Subgraphs and Colourability of Locatable Graphs

We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked whether there exists a characterisation of the graph property of locatable graphs by either forbidden or forbidden induced subgraphs, both of which we answer in the negative. We then proceed to show that such a characterisation does exist for graphs of diameter at most 2, stating it explicitly, and note that this is not true for higher diameter. Exploring a different direction of topic, we also start research in the direction of colourability of locatable graphs, we also show that every locatable graph is 4-colourable, but not necessarily 3-colourable.Comment: 25 page

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic

Subdivisions in the Robber Locating Game

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m \geqslant n$. They conjectured that this bound was best possible for complete graphs, but the present authors showed that in fact the cop wins on $K^{1/m}$ if and only if $m \geqslant n/2$, for all but a few small values of $n$. In this paper we extend this result to general graphs by proving that the cop has a winning strategy on $G^{1/m}$ provided $m \geqslant n/2$ for all but a few small values of $n$; this bound is best possible. We also consider replacing the edges of $G$ with paths of varying lengths.Comment: 13 Page

Shorebirds Breed in Unusually High Densities in the Teshekpuk Lake Special Area, Alaska

On the Arctic Coastal Plain of the National Petroleum Reserve-Alaska (NPR-A), the Teshekpuk Lake Special Area (TLSA) was recognized to protect outstanding wildlife values. Although information has accumulated on the TLSA’s value to caribou and waterfowl, its importance to breeding shorebirds remains largely unquantified. Therefore, we undertook a broad-scale ground study to estimate the population size and density of shorebirds breeding in the TLSA. From a series of plot surveys conducted from 2006 to 2008, we estimated a detection-adjusted total breeding population of more than 573 000 shorebirds and an overall density of 126 shorebirds/km2. Most shorebird species had their greatest densities on the Outer Coastal Plain or had approximately equal densities on Outer and Inner Coastal Plains; only two species had their greatest densities on the Inner Coastal Plain. The greatest densities of breeding shorebirds occurred immediately around Teshekpuk Lake. The TLSA supported more than 10% of the biogeographic populations of black-bellied plover (Pluvialis squatarola), semipalmated sandpiper (Calidris pusilla), and dunlin (C. alpina). Breeding shorebird density in the TLSA is one of the highest in the NPR-A, on Alaska’s North Slope, and throughout the circumpolar Arctic. Our results, coupled with previous information on waterfowl and caribou, indicate that the area around Teshekpuk Lake and the recognized goose molting area northeast of the lake should be protected from oil and gas development.Sur la plaine côtière arctique de la réserve pétrolière nationale-Alaska (NPRA), la région spéciale du lac Teshekpuk (TLSA) a été créée dans le but de protéger les valeurs exceptionnelles de la faune. Même s’il existe beaucoup d’information sur la valeur du caribou et de la sauvagine de la TLSA, l’importance qu’elle revêt en matière d’oiseaux de rivage nicheurs demeure peu quantifiée. Nous avons par conséquent entrepris de faire une étude sur le terrain à grande échelle pour estimer la taille et la densité de la population d’oiseaux de rivage nichant dans la TLSA. À partir d’une série d’enquêtes réalisées de 2006 à 2008, nous avons estimé que le total redressé en fonction de la détection de la population nicheuse s’établissait à plus de 573 000 oiseaux de rivage, et que la densité générale s’élevait à 126 oiseaux de rivage/km2. Les plus grandes densités de la plupart des espèces d’oiseaux de rivage se trouvaient sur la plaine côtière extérieure ou encore, les densités étaient environ égales entre les plaines côtières intérieure et extérieure. Seulement deux espèces avaient leurs plus fortes densités sur la plaine côtière intérieure. Les plus grandes densités d’oiseaux de rivage se manifestaient immédiatement autour du lac Teshekpuk. La TLSA accueillait plus de 10 % des populations biogéographiques de pluviers argentés (Pluvialis squatarola), de bécasseaux semipalmés (Calidris pusilla) et de bécasseaux variables (C. alpina). La densité d’oiseaux nicheurs dans la TLSA est l’une des plus élevées de la NPR-A, sur le versant nord de l’Alaska et à l’échelle de l’Arctique circumpolaire. Nos résultats, jumelés à l’information obtenue antérieurement au sujet de la sauvagine et du caribou, indiquent que la région autour du lac Teshekpuk et la région reconnue pour la mue des oies au nord-est du lac devraient être protégées contre la mise en valeur pétrolière et gazière

The impact of nitrogen contamination and river modification on a Mississippi River floodplain lake

Anthropogenic nitrogen contamination has increased in ecosystems around the world (frequently termed the “nitrogen cascade”). Coke production for steel manufacturing is often overlooked as a source of nitrogen to natural ecosystems. We examined sediment cores from a Horseshoe Lake, a floodplain lake located just East of St. Louis Missouri (USA) to test whether a coking plant effluent could be traced using stable isotopes of nitrogen and diatom microfossils. The distribution of δ15N values in surface sediment samples from the lake shows the highest values near the coking plant effluent. Analysis stable isotopes of nitrogen from sediment cores using a binary mixing model showed three sources of nitrogen since 1688 CE. The first source (active between 1688 and 1920 CE) had a calculated δ15N value of -.8±.4‰. After 1920 a second source with a δ15N of 20.2±2.0 ‰ became active. The diatom microfossil assemblages present from 1688 CE to the late 1800’s are dominated by the planktonic species Aulacoseira granulata and periphytic and benthic genera Gomphonema, Cocconeis, and Lyrella. After the late 1800’s the diatom assemblages are dominated by Staurosira species indicating a shift of species from high flow riverine environments to epipelic species from a lake environment. Our results show how stable isotopes of nitrogen can be used to track nitrogen inputs from industrial sources. They suggest that the high nitrogen input has not been a major source of eutrophication in the lake

Intragenic alternative splicing coordination is essential for Caenorhabditis elegans slo-1 gene function

Alternative splicing is critical for diversifying eukaryotic proteomes, but the rules governing and coordinating splicing events among multiple alternate splice sites within individual genes are not well understood. We developed a quantitative PCR-based strategy to quantify the expression of the 12 transcripts encoded by the Caenorhabditis elegans slo-1 gene, containing three alternate splice sites. Using conditional probability-based models, we show that splicing events are coordinated across these sites. Further, we identify a point mutation in an intron adjacent to one alternate splice site that disrupts alternative splicing at all three sites. This mutation leads to aberrant synaptic transmission at the neuromuscular junction. In a genomic survey, we found that a UAAAUC element disrupted by this mutation is enriched in introns flanking alternate exons in genes with multiple alternate splice sites. These results establish that proper coordination of intragenic alternative splicing is essential for normal physiology of slo-1 in vivo and identify putative specialized cis-regulatory elements that regulate the coordination of intragenic alternative splicing

Sources by Which Students Perceive Professional Counselors\u27 Effectiveness

Using qualitative research methods interviews were conducted with college students regarding the sources they used in generating perceptions of professional counselors. Respondents believed that word of mouth, media sources, and personal experiences were responsible for their understandings of professional counselors. The findings have applications for leaders in professional counseling organizations