Yu Shi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Yu Shi has a total of 26 co-authors. Here are the top co-authors by number of shared publications:
- Weifeng Wang
School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
3 shared publications - Heping Ma
School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China
2 shared publications - Xinping Xiao
School of Science, Wuhan University of Technology, Wuhan, China
2 shared publications - Bin Liu
Dalian University of Technology, Dalian, Liaoning Province, China
1 shared publication - Bin Liu1 shared publication
Chaozhong Wu
Intelligent Transport Systems Research Center, Wuhan University of Technology, Wuhan, 430063, PR China
1 shared publication
Latest Publications
- Open Access
- 9 May 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (10) , 1561
Kolmogorov Equation for a Stochastic Reaction–Diffusion Equation with Multiplicative Noise
Reaction–diffusion equations can model complex systems where randomness plays a role, capturing the interaction between diffusion processes and random fluctuations. The Kolmogorov equations associated with these systems play an important role in understanding the long-term behavior, stability, and control of such complex systems. In this paper, we investigate the existence of a classical solution for the Kolmogorov equation associated with a stochastic reaction–diffusion equation driven by nonlinear multiplicative trace-class noise. We also establish the existence of an invariant measure for the corresponding transition semigroup , where the infinitesimal generator in is identified as the closure of the Kolmogorov operator .- 9 May 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (10) , 1561
Open AccessKolmogorov Equation for a Stochastic Reaction–Diffusion Equation with Multiplicative Noise
Reaction–diffusion equations can model complex systems where randomness plays a role, capturing the interaction between diffusion processes and random fluctuations. The Kolmogorov equations associated with these systems play an important role in understanding the long-term behavior, stability, and control of such complex systems. In this paper, we investigate the existence of a classical solution for the Kolmogorov equation associated with a stochastic reaction–diffusion equation driven by nonlinear multiplicative trace-class noise. We also establish the existence of an invariant measure for the corresponding transition semigroup , where the infinitesimal generator in is identified as the closure of the Kolmogorov operator . - 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in Probability, Uncertainty and Quantitative Risk
- Vol. 9 (3) , 389-404
ϵ-Nash mean-field games for stochastic linear-quadratic systems with delay and applications
In this paper, we focus on mean-field linear-quadratic games for stochastic large-population systems with time delays. The $ \epsilon $ -Nash equilibrium for decentralized strategies in linear-quadratic games is derived via the consistency condition. By means of variational analysis, the system of consistency conditions can be expressed by forward-backward stochastic differential equations. Numerical examples illustrate the sensitivity of solutions of advanced backward stochastic differential equations to time delays, the effect of the the population’s collective behaviors, and the consistency of mean-field estimates.- 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in Probability, Uncertainty and Quantitative Risk
- Vol. 9 (3) , 389-404
ϵ-Nash mean-field games for stochastic linear-quadratic systems with delay and applications
In this paper, we focus on mean-field linear-quadratic games for stochastic large-population systems with time delays. The $ \epsilon $ -Nash equilibrium for decentralized strategies in linear-quadratic games is derived via the consistency condition. By means of variational analysis, the system of consistency conditions can be expressed by forward-backward stochastic differential equations. Numerical examples illustrate the sensitivity of solutions of advanced backward stochastic differential equations to time delays, the effect of the the population’s collective behaviors, and the consistency of mean-field estimates.- 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in Evolution Equations and Control Theory
- Vol. 13 (6) , 1436-1459
Sufficient maximum principle for partially observed mean-field stochastic optimal control problems with delays
This paper deals with partially observed optimal control of mean-field system with noisy memory and discrete delay. By means of the maximum principle, a sufficient optimality condition is established with an assumption of concavity. The main features of this paper include the introduction of a unified adjoint equation. Three examples that shed light on the theoretical results are established in this paper. In particular, a pension fund problem is solved, and an explicit expression for the optimal consumption rate is obtained by means of the maximum principle. Finally, analytic optimal controls are given in the paper and the numerical simulation shows the effect of delay on the optimal solution.
