28 research outputs found

    M 221.01: Introduction to Linear Algebra

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    M 221.02: Introduction to Linear Algebra

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    M 274.01: Introduction to Differential Equation (Applied Differential Equations)

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    M 221.01: Introduction to Linear Algebra

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    M 412.01: Partial Differential Equations

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    M 514.01Introduction to Computational Inverse Problems: Mathematical and Statistical Methods

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    M 414.01: Deterministic Models

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    Consequences of a Refuge for the Predator-Prey Dynamics of a Wolf-Elk System in Banff National Park, Alberta, Canada

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    Refugia can affect predator-prey dynamics via movements between refuge and non-refuge areas. We examine the influence of a refuge on population dynamics in a large mammal predator-prey system. Wolves (Canis lupus) have recolonized much of their former range in North America, and as a result, ungulate prey have exploited refugia to reduce predation risk with unknown impacts on wolf-prey dynamics. We examined the influence of a refuge on elk (Cervus elaphus) and wolf population dynamics in Banff National Park. Elk occupy the Banff townsite with little predation, whereas elk in the adjoining Bow Valley experience higher wolf predation. The Banff refuge may influence Bow Valley predator-prey dynamics through source-sink movements. To test this hypothesis, we used 26 years of wolf and elk population counts and the Delayed Rejection Adaptive Metropolis Markov chain Monte Carlo method to fit five predator-prey models: 1) with no source-sink movements, 2) with elk density-dependent dispersal from the refuge to the non-refuge, 3) with elk predation risk avoidance movements from the non-refuge to the refuge, 4) with differential movement rates between refuge and non-refuge, and 5) with short-term, source-sink wolf movements. Model 1 provided the best fit of the data, as measured by Akaike Information Criterion (AIC). In the top model, Banff and Bow Valley elk had median growth rates of 0.08 and 0.03 (95% credibility intervals [CIs]: 0.027–0.186 and 0.001–0.143), respectively, Banff had a median carrying capacity of 630 elk (95% CI: 471.9– 2676.9), Bow Valley elk had a median wolf encounter rate of 0.02 (95% CI: 0.013–0.030), and wolves had a median death rate of 0.23 (95% CI: 0.146–0.335) and a median conversion efficiency of 0.07 (95% CI: 0.031–0.124). We found little evidence for potential source-sink movements influencing the predator-prey dynamics of this system. This result suggests that the refuge was isolated from the non-refuge

    Hedgehog pathway dysregulation contributes to the pathogenesis of human gastrointestinal stromal tumors via GLI-mediated activation of KIT expression.

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    Gastrointestinal stromal tumors (GIST) arise within the interstitial cell of Cajal (ICC) lineage due to activating KIT/PDGFRA mutations. Both ICC and GIST possess primary cilia (PC), which coordinate PDGFRA and Hedgehog signaling, regulators of gastrointestinal mesenchymal development. Therefore, we hypothesized that Hedgehog signaling may be altered in human GIST and controls KIT expression. Quantitative RT-PCR, microarrays, and next generation sequencing were used to describe Hedgehog/PC-related genes in purified human ICC and GIST. Genetic and pharmacologic approaches were employed to investigate the effects of GLI manipulation on KIT expression and GIST cell viability. We report that Hedgehog pathway and PC components are expressed in ICC and GIST and subject to dysregulation during GIST oncogenesis, irrespective of KIT/PDGFRA mutation status. Using genomic profiling, 10.2% of 186 GIST studied had potentially deleterious genomic alterations in 5 Hedgehog-related genes analyzed, including in the PTCH1 tumor suppressor (1.6%). Expression of the predominantly repressive GLI isoform, GLI3, was inversely correlated with KIT mRNA levels in GIST cells and non-KIT/non-PDGFRA mutant GIST. Overexpression of the 83-kDa repressive form of GLI3 or small interfering RNA-mediated knockdown of the activating isoforms GLI1/2 reduced KIT mRNA. Treatment with GLI1/2 inhibitors, including arsenic trioxide, significantly increased GLI3 binding to the KIT promoter, decreased KIT expression, and reduced viability in imatinib-sensitive and imatinib-resistant GIST cells. These data offer new evidence that genes necessary for Hedgehog signaling and PC function in ICC are dysregulated in GIST. Hedgehog signaling activates KIT expression irrespective of mutation status, offering a novel approach to treat imatinib-resistant GIST
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