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Abstract In this note we examine the following random graph model: for an arbitrary graph , with quadratic many edges, construct a graph by randomly adding edges to and randomly coloring the edges of with colors. We show that for a large enough constant and , every pair of vertices in are joined by a rainbow path, that is, israinbow connected, with high probability. This confirms a conjecture of Anastos and Frieze, who proved the statement for and resolved the case when and is a function of .
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Analyzing colors and spectra of natural rainbows with hyperspectral imaging
Few colorimetric analyses of natural rainbows (i.e., bows seen in rain showers) have been published, and these are limited either to approximate techniques (colorimetrically calibrated red–green–blue (RGB) cameras) or to rainbow proxies (bows seen in sunlit water-drop sprays). Furthermore, no research papers provide angularly detailed spectra of natural rainbows in the visible and near-IR. Thus some uncertainty exists about whether the published spectra and colors differ perceptibly from those in natural rainbows. However, battery-powered imaging spectrometers now make possible direct field measurements of the observed chromaticities and spectra in such bows. These data (1) show consistent spectral and colorimetric patterns along rainbow radii and (2) let one subtract additively mixed background light to reveal the intrinsic colors and spectra produced by rainbow scattering in nature.
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- Award ID(s):
- 1936028
- PAR ID:
- 10161093
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Applied Optics
- Volume:
- 59
- Issue:
- 21
- ISSN:
- 1559-128X; APOPAI
- Format(s):
- Medium: X Size: Article No. F63
- Size(s):
- Article No. F63
- Sponsoring Org:
- National Science Foundation
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