Complex-Valued Ordinary Differential Equation Modeling for Time Series Identification

Yang, Bin; Bao, Wenzheng

doi:10.1109/access.2019.2902958

Cited by 12 publications

(5 citation statements)

References 45 publications

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“…Complex-valued ordinary differential equation (CVODE) model is a variant of ODE model, whose coefficients and functions are complex-valued. Its expression is given as followed [ 59 ]. …”

Section: Methodsmentioning

confidence: 99%

Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model

et al. 2021

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Background The growing researches of molecular biology reveal that complex life phenomena have the ability to demonstrating various types of interactions in the level of genomics. To establish the interactions between genes or proteins and understand the intrinsic mechanisms of biological systems have become an urgent need and study hotspot. Results In order to forecast gene expression data and identify more accurate gene regulatory network, complex-valued version of ordinary differential equation (CVODE) is proposed in this paper. In order to optimize CVODE model, a complex-valued hybrid evolutionary method based on Grammar-guided genetic programming and complex-valued firefly algorithm is presented. Conclusions When tested on three real gene expression datasets from E.coli and Human Cell, the experiment results suggest that CVODE model could improve 20–50% prediction accuracy of gene expression data, which could also infer more true-positive regulatory relationships and less false-positive regulations than ordinary differential equation.

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“…Complex-valued ordinary differential equation (CVODE) model is a variant of ODE model, whose coefficients and functions are complex-valued. Its expression is given as followed [ 59 ]. …”

Section: Methodsmentioning

confidence: 99%

Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model

et al. 2021

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“…ODE (in the real domain and real-valued function) can be extended both in the domain part and in the function value. In Figure 4, the expansion of ODE based on the function value, including vector-valued, complex-valued [55], quaternion-valued [36][37][38]42,56], Banach space [54], etc. While the extension of ODE based on the domain is from real to complex, which is often said as ODE in the complex domain [57][58][59].…”

Section: Development Of Quaternion Differential Equationmentioning

confidence: 99%

Review of Quaternion Differential Equations: Historical Development, Applications, and Future Direction

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Rusyaman

et al. 2023

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Quaternion is a four-dimensional and an extension of the complex number system. It is often viewed from various fields, such as analysis, algebra, and geometry. Several applications of quaternions are related to an object’s rotation and motion in three-dimensional space in the form of a differential equation. In this paper, we do a systematic literature review on the development of quaternion differential equations. We utilize PRISMA (preferred reporting items for systematic review and meta-analyses) framework in the review process as well as content analysis. The expected result is a state-of-the-art and the gap of concepts or problems that still need to develop or answer. It was concluded that there are still some opportunities to develop a quaternion differential equation using a quaternion function domain.

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“…In order to investigate the optimization ability of CVWWO, we make the comparison experiments with the complexvalued versions (CVPSO [32] and CVCSA [33]) of classical swarm intelligent algorithm (particle swarm optimization) and new evolutionary algorithm (crow search algorithm). The maximum iteration is set as 100 and population size is set as 20.…”

Section: B Optimization Ability Investigation Of Cvwwomentioning

confidence: 99%

CSE: Complex-Valued System With Evolutionary Algorithm

et al. 2019

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Complex-valued system identification has the ability to provide the basis for system analysis. So as to demonstrate the potential and internal mechanism of the complex-valued system, this paper proposes a novel complex-valued hybrid evolutionary (CSE) algorithm to optimize the complex-valued expression model (CEM). Complex-valued gene expression programming (CVGEP) is proposed to optimize the architectures of the CEM. Complex-valued water wave optimization (CVWWO) is first proposed to optimize complex-valued coefficients and constants of the CEM. The two artificial complex-valued function approximation problems and non-minimum phase equalization problem are utilized to test the performance of the proposed algorithm. The results demonstrate that this method could identify complex-valued systems more correctly than complex-valued neural networks, which could obtain above 90% smaller mean-squared error (MSE) performance than other complex-valued models. With 10% Gaussian white noise, the CSE could identify accurate complex-valued structure and parameters containing coefficients and constants. The CVWWO has better convergence performance than complex-valued particle swarm optimization and crow search algorithm.INDEX TERMS Complex-valued expression model, gene expression programming, water wave optimization.

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Complex-Valued Ordinary Differential Equation Modeling for Time Series Identification

Cited by 12 publications

References 45 publications

Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model

Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model

Review of Quaternion Differential Equations: Historical Development, Applications, and Future Direction

CSE: Complex-Valued System With Evolutionary Algorithm

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