Color-blind index in graphs of very low degree

Let $c:E(G)\to [k]$ be an edge-coloring of a graph $G$, not necessarily proper. For each vertex $v$, let $\bar{c}(v)=(a_1,\ldots,a_k)$, where $a_i$ is the number of edges incident to $v$ with color $i$. Reorder $\bar{c}(v)$ for every $v$ in $G$ in nonincreasing order to obtain $c^*(v)$, the color-blind partition of $v$. When $c^*$ induces a proper vertex coloring, that is, $c^*(u)\neq c^*(v)$ for every edge $uv$ in $G$, we say that $c$ is color-blind distinguishing. The minimum $k$ for which there exists a color-blind distinguishing edge coloring $c:E(G)\to [k]$ is the color-blind index of $G$, denoted $\operatorname{dal}(G)$. We demonstrate that determining the color-blind index is more subtle than previously thought. In particular, determining if $\operatorname{dal}(G) \leq 2$ is NP-complete. We also connect the color-blind index of a regular bipartite graph to 2-colorable regular hypergraphs and characterize when $\operatorname{dal}(G)$ is finite for a class of 3-regular graphs.Comment: 10 pages, 3 figures, and a 4 page appendi

Daylight Spectrum Index: A New Metric to Assess the Affinity of Light Sources with Daylighting

The current scenario of colorimetry shows a wide variety of different metrics which do not converge in the assessment of the color rendering of light sources. The limitations of the Color Rendering Index have promoted the emergence of new metrics, such as the Color Quality Scale. As in the case of the previous metric, these new concepts are based on the analysis of the deviation of different color samples in a color space, contrasting the results with those obtained with a light source reference, which can vary depending on the color temperature. Within this context, the Daylight Spectrum Index is proposed. This new concept aims to determine the affinity with daylighting of electric light sources, comparing the resulting spectral power distributions of the lamps studied and that observed under natural light. The affinity of an electric light source with daylighting allows for lower energy consumption due to the better performance of human vision. The new metric proposed is evaluated following the results obtained from 80 surveys, demonstrating the usefulness of this new concept in the quantification of color rendering of LED lamps and the affinity of electric light sources with daylighting.Government of Spain BIA2017-86997-

Porcelain Surface Roughness, Color and Gloss Changes after Orthodontic Bonding

The purpose of this study was to evaluate the alteration in surface characteristics after orthodontic debonding of two types of porcelain systems commonly used in prosthetic dentistry. For this purpose, porcelain specimens were fabricated from low-fusing (n = 20) and high-fusing (n = 20) porcelain. The baseline surface roughness, color, and gloss were evaluated using profilometry, color shade index, and gloss study. All specimens were bonded with brackets and debonded using a testing machine at a rate of 0.1 mm/minute crosshead speed. The porcelain surfaces were polished using a 12-fluted carbide composite removal bur (low-fusing, n = 20; high-fusing, n = 20). In addition, half of each porcelain group was further polished using a series of Sof-Lex discs (low-fusing, n = 10; high-fusing, n = 10). The postdebond porcelain surface characteristics roughness, color, and gloss were reevaluated and compared with baseline measurements. The results were analyzed with two-way analysis of variance and Tukey multiple comparisons test, with porcelain type (low-fusing or high-fusing) and polishing protocol (carbide bur or carbide bur and discs) serving as discriminate variables at α = 0.05 level of significance. Bonding and debonding increased all roughness parameters tested; however, no change was revealed between the two polishing protocols. Similarly, gloss and color index changes were significantly altered after resin grinding, regardless of the polishing method used. No difference was identified between the two porcelain types with respect to roughness, color index, or gloss. Orthodontic bonding alters the porcelain surfaces, and postdebond polishing does not restore the surface to the prebond state

Why are the K dwarfs in the Pleiades so Blue?

The K dwarfs in the Pleiades fall nearly one half magnitude below a main sequence isochrone when plotted in a color-magnitude diagram utilizing V magnitude as the luminosity index and B-V as the color index. This peculiarity has been known for forty years but has gone unexplained and mostly ignored. When compared to Praesepe members, the Pleiades K dwarfs again are subluminous (or blue) in a color-magnitude diagram using B-V as the color index. However, using V-I as the color index, stars in the two clusters are coincident to M_V ~ 10; using V-K as the color index, Pleiades late K and M stars fall above the main sequence locus defined by Praesepe members. We believe that the anomalous spectral energy distributions for the Pleiades K dwarfs, as compared to older clusters, are a consequence of rapid stellar rotation and may be primarily due to spottedness. If so, the required areal filling factor for the cool component has to be very large (=> 50%). Weak-lined T Tauri stars have similar color anomalies, and we suspect this is a common feature of all very young K dwarfs (sp. type > K3). The peculiar spectral energy distribution needs to be considered in deriving accurate pre-main sequence isochrone-fitting ages for clusters like the Pleiades since the age derived will depend on the temperature index used.Comment: 41 pages, 15 figures, AASTeX5.0. Accepted 05 May 2003; Scheduled for publication in the Astronomical Journal (August 2003

On martingale tail sums in affine two-color urn models with multiple drawings

In two recent works, Kuba and Mahmoud (arXiv:1503.090691 and arXiv:1509.09053) introduced the family of two-color affine balanced Polya urn schemes with multiple drawings. We show that, in large-index urns (urn index between $1/2$ and $1$) and triangular urns, the martingale tail sum for the number of balls of a given color admits both a Gaussian central limit theorem as well as a law of the iterated logarithm. The laws of the iterated logarithm are new even in the standard model when only one ball is drawn from the urn in each step (except for the classical Polya urn model). Finally, we prove that the martingale limits exhibit densities (bounded under suitable assumptions) and exponentially decaying tails. Applications are given in the context of node degrees in random linear recursive trees and random circuits.Comment: 17 page

W UMa-type Binary Stars in Globular Clusters

A sample of 86 contact binary systems in 14 globular clusters with available color index data in (B-V) or in (V-I) has been analyzed. At least one third of all systems are numerous foreground Galactic Disk projections over long lines of sight to the clusters. Since the selection of the cluster members has been based on the MV(logP, color) calibrations, the matter of a metallicity-correction required particular attention with the result that such a correction is apparently not needed at the present level of accuracy. Analysis of the color-magnitude and period-color relations shows that globular cluster members are under-luminous relative to the Galactic Disk contact systems mainly because of the smaller sizes and, consequently, shorter orbital periods; the color-index effect of the diminished blanketing is less important, especially for (V-I). The variability amplitudes for the Blue Straggler systems show a significantly different distribution from that for systems below the Turn Off Point (TOP): The BS systems show only small amplitudes while the distribution for the systems below the TOP is peculiar in containing only large amplitude systems. This difference is linked to an observational selection effect so that efforts at determining the frequency of occurrence of the contact systems below the TOP have been judged to be premature; the frequency among the BS stars could be at about 45+-10 BS stars per one contact BS binary.Comment: submitted for publication in Astronomical Journal; 8 figures, 3 tables (Table 1 in landscape

Optical Surface Photometry of a Sample of Disk Galaxies. II Structural Components

This work presents the structural decomposition of a sample of 11 disk galaxies, which span a range of different morphological types. The U, B, V, R, and I photometric information given in Paper I (color and color-index images and luminosity, ellipticity, and position-angle profiles) has been used to decide what types of components form the galaxies before carrying out the decomposition. We find and model such components as bulges, disks, bars, lenses and rings.Comment: 14 figures. Accepted for publication in A&