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Summary: In this article, the asymptotic synchronization of a class of fuzzy inertial neural networks (FINNs) with time‐varying delays is investigated. First, the direct analysis approach is applied to replace the accustomed variable transformation and the reduced‐order method for addressing the inertial term. Second, a suitable Lyapunov function and control scheme are devised to obtain several new sufficient conditions to guarantee the asymptotic synchronization of the class of FINNs with time‐varying delays. It turns out that the obtained criteria are simpler and more effective. Meanwhile, some numerical examples demonstrate the effectiveness of the proposed strategies and verify the theoretical results. [ABSTRACT FROM AUTHOR]

Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an efficient multi-scale wavelet method for dehazing and denoising ultrasound images using a fractional-order filter, which integrates a guided filter, directional filter, fractional-order filter, and haze removal to the different resolution images generated by a multi-scale wavelet. In the directional filter stage, an eigen-analysis of each pixel is conducted to extract structural features, which are then classified into edges for targeted filtering. The guided filter subsequently reduces speckle noise in homogeneous anatomical regions. The fractional-order filter allows the algorithm to effectively denoise while improving edge definition, irrespective of the edge size. Haze removal can effectively eliminate the haze caused by attenuation. Our method achieved significant improvements, with PSNR reaching 31.25 and SSIM 0.905 on our ultrasound dataset, outperforming other methods. Additionally, on external datasets like McMaster and Kodak24, it achieved the highest PSNR (29.68, 28.62) and SSIM (0.858, 0.803). Clinical evaluations by four radiologists confirmed its superiority in liver and carotid artery images. Overall, our approach outperforms existing speckle reduction and structural preservation techniques, making it highly suitable for clinical ultrasound imaging. [ABSTRACT FROM AUTHOR]

This article addresses the robust fixed‐time synchronization of fuzzy shunting‐inhibitory cellular neural networks (FSICNNs) with delays by utilizing two different types of control strategies. First, a feedback controller is proposed to achieve fixed‐time synchronization of FSICNNs. Secondly, a novel adaptive controller is designed to guarantee fixed‐time synchronization of FSICNNs, automatically adjusting all control gains without the need for advanced settings. The use of differential inequality techniques and the Lyapunov function method yields several sufficient conditions to ensure fixed‐time synchronization for the considered FSICNNs. Finally, an example, along with its numerical simulation, is presented to demonstrate the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Images captured under varying light conditions have deficient contrast, low brightness, latent colors, and high noise. Numerous methods have been developed for image enhancement. However, these methods are only suitable for enhancing specific type of images (e.g., over-exposed or underexposed), and also fail to restore artifact-free results for various other types of images. Therefore, to meet this goal, in this paper, we present an automatic image enhancement method, which is capable of producing quality results for all types of images captured under uneven exposure conditions (e.g., backlit, non-uniform, over-exposed, one-sided illumination and night-time images). Firstly, images are categorized using a convolutional neural network (CNN) to determine their class, and different values of weight coefficients are achieved for further processing. Then, images are converted into photonegative form to obtain an initial transmission map using a bright channel prior. Next, L1-norm regularization is adopted to refine scene transmission. Besides, environmental light is estimated based on an effective filter. Finally, the image degradation model is applied to achieve enhanced results. Furthermore, post-processing of the images is comprised of two steps, such as denoising and details enhancement. The denoised model is only applied when the images are captured in extreme low-light conditions. Whereas, a smooth layer is obtained using L1-norm regularization to enhance details in partially over-and under-exposed images. Extensive experiments reveal the effectives of the proposed approach as compared to other state-of-the-art algorithms.

