Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(...Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(CSI)as real-valued inputs,potentially discarding useful information embedded in the original CSI.In addition,existing positioning models generally face the contradiction between computational complexity and positioning accuracy.To address these issues,we combine graph neural network(GNN)with complex-valued neural network(CVNN)to construct a lightweight indoor positioning model named CGNet.CGNet employs complexvalued convolution operation to directly process the original CSI data,fully exploiting the correlation between real and imaginary parts of CSI while extracting local features.Subsequently,the feature values are treated as nodes,and conditional position encoding(CPE)module is applied to add positional information.To reduce the number of connections in the graph structure and lower themodel complexity,feature information is mapped to an efficient graph structure through a dynamic axial graph construction(DAGC)method,with global features extracted usingmaximum relative graph convolution(MRConv).Experimental results show that,on the CTW dataset,CGNet achieves a 10%improvement in positioning accuracy compared to existing methods,while the number of model parameters is only 0.8 M.CGNet achieves excellent positioning accuracy with very few parameters.展开更多
Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts ...Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.展开更多
In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. S...In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain su...Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.展开更多
Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link....Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.展开更多
This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural ...This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valu...Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.展开更多
In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued n...In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.展开更多
Despite the superior advantages of specific emitter identification in extracting emitter features from in-phase and quadrature(I/Q)signals,challenges persist due to signal-type confusion and background noise interfere...Despite the superior advantages of specific emitter identification in extracting emitter features from in-phase and quadrature(I/Q)signals,challenges persist due to signal-type confusion and background noise interference.To address those limitations,this paper proposes a multi-channel contrast prediction coding and complex-valued residuals network(MCPC-MCVResNet)framework.This model employs contrast prediction techniques to directly extract discriminative features from electromagnetic signal sequences,effectively capturing both amplitude and phase information within I/Q data.A core innovation of this approach is the sphere space softmax(SS-softmax)loss,which optimizes intra-class clustering density of while establishing well-defined boundaries between distinct emitters.The SS-softmax mechanism significantly enhances the model's capacity to discern subtle variations among radiation emitters.Experimental results demonstrate superior identification accuracy,rapid convergence,and exceptional robustness in low signal-to-noise ratio environments.展开更多
For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer...For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.展开更多
In this paper,we propose,to our knowledge,a new complex-valued dense atrous neural network(CDANN)for phase-only hologram(POH)generation.The network architecture integrates a complex-valued partial convolution(C-PConv)...In this paper,we propose,to our knowledge,a new complex-valued dense atrous neural network(CDANN)for phase-only hologram(POH)generation.The network architecture integrates a complex-valued partial convolution(C-PConv)module into the down-sampling stages of dual U-Net structures,enhancing computational efficiency through selective channelwise processing.To improve feature extraction,we introduce a novel complex-value dense atrous convolution(DAC)module,which employs four cascaded branches with multi-scale atrous convolutions to capture intricate features while maintaining spatial resolution.Additionally,we integrate a spatial pyramid pooling(SPP)module into the U-Net architecture to encode multi-scale contextual features derived from the DAC module.This hierarchical integration expands the U-Net's receptive field while facilitating cross-layer feature fusion.The proposed method achieves an average peak signal-to-noise ratio(PSNR)of 32.19 d B and an average structural similarity index measure(SSIM)of 0.892 within a running time of 24 ms,outperforming conventional approaches.Experiments confirm significant improvements in both reconstruction quality and computational efficiency,making the CDANN suitable for real-time holographic displays.展开更多
In this paper,we propose a novel complex-valued hierarchical multi-fusion neural network(CHMFNet)for generating highquality holograms.The proposed architecture builds upon a U-Net framework,incorporating a complex-val...In this paper,we propose a novel complex-valued hierarchical multi-fusion neural network(CHMFNet)for generating highquality holograms.The proposed architecture builds upon a U-Net framework,incorporating a complex-valued multi-level perceptron(CMP)module that enhances complex feature representation through optimized convolutional operations and advanced activation functions,enabling effective extraction of intricate holographic patterns.The framework further integrates an innovative complex-valued hierarchical multi-fusion(CHMF)block,which implements multi-scale hierarchical processing and advanced feature fusion through its specialized design.This integration of complex-valued convolution and specialized CHMF design enables superior optical information representation,generating artifact-reduced high-fidelity holograms.The computational results demonstrate the superior performance of the proposed method,achieving an average peak signal-to-noise ratio(PSNR)of 34.11 dB and structural similarity index measure(SSIM)of 0.95,representing significant improvements over conventional approaches.Both numerical simulations and experimental validations confirm CHMFNet's enhanced capability in hologram generation,particularly in terms of detail reproduction accuracy and overall image fidelity.展开更多
