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Thep‐dispersion problem is a spatial optimization problem that aims to maximize the minimum separation distance among all assigned nodes. This problem is characterized by an innate spatial structure based on distance attributes. This research proposes a novel approach, named thedistance‐based spatially informed property(D‐SIP) method to reduce the problem size of thep‐dispersion instances, facilitating a more efficient solution while maintaining optimality in nearly all cases. The D‐SIP is derived from investigating the underlying spatial characteristics from the behaviors of thep‐dispersion problem in determining the optimal location of nodes. To define the D‐SIP, this research applies Ripley'sK‐function to the different types of point patterns, given that the optimal solutions of thep‐dispersion problem are strongly associated with the spatial proximity among points discovered by Ripley'sK‐function. The results demonstrate that the D‐SIP identifies collective dominances of optimal solutions, leading to buildingthe spatially informed p‐dispersion model. The simulation‐based experiments show that the proposed method significantly diminishes the size of problems, improves computational performance, and secures optimal solutions for 99.9% of instances (999 out of 1,000 instances) under diverse conditions.
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Life cycle size dynamics in Didymosphenia geminata (Bacillariophyceae)
Didymosphenia geminatahas received a great deal of attention in the last 25 years, and considerable effort has gone into determining the origin, ecological impact, and economic consequences of its invasive behavior. While environmental conditions are a controlling influence in distribution, the extreme success of the species may be tied to its basic biology and life history. Little is known, however, about population dynamics, size restoration and reproduction ofD. geminata. The objective of this study was to determine the temporal patterns in cell size frequency, size restoration strategy, and synchronization of life cycles between populations in close proximity. We implemented FlowCam technology to measure the length of more than 100,000D. geminatacells from two sites in South Boulder Creek, Colorado over 1 year. We applied finite mixture modeling to uncover temporal patterns in size distribution. Our results show that collections ofD. geminataexhibited a complex, multimodal size distribution, almost always containing four overlapping age cohorts. We failed to observe direct visual evidence of the sexual phase. Multiple abrupt and directional shifts in size distribution, however, were documented providing conclusive evidence of cell size restoration. Lastly, nodules in close proximity were asynchronous with respect to size frequency profiles and size diminution, highlighting the relevance of spatial heterogeneity in in situ diatom size dynamics. This study is the first to document the complexity of diatom cell size distribution in a lotic system, size restoration inD. geminata, and the variability in rates of size reduction at microhabitat spatial scales.
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- Award ID(s):
- 1637708
- PAR ID:
- 10034541
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Journal of Phycology
- Volume:
- 53
- Issue:
- 3
- ISSN:
- 0022-3646
- Format(s):
- Medium: X Size: p. 652-663
- Size(s):
- p. 652-663
- Sponsoring Org:
- National Science Foundation
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