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Let Gσ be an oriented graph of a simple undirected graph G with an orientation σ, which assigns to each edge of G a direction so that the resultant graph Gσ becomes a directed graph. The skew energy of Gσ is defined as the sum of the absolute values of all eigenvalues of the skew-adjacency matrix of Gσ. Denote by Uσ (2k) the set of all oriented unicyclic graphs on 2k vertices with a perfect matching which contain no cycle of length l with l ≡ 2(mod 4). In this paper, we characterize the oriented graphs of Uσ (2k) with the minimal skew energy for k ≥ 4. [ABSTRACT FROM AUTHOR]

The global stress distribution and state parameter analysis of the building's main structure is an urgent problem to be solved in the online state assessment technology of building structure health. In this paper, a stress curve clustering algorithm of fiber Bragg grating stress sensor based on density clustering algorithm is proposed. To solve the problem of large dimension and sparse sample space of sensor stress curve, the distance between samples is measured based on improved cosine similarity. Aiming at the problem of low efficiency and poor effect of traditional clustering algorithm, density clustering algorithm based on mutual nearest neighbor is used to cluster. Finally, the classification of the daily stress load characteristics of the sensor is realized, which provides a basis for constructing the mathematical analysis model of building health. The experimental results show that the stress curve clustering method proposed in this paper is better than the latest clustering algorithms such as HDBSCAN, CBKM, K-mean++,FINCH and NPIR, and is suitable for the feature classification of stress curves of fiber Bragg grating sensors. [ABSTRACT FROM AUTHOR]

Meshfree methods such as the Reproducing Kernel Particle Method and the Element Free Galerkin method have proven to be excellent choices for problems involving complex geometry, evolving topology, and large deformation, owing to their ability to model the problem domain without the constraints imposed on the Finite Element Method (FEM) meshes. However, meshfree methods have an added computational cost over FEM that come from at least two sources: increased cost of shape function evaluation and the determination of adjacency or connectivity. The focus of this paper is to formally address the types of adjacency information that arises in various uses of meshfree methods; a discussion of available techniques for computing the various adjacency graphs; propose a new search algorithm and data structure; and finally compare the memory and run time performance of the methods. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph and $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the conjecture of Guan et al. (J. Inequal. Appl. 2014:242, 2014) for the case of bicyclic graphs. .. [ABSTRACT FROM AUTHOR]

In this paper, we consider the flocking problem for a discrete Cucker-Smale model with packet loss. For describing the packet loss process, a more general condition including four different cases is adopted in this paper. Then a sufficient condition for achieving flocking under this condition is obtained. [ABSTRACT FROM AUTHOR]

Several systems can be represented as multiplex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical quantities aiming at capturing the added level of complexity of those systems is required. Various steps in this direction have been made. In the simplest case, dependencies between layers are measured via correlation-based metrics, a procedure that we show to be equivalent to the use of completely homogeneous benchmarks specifying only global constraints. However, this approach does not take into account the heterogeneity in the degree and strength distributions, which is instead a fundamental feature of real-world multiplexes. In this work, we compare the observed dependencies between layers with the expected values obtained from maximum-entropy reference models that appropriately control for the observed heterogeneity in the degree and strength distributions. This information-theoretic approach results in the introduction of novel and improved multiplexity measures that we test on different datasets, i.e. the International Trade Network and the European Airport Network. Our findings confirm that the use of homogeneous benchmarks can lead to misleading results, and highlight the important role played by the distribution of hubs across layers. [ABSTRACT FROM AUTHOR]