This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential tran...This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential transformation is applied and an appropriate controller is designed.Then,a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques.In the end,a numerical example is given to illustrate the effectiveness of the obtained result.展开更多
Direction-of-arrival(DOA)estimation is an important task in many unmanned aerial vehicle(UAV)applications.However,the complicated electromagnetic wave propagation in urban environments substantially deteriorates the p...Direction-of-arrival(DOA)estimation is an important task in many unmanned aerial vehicle(UAV)applications.However,the complicated electromagnetic wave propagation in urban environments substantially deteriorates the performance of many conventional model-driven DOA estimation approaches.To alleviate this,a deep learning based DOA estimation approach is proposed in this paper.Specifically,a complex-valued convolutional neural network(CCNN)is designed to fit the electromagnetic UAV signal with complex envelope better.In the CCNN design,we construct some mapping functions using quantum probabilities,and further analyze some factors which may impact the convergence of complex-valued neural networks.Numerical simulations show that the proposed CCNN converges faster than the real convolutional neural network,and the DOA estimation result is more accurate and robust.展开更多
The problem of exponential module-phase synchronization of complex-valued neural networks(CVNNs)with time-varying delay and stochastic perturbations was investigated.The model of CVNNs with time-varying delay and stoc...The problem of exponential module-phase synchronization of complex-valued neural networks(CVNNs)with time-varying delay and stochastic perturbations was investigated.The model of CVNNs with time-varying delay and stochastic perturbations was considered.The error system was deduced and the module-phase synchronization was defined.Based on the principle of Lyapunov stability theory,the appropriate controller was designed to control the CVNNs.Finally,the effectiveness and reliability of the method were verified by the numerical simulations.展开更多
Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of couple...Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.展开更多
In order to increase the capacity of future satellite communication systems,faster-than-Nyquist(FTN)signaling is increasingly consideredI..Existing methods for compensating for the high power amplifier(HPA)nonlinearit...In order to increase the capacity of future satellite communication systems,faster-than-Nyquist(FTN)signaling is increasingly consideredI..Existing methods for compensating for the high power amplifier(HPA)nonlinearity require perfect knowledge of the HPA model.To address this issue,we analyze the FTN symbol distribution and propose a complex-valued deep neural network(CVDNN)aided compensation scheme for the HPA nonlinearity,which does not require perfect knowledge of the HPA model and can learn the HPA nonlinearity during the training process.A model-driven network for nonlinearity compensation is proposed to further enhance the performance.Furthermore,two training sets based on the FTN symbol distribution are designed for training the network.Extensive simulations show that the Gaussian distribution is a good approximation of the FTN symbol distribution.The proposed model-driven network trained by employing a Gaussian distribution to approximate an FTN signaling can achieve a performance gain of 0.5 dB compared with existing methods without HPA's parameters at the receiver.The proposed neural network is also applicable for non-linear compensation in other systems,including orthogonal frequency-division multiplexing(OFDM).展开更多
文摘Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(CSI)as real-valued inputs,potentially discarding useful information embedded in the original CSI.In addition,existing positioning models generally face the contradiction between computational complexity and positioning accuracy.To address these issues,we combine graph neural network(GNN)with complex-valued neural network(CVNN)to construct a lightweight indoor positioning model named CGNet.CGNet employs complexvalued convolution operation to directly process the original CSI data,fully exploiting the correlation between real and imaginary parts of CSI while extracting local features.Subsequently,the feature values are treated as nodes,and conditional position encoding(CPE)module is applied to add positional information.To reduce the number of connections in the graph structure and lower themodel complexity,feature information is mapped to an efficient graph structure through a dynamic axial graph construction(DAGC)method,with global features extracted usingmaximum relative graph convolution(MRConv).Experimental results show that,on the CTW dataset,CGNet achieves a 10%improvement in positioning accuracy compared to existing methods,while the number of model parameters is only 0.8 M.CGNet achieves excellent positioning accuracy with very few parameters.