With the rise of social media and the internet, the rapid dissemination of information has increased the likelihood of reputation infringement. This study utilizes judicial big data and AI to analyze intrinsic connections in reputation infringement cases, aiding judges in delivering consistent rulings. The challenge lies in balancing freedom of speech with the right to reputation and addressing the ambiguity and subjectivity in infringement cases. This research constructs a structured reputation infringement case dataset from Chinese Judgments Online. It introduces a Fractional Fuzzy Neural System (FFNS) to tackle the vagueness in reputation infringement acts and judicial language, enhancing prediction accuracy for case outcomes. The FFNS, integrating fractional calculus, fuzzy logic, and neural networks, excels in adaptability and nonlinear modeling. It uses fractional order fuzzy membership functions to depict the extent and severity of reputation infringement accurately, combining these outputs with neural networks for predictive analysis. The result is a more precise adjudication tool, demonstrating significant potential for judicial application. [ABSTRACT FROM AUTHOR]

Edge detection is a highly researched topic in the field of image processing, with numerous methods proposed by previous scholars. Among these, ant colony algorithms have emerged as a promising approach for detecting image edges. These algorithms have demonstrated high efficacy in accurately identifying edges within images. For this paper, due to the long-term memory, nonlocality, and weak singularity of fractional calculus, fractional-order ant colony algorithm combined with fractional differential mask and coefficient of variation (FACAFCV) for image edge detection is proposed. If we set the order of the fractional-order ant colony algorithm and fractional differential mask to v = 0 , the edge detection method we propose becomes an integer-order edge detection method. We conduct experiments on images that are corrupted by multiplicative noise, as well as on an edge detection dataset. Our experimental results demonstrate that our method is able to detect image edges, while also mitigating the impact of multiplicative noise. These results indicate that our method has the potential to be a valuable tool for edge detection in practical applications. [ABSTRACT FROM AUTHOR]

Since the existing fracmemristors (fractional-order + memristors) have incremental structures and are designed based on original fractors (a circuit element with fractional-order impedance), this brief presents a new fracmemristor implementation, the Quadratic Chain Scaling Fracmemristor (QCSF), based on the optimized chain scaling fractor. Both the incremental and decremental QCSFs are presented. The design principle is investigated and the time-domain analysis approach is proposed to design an achievable QCSF and to analyze its electrical characteristics. The voltage-current characteristics of a QCSF are not only related to the input signal frequency and amplitude, but also to its operational order. The voltage-current curve of a QCSF is either a pinched hysteresis loop but with the pinched point in the first or third quadrant, or an elliptical hysteresis loop. Compared with existing memristors and fracmemristors, electrical characteristics of the QCSF are more complex. [ABSTRACT FROM AUTHOR]

Considering the $ \alpha$ -stable input signals and noises, several robust fractional-order adaptive filtering algorithms have been proposed in recent years. However, the mean-square performance analysis of the FoAF algorithm has not been well studied in the literature. Toward that end, this letter provide a theoretical mean-square performance analysis of the FoAF algorithm, involving transient and steady-state behavior. Furthermore, an improved fractional-order adaptive filtering algorithm is derived by utilizing the M-estimate technique. Simulation experiments verify the results of the theoretical analysis and demonstrate the advantages of the proposed algorithm in heavy-tailed non-Gaussian environments. [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]

This brief proposes an enhanced fractional derivative that can prevent the tap weight coefficients from destroying the gradient information, solve the problem caused by the fractional extreme point, and improve the convergence speed with the help of error estimation information and Sign function. Based on this fractional derivative, an enhanced fractional least mean square (EFLMS) filter algorithm is proposed. We analyze the influence of unknown system vector on the convergence performance of the EFLMS algorithm. The computational complexity of the proposed algorithm is also analyzed. Simulation experiments show that the EFLMS algorithm achieves better performance in system identification than the classic least mean square (LMS) algorithm and the existing algorithms based on fractional calculus. [ABSTRACT FROM AUTHOR]

This brief proposes a novel perspective for solving single input and multiple output (SIMO) nonlinear systems with multi-cost function adaptive algorithm. Based on Euler polynomials, the Euler filter with finite memory is proposed to construct a filter bank, which realizes the accurate identification of high-dimensional nonlinear systems. To improve the algorithm performance, a multi-cost function is proposed. Moreover, the mean-square stability and steady-state performance of the proposed method are rigorously analyzed. The typical FitzHugh-Nagumo (FHN) system, which fiercely exhibits chaotic dynamics, is considered for justifying the performance of this new algorithm. Numerical results highlight the solution accuracy via comparison with existing approaches. [ABSTRACT FROM AUTHOR]

