Set Of Colors Research Articles

Visibility of color symbology in head-up and head-mounted displays in daylight environments

Color-coded symbology has the potential to enhance the performance of people using head-up and head-mounted displays, as well as head-worn, optical see-through, augmented-reality displays. The distinguishing feature of these displays is the optical combiner that presents symbology overlaid upon the forward natural scene. The presence of high-ambient daylight can desaturate the symbol colors, making them difficult to identify. This is especially true for blue symbols that become faint and colorless in even moderate daylight. We defined a set of colors for testing based on color coding conventions, color symbology research, and results from our previous testing. Included in this set was blue-prime, a color that lies between blue and cyan. We then conducted an experiment to test the visibility of color symbols, the naming of symbol colors, and the legibility of color text mixed with daylight. Results were statistically analyzed and modeled using color-difference formulae. Additional experiments were conducted to test the effects of increasing the luminance of blue symbols and shifting primary colors to increase the luminance. Specific attention was given to the symbol color blue, where the alternative color blue-prime was shown to always outperform the color blue while retaining the color name blue.

Rage – beyond the Point of Boiling Over

Rage – beyond the Point of Boiling Over

The edge coloring game on trees with the number of colors greater than the game chromatic index

Let $$X\in \{A,B\}$$ and $$Y\in \{A,B,-\}$$ , where A, B and − denote (player) Alice, (player) Bob and none of the players, respectively. In the k-[X, Y]-edge-coloring game, Alice and Bob alternately choose a color from a given color set with k colors to color an uncolored edge of a graph G such that no adjacent edges receive the same color. Player X begins and Player Y has the right to skip any number of turns. Alice wins the game if all the edges of G are finally colored; otherwise, Bob wins. The [X, Y]-game chromatic index of an uncolored graph G, denoted by $$\chi '_{[X,Y]}(G)$$ , is the least k such that Alice has a winning strategy for the game. We prove that, for any [X, Y], Alice has a winning strategy for the k-[X, Y]-edge-coloring game on any tree T when $$k>\chi '_{[X,Y]}(T)$$ . Moreover, using some parts of the proofs of the above results, we show that there is a tree T satisfying $$\chi '_{[A,-]}(T)<\chi '_{[B,-]}(T)$$ and $$\chi '_{[A,-]}(T-e)<\chi '_{[B,-]}(T-e)$$ for some edge e of T. This solves an open problem proposed by Andres et al. (Discrete Appl Math 159:1660–1665, 2011).

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9

Let k be a positive integer. An adjacent vertex distinguishing (for short, AVD) total-k-coloring of a graph G is a proper total-k-coloring of G such that any two adjacent vertices have different color sets, where the color set of a vertex v contains the color of v and the colors of its incident edges. It was conjectured that any graph with maximum degree Δ has an AVD total-(Δ+3)-coloring. The conjecture was confirmed for any graph with maximum degree at most 4 and any planar graph with maximum degree at least 10. In this paper, we verify the conjecture for all planar graphs with maximum degree at least 9. Moreover, we prove that any planar graph with maximum degree at least 10 has an AVD total-(Δ+2)-coloring and the bound Δ+2 is sharp.

Two problems on matchings in set families – In the footsteps of Erdős and Kleitman

The families F1,…,Fs⊂2[n] are called q-dependent if there are no pairwise disjoint F1∈F1,…,Fs∈Fs satisfying |F1∪…∪Fs|≤q. We determine max⁡|F1|+…+|Fs| for all values n≥q,s≥2. The result provides a far-reaching generalization of an important classical result of Kleitman.The well-known Erdős Matching Conjecture suggests the largest size of a family F⊂([n]k) with no s pairwise disjoint sets. After more than 50 years its full solution is still not in sight. In the present paper we provide a Hilton–Milner-type stability theorem for the Erdős Matching Conjecture in a relatively wide range, in particular, for n≥(2+o(1))sk with o(1) depending on s only. This is a considerable improvement of a classical result due to Bollobás, Daykin and Erdős.We apply our results to advance in the following anti-Ramsey-type problem, proposed by Özkahya and Young. Let ar(n,k,s) be the minimum number x of colors such that in any coloring of the k-element subsets of [n] with x (non-empty) colors there is a rainbow matching of size s, that is, s sets of different colors that are pairwise disjoint. We prove a stability result for the problem, which allows to determine ar(n,k,s) for all k≥3 and n≥sk+(s−1)(k−1). Some other consequences of our results are presented as well.