- 1 January 2024
- Published by American Institute of Mathematical Sciences (AIMS) in Evolution Equations and Control Theory
- Vol. 13 (6) , 1436-1459
Sufficient maximum principle for partially observed mean-field stochastic optimal control problems with delays
This paper deals with partially observed optimal control of mean-field system with noisy memory and discrete delay. By means of the maximum principle, a sufficient optimality condition is established with an assumption of concavity. The main features of this paper include the introduction of a unified adjoint equation. Three examples that shed light on the theoretical results are established in this paper. In particular, a pension fund problem is solved, and an explicit expression for the optimal consumption rate is obtained by means of the maximum principle. Finally, analytic optimal controls are given in the paper and the numerical simulation shows the effect of delay on the optimal solution.
- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 27 (12) , 7021-7042
Global generalized solutions to a three species predator-prey model with prey-taxis
In this paper, we study the following three species predator-prey model with prey-taxis: * \begin{document}$ \left\{ \begin{array}{lll} u_t = d_1\Delta u+\chi_1\nabla\cdot(u\nabla v)+r_1u(1-u-kv-b_1w), &\quad x\in \Omega, t>0, \\ v_t = d_2\Delta v+r_2v(1-hu-v-b_2w), &\quad x\in \Omega, t>0, \\ w_t = d_3\Delta w-\chi_2\nabla\cdot(w\nabla u)-\chi_3\nabla\cdot(w\nabla v)\\ \ \ \ \ \ \ \ +r_3w(-1+au+av-w), &\quad x\in \Omega, t>0. \end{array}\right. $\end{document} We prove that if (1.7) and (1.6) hold, the model (\begin{document}$ \ast $\end{document}) admits at least one global generalized solution in any dimension.- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 27 (12) , 7021-7042
Global generalized solutions to a three species predator-prey model with prey-taxis
In this paper, we study the following three species predator-prey model with prey-taxis: * \begin{document}$ \left\{ \begin{array}{lll} u_t = d_1\Delta u+\chi_1\nabla\cdot(u\nabla v)+r_1u(1-u-kv-b_1w), &\quad x\in \Omega, t>0, \\ v_t = d_2\Delta v+r_2v(1-hu-v-b_2w), &\quad x\in \Omega, t>0, \\ w_t = d_3\Delta w-\chi_2\nabla\cdot(w\nabla u)-\chi_3\nabla\cdot(w\nabla v)\\ \ \ \ \ \ \ \ +r_3w(-1+au+av-w), &\quad x\in \Omega, t>0. \end{array}\right. $\end{document} We prove that if (1.7) and (1.6) hold, the model (\begin{document}$ \ast $\end{document}) admits at least one global generalized solution in any dimension.- 1 December 2020
- Published by Elsevier in Accident Analysis & Prevention
- Vol. 148, 105800
Rear-end collision warning of connected automated vehicles based on a novel stochastic local multivehicle optimal velocity model
- 1 December 2020
- Published by Elsevier in Accident Analysis & Prevention
- Vol. 148, 105800
Rear-end collision warning of connected automated vehicles based on a novel stochastic local multivehicle optimal velocity model
- Open Access
The influence of stochastic forcing on strong solutions to the Incompressible Slice Model in 2D bounded domain
The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior of whether and specifically the formulation of atmospheric fronts, whose prediction is fundamental in meteorology. Considered herein is the influence of stochastic forcing on the Incompressible Slice Model (ISM) in a smooth 2D bounded domain, which can be derived by adapting the Lagrangian function in Hamilton's principle for CHSM to the Euler-Boussinesq Eady incompressible case. First, we establish the existence and uniqueness of local pathwise solution (probability strong solution) to the ISM perturbed by nonlinear multiplicative stochastic forcing in Banach spaces $W^{k,p}(D)$ with $k>1+1/p$ and $p\geq 2$. The