Set Of Colors Research Articles

Seasonal Changes in Color Preferences Are Linked to Variations in Environmental Colors: A Longitudinal Study of Fall.

People form associations between colors and entities, which influence their evaluations of the world. These evaluations are dynamic, as specific associations become more or less active in people’s minds over time. We investigated how evaluations of colors (color preferences) changed over the course of fall, as color-associated fall entities became more prevalent in the environment. Participants judged their preferences for the same set of colors during nine testing sessions over 11 weeks during fall. We categorized the colors as Leaf and Non-Leaf Colors by matching them to leaves collected during the same period. Changes in preferences for Leaf Colors followed a quadratic pattern, peaking around when the leaves were most colorful and declining as winter approached. Preferences for Non-Leaf Colors did not significantly change. Individual differences in these changes could be explained by preferences for seasonal entities, as predicted by the differential activation hypothesis within the Ecological Valence Theory. The more a given individual liked fall-associated entities, the more their preference for Leaf Colors increased during fall. No analogous relations existed with winter-associated entities or Non-Leaf Colors. These results demonstrate the importance of studying temporal and individual differences for understanding preferences.

Singular knots and involutive quandles

The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular links. As an application, we distinguish several singular knots and links.

An improved upper bound on the adjacent vertex distinguishing total chromatic number of graphs

An adjacent vertex distinguishing total k-coloring of a graph G is a proper total k-coloring of G such that any pair of adjacent vertices have different sets of colors. The minimum number k needed for such a total coloring of G is denoted by χa′′(G). In this paper we prove that χa′′(G)≤2Δ(G)−1 if Δ(G)≥4, and χa′′(G)≤⌈5Δ(G)+83⌉ in general. This improves a result in Huang et al. (2012) which states that χa′′(G)≤2Δ(G) for any graph with Δ(G)≥3.

Pólya urn schemes with infinitely many colors

In this work we introduce a new type of urn model with infinite but countable many colors indexed by an appropriate infinite set. We mainly consider the indexing set of colors to be the $d$-dimensional integer lattice and consider balanced replacement schemes associated with bounded increment random walks on it. We prove central and local limit theorems for the random color of the $n$-th selected ball and show that irrespective of the null recurrent or transient behavior of the underlying random walks, the asymptotic distribution is Gaussian after appropriate centering and scaling. We show that the order of any non-zero centering is always ${\mathcal O}\left(\log n\right)$ and the scaling is ${\mathcal O}\left(\sqrt{\log n}\right)$. The work also provides similar results for urn models with infinitely many colors indexed by more general lattices in ${\mathbb R}^d$. We introduce a novel technique of representing the random color of the $n$-th selected ball as a suitably sampled point on the path of the underlying random walk. This helps us to derive the central and local limit theorems.

3D printed versus conventionally cured provisional crown and bridge dental materials

ObjectivesTo optimize the 3D printing of a dental material for provisional crown and bridge restorations using a low-cost stereolithography 3D printer; and compare its mechanical properties against conventionally cured provisional dental materials. MethodsSamples were 3D printed (25×2×2mm) using a commercial printable resin (NextDent C&B Vertex Dental) in a FormLabs1+ stereolithography 3D printer. The printing accuracy of printed bars was determined by comparing the width, length and thickness of samples for different printer settings (printing orientation and resin color) versus the set dimensions of CAD designs. The degree of conversion of the resin was measured with FTIR, and both the elastic modulus and peak stress of 3D printed bars was determined using a 3-point being test for different printing layer thicknesses. The results were compared to those for two conventionally cured provisional materials (Integrity®, Dentsply; and Jet®, Lang Dental Inc.). ResultsSamples printed at 90° orientation and in a white resin color setting was chosen as the most optimal combination of printing parameters, due to the comparatively higher printing accuracy (up to 22% error), reproducibility and material usage. There was no direct correlation between printing layer thickness and elastic modulus or peak stress. 3D printed samples had comparable modulus to Jet®, but significantly lower than Integrity®. Peak stress for 3D printed samples was comparable to Integrity®, and significantly higher than Jet®. The degree of conversion of 3D printed samples also appeared higher than that of Integrity® or Jet®. SignificanceOur results suggest that a 3D printable provisional restorative material allows for sufficient mechanical properties for intraoral use, despite the limited 3D printing accuracy of the printing system of choice.

The minimum chromatic violation problem: a polyhedral study

We propose a generalization of the k-coloring problem, namely the minimum chromatic violation problem (MCVP). Given a graph G=(V,E), a set of weak edgesF⊂E and a set of colors C, the MCVP asks for a |C|-coloring of the graph G′=(V,E\\F) minimizing the number of weak edges with both endpoints receiving the same color. We present an integer programming formulation for this problem and provide an initial polyhedral study of the polytopes arising from this formulation. We give partial characterizations of facet-inducing inequalities and we show how facets from weaker and stronger instances of MCVP (i.e., more/less weak edges) are related. We then introduce a general lifting procedure which generates (sometimes facet-inducing) valid inequalities from generic valid inequalities and we present several facet-inducing families arising from this procedure. Finally, we present another family of facet-inducing inequalities which is not obtained from the prior lifting procedure.

