In this study, we have proposed an alternative approach for sentence modeling problem. The difficulty of the choice of answer, the semantically related questions and the lack of syntactic closeness of the answers give rise to the difficulty of selecting the answer. The deep learning field has recently achieved a pivotal success in semantic analysis, machine translation, and text summaries. The essence of this work, inspired by the human orthographic processing mechanism and using multiple convolution filters with pre-rendered 2-Dimension (2D) representations of sentences, input or output size is to learn the basic features of the language without concerns. For this reason, the semantic relations in the sentence structure are learned by the convolutional variational auto-encoders first, and then the question and answer spaces learned by the auto-encoders are linked with proposed intermediate models. We have benchmarked five variations of our proposed model, which is based on Variational Auto-Encoder with multiple latent spaces and able to achieve lower error rates than the baseline model, which is the base Convolutional LSTM.
The binding number of a graph G is defined to be the minimum of [Formula: see text] taken over all nonempty [Formula: see text] such that [Formula: see text]. Binding number, one indicator to better understand graph, is an important characteristic quantity of a graph. In this paper, the relationships between the binding number and some other graph vulnerability parameters, namely the toughness, integrity, rupture degree and scattering number, are established. Exact values for the binding numbers of wheel related graphs namely gear, helm, sunflower and friendship graph are obtained.
Let G(V (G), E(G)) be a simple connected graph and dG(u) be the degree of the vertex u. Topological indices are numerical parameters of a graph which are invariant under graph isomorphisms. Recently, people are studying various topological measures such as the arithmetic-geometric index and the edge version of arithmeticgeometric index of a graph G. Topological index based on the ratios of geometrical and arithmetical means of end vertex degrees of edges. In this paper, exact values for the arithmetic-geometric index and the edge version of arithmetic-geometric index of wheel related graphs namely gear, helm, sunflower and friendship graph are obtained.
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