基金partially supported by the JSPS KAKENHI(JP22H03643,JP19K22891)。
文摘Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503338,61573316,61374152,and 11302195)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金support from the National Natural Science Foundation of China (Grant Nos.62027820,61975143,61735012,and 62205380).
文摘Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.
文摘Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.
基金Project supported by the Science and Technology Support Program of Xingtai,China(Grant No.2019ZC054)。
文摘This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62176189 and 62106181)the Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Grant No. Y202002)。
文摘Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.
文摘In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.
基金supported by the National Natural Science Foundation of China(62201602)。
文摘Despite the superior advantages of specific emitter identification in extracting emitter features from in-phase and quadrature(I/Q)signals,challenges persist due to signal-type confusion and background noise interference.To address those limitations,this paper proposes a multi-channel contrast prediction coding and complex-valued residuals network(MCPC-MCVResNet)framework.This model employs contrast prediction techniques to directly extract discriminative features from electromagnetic signal sequences,effectively capturing both amplitude and phase information within I/Q data.A core innovation of this approach is the sphere space softmax(SS-softmax)loss,which optimizes intra-class clustering density of while establishing well-defined boundaries between distinct emitters.The SS-softmax mechanism significantly enhances the model's capacity to discern subtle variations among radiation emitters.Experimental results demonstrate superior identification accuracy,rapid convergence,and exceptional robustness in low signal-to-noise ratio environments.
文摘For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.
基金supported by the National Natural Science Foundation of China(No.62265006)the Jiangxi Provincial Department of Science and Technology(Nos.20212BCJL23050 and 20232BAB212017)+4 种基金the Foundation of Jiangxi Educational Commission(No.GJJ200623)the China Postdoctoral Science Foundation(No.2021M691344)the Jiangxi Provincial Postdoctoral Science Foundation of China(No.2020KY16)the Natural Science Foundation of Zhejiang Province(No.LQ22F050005)the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.2022YW53)。
文摘In this paper,we propose,to our knowledge,a new complex-valued dense atrous neural network(CDANN)for phase-only hologram(POH)generation.The network architecture integrates a complex-valued partial convolution(C-PConv)module into the down-sampling stages of dual U-Net structures,enhancing computational efficiency through selective channelwise processing.To improve feature extraction,we introduce a novel complex-value dense atrous convolution(DAC)module,which employs four cascaded branches with multi-scale atrous convolutions to capture intricate features while maintaining spatial resolution.Additionally,we integrate a spatial pyramid pooling(SPP)module into the U-Net architecture to encode multi-scale contextual features derived from the DAC module.This hierarchical integration expands the U-Net's receptive field while facilitating cross-layer feature fusion.The proposed method achieves an average peak signal-to-noise ratio(PSNR)of 32.19 d B and an average structural similarity index measure(SSIM)of 0.892 within a running time of 24 ms,outperforming conventional approaches.Experiments confirm significant improvements in both reconstruction quality and computational efficiency,making the CDANN suitable for real-time holographic displays.
