363 research outputs found

    The Betti poset in monomial resolutions

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    Let PP be a finite partially ordered set with unique minimal element 0^\hat{0}. We study the Betti poset of PP, created by deleting elements q∈Pq\in P for which the open interval (0^,q)(\hat{0}, q) is acyclic. Using basic simplicial topology, we demonstrate an isomorphism in homology between open intervals of the form (0^,p)⊂P(\hat{0},p)\subset P and corresponding open intervals in the Betti poset. Our motivating application is that the Betti poset of a monomial ideal's lcm-lattice encodes both its Zd\mathbb{Z}^{d}-graded Betti numbers and the structure of its minimal free resolution. In the case of rigid monomial ideals, we use the data of the Betti poset to explicitly construct the minimal free resolution. Subsequently, we introduce the notion of rigid deformation, a generalization of Bayer, Peeva, and Sturmfels' generic deformation

    LS 152.13: Introduction to Humanities

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    This ain\u27t the Amazon

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    LS 395.01: Modern Humanities

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    LS 152.16: Introduction to Humanities

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    Developing Dementia-Friendly Tourism Destinations: An Exploratory Analysis

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    Dementia is emerging as a global issue. Increases in life expectancy create an older population structure with accompanying health needs but also high lifestyle expectations. For example existing generations have come to expect to be able to participate in leisure and tourism activities in later life, which can be constrained by the onset of dementia. Leading healthy lifestyles and engaging in tourism activities are viewed as fundamental to remaining active and contributing to slowing the progress of dementia. This study is the first to examine the challenges and implications of the growing scale of dementia and the business opportunities this may create for destinations wishing to achieve dementia-friendly status. The paper reports results from an initial scoping study with tourism businesses in a coastal resort in the United Kingdom with such ambitions to assess the nature of the issues that arose from a series of face-to-face interviews

    Observing convective aggregation

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    Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad a distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network
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