solution is obtained by introducing suitable cut-off operators applied to the $W^{1,\infty}$-norm of the velocity and temperature fields, using the stochastic compactness method and the Yamada-Watanabe type argument based on the Gy\"{o}ngy-Krylov characterization of convergence in probability. Then, when the ISM is perturbed by linear multiplicative stochastic forcing and the potential temperature does not vary linearly on the $y$-direction, we prove that the associated Cauchy problem admits a unique global-in-time pathwise solution with high probability, provided that the initial data is sufficiently small or the diffusion parameter is large enough. The results partially answer the problems left open in Alonso-Or{\'a}n et al. (Physica D 392:99--118, 2019, pp. 117).Open AccessThe influence of stochastic forcing on strong solutions to the Incompressible Slice Model in 2D bounded domain
The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior of whether and specifically the formulation of atmospheric fronts, whose prediction is fundamental in meteorology. Considered herein is the influence of stochastic forcing on the Incompressible Slice Model (ISM) in a smooth 2D bounded domain, which can be derived by adapting the Lagrangian function in Hamilton's principle for CHSM to the Euler-Boussinesq Eady incompressible case. First, we establish the existence and uniqueness of local pathwise solution (probability strong solution) to the ISM perturbed by nonlinear multiplicative stochastic forcing in Banach spaces $W^{k,p}(D)$ with $k>1+1/p$ and $p\geq 2$. The solution is obtained by introducing suitable cut-off operators applied to the $W^{1,\infty}$-norm of the velocity and temperature fields, using the stochastic compactness method and the Yamada-Watanabe type argument based on the Gy\"{o}ngy-Krylov characterization of convergence in probability. Then, when the ISM is perturbed by linear multiplicative stochastic forcing and the potential temperature does not vary linearly on the $y$-direction, we prove that the associated Cauchy problem admits a unique global-in-time pathwise solution with high probability, provided that the initial data is sufficiently small or the diffusion parameter is large enough. The results partially answer the problems left open in Alonso-Or{\'a}n et al. (Physica D 392:99--118, 2019, pp. 117). - Open Access
Identification of Diagnostic Biomarkers and Subtypes of Liver Hepatocellular Carcinoma by Multi-Omics Data Analysis
As liver hepatocellular carcinoma (LIHC) has high morbidity and mortality rates, improving the clinical diagnosis and treatment of LIHC is an important issue. The advent of the era of precision medicine provides us with new opportunities to cure cancers, including the accumulation of multi-omics data of cancers. Here, we proposed an integration method that involved the Fisher ratio, Spearman correlation coefficient, classified information index, and an ensemble of decision trees (DTs) for biomarker identification based on an unbalanced dataset of LIHC. Then, we obtained 34 differentially expressed genes (DEGs). The ability of the 34 DEGs to discriminate tumor samples from normal samples was evaluated by classification, and a high area under the curve (AUC) was achieved in our studied dataset and in two external validation datasets (AUC = 0.997, 0.973, and 0.949, respectively). Additionally, we also found three subtypes of LIHC, and revealed different biological mechanisms behind the three subtypes. Mutation enrichment analysis showed that subtype 3 had many enriched mutations, including tumor protein p53 (TP53) mutations. Overall, our study suggested that the 34 DEGs could serve as diagnostic biomarkers, and the three subtypes could help with precise treatment for LIHC.
