3,069 research outputs found

    On distinguishing trees by their chromatic symmetric functions

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    Let TT be an unrooted tree. The \emph{chromatic symmetric function} XTX_T, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of TT. The \emph{subtree polynomial} STS_T, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of TT by their numbers of edges and leaves. We prove that ST=S_T = , where is the Hall inner product on symmetric functions and Φ\Phi is a certain symmetric function that does not depend on TT. Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (\emph{spiders} and some \emph{caterpillars}), and one family of unicyclic graphs (\emph{squids}) whose members are determined completely by their chromatic symmetric functions.Comment: 16 pages, 3 figures. Added references [2], [13], and [15

    On distinguishing trees by their chromatic symmetric functions

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    This is the author's accepted manuscript

    Depression in Husbands of Breast Cancer Patients: Relationships to Coping and Social Support

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    PURPOSE: The purpose of the present study was to examine depression in husbands of women with breast cancer, as depression is typically as high in husbands as in patients, and impacts functioning in both. METHODS: We compared husbands of patients to husbands of women without chronic illness on depressive symptoms with the Center for Epidemiological Studies Depression Scale, social support with the Interpersonal Support Evaluation List, and coping with the Ways of Coping Questionnaire. Using the stress and coping model, we examined whether coping mediated social support and depression differently by group, as has been found in the literature. RESULTS: Husbands of patients reported higher scores on the measure of depression and lower use of problem-focused coping, while groups reported equivalent social support. Escape-avoidance coping emerged as a full mediator between social support and depression in husbands of patients, but only a partial mediator in comparison husbands. Accepting responsibility coping partially mediated social support and depression in both groups. Low social support appears particularly detrimental in husbands of patients as it is associated with ineffective coping and depression. CONCLUSIONS: Findings suggest that among husbands of patients, social support relates to depression only through its relationship with coping, indicating healthcare providers should direct attention and intervention to the coping strategies employed by husbands with low social support

    Sensory and affective response to chocolate differing in cocoa content:a TDS and facial electromyography approach

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    Existing research has offered insight into facial activities and their associations with hedonic liking during the consumption of basic food samples and suggests facial changes during consumption are linked to the hedonic evaluation of tastes and, thus related to the taster's perception rather than the tastes themselves. This study tests whether, during the consumption of commercially available dark chocolate, a complex food product, which can be high in bitterness but expectedly so, how facial activities are linked to the bitterness levels and the hedonic liking of the samples. To do this we carried out two studies with untrained consumers, the first of which captured temporally dynamic sensory perception during the consumption of dark chocolate samples of 36% and 85% cocoa content, using the Temporal Dominance of Sensations (TDS) approach. The second study captured facial EMG over the corrugator and zygomaticus muscles during the consumption of dark chocolate samples (36%, 70%, and 85% cocoa). Specifically, the aim of this research was to investigate whether corrugator activity had a greater association with bitterness perception, linked to cocoa, or hedonic evaluation. Capturing the dynamic sensory profile of chocolate samples allowed an investigation into the time points most evident of sensory variation related to the bitterness and sweetness of the taste, allowing insight into whether facial activities also deviated during this time. These data offer evidence to suggest that corrugator was associated with hedonic evaluation during consumption of the samples, with the most liked samples (being those with 70% and 36% cocoa) eliciting similar corrugator activities and less activity than the least liked 85% cocoa content sample; however, there was also evidence to suggest a significant variation in participants' corrugator activity during the period of oral processing when bitterness was most evident in the 85% cocoa sample and sweetness was most evident in the 36% cocoa sample (i.e., the time when bitterness and sweetness were most divergent) Further investigation showed a variation in facial activities elicited during consumption of the 36% cocoa sample based on whether individuals were part of the group who favoured the 85% cocoa sample or the group favouring the 36% cocoa sample. The findings, therefore, suggest facial EMG, specifically over the corrugator, appears to be related to the hedonic evaluation of a complex food product and not the taste itself. Furthermore, being aware of the time points where sensory variations are most apparent between samples can allow for targeted investigation into facial EMG and its ability to distinguish food samples. [Abstract copyright: Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.

