Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

TRACKING THE EVOLUTION OF E-GROCERS: A QUANTITATIVE ASSESSMENT

Forecasts of the proportion of food retailing likely to be conducted over the Internet remain small, perhaps only contributing 2 percent of sales. One reason for this low market share is the challenge E-Grocers face in developing strategies which respond to four key areas of interest to consumers: signals of firm quality; signals of product quality; the range of products offered; and service, or customer-relationship management (CRM). Careful attention to these consumer concerns is important in all retail relationships–-online or offline. This paper compares indicators of these factors across U.S. E-Grocers. A quantitative four-period ranking of online food-retailing strategies is presented for the nascent industry. Data from the third and fourth quarters of 2001, the fourth quarter of 2002, and the first quarter of 2004 provide the basis of this discussion. After initial setbacks, data show traditional ("“bricks”") grocery retailers successfully developing online strategies. Firms not primarily focused on groceries exited the E-Grocery sector, while the development of specialty food suppliers blurred the concept of online food retailing. Gaps in current strategies are indicated using content analyses of E-Grocery web sites.Agribusiness,

Attraction of Adult Chironomidae (Diptera) to Incandescent Light Under Laboratory Conditions

The attraction of three chironomid species, Glyptotendipes paripes Edwards, Chironomus crassicaudatus Malloch, and Polypedilum halterale (Coquillett), to incandescent light of different colors and wattages was studied. Field-captured adults were released from the center of a dark room (9 by 9 m) equipped with a New Jersey light trap in each corner. The effects of color were determined by using 100-W lamps of red, orange, yellow, green, blue, and white. The effects of light intensity were studied by using 100, 60, 40, and 25-W white lamps. Measurements of light intensity of each lamp were taken. Among the colors tested in two separate combinations, white light attracted the maximum numbers of adults and red light the least. The three species exhibited a similar behavior. Among white light of different intensities, the maximum attraction of G. paripes occurred toward the highest intensity and the minimum toward the lowest intensity. The midge species responded more to the quantity (power or intensity) than to the quality (color or wavelength) of ligh

Converting Treatment Plans From Helical Tomotherapy to L-Shape Linac: Clinical Workflow and Dosimetric Evaluation.

This work evaluated a commercial fallback planning workflow designed to provide cross-platform treatment planning and delivery. A total of 27 helical tomotherapy intensity-modulated radiotherapy plans covering 4 anatomical sites were selected, including 7 brain, 5 unilateral head and neck, 5 bilateral head and neck, 5 pelvis, and 5 prostate cases. All helical tomotherapy plans were converted to 7-field/9-field intensity-modulated radiotherapy and volumetric-modulated radiotherapy plans through fallback dose-mimicking algorithm using a 6-MV beam model. The planning target volume (PTV) coverage ( D1, D99, and homogeneity index) and organs at risk dose constraints were evaluated and compared. Overall, all 3 techniques resulted in relatively inferior target dose coverage compared to helical tomotherapy plans, with higher homogeneity index and maximum dose. The organs at risk dose ratio of fallback to helical tomotherapy plans covered a wide spectrum, from 0.87 to 1.11 on average for all sites, with fallback plans being superior for brain, pelvis, and prostate sites. The quality of fallback plans depends on the delivery technique, field numbers, and angles, as well as user selection of structures for organs at risk. In actual clinical scenario, fallback plans would typically be needed for 1 to 5 fractions of a treatment course in the event of machine breakdown. Our results suggested that <1% dose variance can be introduced in target coverage and/or organs at risk from fallback plans. The presented clinical workflow showed that the fallback plan generation typically takes 10 to 20 minutes per case. Fallback planning provides an expeditious and effective strategy for transferring patients cross platforms, and minimizing the untold risk of a patient missing treatment(s)

Staircase polygons: moments of diagonal lengths and column heights

We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10-15 July 2005, Queensland, Australi