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Automatic modulation recognition (AMR) stands as a pivotal operation within industrial cognitive radio systems. State-of-the-art real-valued convolutional neural networks (CNNs) have innovated modulation recognition but view complex signal components as separate real inputs, impairing signal phase integrity and model interpretability. This paper presents an innovative AMR method known as the CVCNN-LSTM. Our study aims to leverage CNNs in conjunction with a long short-term memory network (LSTM) to harness the strengths of both networks while mitigating their weaknesses. This approach enhances the learning of original I/Q signal features, thus improving recognition performance. The proposed network is composed of multiple LFLBs and an LSTM layer. Each LFLBs is primarily composed of a convolutional layer and an average pooling layer, which play a key role in enabling local correlation learning and hierarchical correlation extraction. Recognizing that I/Q data inherently possesses a complex-valued structure, we advocate using end-to-end complex-valued CNN and complex-valued LSTM instead of dual-channel real-valued networks for modulation recognition. We conduct experiments to evaluate complex-valued networks and demonstrate that our method surpasses current state-of-the-art approaches in the AMR field.

Automatic modulation recognition (AMR) stands as a pivotal operation within industrial cognitive radio systems. State-of-the-art real-valued convolutional neural networks (CNNs) have innovated modulation recognition but view complex signal components as separate real inputs, impairing signal phase integrity and model interpretability. This paper presents an innovative AMR method known as the CVCNN-LSTM. Our study aims to leverage CNNs in conjunction with a long short-term memory network (LSTM) to harness the strengths of both networks while mitigating their weaknesses. This approach enhances the learning of original I/Q signal features, thus improving recognition performance. The proposed network is composed of multiple LFLBs and an LSTM layer. Each LFLBs is primarily composed of a convolutional layer and an average pooling layer, which play a key role in enabling local correlation learning and hierarchical correlation extraction. Recognizing that I/Q data inherently possesses a complex-valued structure, we advocate using end-to-end complex-valued CNN and complex-valued LSTM instead of dual-channel real-valued networks for modulation recognition. We conduct experiments to evaluate complex-valued networks and demonstrate that our method surpasses current state-of-the-art approaches in the AMR field. [ABSTRACT FROM AUTHOR]

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]

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings. [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 article analyzes the quasi-projective synchronization (QPS) issues of delayed Caputo-type BAM neural networks in the complex field. In order to facilitate calculation and realize QPS, the non-decomposition method is adopted. Moreover, a novel lemma in the form of algebraic inequality is established based on the Laplace transform, which makes it more convenient to deal with the delay term. Applying the proposed lemma, inequality techniques and Lyapunov method, some criteria of QPS are obtained via the designed different controllers. Meanwhile, the error bound is effectively derived. Eventually, the rationality of the gained criteria is tested by two simulations. [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]

This paper addresses the problem of Mittag-Leffler synchronization of T–S fuzzy fractional-order discrete-time complex-valued molecular models of mRNA and protein in regulatory mechanisms with two kinds of regulation functions, respectively. A novel approach is proposed to effectively deal with the joint effects from leakage delay and time varying delay for the class of T–S fuzzy fractional-order discrete-time complex-valued genetic regulatory networks (FDTCVGRNs). By employing Lyapunov stability method and Caputo fractional difference inequalities, several effective conditions according to algebraic inequality and complex-valued linear matrix inequalities are deduced to guarantee the synchronization of the addressed FDTCVGRNs. Moreover, Mittag-Leffler synchronization problem of the nonlinear regulation function in complex-valued molecular models on the basis of general regulation function and linear threshold one. Compared with existing results in the literature, our results are less conservative than existing ones. Finally, simulation results with two numerical examples are demonstrated, which proves the validity of the proposed method. [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.

