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Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of annvertex graph, and need to output a clique. We show that if the input graph is drawn at random from(and hence is likely to have a clique of size roughly), then for everyδ<2 and constantℓ, there is anα<2 (that may depend onδandℓ) such that no algorithm that makesnδprobes inℓrounds is likely (over the choice of the random graph) to output a clique of size larger than.
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Nearshore Lagrangian Connectivity: Submesoscale Influence and Resolution Sensitivity
Abstract Realistic simulation of nearshore (from the shoreline to approximately 10‐km offshore) Lagrangian material transport is required for physical, biological, and ecological investigations of the coastal ocean. Recently, high‐resolution simulations of the coastal ocean have revealed a shelf populated with small‐scale, rapidly evolving currents that arise at resolutions100 m. However, many historical and recent investigations of coastal connectivity utilize circulation models with ≈1‐km resolution. Here we show a resolution sensitivity to simulated Lagrangian transport and coastal connectivity with a hierarchy of Regional Oceanic Modeling System simulations of the Santa Barbara Channel at Δx= 1, 0.3, 0.1, and 0.036 km. At higher resolution ( 100 m), rapid alongshore and vertical transport occurs in regions less than 1 km from the shoreline due to submesoscale shelf currents that open up new transport pathways on the shelf: submesoscale fronts and filaments, topographic wakes, and narrow alongshore jets. Shallow‐water fronts and filaments induce early time downwelling and subsequent dispersal at depth of surface material; this is not captured at coarser resolution (Δx= 1 km). Differences in three‐dimensional and two‐dimensional transport are explored in a higher‐resolution simulation: In general, three‐dimensional trajectories are more dispersive than two‐dimensional, due to a separation in their respective trajectories.
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- PAR ID:
- 10453979
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Oceans
- Volume:
- 124
- Issue:
- 7
- ISSN:
- 2169-9275
- Page Range / eLocation ID:
- p. 5180-5204
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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