Local Properties in Colored Graphs, Distinct Distances, and Difference Sets

We study Extremal Combinatorics problems where local properties are used to derive global properties. That is, we consider a given configuration where every small piece of the configuration satisfies some restriction, and use this local property to derive global properties of the entire configuration. We study one such Ramsey problem of Erdős and Shelah, where the configurations are complete graphs with colored edges and every small induced subgraph contains many distinct colors. Our bounds for this Ramsey problem show that the known probabilistic construction is tight in various cases. We study one Discrete Geometry variant, also by Erdős, where we have a set of points in the plane such that every small subset spans many distinct distances. Finally, we consider an Additive Combinatorics problem, where we are given sets of real numbers such that every small subset has a large difference set. We derive new bounds for all of the above problems. Our proof technique is based on introducing a variant of additive energy, which is based on edge colors in graphs.

Neighbor-locating colorings in graphs

A k-coloring of a graph G is a k-partition Π={S1,…,Sk} of V(G) into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color Si, the set of colors of the neighborhood of u is different from the set of colors of the neighborhood of v. The neighbor-locating chromatic numberχNL(G) is the minimum cardinality of a neighbor-locating coloring of G.We establish some tight bounds for the neighbor-locating chromatic number of a graph, in terms of its order, maximum degree and independence number. We determine all connected graphs of order n≥5 with neighbor-locating chromatic number n or n−1. We examine the neighbor-locating chromatic number for two graph operations: join and disjoint union, and also for two graph families: split graphs and Mycielski graphs.

Detecting list-colored graph motifs in biological networks using branch-and-bound strategy

In this work, we study the list-colored graph motif problem, which was introduced to detect functional motifs in biological networks. Given a multi-set M of colors as the query motif and a list-colored graph G where each vertex in G is associated with a set of colors, the aim of this problem is to find a sub-graph of G whose vertex set is colored exactly as motif M. To solve this problem, we present a heuristic method to efficiently and accurately detect list-colored graph motifs in biological networks using branch-and-bound strategy. We transform the detection of list-colored graph motif to the search of connected induced sub-graphs in list-colored graph, where the vertices in the sub-graph are assigned to distinctive colors of query motif. This transformation enables our method to accurately discover the occurrences of query motif without enumerating and verifying all sub-graphs. Furthermore, a new initial vertex selection strategy based on the colors of vertices is proposed to accurately determine the search scope of motifs. Experiments conducted on metabolic networks and protein-interaction networks demonstrate that our method can achieve better performance in accuracy and efficiency in comparison to other existing methods.

A broken cycle theorem for the restrained chromatic function

A restraint r role=presentation> r r r on a graph G role=presentation> G G G is a function that assigns each vertex of the graph a finite subset of N role=presentation> ℕ N \mathbb{N} . For each vertex v role=presentation> v v v of the graph, r ( v ) role=presentation> r ( v ) r ( v ) r(v) is called the set of colors forbidden at v role=presentation> v v v . A proper coloring of G role=presentation> G G G is said to be permitted by a given restraint r role=presentation> r r r if each vertex v role=presentation> v v v of the graph receives a color that is not from its set of forbidden colors r ( v ) role=presentation> r ( v ) r ( v ) r(v) . The restrained chromatic function, denoted by π r ( G , x ) role=presentation> π r ( G , x ) π r ( G , x ) \pi_r(G,x) , is a function whose evaluations at integer x role=presentation> x x x values count the number of proper x role=presentation> x x x -colorings of the graph G role=presentation> G G G permitted by the restraint r role=presentation> r r r and this function is known to be a polynomial function of x role=presentation> x x x for large enough x role=presentation> x x x . The restrained chromatic function π r ( G , x ) role=presentation> π r ( G , x ) π r ( G , x ) \pi_r(G,x) is a generalization of the well-known chromatic polynomial π ( G , x ) role=presentation> π ( G , x ) π ( G , x ) \pi(G,x) , as π r ( G , x ) = π ( G , x ) role=presentation> π r ( G , x ) = π ( G , x ) π r ( G , x ) = π ( G , x ) \pi_r(G,x)=\pi(G,x) if r ( v ) = ∅ role=presentation> r ( v ) = ∅ r ( v ) = ∅ r(v)=\emptyset for each vertex v role=presentation> v v v of the graph. Whitney's celebrated broken cycle theorem gives a combinatorial interpretation of the coefficients of the chromatic polynomial via certain subgraphs (the so-called broken cycles). We provide an extension of this result by finding combinatorial interpretations of the coefficients of the restrained chromatic function.

Quandle coloring quivers

We consider a quiver structure on the set of quandle colorings of an oriented knot or link diagram. This structure contains a wealth of knot and link invariants and provides a categorification of the quandle counting invariant in the most literal sense, i.e. giving the set of quandle colorings the structure of a small category which is unchanged by Reidemeister moves. We derive some new enhancements of the counting invariant from this quiver structure and show that the enhancements are proper with explicit examples.

