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In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results. [ABSTRACT FROM AUTHOR]

This study is focused on analyzing the L 1 -stochastic internal stability and the design of an L 1 -gain controller for two-dimensional (2D) continuous positive Markov jumping systems (PMJSs) with constraints on the inputs and states. An algorithm is developed to explicitly determine the state feedback control law with the optional L 1 -gain performance. First, by constructing a co-positive stochastic Lyapunov function for the positive system and establishing the equation for the Markov states' mathematical expectation, several sufficient and necessary conditions for L 1 -stochastic internal stability are derived. This analysis indicates that 2D PMJSs with directional delays are influenced by sizes of the system matrices and magnitude of delays, and transition matrix. Second, a method for calculating the L 1 -gain is formulated utilizing linear programming (LP), thus, an L 1 -gain controller is designed to guarantee that the closed-loop system is positive and L 1 -stochastically internally stable, while achieving optimal L 1 -gain performance. Two numerical and practical examples are considered, and the influence of delays and transition probability matrices on the L 1 -gain is specified to validate the preceding theoretical findings. [ABSTRACT FROM AUTHOR]

• The syntactic structure of natural language is import for the model to understand the sentences comprehensively. • The relative syntactic distance can be used to describe the degree of dependency between adjacent words in a sentence. • A relative syntactic distance-based language model RSD-LSTM is proposed to integrate syntactic information into LSTM. • Low-level and high-level syntactic structure features can be fused to generate hidden representations. • The experimental results of RSD-LSTM outperform existing state-of-the-art models on different tasks. In natural language, the relationship among the constituents of a sentence is usually tree-like: words, phrases, and clauses constitute a sentence hierarchically, and the dependency between different constituents induces the syntactic structure. Such a complex tree-like structure is vital for understanding natural languages. However, recurrent neural networks (RNNs) model languages sequentially and fail to encode a hierarchical syntactic dependency comprehensively, therefore causing the networks to underperform on comprehension-based tasks. In this paper, we propose a novel neural language model, called relative syntactic distance LSTM (RSD-LSTM), to capture the syntactic structure dependency dynamically. RSD-LSTM employs a convolutional neural network to compute the relative syntactic distance between sentences to represent the degree of dependency between words and modifies the gating mechanism of LSTM through the relative syntactic distance. Furthermore, we add a direct connection between hidden states to fuse high-level and low-level syntactic features. We conducted extensive experiments on language modeling. The results suggest that RSD-LSTM achieves improvements of 1.82 and 2.03 in perplexity compared with current top methods on the Penn Treebank and WikiText-2 datasets, respectively. Moreover, we conducted experiments on a machine translation application task. Experimental results of this task also show significant improvements of RSD-LSTM compared with baseline models. [ABSTRACT FROM AUTHOR]