The Firefighter Problem: A Structural Analysis

We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of bounded degree b+3 for any fixed budget b>=2 (Bazgan et al.,2012). In this paper, we provide further insight into the complexity landscape of the problem by showing that the pathwidth and the maximum degree of the input graph govern its complexity. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any fixed budget b>=1. We then show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter "pathwidth" and "maximum degree" of the input graph

Modelling and optimal control of blood glucose levels in the human body

Regulating the blood glucose level is a challenging control problem for the human body. Abnormal blood glucose levels can cause serious health problems over time, including diabetes. Although several mathematical models have been proposed to describe the dynamics of glucose-insulin interaction, none of them have been universally adopted by the research community. In this paper, we consider a dynamic model of the blood glucose regulatory system originally proposed by Liu and Tang in 2008. This model consists of eight state variables naturally divided into three subsystems: the glucagon and insulin transition subsystem, the receptor binding subsystem and the glucosesubsystem. The model contains 36 model parameters, many of which are unknown and difficult to determine accurately. We formulate an optimal parameter selection problem in which optimal values for the model parameters must be selected so that the resulting model best its given experimental data.We demonstrate that this optimal parameter selection problem can be solved readily using the optimal control software MISER 3.3. Using this approach, significant improvements can be made in matching the model to the experimental data. We also investigate the sensitivity of the resulting optimizedmodel with respect to the insulin release rate. Finally, we use MISER 3.3 to determine optimal open loop controls for the optimized model

Environmental Exposure to Polychlorinated Biphenyls and p,p´-DDE and Sperm Sex-Chromosome Disomy

Background: Chromosomal abnormalities contribute substantially to reproductive problems, but the role of environmental risk factors has received little attention

Comparison of Short-Term Estrogenicity Tests for Identification of Hormone-Disrupting Chemicals

The aim of this study was to compare results obtained by eight different short-term assays of estrogenlike actions of chemicals conducted in 10 different laboratories in five countries. Twenty chemicals were selected to represent direct-acting estrogens, compounds with estrogenic metabolites, estrogenic antagonists, and a known cytotoxic agent. Also included in the test panel were 17β-estradiol as a positive control and ethanol as solvent control. The test compounds were coded before distribution. Test methods included direct binding to the estrogen receptor (ER), proliferation of MCF-7 cells, transient reporter gene expression in MCF-7 cells, reporter gene expression in yeast strains stably transfected with the human ER and an estrogen-responsive reporter gene, and vitellogenin production in juvenile rainbow trout. 17β-Estradiol, 17α-ethynyl estradiol, and diethylstilbestrol induced a strong estrogenic response in all test systems. Colchicine caused cytotoxicity only. Bisphenol A induced an estrogenic response in all assays. The results obtained for the remaining test compounds—tamoxifen, ICI 182.780, testosterone, bisphenol A dimethacrylate, 4-n-octylphenol, 4-n-nonylphenol, nonylphenol dodecylethoxylate, butylbenzylphthalate, dibutylphthalate, methoxychlor, o,p′-DDT, p,p′-DDE, endosulfan, chlomequat chloride, and ethanol—varied among the assays. The results demonstrate that careful standardization is necessary to obtain a reasonable degree of reproducibility. Also, similar methods vary in their sensitivity to estrogenic compounds. Thus, short-term tests are useful for screening purposes, but the methods must be further validated by additional interlaboratory and interassay comparisons to document the reliability of the methods