This paper discusses the capabilities of the fractional differential approach for the detection of textural features in two-dimensional digital images and the involved Lateral Inhibition Principle, and fractional differential masks and algorithms of digital image. Firstly, the kinetic physical meaning of fractional differential and the relationship between fractional calculus and classical time-frequency analysis and the separability of two-dimensional fractional calculus on certain conditions are deduced. Secondly, the difference between two Gaussians receptive fields for fractional differential of digital image involved signal processing and biologic vision nerve model is discussed. An analysis of its Mach band is also included. Thirdly, the implements and parameters of eight n × n fractional differential masks, which are mutual central symmetric, on negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left lower diagonal, left upper diagonal, right lower diagonal, right upper diagonal respectively are discussed. Lastly, the numerical implementation algorithms of fractional differential mask for digital image are discussed. Numerical experiments show that the textural details enhance capabilities of fractional differential-based texture operator and are better than that of integral differential based one for rich-grained digital images.

In this paper, a Fractional-order Retinex (FR) for the adaptive contrast enhancement of Under-Exposed Traffic Images (UETI) is proposed to be achieved by the fractional-order variational method. The disposable reconstructive results of the contrast enhancement of UETI play a significant role in traffic safety and are often taken as intermediate results for the traffic virtual reality and augmented reality of intelligent transportation systems. To this end, this paper proposes a state-ofthe-art application of a promising mathematical method, fractional calculus, to extend the classic integer-order Retinex to the fractional-order one, a FR, which leads to a fractional-order algebraic regularization term and contributes to better conditioning of the reconstruction problem. At first, the fractional-order isotropic equation related to a FR is implemented by the Fractional-order Steepest Descent Method (FSDM). Secondly, the corresponding restrictive fractional-order optimization is achieved. Finally, the capability of a FR to non-linearly preserve complex textural details as well as desired contrast enhancing is validated by experimental analysis, which is a major advantage superior to conventional contrast enhancement algorithms, especially for UETI rich in textural details. The paper gives a novel mathematical approach, fractional calculus, to the family of Retinex algorithms that differs from most of the previous approaches and as such, it represents an interesting theoretical contribution. [ABSTRACT FROM AUTHOR]

A class of fractal-chain fractance approximation circuit (FCFAC) has been discussed in this paper. The FCFAC type 1 (FCFAC-1) can achieve the rational approximation of negative-half-order fractances. Changing the series and parallel connections or the positions of resistors and capacitors in FCFAC-1 produces another three FCFACs of negative-half-order. Making scaling extensions to the four original FCFACs, the scaling FCFACs can be obtained and achieve the rational approximation of fractances of arbitrary-order. The operational order, which is determined by the progression ratio of resistance α and the progression ratio of capacitance β , can be expressed as μ = − lg α / lg (α β). The approximation performance of the scaling FCFACs has been improved and the optimised circuits are really simple. The oscillation phenomena of the frequency-domain characteristics of the scaling FCFACs have been described quantitatively. In addition, a comparison of approximation performance shows the scaling FCFACs provide a good choice in available fractance approximation circuits (FACs). [ABSTRACT FROM AUTHOR]

The dual-slope integral analog-to-digital converter is widely used in low-speed, high-precision measurement owing to its high precision and strong resistance on crosstalk interference. To meet the requirements of higher accuracy and faster measurement, the integral sensitivity and conversion speed of the dual-slope integral analog-to-digital converter must be improved. Therefore, based on fractional-order calculus, we propose a fractional-order dual-slope integral analog-to-digital converter. First, constant-current charging curves were provided to explain the source of the idea of the fractional-order dual-slope integral analog-to-digital converter. Then, the working principle of the fractional-order dual-slope integral analog-to-digital converter is described in detail. The calculation formula of analog-to-digital conversion is derived and analyzed. Moreover, the relationship of the voltage-measurement error with the operation-order error of the fractor and the reference voltage error is theoretically derived. Furthermore, we theoretically analyze the resistance of the proposed analog-to-digital converter to crosstalk interference, as well as the requirements for the first fractional integral time when crosstalk interference is suppressed. Specifically, we prove that the proposed analog-to-digital converter has a higher sensitivity and conversion speed than the classical converter, and we provide a quantitative calculation formula. [ABSTRACT FROM AUTHOR]

