Throttling for the game of Cops and Robbers on graphs

We consider the cop-throttling number of a graph $G$ for the game of Cops and Robbers, which is defined to be the minimum of $(k + \text{capt}_k(G))$, where $k$ is the number of cops and $\text{capt}_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber on $G$ over all possible games. We provide some tools for bounding the cop-throttling number, including showing that the positive semidefinite (PSD) throttling number, a variant of zero forcing throttling, is an upper bound for the cop-throttling number. We also characterize graphs having low cop-throttling number and investigate how large the cop-throttling number can be for a given graph. We consider trees, unicyclic graphs, incidence graphs of finite projective planes (a Meyniel extremal family of graphs), a family of cop-win graphs with maximum capture time, grids, and hypercubes. All the upper bounds on the cop-throttling number we obtain for families of graphs are $O(\sqrt n)$.Comment: 22 pages, 4 figure

Optimizing the trade-off between number of cops and capture time in Cops and Robbers

The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber on $G$ over all possible games in which both players play optimally. In this paper, we construct a family of graphs having $th_c(G)= \Omega(n^{2/3})$, establish a sublinear upper bound on the cop throttling number, and show that the cop throttling number of chordal graphs is $O(\sqrt{n})$. We also introduce the product cop throttling number $th_c^{\times}(G)$ as a parameter that minimizes the person-hours used by the cops. This parameter extends the notion of speed-up that has been studied in the context of parallel processing and network decontamination. We establish bounds on the product cop throttling number in terms of the cop throttling number, characterize graphs with low product cop throttling number, and show that for a chordal graph $G$, $th_c^{\times}=1+rad(G)$.Comment: 19 pages, 3 figure

Morbid adherence of the placenta: lack of specificity should remind us that ultrasound is a screening tool.

Excellent performance has been reported with prenatal diagnosis of abnormal placental invasion using ultrasound. We describe a case which illustrates the validity of ultrasound features of abnormally invasive placentation in women without previous caesarean delivery. CASE: Ms. CB, a 27 year-old G3 P1+1 was seen in her pregnancy at 36 weeks of gestation. Her first pregnancy was uncomplicated and she gave vaginal birth to a normally grown baby at term. Before the current pregnancy, she suffered a miscarriage in the first trimester, and underwent surgical evacuation. She suffered prolonged vaginal blood loss for which she was investigated, and a diagnosis of A-V malformation (AVM) was made on the basis of the ultrasound findings (Figure 1). She conceived spontaneously before intervention

The Electronic and Superconducting Properties of Oxygen-Ordered MgB2 compounds of the form Mg2B3Ox

Possible candidates for the Mg2B3Ox nanostructures observed in bulk of polycrystalline MgB2 (Ref.1) have been studied using a combination of Z-contrast imaging, electron energy loss spectroscopy (EELS) and first-principles calculations. The electronic structures, phonon modes, and electron phonon coupling parameters are calculated for two oxygen-ordered MgB2 compounds of composition Mg2B3O and Mg2B3O2, and compared with those of MgB2. We find that the density of states for both Mg2B3Ox structures show very good agreement with EELS, indicating that they are excellent candidates to explain the observed coherent oxygen precipitates. Incorporation of oxygen reduces the transition temperature and gives calculated TC values of 18.3 K and 1.6 K for Mg2B3O and Mg2B3O2, respectively.Comment: Submitted to PR

Computation of Kolmogorov's Constant in Magnetohydrodynamic Turbulence

In this paper we calculate Kolmogorov's constant for magnetohydrodynamic turbulence to one loop order in perturbation theory using the direct interaction approximation technique of Kraichnan. We have computed the constants for various $E^u(k)/E^b(k)$, i.e., fluid to magnetic energy ratios when the normalized cross helicity is zero. We find that $K$ increases from 1.47 to 4.12 as we go from fully fluid case $(E^b=0)$ to a situation when $E^u/E^b=0.5$, then it decreases to 3.55 in a fully magnetic limit $(E^u=0)$. When $E^u/E^b=1$, we find that $K=3.43$.Comment: Latex, 10 pages, no figures, To appear in Euro. Phys. Lett., 199

The growth of leading-edge distortions on a viscous sheet

The results of a set of experiments to determine some features of the undulations that develop on the leading edge of a sheet of fluid on an inclined plane are presented. A range of fluid viscosities, fluid volumes, and plate angles was used. In nearly all the cases, the observed disturbances had a triangular or sawtooth shape, with only a single example of a finger or parallel-sided shape appearing. The power-law exponents for the position down the plate of both the tips of the disturbances and their roots, that is, the points where they join the uniform sheet above them, were calculated from a series of photographs, and the corresponding wavelengths measured. The exponents are broadly in line with those that can be deduced from a simple model including viscosity, gravity, and volume flux, and ignoring all capillary effects. This conclusion suggests that the criterion for distinguishing the two types of disturbance does not depend on the global dynamics of the developing structures, and that a detailed analysis of the tip and root regions, where capillarity will be significant, is needed for further progress to be made. © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70941/2/PHFLE6-11-2-307-1.pd

Determining the effects of cattle grazing treatments on Yosemite toads (Anaxyrus [=Bufo] canorus) in montane meadows.