AVD-edge coloring on powers of paths

In a proper edge coloring of a graph, the set of colors of a vertex v is the set of colors of the edges incident to v, C(v). If C(u)≠C(v) for every adjacent vertices u and v, this edge coloring is an AVD-edge coloring. The least number of colors for which G has an AVD-edge coloring is called the AVD-chromatic index, χa′(G). We determine the AVD-chromatic index for the powers of paths.

Webサイトの配色に基づく視認性に関する分析 : 白色背景における文字色の自己組織化マップによる検討(一般講演 B1)

Webサイトの配色に基づく視認性に関する分析 : 白色背景における文字色の自己組織化マップによる検討(一般講演 B1)

Webサイトの配色に基づく視認性に関する分析 : 自己組織化マップによる個人差の検討(一般講演1B)

Webサイトの配色に基づく視認性に関する分析 : 自己組織化マップによる個人差の検討(一般講演1B)

Locally identifying coloring of graphs with few P4s

A lid-coloring (locally identifying coloring) of a graph is a proper coloring such that, for any edge uv, if u and v have distinct closed neighborhoods, then the set of colors used on vertices of the closed neighborhoods of u and v are distinct. The lid-chromatic number is the minimum number of colors used in a lid-coloring. In this paper we prove a relation between lid-coloring and a variation, called strong lid-coloring. With this, we obtain linear time algorithms to calculate the lid-chromatic number for some classes of graphs with few P4's, such as cographs, P4-sparse graphs and (q,q−4)-graphs. We also prove that the lid-chromatic number is O(n1−ε)-inapproximable in polynomial time for every ε>0, unless P=NP.

Upper bounds for adjacent vertex-distinguishing edge coloring

An adjacent vertex-distinguishing edge coloring of a graph is a proper edge coloring such that no pair of adjacent vertices meets the same set of colors. The adjacent vertex-distinguishing edge chromatic number is the minimum number of colors required for an adjacent vertex-distinguishing edge coloring, denoted as $$\chi '_{as}(G)$$ . In this paper, we prove that for a connected graph G with maximum degree $$\Delta \ge 3$$ , $$\chi '_{as}(G)\le 3\Delta -1$$ , which proves the previous upper bound. We also prove that for a graph G with maximum degree $$\Delta \ge 458$$ and minimum degree $$\delta \ge 8\sqrt{\Delta ln \Delta }$$ , $$\chi '_{as}(G)\le \Delta +1+5\sqrt{\Delta ln \Delta }$$ .

Monochromatic tree covers and Ramsey numbers for set-coloured graphs

We consider a generalisation of the classical Ramsey theory setting to a setting where each of the edges of the underlying host graph is coloured with a set of colours (instead of just one colour). We give bounds for monochromatic tree covers in this setting, both for an underlying complete graph, and an underlying complete bipartite graph. We also discuss a generalisation of Ramsey numbers to our setting and propose some other new directions.Our results for tree covers in complete graphs imply that a stronger version of Ryser’s conjecture holds for k-intersecting r-partite r-uniform hypergraphs: they have a transversal of size at most r−k. (Similar results have been obtained by Király et al., see below.) However, we also show that the bound r−k is not best possible in general.

Random subgraphs of properly edge-coloured complete graphs and long rainbow cycles

A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. In 1980 Hahn conjectured that every properly edge-coloured complete graph K n has a rainbow Hamiltonian path. Although this conjecture turned out to be false, it was widely believed that such a colouring always contains a rainbow cycle of length almost n. In this paper, improving on several earlier results, we confirm this by proving that every properly edge-coloured K n has a rainbow cycle of length n − O(n 3/4). One of the main ingredients of our proof, which is of independent interest, shows that a random subgraph of a properly edge-coloured K n formed by the edges of a random set of colours has a similar edge distribution as a truly random graph with the same edge density. In particular, it has very good expansion properties.

Upper bounds on adjacent vertex distinguishing total chromatic number of graphs

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that for any pair of adjacent vertices, the set of colors appearing on the vertex and incident edges are different. The minimum number of colors required for an adjacent vertex distinguishing total coloring of G is denoted by χa′′(G). Let G be a graph, and χ(G) and χ′(G) be the chromatic number and edge chromatic number of G, respectively. In this paper we show that χa′′(G)≤χ(G)+χ′(G)−1 for any graph G with χ(G)≥6, and χa′′(G)≤χ(G)+Δ(G) for any graph G. Our results improve the only known upper bound 2Δ obtained by Huang et al. (2012). As a direct consequence, we have χa′′(G)≤Δ(G)+3 if χ(G)=3 and thus it implies the known results on graphs with maximum degree 3, K4-minor-free graphs, outerplanar graphs, graphs with maximum average degree less than 3, planar graphs with girth at least 4 and 2-degenerate graphs.

Effect of different types of disinfection solution and aging on the hardness and colour stability of maxillofacial silicone elastomers.

