Visibility Graphs, Dismantlability, and the Cops and Robbers Game

We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit-evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.Comment: 23 page

Effect of Uveal Melanocytes on Choroidal Morphology in Rhesus Macaques and Humans on Enhanced-Depth Imaging Optical Coherence Tomography.

PurposeTo compare cross-sectional choroidal morphology in rhesus macaque and human eyes using enhanced-depth imaging optical coherence tomography (EDI-OCT) and histologic analysis.MethodsEnhanced-depth imaging-OCT images from 25 rhesus macaque and 30 human eyes were evaluated for choriocapillaris and choroidal-scleral junction (CSJ) visibility in the central macula based on OCT reflectivity profiles, and compared with age-matched histologic sections. Semiautomated segmentation of the choriocapillaris and CSJ was used to measure choriocapillary and choroidal thickness, respectively. Multivariate regression was performed to determine the association of age, refractive error, and race with choriocapillaris and CSJ visibility.ResultsRhesus macaques exhibit a distinct hyporeflective choriocapillaris layer on EDI-OCT, while the CSJ cannot be visualized. In contrast, humans show variable reflectivities of the choriocapillaris, with a distinct CSJ seen in many subjects. Histologic sections demonstrate large, darkly pigmented melanocytes that are densely distributed in the macaque choroid, while melanocytes in humans are smaller, less pigmented, and variably distributed. Optical coherence tomography reflectivity patterns of the choroid appear to correspond to the density, size, and pigmentation of choroidal melanocytes. Mean choriocapillary thickness was similar between the two species (19.3 ± 3.4 vs. 19.8 ± 3.4 μm, P = 0.615), but choroidal thickness may be lower in macaques than in humans (191.2 ± 43.0 vs. 266.8 ± 78.0 μm, P < 0.001). Racial differences in uveal pigmentation also appear to affect the visibility of the choriocapillaris and CSJ on EDI-OCT.ConclusionsPigmented uveal melanocytes affect choroidal morphology on EDI-OCT in rhesus macaque and human eyes. Racial differences in pigmentation may affect choriocapillaris and CSJ visibility, and may influence the accuracy of choroidal thickness measurements

Pigment Intensity in Dogs is Associated with a Copy Number Variant Upstream of KITLG.

Dogs exhibit a wide variety of coat color types, and many genes have been identified that control pigment production, appearance, and distribution. Some breeds, such as the Nova Scotia Duck Tolling Retriever (NSDTR), exhibit variation in pheomelanin pigment intensity that is not explained by known genetic variants. A genome-wide association study comparing light red to dark red in the NSDTR identified a significantly associated region on canine chromosome 15 (CFA 15:23 Mb-38 Mb). Coverage analysis of whole genome sequence data from eight dogs identified a 6 kb copy number variant (CNV) 152 kb upstream of KITLG. Genotyping with digital droplet PCR (ddPCR) confirmed a significant association between an increased copy number with the dark-red coat color in NSDTR (p = 6.1 × 10-7). The copy number of the CNV was also significantly associated with coat color variation in both eumelanin and pheomelanin-based Poodles (p = 1.5 × 10-8, 4.0 × 10-9) and across other breeds. Moreover, the copy number correlated with pigment intensity along the hair shaft in both pheomelanin and eumelanin coats. KITLG plays an important role in melanogenesis, and variants upstream of KITLG have been associated with coat color variation in mice as well as hair color in humans consistent with its role in the domestic dog

Income dynamics and the life cycle

This paper argues that our understanding of income and poverty dynamics benefits from taking a life cycle perspective. A person¿s age and family circumstances ¿ the factors that shape their life cycle ¿ affect the likelihood of experiencing key life events, such as partnership formation, having children, or retirement; this in turn affects their probability of experiencing rising, falling, or other income trajectories. Using ten waves of the British Household Panel Survey, we analyse the income trajectories of people at different stages in their lives in order to build a picture of income dynamics over the whole life cycle. We find that particular life events are closely associated with either rising or falling trajectories, but that there is considerable heterogeneity in income trajectories following these different events. Typically, individuals experiencing one of these life events are around twice as likely to experience a particular income trajectory, but most individuals will not follow the trajectory most commonly associated with that life event. This work improves our understanding of the financial impact of different life events and provides an indication of how effectively the welfare state cushions people against the potentially adverse impact of certain events