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]

In this paper, the quasi-synchronization and global asymptotic synchronization of memristor-based complex-valued neural networks with time-varying delays are studied respectively. Two suitable controllers are designed to achieve the control objective. To get the corresponding conclusion, the method of vector ordering is employed, which can be used to compare the size of two different complex numbers, as a result, the closed convex hull derived by the complex-valued connections can be derived. Finally, the effectiveness of the proposed method is verified by two simulation examples. [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]

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.

Gene regulatory network (GRN) inference with biology data is a difficult and serious issue in the field of system biology. In order to detect the direct associations of GRN more accurately, a novel two-step GRN inference technique based on the time-delayed correlation coefficient (TDCC) and time-delayed complex-valued S-system model (TDCVSS) is proposed. First, a TDCC algorithm is utilized to construct an initial network. Second, a TDCVSS model is utilized to prune the network topology in order to delete false-positive regulatory relationships for each target gene. The complex-valued restricted additive tree and complex-valued differential evolution are proposed to approximate the optimal TDCVSS model. Finally, the overall network could be inferred by integrating the regulations of all target genes. Two real gene expression datasets from E. coli and S. cerevisiae gene networks are utilized to evaluate the performances of our proposed two-step GRN inference algorithm. The results demonstrated that the proposed algorithm could infer GRN more correct than classical methods and time-delayed methods. [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]

Gene regulatory network (GRN) inference with biology data is a difficult and serious issue in the field of system biology. In order to detect the direct associations of GRN more accurately, a novel two-step GRN inference technique based on the time-delayed correlation coefficient (TDCC) and time-delayed complex-valued S-system model (TDCVSS) is proposed. First, a TDCC algorithm is utilized to construct an initial network. Second, a TDCVSS model is utilized to prune the network topology in order to delete false-positive regulatory relationships for each target gene. The complex-valued restricted additive tree and complex-valued differential evolution are proposed to approximate the optimal TDCVSS model. Finally, the overall network could be inferred by integrating the regulations of all target genes. Two real gene expression datasets from E. coli and S. cerevisiae gene networks are utilized to evaluate the performances of our proposed two-step GRN inference algorithm. The results demonstrated that the proposed algorithm could infer GRN more correct than classical methods and time-delayed methods.

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 presents the analytical and numerical investigation on the global synchronization and anti-synchronization for a class of drive-response systems of fractional-order complex-valued gene regulatory networks with time-varying delays (DFGRNs). In our design, two kinds of adaptive feedback controllers are used to synchronize and anti-synchronize the proposed drive-response systems, and some sufficient conditions on the global asymptotical synchronization and anti-synchronization are given with the methods of the fractional Lyapunov-like functions and the fractional-order inequalities. In the numerical simulations, two minimum “estimated time”, T1 and T2, are computed to achieve the synchronization and anti-synchronization. We find that T1 and T2 increase with the decreasing of the fractional order of DFGRNs.

Noncoherent demodulation is an attractive choice for many wireless communication systems. It requires minimal protocol overhead for carrier synchronization, and it is robust to radio impairments commonly found in low-cost transceivers. Machine learning techniques, such as neural networks and deep learning, offer additional benefits for these systems. Practical communication systems often include nonlinearities, non-stationarity, and non-Gaussian noise, which complicate mathematical derivation of optimum demodulators. Learning approaches can optimize demodulator performance directly from simulated or measured radio data, which is often plentiful in the design and verification of today's integrated transceivers. This paper examines several candidate neural network topologies for use in noncoherent demodulation and provides a mathematical framework for their comparison. Each is based on a complex-valued feature detection layer, which may be characterized as coherent or noncoherent, followed by one or more real-valued classification layers. Backpropagation equations for the noncoherent feature layer include a synchronization term that facilitates training with noncoherent input data. The coherent layer does not synchronize training data, however a noncoherent demodulator can still be constructed by increasing the coherent layer capacity and adding a max pooling layer to marginalize the unknown signal phase. A frequency classification example highlights the differences between the topologies and confirms that optimum noncoherent demodulation can be learned in the presence of AWGN and random phase offsets. The topologies considered here are suitable for noncoherent demodulation of power-efficient modulations such as FSK and ASK, which are typical in today's short-range wireless communication systems. It is hoped that such topologies will lead to a future common architecture that can support the wide range of modulation formats in this space.

