Shift maps are not type-preserving

Codes from lattice and related graphs, and permutation decoding

For a connected graph G, there are several related graphs such as line graph L(G), subdivision graph S(G), vertex-semitotal graph R(G), edge-semitotal graph Q(G) and total graph T(G) [I. Gutman, B. Furtula, Ž. K. Vukićević and G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015), 5-16, W. Yan, B.-Y. Yang and Y. -N. Yeh, The behavior of Wiener indices and polynomials of graphs under five graph decorations, Appl. Math. Lett. 20 (2007), 290-295]. Let F be one of symbols S, R, Q or T. The F-sum G1+FG2 of two connected graphs G1 and G2 is a graph with vertex set (V (G1) U E(G1)) × V (G2) in which two vertices (u1, v1) and (u2, v2) of G1 +F G2 are adjacent if and only if [u1 = u2 _ V (G1) and u1v2 _ E(G2)] or [v1 = v2 and u1u2 2 E(F(G))] [M. Eliasi and B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157 (2009), 794-803]. In this paper, we investigate the harmonic index of edge-semitotal graphs, total graphs and F-sum of graphs, where F = Q or T.

Until now, the search carried out in devices using the conventional, textual form of search now seems tedious, considering the advances made in human software interaction since the emergence and development in touch-screen interfaces. In the past decade finger-touch or multi-touch interfaces have completely altered the way we interact with the devices. The input method implemented in search mechanisms, use the textual form of string input method that can be extended to graphical search which would enhance the interaction of human to software and also is efficient. This Paper proposes a new content based Image search Algorithm using Rough Set and Relational Graph.

Identifying synergistic drug combinations (SDCs) is a great challenge due to the combinatorial complexity and the fact that SDC is cell line specific. The existing computational methods either did not consider the cell line specificity of SDC, or did not perform well by building model for each cell line independently. In this paper, we present a novel encoder-decoder network named SDCNet for predicting cell line-specific SDCs. SDCNet learns common patterns across different cell lines as well as cell line-specific features in one model for drug combinations. This is realized by considering the SDC graphs of different cell lines as a relational graph, and constructing a relational graph convolutional network (R-GCN) as the encoder to learn and fuse the deep representations of drugs for different cell lines. An attention mechanism is devised to integrate the drug features from different layers of the R-GCN according to their relative importance so that representation learning is further enhanced. The common patterns are exploited through partial parameter sharing in cell line-specific decoders, which not only reconstruct the known SDCs but also predict new ones for each cell line. Experiments on various datasets demonstrate that SDCNet is superior to state-of-the-art methods and is also robust when generalized to new cell lines that are different from the training ones. Finally, the case study again confirms the effectiveness of our method in predicting novel reliable cell line-specific SDCs.

We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.

Permanent magnet linear synchronous motor (PMLSM) is a new type of motor with high positioning accuracy. This paper introduces the related design theory of PMLSM with the utilization of finite element software. we refer to the sample transient electromagnetic analysis, firstly. And then get the Thrust fluctuation map and compare to its winding back EMF curve and other related graphs. Through altering of the thickness, air gap length, junior core’s structure and size and other parameters, we finally conclude the designed requirements will be eventually fulfilled this optimization.

We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pure) mapping class groups are not co-Hopfian; these are first such examples of injective endomorphisms of mapping class groups that fail to be surjective. We then prove that, subject to some topological conditions on the domain surface, any continuous injective homomorphism between (arbitrary) big mapping class groups that sends Dehn twists to Dehn twists is induced by a subsurface embedding. Finally, we explore the extent to which, in stark contrast to the finite-type case, superinjective maps between curve graphs impose no topological restrictions on the underlying surfaces.

Capturing the complex time pattern of physical activity (PA) and sedentary behavior (SB) using accelerometry remains a challenge. Research from occupational health suggests exposure variation analysis (EVA) could provide a meaningful tool. This paper (1) explains the application of EVA to accelerometer data, (2) demonstrates how EVA thresholds and derivatives could be chosen and used to examine adherence to PA and SB guidelines, and (3) explores the validity of EVA outputs. EVA outputs are compared with accelerometer data from 4 individuals (Study 1a and 1b) and 3 occupational groups (Study 2): seated workstation office workers (n = 8), standing workstation office workers (n = 8), and teachers (n = 8). Line graphs and related EVA graphs highlight the use of EVA derivatives for examining compliance with guidelines. EVA derivatives of occupational groups confirm no difference in bouts of activity but clear differences as expected in extended bouts of SB and brief bursts of activity, thus providing evidence of construct validity. EVA offers a unique and comprehensive generic method that is able, for the first time, to capture the time pattern (both frequency and intensity) of PA and SB, which can be tailored for both occupational and public health research.

Capturing the pattern of activity: Exposure variation analysis of accelerometer data

The relative neighbourhood graph is a part of every 30°-triangulation

Efficacy of information extraction from bar, line, circular, bubble and radar graphs

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces. We also study the subgraph of the curve graph spanned by those elements which intersect a fixed separating curve on the surface. We show that this graph has infinite diameter and geometric rank 3, and thus is not hyperbolic.

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we study intersection numbers of curves contained in geodesics in the curve graph. Furthermore, we generalize a well-known result on intersection number growth of curves under iteration of Dehn twists and multitwists for all kinds of pure mapping classes.

Analyzing a large and unobtainable relationship graph using a streaming activity graph

Bioinformatics studies the acquisition, process, store, distribution, analysis, etc of biological information so as to understand the meanings of biological data by means of mathematics, computer science and biological techniques. Some researches on Bioinformatics, such as the properties of DNA and the Watson-Crick’s law, provide a probability of computing with DNA molecules. DNA computing is a new computational paradigm that executes parallel computation with DNA molecules based on the Watson-Crick’s law. The procedure of DNA computing can be divided into three stages: encoding information, computation (molecular operations) and extraction of solution. The stage of encoding information is the first and most important step, which directly affects the formation of optimal solution. The methods of encoding information can be divided into two classes: the methods of encoding information in graphs without weights and the methods of encoding information in graphs with weights. The previous researches, which belong to the first class, such as Adleman’s encoding method [1] for the directed Hamiltonian path problem, Lipton’s encoding method [2] for the SAT problem, and Ouyang’s encoding method [3] for the maximal clique problem, do not require the consideration of weight representation in DNA strands. However, there are many practical applications related to weights. Therefore, weight representation in DNA strand is an important issue toward expanding the capability of DNA computing to solve optimization problems. Narayanan et al [6] presented a method of encoding weights by the lengths of DNA strands. Shin et al [6] proposed a method of encoding weights by the number of hydrogen bonds in fixed-length DNA strand. Yamamoto et al [7] proposed a method of encoding weights by the concentrations of DNA strands. Lee et al [9] proposed a method of encoding weights by the melting temperatures of fixed-length DNA strands. Han et al [10, 11] proposed a method of encoding weights by means of the general line graph. They also gave a method of encoding weights [12] by means of the relative length graph and several improved DNA encoding methods [13–16] for the maximal weight clique problem, the traveling salesman problem, the minimum spanning tree problem and the 0/1 knapsack problem. In this chapter, I collect and classify the present methods of encoding information in DNA strands, which will benefit the further research on DNA computing.