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In this study, we introduce a novel approach to speech enhancement through the design of a complex temporal convolutional network (Complex-TCN). This model leverages the power of complex networks, enabling the simultaneous capture of both magnitude and phase information inherent in speech signals. By employing a temporal convolutional network, the Complex-TCN excels at extracting contextual information within the time domain of speech. Our findings underscore the substantial performance improvements achieved through the synergistic use of the temporal convolutional network and the incorporation of complex representations. [ABSTRACT FROM AUTHOR]

In this paper, we ponder a kind of discrete-time fractional-order complex-valued fuzzy BAM neural network. Firstly, in order to guarantee the quasi-projective synchronization of the considered networks, an original quantitative control strategy is designed. Next, by virtue of the relevant definitions and properties of the Mittag-Leffler function, we propose a novel discrete-time fractional-order Halanay inequality, which is more efficient for disposing of the discrete-time fractional-order models with time delays. Then, based on the new lemma, fractional-order h-difference theory, and comparison principle, we obtain some easy-to-verify synchronization criteria in terms of algebraic inequalities. Finally, numerical simulations are provided to check the accuracy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction–diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples. [ABSTRACT FROM AUTHOR]

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov's direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples. [ABSTRACT FROM AUTHOR]

A novel variable kernel width generalized complex-valued least mean-square (VKW-GCKLMS) algorithm aims to optimize kernel width in online way to tackle with the problem that the performance of nonlinear kernel algorithms with fixed values of kernel widths is degraded by inappropriate choice of kernel widths. The proposed VKW-GCKLMS algorithm is able to continuously optimize values of kernel widths by using stochastic gradient algorithm in the task of complex-valued nonlinear filtering. Numerical simulations illustrate that the VKW-GCKLMS algorithm is capable of guiding values of kernel widths of different kernels toward those that can achieve the optimal filtering performances. In addition, it is also shown that initial values of kernel widths do not have evident effect on the filtering performance of the VKW-GCKLMS algorithm, which demonstrates the high effectiveness of the VKW-GCKLMS algorithm. [ABSTRACT FROM AUTHOR]

To utilize the full second-order statistical information of the complex-valued signal, a widely linear complex-valued LMM (WL-CLMM) algorithm is proposed by using different M-estimate functions. The proposed WL-CLMM algorithm can process both circular and noncircular complex-valued signals in impulsive noise environments. Moreover, a novel adaptive threshold adjustment method for the M-estimate function is designed according to the probability density function of the complex-valued error signal. In addition, to decrease the sensitivity of the input signal to the performance of the algorithm, the normalized version of WL-CLMM (WL-CNLMM) has been developed. Then, we carry out the mean behavior and mean square behavior analysis of the proposed algorithms. Simulation results show that the proposed algorithms outperform some existing complex-valued algorithms and the theoretical results are well matched. [ABSTRACT FROM AUTHOR]

In this paper, without dividing the fractional-order complex-valued coupled neural networks (FCVCNNs) into two real-valued systems, the problem of synchronization is investigated for FCVCNNs with time-varying coupling strength. To achieve synchronization, by updating coupling strength, two feasible adaptive protocols are designed, 1) a fractional-order adaptive strategy depending on global information; 2) a fractional-order adaptive law relying on the local information based on the connected dominating set theory. Additionally, instead of making the weighted average technique or the solution of the isolated node equation as synchronization reference value, direct error method is adopted to realize synchronization, which offers a flexible way in analysis of FCVCNNs. At last, a numerical simulation is provided to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

Complex-valued neural network is a kind of learning model which can deal with problems in complex domain. Fully complex extreme learning machine (CELM) is a much faster training algorithm than the complex backpropagation (CBP) scheme. However, it is at the cost of using more hidden nodes to obtain the comparable performance. An upper-layer-solution-aware algorithm has been proposed for training single-hidden layer feedforward neural networks, which performs much better than its counterparts, pseudo-inverse learning (PIL)/extreme learning machine and gradient decent-based backpropagation neural networks. Consequently, there exist two challenges that need to be dealt with: 1) How to combine the advantages of CBP and CELM to develop a novel complex learning algorithm? and 2) What is the convergent behavior of the presented algorithm? In this article, an input weights dependent complex-valued (IWDCV) learning algorithm based on Wirtinger calculus has been proposed, which effectively solves the nonanalytic problem of the common activation functions during training neural networks. In addition, the monotonicity of the error function and the deterministic convergence of the proposed model have been strictly proved, which theoretically guarantee the efficiency and effectiveness of the given model, IWDCV. Finally, for real and complex-valued problems, a variety of simulations have been done to demonstrate the comparable performance of the proposed algorithm which support the theoretical observations as well. [ABSTRACT FROM AUTHOR]

