8,230 research outputs found

    Recursive strategy for decomposing Betti tables of complete intersections

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    We introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition. We also provide a detailed analysis of the Boij-Soederberg decomposition for Betti diagrams of codimension four complete intersections where the largest generating degree satisfies the size condition

    Critical Pebbling Numbers of Graphs

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    We define three new pebbling parameters of a connected graph GG, the rr-, gg-, and uu-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices nn and the diameter dd of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the rr-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the rr-critical pebbling number is 2d2^d.Comment: 26 page

    Comprehension Models of Audiovisual Discourse Processing

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    Comprehension is integral to enjoyment of media narratives, yet our understanding of how viewers create the situation models that underlie comprehension is limited.This study utilizes two models of comprehension that had previously been tested with factual texts/videos to predict viewers’ recall of entertainment media. Across five television/film clips, the landscape model explained at least 29% of the variance in recall. A dual coding version that assumed separate verbal and visual representations of the story significantly improved the model fit in four of the clips, accounting for an additional 15–29% of the variance. The dimensions of the event-indexingmodel (time, space, protagonist, causality, and intentionality) significantly moderated the relationship between the dual coding model and participant recall in all clips

    Unimolecular reaction rates in solution and in the isolated molecule: Comparison of diphenyl butadiene nonradiative decay in solutions and supersonic jets

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    The recent study of diphenyl butadiene (DPB) in supersonic jets and in solution by Shepanski et al.(1) and by Courtney and Felming(2), respectively, provides an opportunity to compare the isomerization rates measured in the isolated molecule (jet) with those measured at very low viscosity in solution. These comparisons should shed light on the vibrational energy flows between “optical” and “reactive” modes in the isolated molecule and on the connection between activated, friction dependent, models of barrier crossing in solution,(3-5) and statistical RRK (or RRKM) theories of gas phase unimolecular reactions(6)
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