The traditional minimum spanning tree clustering algorithm uses a simple Euclidean distance metric method to calculate the distance between two entities. For the processing of noise data, the similarity can’t be well...
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In this paper we obtain a numerically tractable test (sufficient condition) for the exponential stability of the unique positive equilibrium point of an ODE system. The result (Theorem 3.1) is based on Lyapunov theory...
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The two-dimensional threshold segmentation algorithm is time-consuming and cannot detect multiple paper defects. Considering these problems, a fast two-dimensional threshold method for on-line segmentation of multiple...
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Modeling Instruction (MI), an active-learning introductory physics curriculum, has been shown to improve student academic success. Peer-to-peer interactions play a salient role in the MI classroom. Their impact on stu...
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Traditional paper defect detection algorithms have the problems of low detection rate and poor anti-interference ability for low contrast paper defects such as cracks and folds. Considering these problems, an algorith...
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Self-expression learning methods often obtain a coefficient matrix to measure the similarity between pairs of samples. However, directly using the raw data to represent each sample under the self-expression framework ...
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In order to gain a high-performance analysis for electroencephalogram (EEG) signal, denoising has become a hot topic in this field. Due to the good performance of Volterra model, it has been widely applied to remove t...
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Cognitive diagnosis plays a crucial role in Intelligent Tutor Systems, which aims to diagnose learners' cognitive states according to learners' observable records, such as exercise records. However, this paper...
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In this study, we first develop SIV model by incorporating the intercellular time delay and analyze the stability of the equilibrium points. The model dynamics admits disease-free equilibrium and the infected equilibr...
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Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rat...
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The urn model with triggering (UMT) has been instrumental in modeling these innovation dynamics. Yet a generalization is needed to capture the richer empirical phenomenology. Here we introduce a time-dependent urn model with triggering (TUMT), a generalization of the UMT that crucially integrates time-dependent parameters for reinforcement and triggering to offer a broader framework for modeling innovation in nonstationary systems. Through analytical computation and numerical simulations, we show that the TUMT reconciles various behaviors observed in a broad spectrum of systems from patenting activity to the analysis of gene mutations. We highlight how the TUMT features a “critical” region where both Heaps' and Zipf's laws coexist, for which we compute the exponents.
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