Finite-time synchronization is concerned for the fractional-order complex-valued fuzzy cellular neural networks (FOCVFCNNs) with leakage delay and time-varying delays. Without using the usual complex-valued system decomposition method, this paper designs the different forms of the controllers by using 2-norm. And we construct the appropriate Lyapunov functional and apply inequality analytical techniques, some new sufficient conditions are obtained to ensure finite-time synchronization of the FOCVFCNNs. The upper bound of setting-time function is obtained. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This article investigates exponential synchronization of complex-valued memristor-based delayed neural networks (CVMDNNs). Firstly, the CVMDNNs are divided into two real-valued systems: the real and the imaginary part. These two parts are not isolated, they are interrelated. Secondly, integrating the theory of differential inclusion with the definition of Filippov solution, the interval parameter system is established, and the synchronization problem of CVMDNNs is studied. Thirdly, an innovative quantized intermittent controller is designed that takes full advantage of the networks' transmission capacity and reduces control costs. Moreover, the exponential synchronization sufficient condition of CVMDNNs can be obtained via applying the Lyapunov function technique and quantized intermittent control. Finally, an explanatory illustration is offered to certify the validity of the theoretical outcomes. [ABSTRACT FROM AUTHOR]

We propose a novel adaptive kernel-based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by the authors. This paper shows that in the adaptive version of the kernel regression for complex-valued signals we need to include another kernel term, the so-called pseudo-kernel. This new solution is endowed with better representation capabilities in complex-valued fields since it can efficiently decouple the learning of the real and the imaginary part. Also, we review previous realizations of the complex KLMS algorithm and its augmented version to prove that they can be rewritten as particular cases of the gCKLMS. Furthermore, important conclusions on the design of the kernels are drawn that help to greatly improve the convergence of the algorithms. In the experiments, we revisit the nonlinear channel equalization problem to highlight the better convergence of the gCKLMS compared to previous solutions. Also, the flexibility of the proposed generalized approach is tested in a second experiment with non-independent real and imaginary parts. The results illustrate the significant performance improvements of the gCKLMS approach when the complex-valued signals have different properties for the real and imaginary parts. [ABSTRACT FROM AUTHOR]

Recent studies have shown that complex information in single-channel synthetic aperture radar (SAR) imagery has practically always been underrated. This improves the perception of their potential for ocean monitoring. Based on the in-depth interpretation of complex signal kurtosis (CSK), this paper proposes a new ship detection method based on CSK in single-channel SAR imagery. The proposed method consists of two main parts, i.e., region proposal and target identification. The basic idea is to first detect potential ship locations based on the region proposal. Then, the final ship target is acquired based on the target identification. Compared to conventional methods based on detected products, e.g., the constant false alarm rate (CFAR), the proposed method has three advantages. First, CSK can take advantage of both non-Gaussianity and noncircularity, which is the fundamental concept distinguishing complex signal analysis from the real case. Second, the proposed method can be intrinsically free of false alarms caused by radio frequency interference (RFI). Finally, the proposed method can avoid missing detection in dense target situations. This methodology has been demonstrated over significant data sets acquired from Sentinel-1, TerraSAR-X, and Gaofen-3. These results validate that CSK is a vital indicator of ship detection. Complex information is expected to play a more important role in single-channel SAR imagery. [ABSTRACT FROM AUTHOR]

Compared with real-valued complex networks, complex-valued dynamic networks have a wider application space. In addition, considering the existence of time delay and uncertainty in the actual system, the synchronization problem of fractional-order complex-valued dynamic networks with uncertain parameter and coupled delay is studied in this paper. In particular, the uncertain parameter is correlated with time delay. By using fractional derivative inequalities and linear delay fractional order equations, the synchronization of uncertainty complex networks with coupling delay is realized. Sufficient conditions for global asymptotic synchronization are obtained. The obtained synchronization results are applicable to most complex network systems with or without delay. Finally, numerical simulations verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract The robust stability for memristor-based fractional-order Complex-Valued Neural Networks (FCVNNs) with time delay is investigated here. In complex plane, by using the Lyapunov method, and under the sense of Filippov solutions, the existence of unique equilibrium and globally asymptotic stability for such Neural Networks (NNs) have been obtained when the nonlinear complex-valued activation functions could be split into two(real and imaginary) parts. Moreover, locally asymptotic stability for such Neural NNs have been proposed when the nonlinear complex activation functions are bounded. Lastly, three numerical examples are given to confirm the efficiency of theorems. [ABSTRACT FROM AUTHOR]