Understanding the effect of aging and different disinfecting agents on the physical properties of pigmented maxillofacial silicones may help eliminate the current uncertainty as to the best follow-up suggestions for the patients treated with silicone prostheses. One hundred fifty specimens (14 × 2 mm) were evaluated for colour and 75 specimens (30 × 10 mm) for hardness (total, 225 specimens). Five specimens were used for hardness testing in each disinfecting solution while 10 silicone specimens were used for colour evaluation. The samples were separated into 5 groups and the initial hardness and colour evaluations were performed and placed in disinfectant solution (neutral soap, effervescent tablet, 0.2% chlorhexidine, 4% chlorhexidine, sodium hypochlorite). A second set of colour and hardness measurements was taken after 48 hours of disinfection and 1,008 hours of artificial aging in a QUV-accelerated weathering tester. Two-way and 1-way analysis of variance with Tukey tests and paired t-test were used for statistical analysis (α = 0.05). Before artificial aging, the hardness value of the red pigment group was found to be significantly lower than that of the brown pigment group. After aging, the lowest Shore A value was seen in the neutral soap group, while the highest was seen in the effervescent tablet. Based on the results of this study, chlorohexidine 0.2% was found to be most suitable agent for disinfection of the prostheses. Washing with neutral soap caused loss of pigment from the surface of the silicones. Sodium hypochlorite was found to have a colour-fading effect on silicone specimens.

No evidence of task co-representation in a joint Stroop task.

People working together on a task must often represent the goals and salient items of their partner. The aim of the present study was to study the influence of joint task representations in an interference task in which the congruency relies on semantic identity. If task representations are shared between partners in a joint Stroop task (co-representation account), we hypothesized that items in the response set of one partner might influence performance of the other. In Experiment 1, pairs of participants sat side by side. Each participant was instructed to press one of two buttons to indicate which of two colors assigned to them was present, ignoring the text and responding only to the pixel color. There were three types of incongruent distractor words: names of colors from their own response set, names of colors from the other partner's response set, and neutral words for colors not used as font colors. The results of Experiment 1 showed that when people were doing this task together, distractor words from the partner's response set interfered more than neutral words and just as much as the words from their own response color set. However, in three follow-up experiments (Experiments 2a, 2b, and 2c), we found an elevated interference for the other response-set words even though no co-actor was present. The overall pattern of results across our study suggests that an alternative response set, regardless of whether it belonged to a co-actor or to a non-social no-go condition, evoked equal amounts of interference comparable to those of the own response set. Our findings are in line with a theory of common coding, in which all events-irrespective of their social nature-are represented and can influence behavior.

Coloring graphs of various maximum degree from random lists

AbstractLet G = G(n) be a graph on n vertices with maximum degree Δ =Δ (n). Assign to each vertex v of G a list L(v) of colors by choosing each list independently and uniformly at random from all k‐subsets of a color set of size . Such a list assignment is called a random ‐list assignment. In this paper, we are interested in determining the asymptotic probability (as n →∞) of the existence of a proper coloring φ of G, such that for every vertex v of G, a so‐called L‐coloring. We give various lower bounds on σ, in terms of n, k, and Δ, which ensures that with probability tending to 1 as n →∞ there is an L‐coloring of G. In particular, we show, for all fixed k and growing n, that if and , then the probability that G has an L‐coloring tends to 1 as . If and , then the same conclusion holds provided that . We also give related results for other bounds on Δ, when k is constant or a strictly increasing function of n.

A Vizing-like theorem for union vertex-distinguishing edge coloring

We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the problem of finding a coloring with the minimum number of colors where every vertex receives a distinct label. Finding such a coloring generalizes several other well-known problems of vertex-distinguishing colorings in graphs.We show that for any graph (without connected component reduced to an edge or a single vertex), the minimum number of colors for which such a coloring exists can only take 3 possible values depending on the order of the graph. Moreover, we provide the exact value for paths, cycles and complete binary trees.

Minimal sufficient sets of colors and minimum number of colors

In this paper, we first investigate the minimal sufficient sets of colors for [Formula: see text] and [Formula: see text]. For odd prime [Formula: see text] and any [Formula: see text]-colorable link [Formula: see text] with [Formula: see text], we give alternative proofs of [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text]. We also elaborate on equivalence classes of sets of distinct colors (on a given modulus) and prove that there are two such classes of five colors modulo [Formula: see text], and only one such class of five colors modulo 13.

Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images

A fuzzy logic-based color histogram analysis technique is presented for discriminating benign skin lesions from malignant melanomas in dermoscopy images. The approach extends previous research for utilizing a fuzzy set for skin lesion color for a specified class of skin lesions, using alpha-cut and support set cardinality for quantifying a fuzzy ratio skin lesion color feature. Skin lesion discrimination results are reported for the fuzzy clustering ratio over different regions of the lesion over a data set of 517 dermoscopy images consisting of 175 invasive melanomas and 342 benign lesions. Experimental results show that the fuzzy clustering ratio applied over an eight-connected neighborhood on the outer 25% of the skin lesion with an alpha-cut of 0.08 can recognize 92.6% of melanomas with approximately 13.5% false positive lesions. These results show the critical importance of colors in the lesion periphery. Our fuzzy logic-based description of lesion colors offers relevance to clinical descriptions of malignant melanoma.