Open AccessIdentification of Diagnostic Biomarkers and Subtypes of Liver Hepatocellular Carcinoma by Multi-Omics Data Analysis
As liver hepatocellular carcinoma (LIHC) has high morbidity and mortality rates, improving the clinical diagnosis and treatment of LIHC is an important issue. The advent of the era of precision medicine provides us with new opportunities to cure cancers, including the accumulation of multi-omics data of cancers. Here, we proposed an integration method that involved the Fisher ratio, Spearman correlation coefficient, classified information index, and an ensemble of decision trees (DTs) for biomarker identification based on an unbalanced dataset of LIHC. Then, we obtained 34 differentially expressed genes (DEGs). The ability of the 34 DEGs to discriminate tumor samples from normal samples was evaluated by classification, and a high area under the curve (AUC) was achieved in our studied dataset and in two external validation datasets (AUC = 0.997, 0.973, and 0.949, respectively). Additionally, we also found three subtypes of LIHC, and revealed different biological mechanisms behind the three subtypes. Mutation enrichment analysis showed that subtype 3 had many enriched mutations, including tumor protein p53 (TP53) mutations. Overall, our study suggested that the 34 DEGs could serve as diagnostic biomarkers, and the three subtypes could help with precise treatment for LIHC.
- Open Access
- 26 April 2020
- Published by Wiley in Computational Intelligence and Neuroscience
- Vol. 2020, 1-15
Optimized Mahalanobis–Taguchi System for High-Dimensional Small Sample Data Classification
The Mahalanobis–Taguchi system (MTS) is a multivariate data diagnosis and prediction technology, which is widely used to optimize large sample data or unbalanced data, but it is rarely used for high-dimensional small sample data. In this paper, the optimized MTS for the classification of high-dimensional small sample data is discussed from two aspects, namely, the inverse matrix instability of the covariance matrix and the instability of feature selection. Firstly, based on regularization and smoothing techniques, this paper proposes a modified Mahalanobis metric to calculate the Mahalanobis distance, which is aimed at reducing the influence of the inverse matrix instability under small sample conditions. Secondly, the minimum redundancy-maximum relevance (mRMR) algorithm is introduced into the MTS for the instability problem of feature selection. By using the mRMR algorithm and signal-to-noise ratio (SNR), a two-stage feature selection method is proposed: the mRMR algorithm is first used to remove noise and redundant variables; the orthogonal table and SNR are then used to screen the combination of variables that make great contribution to classification. Then, the feasibility and simplicity of the optimized MTS are shown in five datasets from the UCI database. The Mahalanobis distance based on regularization and smoothing techniques (RS-MD) is more robust than the traditional Mahalanobis distance. The two-stage feature selection method improves the effectiveness of feature selection for MTS. Finally, the optimized MTS is applied to email classification of the Spambase dataset. The results show that the optimized MTS outperforms the classical MTS and the other 3 machine learning algorithms.
- 26 April 2020
- Published by Wiley in Computational Intelligence and Neuroscience
- Vol. 2020, 1-15
Open AccessOptimized Mahalanobis–Taguchi System for High-Dimensional Small Sample Data Classification
The Mahalanobis–Taguchi system (MTS) is a multivariate data diagnosis and prediction technology, which is widely used to optimize large sample data or unbalanced data, but it is rarely used for high-dimensional small sample data. In this paper, the optimized MTS for the classification of high-dimensional small sample data is discussed from two aspects, namely, the inverse matrix instability of the covariance matrix and the instability of feature selection. Firstly, based on regularization and smoothing techniques, this paper proposes a modified Mahalanobis metric to calculate the Mahalanobis distance, which is aimed at reducing the influence of the inverse matrix instability under small sample conditions. Secondly, the minimum redundancy-maximum relevance (mRMR) algorithm is introduced into the MTS for the instability problem of feature selection. By using the mRMR algorithm and signal-to-noise ratio (SNR), a two-stage feature selection method is proposed: the mRMR algorithm is first used to remove noise and redundant variables; the orthogonal table and SNR are then used to screen the combination of variables that make great contribution to classification. Then, the feasibility and simplicity of the optimized MTS are shown in five datasets from the UCI database. The Mahalanobis distance based on regularization and smoothing techniques (RS-MD) is more robust than the traditional Mahalanobis distance. The two-stage feature selection method improves the effectiveness of feature selection for MTS. Finally, the optimized MTS is applied to email classification of the Spambase dataset. The results show that the optimized MTS outperforms the classical MTS and the other 3 machine learning algorithms.