Computing complex-valued time-dependent matrix inverse is an important procedure in statistics and control theory. Zeroing neural network (ZNN) becomes an effective method for solving time-dependent issues. This paper proposes a complex-valued synthetical ZNN (CVSZNN) model for computing complex-valued time-dependent matrix inverse within different noise environments. Two important property is synthetically dissected in the construction process of CVSZNN model. First, the finite-time convergence, to ensure the efficiency of CVSZNN model for solving complex-valued time-dependent issue. Secondly, the anti-noise property, to guarantee the robustness of CVSZNN model in presence of noises. Two important aspects above have been validated by theoretical analysis and numerical experiments. Furthermore, the impact of parameters values is investigated based on the experimental results. As compared with the existing ZNN models for computing complex-valued time-dependent matrix inverse, the superiority of the proposed CVSZNN model is displayed fully.

A dynamic complex-valued matrix pseudoinversion (DCVMP) is encountered in some special environments, where the system parameters contain the dynamic, magnitude, and phase information. Currently, most of the existing models are employed to the DCVMP under a noise-free workspace. However, the noise perturbation is unavoidable in the practical application scenarios. Therefore, the motivation of this article is to design a computational model for the DCVMP with strong robustness and high-precision computing solutions. To this end, a modified Newton integration (MNI) neural algorithm is proposed for the DCVMP with noise-suppressing ability in this article. Besides, the corresponding convergence proofs on the MNI neural algorithm are provided. Furthermore, the numerical simulations and an application to the estimation of mobile object localization, are demonstrated to illustrate the superiority of the MNI neural algorithm. [ABSTRACT FROM AUTHOR]

The issue of complex-valued time-dependent pseudoinverse often exists in science and engineering fields. In the existing studies, many models were presented for solving complex-valued time-dependent pseudoinverse in the noiseless environments. However, the appearance of noise is unavoidable in practice. In this paper, a novel noise-acceptable zeroing neural network (NAZNN) model is first proposed for computing complex-valued time-dependent matrix pseudoinverse with different noise situations. For comparison, the traditional zeroing neural network and the gradient neural network are adopted to complete the same task. Theoretical analyses prove that the proposed NAZNN model obtains the global exponential convergence performance. Moreover, the proposed NAZNN is also proven to obtain strong resistance to various sorts of noise. Finally, the results of numerical experiments further substantiate the theoretical analysis and indicate the effectiveness and superiority of the proposed NAZNN model for computing complex-valued time-dependent matrix pseudoinverse in various kinds of noise.

This paper discusses synchronization problem of two delayed stochastic neural networks. By constructing the Lyapunov functions, using stochastic analysis technique, some sufficient conditions guaranteeing the synchronization in mean square for the drive system with the response system have been derived in terms of linear matrix inequalities (LMIs) approach. Moreover, the main feature of this paper lies in that the present results are applicable for the drive system and the response system which all are considered not only in complex-valued domain but also with stochastic noise case. Two numerical examples are given to illustrate the effectiveness and merits of the present results.

Time series identification is one of the key approaches to dealing with time series data and discovering the change rules. Therefore, time series forecasting can be treated as one of the most challenging issues in this field. In order to improve the forecasting performance, we propose a novel time series prediction model based on a complex-valued ordinary differential equation (CVODE) to predict time series. A multi expression programming (MEP) algorithm is utilized to optimize the structure of the CVODE model. So as to achieve the optimal complex-valued coefficients, a novel optimization algorithm based on a complex-valued crow search algorithm (CVCSA) is proposed. The chaotic Mackey-Glass time series, small-time scale traffic measurements, Nasdaq-100 index, and Shanghai stock exchange composite index are utilized to evaluate the performance of our method. The results prove that our proposed method could predict more accurately than state-of-the-art real-valued neural networks and an ordinary differential equation (ODE). The CVCSA has faster convergence speed and stronger optimization ability than the crow search algorithm (CSA) and particle swarm optimization (PSO).