Pattern Colored Hamilton Cycles in Random Graphs

We consider the existence of patterned Hamilton cycles in randomly colored random graphs. Given a string $\Pi$ over a set of colors $\{1,2,\ldots,r\}$, we say that a Hamilton cycle is $\Pi$-colored if the pattern repeats at intervals of length $|\Pi|$ as we go around the cycle. We prove a hitting time result for the existence of such a cycle. We also prove a hitting time result for the related notion of $\Pi$-connected.

Multi Features Based Approach for White Blood Cells Segmentation and Classification in Peripheral Blood and Bone Marrow Images

In this paper, we propose a complete automated framework for white blood cells differential count in peripheral blood and bone marrow images, in order to reduce the analysis time and increase the accuracy of several blood disorders diagnosis. A new colour transformation is first proposed to highlight the white blood cells regions. Then, a marker controlled watershed algorithm is used to segment the region of interest. The nucleus and cytoplasm are subsequently separated. In the identification step, a set of colour, texture and morphological features are extracted from both nucleus and cytoplasm regions. Next, the performances of a random forest classifier on a set of microscopic images are compared and evaluated. The obtained results reveal high recognition accuracies for both segmentation and classification stage.

Classification of Marble Using Image Processing

Classification of marble image according to usage purpose and quality is an important procedure for export. Discrimination between marble varieties is a difficult task during selection, since it requires trainings and experience. Therefore, the development of automatic prediction model based on image processing is a potential application area to support experts across the world. In this study an attempt has been made to develop marble variety classification model by comparing color, texture and ensemble of color and texture. In view of this, a digital image processing technique based on combined texture and color features have been explored good classification performance to classify varieties of marble image. On the average 60 images were taken from each of the three marble varieties (Grade A, Grade B, Grade C). The total number of images taken was 180. For the classification model we applied image preprocessing techniques; image acquisition, image conversion, noise removal, image enhancement, edge detection and image binarization. For texture extraction gray level co-occurrence matrix, for color extraction color histogram was applied. For classification five textures and six color features were extracted from each marble image. To build the classification models for prediction of marble varieties, K-Nearest Neighbors (KNN), Artificial Neural Network (ANN) are investigated. Based on experimental results, ANN outperforms KNN. Quantitatively, an average accuracy of 83.3% and 93.7% is achieved KNN and ANN respectively for Grade A, Grade B, Grade C varieties with the combined feature sets of color and texture. This shows an encouraging result to design an applicable marble classification model. Marble fractured and vines of the images affect greatly the performance of the classifier and hence they are the future research direction that needs an investigation of generic noise removal and feature extraction techniques.

2-distance colorings of integer distance graphs

A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1,. .. , k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ 2 (G) of G is then the mallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d 1 ,. .. , d k }, the integer distance graph G = G(D) is the infinite graph defined by V (G) = Z and uv ∈ E(G) if and only if |v − u| ∈ D. We study the 2-distance chromatic number of integer distance graphs for several types of sets D. In each case, we provide exact values or upper bounds on this parameter and characterize those graphs G(D) with χ 2 (G(D)) = ∆(G(D)) + 1.

RGB Color Cluster and Graph Coloring Algorithm for Partial Color Blind Correction

Partial color blindness is an anomaly occurring to 5-8% of the world's population. Color correction using re-coloring algorithm usually can be used to help partial color blindness patient. One of the existing re-coloring techniques is to use the RGB color cluster technique and combine it by utilizing the brute force algorithm to perform color tracing for correcting the color. It has massive time and memory complexity. This research aims to create a correction technique for color blind people using RGB Color Cluster combined with Graph Coloring Algorithm. The first process is to get the RGB color cluster for color blind subject. After getting RGB color cluster from the subject then the image which want to be corrected is grouped based on RGB color cluster. The threshold of color grouping in image is done by utilizing the upper and lower bound values of the RGB color cluster. After the cluster is grouped, then we can represent neighbourhood between the colors by utilizing graph. The adjacent color group will be a neighbour. The next process is color re-coloring using graph coloring algorithm. In graph coloring algorithm, same color group is prohibited to become neighbour. In this research, graph coloring algorithm is used to prevent 2 colors that are look almost similar for become neighbours because it will cause the subject cannot distinguish it. Re-coloring is done by increasing and decreasing the color intensity of a set of colors. This technique succeeds in decreasing the complexity of the brute force algorithm from O(N4) to O(2N2) where the first N2 is the complexity of building the cluster group and the second N2 is the complexity of the re- coloring. In addition, the color of the object becomes more natural because Re-coloring is based on color group not pixel based.

