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger than their height, refuting the second conjecture. On the other hand, we show that any poset of width $2$ has queue-number at most $2$, thus confirming the first conjecture in the first non-trivial case. Moreover, we improve the previously best known bounds and show that planar posets of width $w$ have queue-number at most $3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its width.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

kk-Critical Graphs in P5P_5-Free Graphs

Given two graphs $H_1$ and $H_2$, a graph $G$ is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ be the path on $t$ vertices. A graph $G$ is $k$-vertex-critical if $G$ has chromatic number $k$ but every proper induced subgraph of $G$ has chromatic number less than $k$. The study of $k$-vertex-critical graphs for graph classes is an important topic in algorithmic graph theory because if the number of such graphs that are in a given hereditary graph class is finite, then there is a polynomial-time algorithm to decide if a graph in the class is $(k-1)$-colorable. In this paper, we initiate a systematic study of the finiteness of $k$-vertex-critical graphs in subclasses of $P_5$-free graphs. Our main result is a complete classification of the finiteness of $k$-vertex-critical graphs in the class of $(P_5,H)$-free graphs for all graphs $H$ on 4 vertices. To obtain the complete dichotomy, we prove the finiteness for four new graphs $H$ using various techniques -- such as Ramsey-type arguments and the dual of Dilworth's Theorem -- that may be of independent interest.Comment: 18 page

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure

Linear Extensions and Comparable Pairs in Partial Orders

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also show that a random interval partial order on $n$ elements has close to a third of the pairs comparable with high probability, and the number of linear extensions is $n! \, 2^{-\Theta(n)}$ with high probability

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Carnivore Translocations and Conservation: Insights from Population Models and Field Data for Fishers (Martes pennanti)

Translocations are frequently used to restore extirpated carnivore populations. Understanding the factors that influence translocation success is important because carnivore translocations can be time consuming, expensive, and controversial. Using population viability software, we modeled reintroductions of the fisher, a candidate for endangered or threatened status in the Pacific states of the US. Our model predicts that the most important factor influencing successful re-establishment of a fisher population is the number of adult females reintroduced (provided some males are also released). Data from 38 translocations of fishers in North America, including 30 reintroductions, 5 augmentations and 3 introductions, show that the number of females released was, indeed, a good predictor of success but that the number of males released, geographic region and proximity of the source population to the release site were also important predictors. The contradiction between model and data regarding males may relate to the assumption in the model that all males are equally good breeders. We hypothesize that many males may need to be released to insure a sufficient number of good breeders are included, probably large males. Seventy-seven percent of reintroductions with known outcomes (success or failure) succeeded; all 5 augmentations succeeded; but none of the 3 introductions succeeded. Reintroductions were instrumental in reestablishing fisher populations within their historical range and expanding the range from its most-contracted state (43% of the historical range) to its current state (68% of the historical range). To increase the likelihood of translocation success, we recommend that managers: 1) release as many fishers as possible, 2) release more females than males (55–60% females) when possible, 3) release as many adults as possible, especially large males, 4) release fishers from a nearby source population, 5) conduct a formal feasibility assessment, and 6) develop a comprehensive implementation plan that includes an active monitoring program

Dental and microbiological risk factors for hospital-acquired pneumonia in non-ventilated older patients

We obtained a time series of tongue/throat swabs from 90 patients with lower limb fracture, aged 65-101 in a general hospital in the North East of England between April 2009-July 2010. We used novel real-time multiplex PCR assays to detect S. aureus, MRSA, E. coli, P. aeruginosa, S. pneumoniae, H. influenza and Acinetobacter spp. We collected data on dental/denture plaque (modified Quigley-Hein index) and outcomes of clinician-diagnosed HAP.The crude incidence of HAP was 10% (n = 90), with mortality of 80% at 90 days post discharge. 50% of cases occurred within the first 25 days. HAP was not associated with being dentate, tooth number, or heavy dental/denture plaque. HAP was associated with prior oral carriage with E. coli/S. aureus/P.aeruginosa/MRSA (p = 0.002, OR 9.48 95% CI 2.28-38.78). The incidence of HAP in those with carriage was 35% (4% without), with relative risk 6.44 (95% CI 2.04-20.34, p = 0.002). HAP was associated with increased length of stay (Fishers exact test, p=0.01), with mean 30 excess days (range -11.5-115). Target organisms were first detected within 72 hours of admission in 90% participants, but HAP was significantly associated with S. aureus/MRSA/P. aeruginosa/E. coli being detected at days 5 (OR 4.39, 95%CI1.73-11.16) or 14 (OR 6.69, 95%CI 2.40-18.60).Patients with lower limb fracture who were colonised orally with E. coli/ S. aureus/MRSA/P. aeruginosa after 5 days in hospital were at significantly greater risk of HAP (p = 0.002)