This paper presents the theoretical results about global Mittag–Leffler stabilization for a class of fractional-order complex-valued memristive neural networks with the designed two types of control rules. As the extension of fractional-order real-valued memristive neural networks, fractional-order complex-valued memristive neural networks have complex-valued states, synaptic weights, and the activation functions. By utilizing the set-valued maps, a generalized fractional derivative inequality as well as fractional-order differential inclusions, several stabilization criteria for global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks are established. A numerical example is provided here to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The target of this article is to study almost periodic dynamical behaviors for complex-valued recurrent neural networks with discontinuous activation functions and time-varying delays. We construct an equivalent discontinuous right-hand equation by decomposing real and imaginary parts of complex-valued neural networks. Based on differential inclusions theory, diagonal dominant principle and nonsmooth analysis theory of generalized Lyapunov function method, we achieve the existence, uniqueness and global stability of almost periodic solution for the equivalent delayed differential network. In particular, we derive a series of results on the equivalent neural networks with discontinuous activation functions, constant coefficients as well as periodic coefficients, respectively. Finally, we give a numerical example to demonstrate the effectiveness and feasibility of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• The high-order fractional complex-valued BAM neural networks are proposed and their sufficient stability conditions are given. • Taking time delay as a bifurcation parameter, the general Hopf bifurcation conditions of fractional complex-valued BAM neural networks are obtained. • The relationship between fractional order and critical bifurcation point is also discussed. In this paper dynamical behaviors of a class of high–order fractional complex–valued bidirectional associative memory neural networks with multiple time delays are investigated. Firstly, they are reduced to real–valued systems by separating the real and imaginary parts. Then, stability criteria of fractional complex–valued bidirectional associative memory neural networks without delay are obtained. Concerning the delay case, the time delay is set as a bifurcation parameter and the condition of Hopf bifurcation is given by analyzing roots of characteristic equations. Finally, two numerical examples are presented and illustrate that Hopf bifurcation does happen when time delay exceeds the critical value. [ABSTRACT FROM AUTHOR]

In this paper, a novel version of nonlinear model, i.e. a complex-valued love model with two time delays between two individuals in a love affair, has been proposed. A notable feature in this model is that we separate the emotion of one individual into real and imaginary parts to represent the variation and complexity of psychophysiological emotion in romantic relationship instead of just real domain, and make our model much closer to reality. This is because love is a complicated cognitive and social phenomenon, full of complexity, diversity and unpredictability, which refers to the coexistence of different aspects of feelings, states and attitudes ranging from joy and trust to sadness and disgust. By analyzing associated characteristic equation of linearized equations for our model, it is found that the Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical value. Stability of bifurcating cyclic love dynamics is also derived by applying the normal form theory and the center manifold theorem. In addition, it is also shown that, for some appropriate chosen parameters, chaotic behaviors can appear even without time delay. [ABSTRACT FROM AUTHOR]

We propose a low-complexity, complex-valued sphere decoding (CV-SD) algorithm, which is referred to as circular sphere decoding (CSD) and is applicable to multiple-input–multiple-output (MIMO) systems with arbitrary 2-D constellations. CSD provides a new constraint test. This constraint test is carefully designed so that the elementwise dependence is removed in the metric computation for the test. As a result, the constraint test becomes simple to perform without restriction on its constellation structure. By additionally employing this simple test as a prescreening test, CSD reduces the complexity of the CV-SD search. We show that the complexity reduction is significant, while its maximum-likelihood (ML) performance is not compromised. We also provide a powerful tool to estimate the pruning capacity of any particular search tree. Using this tool, we propose the predict-and-change strategy, which leads to a further complexity reduction in CSD. Extension of the proposed methods to soft output sphere decoding (SD) is also presented. [ABSTRACT FROM PUBLISHER]

Complex-valued neural networks (CVNNs) with integer-order have attracted much attention, and which have been well discussed. Fractional complex-valued neural networks (FCVNNs) are more suitable to describe the dynamical properties of neural networks, but have rarely been studied. It is the first time that the stability and bifurcation of a class of delayed FCVNN is investigated in this paper. The activation function can be expressed by separating into its real and imaginary parts. By using time delay as the bifurcation parameter, the dynamical behaviors that including local asymptotical stability and Hopf bifurcation are discussed, the conditions of emergence of bifurcation are obtained. Furthermore, it reveals that the onset of the bifurcation point can be delayed as the order increases. Finally, an illustrative example is provided to verify the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In probabilistic equalization of channels with inter-symbol interference, the BCJR algorithm and its approximations become intractable for high-order modulations, even for moderate channel dispersions. In this paper, we introduce a novel soft equalizer to approximate the symbol a posteriori probabilities (APP), where the expectation propagation (EP) algorithm is used to provide an accurate estimation. This new soft equalizer is presented as a block solution, denoted as block-EP (BEP), where the structure of the matrices involved is exploited to reduce the complexity order to \mathcal O( L N ^2) , i.e., linear in the length of the channel, $ L$ , and quadratic in the frame length, $ N$ . The solution is presented in complex-valued formulation within a turbo equalization scheme. This algorithm can be cast as a linear minimum-mean-squared-error (LMMSE) turbo equalization with double feedback architecture, where constellations being discrete is a restriction exploited by the EP that provides a first refinement of the APP. In the experiments included, the BEP exhibits a robust performance, regardless of the channel response, with gains in the range 1.5–5 dB compared with the LMMSE equalization. [ABSTRACT FROM PUBLISHER]