Efficient palette-based decomposition and recoloring of images via RGBXY-space geometry

We introduce an extremely scalable and efficient yet simple palette-based image decomposition algorithm. Given an RGB image and set of palette colors, our algorithm decomposes the image into a set of additive mixing layers, each of which corresponds to a palette color applied with varying weight. Our approach is based on the geometry of images in RGBXY-space. This new geometric approach is orders of magnitude more efficient than previous work and requires no numerical optimization. We provide an implementation of the algorithm in 48 lines of Python code. We demonstrate a real-time layer decomposition tool in which users can interactively edit the palette to adjust the layers. After preprocessing, our algorithm can decompose 6 MP images into layers in 20 milliseconds.

Spiking Neural P Systems With Colored Spikes

Spiking neural P systems (SN P systems) are bio-inspired neural-like computing models, which are obtained by abstracting the way of biological neurons’ spiking and communication by means of spikes in central nervous systems. SN P systems performed well in describing and modeling behaviors that occur simultaneously, yet weak at modeling complex systems with the limits of using a single spike. In this paper, drawing on the idea from colored petri nets, SN P systems with colored spikes are proposed, where a finite set of colors is introduced to mark the spikes such that each spike is associated with a unique color. The updated spiking rule is applied by consuming and emitting a number of colored spikes (with the same or different colors). The computation power of the systems is investigated. Specifically, it is shown that SN P systems with colored spikes having three neurons are sufficient to compute Turing computable sets of numbers, and such system having two neurons is able to compute the family of recursive functions. These results improved the corresponding ones on the number of neurons needed to construct universal SN P systems recently appeared in [Neurocomputing, 2016, 193(12): 193–200]. To our best knowledge, this is the smallest number of neurons used to construct Turing universal SN P systems as number generator and function computing device by far.

Generating sets of Reidemeister moves of oriented singular links and quandles

We give a generating set of the generalized Reidemeister moves for oriented singular links. We then introduce an algebraic structure arising from the axiomatization of Reidemeister moves on oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of colorings of a singular knot by this new structure is an invariant of oriented singular knots and use it to distinguish some singular links.

Peculiarities of the Color Epithets Functioning in the Yakut Heroic Epic Olonkho Text

This article devoted to the semantics of color epithets in the text of the Yakut heroic epic olonkho analysis, as well as to the peculiarities of their functioning in the epic text. An epithet, as an artistic and visual mean, has been attracting the interest of linguists since ancient times. Theoretical and methodological basis of the research consists of the works of A.N. Veselovsky, A.A. Potebnya, V.M. Zhirmunsky, V.Ya. Propp, S.Y. Neklyudov, S.L. Neveleva, as well as of the works of the Yakut scientists I.V. Pukhov, G.U. Ergis, P.A. Sleptsov, N.I. Filippova, V.V. Illarionov and other epics of the Russian Federation peoples researchers. The study of color epithets semantics and their functioning in the text of the Yakut heroic epic olonkho has the purpose of expanding linguistic knowledge about national-cultural specifics of the Yakuts, saved in the epic of olonkho. The relevance of this work lies in the fact that the subject of research – color epithets – is a significant part of the epithet layer in the olonkho text, thus, study of them contributes to a systematic analysis of the vocabulary of the Yakut heroic epic olonkho as a whole. Color epithets are a set of color adjectives “үрүҥ/ маҥ(ҕ)ан” white, “хара” black, “кыhыл” red, “аалай” scarlet, “араҕас” yellow, “бороҥ” gray, “күөх” green/light blue/blue. The object of the research is based on the texts of academic editions of “Nyurgun Bootur the Swift” olonkho by K.G. Orosin, “Kyys Debiliye” olonkho by N.P. Burnashev, “Mighty Er Sogotokh” by V.O. Karataev and “Obstinate Kulun Kullustur” by I.G. Timofeev-Teploukhov. At the initial stage, in the paper used the methods of computer analysis for the selection of color epithets from the olonkho text array, further, to characterize the color epithets and the determined words – methods of dictionary definitions analysis, as well as methods of quantitative, descriptive, contextual and comparative analysis. As shown by the study, color epithets are used in the text of the Yakut olonkho in the description of literally all elements of the epic narrative: time, place, appearance, clothing of heroes, weapons of heroes, their emotions and magical properties. It is established that the informativeness of color epithets, inherent into the semantics of the word and revealed in the combinations of color epithets with determined words, is very large – they express the worldview of the Yakuts, their attitude to the world, their assessment of the environment.

Linear de-preferential urn models

Abstract In this paper we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the de-preferential urn scheme. We establish the almost-sure limit of the random configuration for any balanced replacement matrix R. In particular, we show that the limiting configuration is uniform on the set of colours if and only if R is a doubly stochastic matrix. We further establish the almost-sure limit of the vector of colour counts and prove central limit theorems for the random configuration as well as for the colour counts.