    On the Spectra of Simplicial Rook Graphs

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    The simplicial rook graph\textit{simplicial rook graph} SR(d,n)SR(d,n) is the graph whose vertices are the lattice points in the nnth dilate of the standard simplex in Rd\mathbb{R}^d, with two vertices adjacent if they differ in exactly two coordinates. We prove that the adjacency and Laplacian matrices of SR(3,n)SR(3,n) have integral spectra for every nn. We conjecture that SR(d,n)SR(d,n) is integral for all dd and nn, and give a geometric construction of almost all eigenvectors in terms of characteristic vectors of lattice permutohedra. For n(d2)n \leq \binom{d}{2}, we give an explicit construction of smallest-weight eigenvectors in terms of rook placements on Ferrers diagrams. The number of these eigenvectors appears to satisfy a Mahonian distribution

    An ethnographic exploration of drug markets in Kisumu, Kenya.

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    BACKGROUND: Illegal drug markets are shaped by multiple forces, including local actors and broader economic, political, social, and criminal justice systems that intertwine to impact health and social wellbeing. Ethnographic analyses that interrogate multiple dimensions of drug markets may offer both applied and theoretical insights into drug use, particularly in developing nations where new markets and local patterns of use traditionally have not been well understood. This paper explores the emergent drug market in Kisumu, western Kenya, where our research team recently documented evidence of injection drug use. METHODS: Our exploratory study of injection drug use was conducted in Kisumu from 2013 to 2014. We draw on 151 surveys, 29 in-depth interviews, and 8 months of ethnographic fieldwork to describe the drug market from the perspective of injectors, focusing on their perceptions of the market and reports of drug use therein. RESULTS: Injectors described a dynamic market in which the availability of drugs and proliferation of injection drug use have taken on growing importance in Kisumu. In addition to reports of white and brown forms of heroin and concerns about drug adulteration in the market, we unexpectedly documented widespread perceptions of cocaine availability and injection in Kisumu. Examining price data and socio-pharmacological experiences of cocaine injection left us with unconfirmed evidence of its existence, but opened further possibilities about how the chaos of new drug markets and diffusion of injection-related beliefs and practices may lend insight into the sociopolitical context of western Kenya. CONCLUSIONS: We suggest a need for expanded drug surveillance, education and programming responsive to local conditions, and further ethnographic inquiry into the social meanings of emergent drug markets in Kenya and across sub-Saharan Africa

    A Detailed Observational Analysis of V1324 Sco, the Most Gamma-Ray Luminous Classical Nova to Date

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    It has recently been discovered that some, if not all, classical novae emit GeV gamma rays during outburst, but the mechanisms involved in the production of the gamma rays are still not well understood. We present here a comprehensive multi-wavelength dataset---from radio to X-rays---for the most gamma-ray luminous classical nova to-date, V1324 Sco. Using this dataset, we show that V1324 Sco is a canonical dusty Fe-II type nova, with a maximum ejecta velocity of 2600 km s1^{-1} and an ejecta mass of few ×105\times 10^{-5} M_{\odot}. There is also evidence for complex shock interactions, including a double-peaked radio light curve which shows high brightness temperatures at early times. To explore why V1324~Sco was so gamma-ray luminous, we present a model of the nova ejecta featuring strong internal shocks, and find that higher gamma-ray luminosities result from higher ejecta velocities and/or mass-loss rates. Comparison of V1324~Sco with other gamma-ray detected novae does not show clear signatures of either, and we conclude that a larger sample of similarly well-observed novae is needed to understand the origin and variation of gamma rays in novae.Comment: 26 pages, 13 figure

    The effects of moderate prenatal alcohol exposure on the organization of exploratory behavior by adult female rats

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    A large body of research has indicated that moderate Prenatal Alcohol Exposure (PAE - 60 mg/dl peak BAC) can produce impairments on cognitive processes, such as spatial learning and memory. The neurobiological basis of these impairments is poorly understood but is frequently linked to alterations in hippocampal functioning. Although the hippocampus has a central role in learning and memory, damage to the hippocampus can also produce impairments in locomotor and exploratory behaviors by rodents (reviewed in Thompson et al., 2018). Rodent exploratory behavior is organized around home bases, which serves as central points of attraction from which rats and mice organize their exploratory trips into the remaining environment. We are unaware of studies investigating the relationship between moderate prenatal alcohol exposure and exploratory behavior. Thus, in the present study, we tested adult female rats in two experiments where they were allowed to freely explore a circular open field for ~30min. Here, we report that, with respect to home base behavior, exploratory movements were largely intact in rats exposed to alcohol prenatally. Specifically, animals rapidly established home bases within 5min of the beginning of testing and the bases were established in one or two locations in the environment. They made exploratory trips away and back to the home base and made several stops at this location along with bouts of grooming behavior. The results are discussed with respect to theories of hippocampal function and the impact of moderate prenatal alcohol on spatial behavior
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