Clustered Graph Coloring and Layered Treewidth

A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies clustered coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption than previous works, where typically the number of colors depends on an excluded minor. This paper focuses on graph classes with bounded layered treewidth, which include planar graphs, graphs of bounded Euler genus, graphs embeddable on a fixed surface with a bounded number of crossings per edge, amongst other examples. Our main theorem says that for fixed integers $s,t,k$, every graph with layered treewidth at most $k$ and with no $K_{s,t}$ subgraph is $(s+2)$-colorable with bounded clustering. In the $s=1$ case, which corresponds to graphs of bounded maximum degree, we obtain polynomial bounds on the clustering. This greatly improves a corresponding result of Esperet and Joret for graphs of bounded genus. The $s=3$ case implies that every graph with a drawing on a fixed surface with a bounded number of crossings per edge is 5-colorable with bounded clustering. Our main theorem is also a critical component in two companion papers that study clustered coloring of graphs with no $K_{s,t}$-subgraph and excluding a fixed minor, odd minor or topological minor

Automatic Generation of School Bus Routes in Los Angeles

The goal of our project is to automatically generate school bus routes for the Los Angeles Unified School District (LAUSD). We examined four algorithms, including two from the existing literature and two new ones that we developed. A major focus of our work was the construction of “mixed-load routes,” which transport students from multiple schools. Based on our measurements (whose imperfections we discuss), three of the four algorithms perform at least as well as the existing route plan, and one of those three performs better than the existing route plan. We also delivered a user-friendly routing program to LAUSD that uses one of these algorithms, and we have made our software publicly available. Our insights and results are also applicable to other school districts that permit mixed-load routing

Accuracy Assessment on Drone Measured Heights at Different Height Levels

The advancement in unmanned aerial system (UAS) technology has made it possible to attain an aerial unit, commonly known as a drone, at an affordable price with increasing precision and accuracy in positioning and photographing. While aerial photography is the most common use of a drone, many of the models available in the market are also capable of measuring height, the height of the drone above ground, or the altitude above the mean sea level. On board a drone, a barometer is used to control the flight height by detecting the atmospheric pressure change; while a GPS receiver is mainly used to determine the horizontal position of the drone. While both barometer and GPS are capable of measuring height, they are based on different algorithms. Our study goal was to assess the accuracy of height measurement by a drone, with different landing procedures and GPS settings

Hamster leukemia virus: lack of endogenous DNA synthesis and unique structure of its DNA polymerase

Infectious hamster leukemia virus (HaLV) contains a DNA polymerase different from those of murine and avian viruses. No endogenous reaction directed by the 60 to 70S RNA of HaLV could be demonstrated in detergenttreated HaLV virions, nor could the purified DNA polymerase copy added viral RNA. The virion RNA could, however, act as template for added avian myeloblastosis virus DNA polymerase and the HaLV DNA polymerase could efficiently utilize homopolymers as templates. The HaLV enzyme was like other reverse transcriptases in that certain ribohomopolymers were much better templates than the homologous deoxyribohomopolymers. No ribonuclease H activity could be shown in the HaLV enzyme, but neither could activity be found in the murine leukemia virus DNA polymerase. The hamster enzyme was unique in that poly(A) ·oligo(dT) was a poor template, and globin mRNA primed with oligo(dT) was totally inactive as a template. Its uniqueness was also indicated by its subunit composition; electrophoresis of the HaLV DNA polymerase in sodium dodecyl sulfate-containing polyacrylamide gels revealed equimolar amounts of two polypeptides of molecular weight 68,000 and 53,000. The sedimentation rate of the enzyme in glycerol gradients was consistent with a structure containing one each of the two polypeptides. The enzyme thus appears to be structurally distinct from other known virion DNA polymerases. Its inability to carry out an endogenous reaction in vitro might result from an inability to utilize certain primers

Health Information Availability and the Consumption of Eggs: Are Consumers Bayesians?

We use a generalized Bayesian updating model to estimate the impact of health information appearing in the popular media on the consumption of eggs. Our model allows media publications with differing circulation numbers to have differing effects. Further, we explore the possible effects of several known psychological biases in learning.Marketing,