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]

In this paper, the fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects is investigated. We first separate these complex-valued networks into real and imaginary parts, and design the appropriate controllers. Then apply the set-valued map and the differential inclusion theorem to handle the discontinuity problems at the right-hand side of the drive-response systems. By constructing the comparison systems together with the Lyapunov function, we get the fixed-time synchronization conditions. Moreover, the estimate of the settling time is also explicitly obtained. Finally, two examples and their numerical simulations are presented to show the effectiveness of the obtained theoretical 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]

Examples of complex-valued random phenomena in science and engineering are abound, and joint blind source separation (JBSS) provides an effective way to analyze multiset data. Thus there is a need for flexible JBSS algorithms for efficient data-driven feature extraction in the complex domain. Independent vector analysis (IVA) is a prominent recent extension of independent component analysis to multivariate sources, i.e., to perform JBSS, but its effectiveness is determined by how well the source models used match the true latent distributions and the optimization algorithm employed. The complex multivariate generalized Gaussian distribution (CMGGD) is a simple, yet effective parameterized family of distributions that account for full second- and higher-order statistics including noncircularity, a property that has been often omitted for convenience. In this paper, we marry IVA and CMGGD to derive, IVA-CMGGD, with a number of numerical optimization implementations including steepest descent, the quasi-Newton method Broyden–Fletcher–Goldfarb–Shanno (BFGS), and its limited-memory sibling limited-memory BFGS all in the complex-domain. We demonstrate the performance of our algorithm on simulated data as well as a 14-subject real-world complex-valued functional magnetic resonance imaging dataset against a number of competing algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to the global exponential stability (GES) and synchronization control of delayed complex-valued memristive neural networks (CVMNNs). The criterion on the existence, uniqueness and GES of the equilibrium point (EP) for delayed CVMNNs is established by constructing a suitable Lyapunov functional and using the homeomorphism theory as well as linear matrix inequality. Meanwhile, a sampled-data controller is designed to synchronize the master and slave systems under the framework of inequality techniques and Lyapunov method. Finally, two examples are presented to show the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper presents a novel complex-valued polynomial model (CPM) for real-valued prediction and classification problems. In a CPM, function, independent variables and dependent variables are complex-valued. Before CPM optimization, real-valued data need to be converted into complex values. As the linear version of additive tree model, additive expression tree is proposed to optimize the complex-valued structure of CPM. Real parts and imaginary parts of the complex-valued coefficients are encoded into a chromosome and brain storm optimization is utilized to evolve the complex-valued coefficients of CPM. CPM is utilized to predict three financial datasets and classify n-class problems. The prediction results show that CPM presents higher forecasting accuracy than real-valued polynomial model, other real-valued neural networks and ordinary differential equation. The classification performance of CPM is compared with existing methods on IRIS, Liver and Ionosphere datasets. And the results reveal that CPM performs better than well-established and newly proposed real-valued classifiers. [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]

In this paper, a class of delayed complex-valued neural network with diffusion under Dirichlet boundary conditions is considered. By using the properties of the Laplacian operator and separating the neural network into real and imaginary parts, the corresponding characteristic equation of neural network is obtained. Then, the dynamical behaviors including the local stability, the existence of Hopf bifurcation of zero equilibrium are investigated. Furthermore, by using the normal form theory and center manifold theorem of the partial differential equation, the explicit formulae which determine the direction of bifurcations and stability of bifurcating periodic solutions are obtained. Finally, a numerical simulation is carried out to illustrate the results. [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]