An algorithm for matching the weighted sub-graphs based on gradient flows is proposed in this paper. First, the smaller and larger graphs for matching are represented by means of their weighted ...adjacency matrices. Then, an objective function is introduced to measure the differences between two weighted adjacency matrices. Because the permutation matrix for graph matching is usually relaxed to an orthogonal matrix with non-negative elements, an optimization-based approach is adopted to “navigate” the solution toward an appropriate permutation matrix. To accomplish this goal, two gradient flows in the space of orthogonal matrices are defined in such a way that they minimize the objective functions. One minimizes the objective function in the space of orthogonal matrices, and the other minimizes the distance of an orthogonal matrix from the set of permutations. In addition, two cost functions are introduced to force satisfaction (approximately) of the constraint that a translation matrix must have integer entries of different values. The experimental results show that the proposed sub-graph matching is feasible.
Classic And Network Epidemiological Models Hernandez Ramirez, Juan David; Cortes Garcia, Christian Camilo
Scientia et technica,
2021, Letnik:
26, Številka:
4
Journal Article
Odprti dostop
In this work is analyzed the environment and the dynamics of the states for a disease within a constant and closed population, represented by a system of ordinary differential equations, in which the ...individual, besides having the same opportunity to get in contact with any other, can recover or not, acquiring or not immunity through time. With these defined guidelines, the conditions when the disease spreads over time between such models are compared with those represented by a network. As the network can be represented by an adjacency matrix, the dynamics in the epidemiological states depends, besides the conditions in their parameters of the classic models, on largest eigenvalueof such matrix.
En este trabajo se analiza el entorno y la dinámica de los estados para una enfermedad dentro de una población constante y cerrada, representado por un sistema de ecuaciones diferenciales ordinarias, en que el individuo, además de tener la misma oportunidad de entrar en contacto con cualquier otro, se pueda o no recuperar, adquiriendo o no inmunidad a través del tiempo. Con estos lineamientos definidos, se compara las condiciones cuando la enfermedad se propaga a lo largo del tiempo entre dichos modelos con los representados por una red. Como la red puede ser representado por una matriz de adyacencia, la dinámica en los estados epidemiológicos depende, además de las condiciones en sus parámetros de los modelos clásicos, del valor propio más grande de dicha matriz.
In a graph G, if di is the degree of a vertex vi, the geometric-arithmetic matrix GA(G) is a square matrix whose Formula: see text-th entry is Formula: see text whenever vertices i and j are adjacent ...and 0 otherwise. The set of all eigenvalues of GA(G) including multiplicities is known as the geometric-arithmetic spectrum of G. The difference between the largest and the smallest geometric-arithmetic eigenvalue is called the geometric-arithmetic spread Formula: see text of G. In this article, we investigate some properties of Formula: see text We obtain lower and upper bounds of Formula: see text and show the existence of graphs for which equality holds. Further, Formula: see text is computed for various graph operations.
For a simple finite graph G, the generalized adjacency matrix is defined as Aα(G)=αD(G)+(1−α)A(G),α∈0,1, where A(G) and D(G) are respectively the adjacency matrix and diagonal matrix of the vertex ...degrees. The Aα-spread of a graph G is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the Aα(G). In this paper, we answer the question posed in (Lin, Z.; Miao, L.; Guo, S. Bounds on the Aα-spread of a graph. Electron. J. Linear Algebra 2020, 36, 214–227). Furthermore, we show that the path graph, Pn, has the smallest S(Aα) among all trees of order n. We establish a relationship between S(Aα) and S(A). We obtain several bounds for S(Aα).
For α∈0,1, let Aα(Gσ)=αD(G)+(1−α)A(Gσ), where G is a simple undirected graph, D(G) is the diagonal matrix of its vertex degrees and A(Gσ) is the adjacency matrix of the signed graph Gσ whose ...underlying graph is G. In this paper, basic properties of Aα(Gσ) are obtained, its positive semidefiniteness is studied and some bounds on its eigenvalues are derived—in particular, lower and upper bounds on its largest eigenvalue are obtained.
We present some applications of a new matrix approach for studying the properties of the lift Γα of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the ...involved group is Abelian, we completely determine the spectrum of Γα. As some examples of our technique, we study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman–Singleton graph.
An innovative automatic modulation classification using graph-based generalized second-order cyclic spectrum analysis in the background of α-stable noise is presented in this paper. In our proposed ...method, the three-dimensional generalized second-order cyclic spectrum of the modulated signal is first constructed from the nonlinear Hilbert transform. According to the generalized second-order cyclic spectrum, the signal is mapped onto a set of direct weighted rings in the graph domain. Then, the graph features of the modulated signal are extracted from the lower-upper decomposition of the corresponding adjacency matrices. The Hamming distance is employed to measure the distinctions between the feature parameters derived from the training and test data, and the modulation scheme can be identified thereby. Monte Carlo simulation results demonstrate that the proposed approach can achieve better classification accuracy than other existing methods for the α-stable noise scenario.
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