Amphibians are experiencing a precipitous global decline, and population stability on public lands with multiple uses is a key concern for managers. In the Sierra Nevada Mountains (California, USA), managers have specifically identified livestock grazing as an activity that may negatively affect Yosemite toads due to the potential overlap of grazing with toad habitat. Grazing exclusion from Yosemite toad breeding and rearing areas and/or entire meadows have been proposed as possible management actions to alleviate the possible impact of cattle on this species. The primary objective of this study was to determine if different fencing treatments affect Yosemite toad populations. We specifically examined the effect of three fencing treatments on Yosemite toad breeding pool occupancy, tadpoles, and young of the year (YOY). Our hypothesis was that over the course of treatment implementation (2006 through 2010), Yosemite toad breeding pool occupancy and early life stage densities would increase within two fencing treatments relative to actively grazed meadows due to beneficial changes to habitat quality in the absence of grazing. Our results did not support our hypothesis, and showed no benefit to Yosemite toad presence or early life stages in fenced or partially fenced meadows compared to standard USDA Forest Service grazing levels. We found substantial Yosemite toad variation by both meadow and year. This variation was influenced by meadow wetness, with water table depth significant in both the tadpole and YOY models

Information Literacy and Adult Learners: Using Authentic Assessment to Determine Skill Gaps

Information literacy (IL) skills are essential for adult learners in higher education, especially those unfamiliar with information systems. Citing a lack of literature assessing such skills in adult learners, this article examines the IL abilities of adult learners in an information literacy course. Using a rubric and annotated bibliographies from study participants, the authors rank the IL abilities of adult students. Similar to studies assessing IL skills in traditional undergraduates, the authors found adult students struggled to articulate their evaluations of sources. The authors make recommendations for improving IL instruction for adults and suggest future research

Pisatin demethylation by fungal pathogens and nonpathogens of pea: Association with pisatin tolerance and virulence

Previous studies have indicated that detoxification of their hosts’ phytoalexins is a tolerance mechanism for some true fungi, but not the fungus-like Oomycota, and may be involved in determining the virulence of a pathogen. In the present study, the associations between demethylation of the pea phytoalexin pisatin, tolerance to pisatin, and viru­lence on pea were examined for 50 fungal isolates which represent 17 species of pathogens and nonpathogens of pea. All isolates of Pythium coloratum and P. irregulare failed to metabolize and were sensitive to pisatin, consistent with previous observations that members of the Oomycota generally lack the ability to metabolize and are sensitive to their hosts’ phytoalexins. Among true fungi tested, the ability to demethylate pisatin was common, regardless of whether the particular isolate was pathogenic on pea or not. However, when the rate of pisatin demethylation was compared to virulence, all but one of the moderate to highly virulent isolates rapidly demethylated pisatin. In addition, the more rapidly demethylating isolates were generally more tolerant of pisatin. These results suggest that a specialized en­zyme system for quickly detoxifying pisatin might be present in most pea pathogens. In previous studies a specific cy­tochrome P450 enzyme for demethylating pisatin was identified in the pea pathogen Nectria haematococca mating pop­ulation VI, and genes (PDA genes) encoding that enzyme have been cloned from this fungus. When DNA specific for these genes was used to probe genomic DNA from other fungi that demethylate pisatin, significant hybridization was detected with only one fungus, the pea pathogen Fusarium oxysporum f. sp. pisi. If the other pea pathogens possess a specific cytochrome P450 system for detoxification of pisatin, the genes encoding these enzymes apparently share lim­ited nucleotide similarity with N. haematococca PDA genes

Pisatin demethylation by fungal pathogens and nonpathogens of pea: Association with pisatin tolerance and virulence

Previous studies have indicated that detoxification of their hosts’ phytoalexins is a tolerance mechanism for some true fungi, but not the fungus-like Oomycota, and may be involved in determining the virulence of a pathogen. In the present study, the associations between demethylation of the pea phytoalexin pisatin, tolerance to pisatin, and viru­lence on pea were examined for 50 fungal isolates which represent 17 species of pathogens and nonpathogens of pea. All isolates of Pythium coloratum and P. irregulare failed to metabolize and were sensitive to pisatin, consistent with previous observations that members of the Oomycota generally lack the ability to metabolize and are sensitive to their hosts’ phytoalexins. Among true fungi tested, the ability to demethylate pisatin was common, regardless of whether the particular isolate was pathogenic on pea or not. However, when the rate of pisatin demethylation was compared to virulence, all but one of the moderate to highly virulent isolates rapidly demethylated pisatin. In addition, the more rapidly demethylating isolates were generally more tolerant of pisatin. These results suggest that a specialized en­zyme system for quickly detoxifying pisatin might be present in most pea pathogens. In previous studies a specific cy­tochrome P450 enzyme for demethylating pisatin was identified in the pea pathogen Nectria haematococca mating pop­ulation VI, and genes (PDA genes) encoding that enzyme have been cloned from this fungus. When DNA specific for these genes was used to probe genomic DNA from other fungi that demethylate pisatin, significant hybridization was detected with only one fungus, the pea pathogen Fusarium oxysporum f. sp. pisi. If the other pea pathogens possess a specific cytochrome P450 system for detoxification of pisatin, the genes encoding these enzymes apparently share lim­ited nucleotide similarity with N. haematococca PDA genes