Literatura científica selecionada sobre o tema "Edge-colored graph theory"

RNA tertiary structure is crucial to its many non-coding molecular functions. RNA architecture is shaped by its secondary structure composed of stems, stacked canonical base pairs, enclosing loops. While stems are precisely captured by free-energy models, loops composed of non-canonical base pairs are not. Nor are distant interactions linking together those secondary structure elements (SSEs). Databases of conserved 3D geometries (a.k.a. modules) not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local elements, loops. Representing the RNA structure as a graph has recently allowed to expend this work to pairs of SSEs, uncovering a hierarchical organization of these 3D modules, at great computational cost. Systematically capturing recurrent patterns on a large scale is a main challenge in the study of RNA structures. In this paper, we present an efficient algorithm to compute maximal isomorphisms in edge colored graphs. We extend this algorithm to a framework well suited to identify RNA modules, and fast enough to considerably generalize previous approaches. To exhibit the versatility of our framework, we first reproduce results identifying all common modules spanning more than 2 SSEs, in a few hours instead of weeks. The efficiency of our new algorithm is demonstrated by computing the maximal modules between any pair of entire RNA in the non-redundant corpus of known RNA 3D structures. We observe that the biggest modules our method uncovers compose large shared sub-structure spanning hundreds of nucleotides and base pairs between the ribosomes of Thermus thermophilus, Escherichia Coli, and Pseudomonas aeruginosa.

At the beginning of each semester, subjects scheduling is always carried out by the curriculum representatives and academic staff. There were several problems that must be avoided in subjects scheduling, these problems were the schedule of teachers who teach one subject at the same time are scheduled in different classes, teachers who teach more than one subject are scheduled in the same class at the same time, teachers who are lack of scheduled for teaching. In the subject of graph theory, there is a concept of graph coloring, one of which is vertex coloring. In vertex coloring, there is a Welch-Powell Algorithm application which produces a color for each vertex. In subject scheduling, it is assumed that the vertex is the subject and the teacher, while the edge is the class. In vertex coloring, graph vertices are colored so that there's no two neighboring vertices have the same color. The aim of this research was to arrange a lesson schedule so that problems do not occur such as clashes between teachers, subjects, and teaching hours. The method used in arranging this lesson schedule used the Welch-Powell Algorithm. The results obtained were using the Welch-Powell Algorithm to produce a lesson schedule every day where if there are two classes that have the same subject, they can meet the same day requirements but come in different hours and get a lesson schedule that has no clash between teachers, subjects, and teaching hours.

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.