基金supported by the National Natural Science Foundation of China(No.62265006)the Jiangxi Provincial Department of Science and Technology(Nos.20212BCJL23050 and 20232BAB212017)+4 种基金the Natural Science Foundation of Zhejiang Province(No.LQ22F050005)the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.2022YW53)the Foundation of Jiangxi Educational Commission(No.GJJ200623)the China Postdoctoral Science Foundation(No.2021M691344)the Jiangxi Provincial Postdoctoral Science Foundation of China(No.2020KY16)。
文摘In this paper,we propose a novel complex-valued hierarchical multi-fusion neural network(CHMFNet)for generating highquality holograms.The proposed architecture builds upon a U-Net framework,incorporating a complex-valued multi-level perceptron(CMP)module that enhances complex feature representation through optimized convolutional operations and advanced activation functions,enabling effective extraction of intricate holographic patterns.The framework further integrates an innovative complex-valued hierarchical multi-fusion(CHMF)block,which implements multi-scale hierarchical processing and advanced feature fusion through its specialized design.This integration of complex-valued convolution and specialized CHMF design enables superior optical information representation,generating artifact-reduced high-fidelity holograms.The computational results demonstrate the superior performance of the proposed method,achieving an average peak signal-to-noise ratio(PSNR)of 34.11 dB and structural similarity index measure(SSIM)of 0.95,representing significant improvements over conventional approaches.Both numerical simulations and experimental validations confirm CHMFNet's enhanced capability in hologram generation,particularly in terms of detail reproduction accuracy and overall image fidelity.
基金the National Natural Science Foundation of China (61503222, 62173214)the Natural Science Foundation of Shandong Province of China (ZR2021MF100)+2 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of Chinain part by the Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China (2019KJI005)in part by the SDUST Research Fund
文摘This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential transformation is applied and an appropriate controller is designed.Then,a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques.In the end,a numerical example is given to illustrate the effectiveness of the obtained result.
文摘Direction-of-arrival(DOA)estimation is an important task in many unmanned aerial vehicle(UAV)applications.However,the complicated electromagnetic wave propagation in urban environments substantially deteriorates the performance of many conventional model-driven DOA estimation approaches.To alleviate this,a deep learning based DOA estimation approach is proposed in this paper.Specifically,a complex-valued convolutional neural network(CCNN)is designed to fit the electromagnetic UAV signal with complex envelope better.In the CCNN design,we construct some mapping functions using quantum probabilities,and further analyze some factors which may impact the convergence of complex-valued neural networks.Numerical simulations show that the proposed CCNN converges faster than the real convolutional neural network,and the DOA estimation result is more accurate and robust.
基金supported by the National Natural Science Foundation of China under Grant No.61863025International S&T Cooperation Projects of Gansu province under Grant No.144WCGA166Longyuan Young Innovation Talents and the Doctoral Foundation of LUT。
文摘The problem of exponential module-phase synchronization of complex-valued neural networks(CVNNs)with time-varying delay and stochastic perturbations was investigated.The model of CVNNs with time-varying delay and stochastic perturbations was considered.The error system was deduced and the module-phase synchronization was defined.Based on the principle of Lyapunov stability theory,the appropriate controller was designed to control the CVNNs.Finally,the effectiveness and reliability of the method were verified by the numerical simulations.
基金the National Natural Science Foundation of China(Grant No.61773010)。
文摘Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.
基金supported in part by the National Key R&D Program of China under Grant 2021YFB2900501and in part by the National Natural Science Foundation of China under Grant 62171356.
文摘In order to increase the capacity of future satellite communication systems,faster-than-Nyquist(FTN)signaling is increasingly consideredI..Existing methods for compensating for the high power amplifier(HPA)nonlinearity require perfect knowledge of the HPA model.To address this issue,we analyze the FTN symbol distribution and propose a complex-valued deep neural network(CVDNN)aided compensation scheme for the HPA nonlinearity,which does not require perfect knowledge of the HPA model and can learn the HPA nonlinearity during the training process.A model-driven network for nonlinearity compensation is proposed to further enhance the performance.Furthermore,two training sets based on the FTN symbol distribution are designed for training the network.Extensive simulations show that the Gaussian distribution is a good approximation of the FTN symbol distribution.The proposed model-driven network trained by employing a Gaussian distribution to approximate an FTN signaling can achieve a performance gain of 0.5 dB compared with existing methods without HPA's parameters at the receiver.The proposed neural network is also applicable for non-linear compensation in other systems,including orthogonal frequency-division multiplexing(OFDM).