The Rao test is an important method in signal detection in the presence of unknown parameters. The traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real-valued parameter vector and then to use the real Rao test. Alternatively, we present a complex parameter Rao test by reformulating the calculations with respect to the complex-valued quantities directly. Two important examples of the application of the complex parameter Rao test are given to illustrate the procedure. [ABSTRACT FROM PUBLISHER]

Abstract: Since many systems such as quantum system, complex-valued neural network and Lorenz system are complex-valued differential system, in this paper, the stability of complex-valued impulsive system with delay is addressed. By taking advantage of Lyapunov function in complex field, some new criteria for global exponential stability are established, which not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. As an application, a new impulsive controller for complex-valued Lü system with delay is designed. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of the dynamic behaviors of a class of complex-valued neural networks with mixed time delays. Some sufficient conditions for assuring the existence, uniqueness and exponential stability of the equilibrium point of the system are derived using the vector Lyapunov function method, homeomorphism mapping lemma and the matrix theory. The obtained results not only are convenient to check, but also generalize the previously published corresponding results. A numerical example is used to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: Since a quantum system, which is one of the foci of ongoing research, is a classical example of a complex-valued system, in this paper, the issue of asymptotic stability of solutions to complex-valued nonlinear delay differential systems is addressed. By taking advantage of the theory of matrix measure, the exponential stability criteria of a complex-valued nonlinear delay system are established, which not only improve some known results in literature, but also greatly reduce the complexity of analysis and computation. As an application, the exponential stability conditions of 2-dimensional real-valued time-varying delay systems are derived, the conditions are easier to verify in comparison with known results. The effectiveness of the main results are illustrated by some numerical examples. [Copyright &y& Elsevier]

Abstract: This paper presents two new approaches of spatio-temporal data classification using complex-valued neural networks. First approach uses extended complex-valued back-propagation algorithm to train MLP network, whose output’s amplitudes are encoded in one-of-N coding. It makes a classification decision based on accumulated distance between network output and trained pattern. The second approach is inspired in RBF networks with two layer architecture. Neurons from the first layer have fixed position in space and time encoded into theirs weights. This layer is trained by presented extension of neural gas algorithm into complex numbers. The second layer affects which neurons from the first layer belong to specific class. Paper contains details on experimenting with proposed approaches on artificial data of hand-written character recognition and comparison of both methods. [Copyright &y& Elsevier]

In this paper, a complex-valued wavelet network (CWN) is proposed. The network has complex inputs, outputs, connection weights, dilation and translation parameters, but the nonlinearity of the hidden nodes remains a real-valued function (real-valued wavelet function). This kind of network is able to approximate an arbitrary nonlinear function in complex multi-dimensional space, and it provides a powerful tool for nonlinear signal processing involving complex signals. A complex algorithm is derived for the training of the proposed CWN. A numerical example on nonlinear communication channel identification is presented for illustration. [Copyright &y& Elsevier]

• This is the first time to investigate the master-slave synchronization for complex-valued delayed chaotic Lure systems. • The model and results in this paper are more general which treat real valued chaotic Lure systems as special cases. • A novel LKF is constructed and new sampled-data synchronization criteria of CVCLSs are exported. The master-slave synchronization of a type of the complex-valued chaotic Lur'e systems (CVCLSs) with time delay is addressed for the first time, with decomposing complex-valued dynamic systems into two real-valued systems. The complex-valued state variables are introduced in the chaotic Lur'e systems, which expand the application in image processing and remote operation control, and improve the confidentiality in secure communication. Firstly, on the basis of the Lyapunov principle, a Lyapunov-Krasovkii functional (LKF) is established by using certain novel augmented terms, which can take full advantage of the usable information on the sampled-data and the characteristics of the system. Secondly, in the case of a complex-valued delayed chaotic Lur'e system, a more general synchronization criterion is constructed to expand certain current conclusions in the real domain. What's more, the required gain matrices can be designed according to the solution of the linear matrix inequalities (LMIs). In contrast, the conclusions of this paper are more extensive than some existing studies. At last, the validity of the conclusions of this paper is proved by numerical simulations. [ABSTRACT FROM AUTHOR]