In this article, inspired by the state-of-the-art research progress of the fractional-order memristor, a fractional-order memristive prediction model of the trading price of future is attempted to be proposed, which can feasibly predict the variation trend of the following unknown trading price data only depending on a small sampling of the given ones in a previous short time. At first, the analogy analysis of the relationship between an actual system of future trading and a physical memristive system of charge transfer is achieved. Second, the achievement of a corresponding capacitive string scaling fracmemristor (LCSF) is mathematically derived and analyzed in detail. Third, a 5-years data from 2015 to 2019 of the 300 exchange traded fund open-end index securities investment fund of Shanghai Stock Exchange is selected to verify the multiscale prediction ability of trading price of future of the LCSF. The theoretical contribution of this article is the first application of the fractional-order memristive electronic system to feasibly achieve an intelligent prediction model of the financial technology. [ABSTRACT FROM AUTHOR]

Extracting robust visual saliency map and image cropping are fundamental problems in computer vision, graphics, and so on. It is not easy task to accurately detect and crop the entire salient object from images with complex background. In this paper, a deep learning strategy is adopted to train a large data-set of images, to get saliency map from the input image using graph-based segmentation and gray level adjustment to enhance and extract more accurate and clear saliency map. Furthermore, the Gaussian filter and image scaling used along with cropping method to keep better presentation of the visual object. The important task of overall framework is to take care about relevant image contents as well as to identify more region of interest and get optimum rectangle from the saliency map with minimum and maximum rectangular windows. Quality and low computational complexity have been focused while performing the cropping operation because automatic and efficient cropping technique should not only rely on geometric constraints, but it should be fast enough to consider the important image contents. The applied method use different data-set of images, to ensure the efficiency of this technique and the experimental results show that the framework is not only fast as well as much better for image cropping. We used Matlab and Caffe framework for efficient experimental results. [ABSTRACT FROM AUTHOR]

Since we cannot solve the equation, we know nothing about the properties of the fracmemristor circuit. In this paper, HP memristor is used in fracmemristor circuit for the first time. After a series of mathematical processing, the HP fracmemristor can be equivalent to two parts which are represented as F and VM, respectively. The F part is the fractance. The VM part is related to the current, and it can best reflect the fracmemristor property of the circuit. Therefore, we hope that we can understand the fracmemristor circuit by the simulation research of the HP fracmemristor circuit. Firstly, the amplitude frequency characteristic and phase frequency characteristic of HP fracmemristor are obtained by using Matlab. And compared with the fractance, they have different characteristics. After that, the 1/2 order fracmemristor property is studied. By approximating processing the 1/2 Laplasse operator and then using Laplasse transform and inverse Laplasse transform, we can get the total resistance change with time, the changes of total resistance with the current figure, the voltage of part F changes with the current, the voltage of part VM with the current changes, as well as the total voltage with current changes. From these diagrams, the U-I diagram of the VM section intersects at two points. The currents at these two points are symmetrical about the origin, and the voltages at the two points are slightly different. Moreover, the magnitude of the current and voltage is stable at the point of intersection, and does not change with the magnitude of the input current. For HP fracmemristor circuits, its properties depend on the size of the current. When the current is very small, the HP fracmemristor exhibits the characteristics of fractance, and the influence of the VM part can be ignored. With the increase of current, the effect of fractance F is reduced, and the effect of VM is increased. When the current increases to a certain size, the output of the circuit is the same as that of the VM part, and the effect of the fractance F part can be ignored. [ABSTRACT FROM AUTHOR]

This paper presents a state-of-the-art application of fractional hopfield neural networks (FHNNs) to defend against chip cloning attacks, and provides insight into the reason that the proposed method is superior to physically unclonable functions (PUFs). In the past decade, PUFs have been evolving as one of the best types of hardware security. However, the development of the PUFs has been somewhat limited by its implementation cost, its temperature variation effect, its electromagnetic interference effect, the amount of entropy in it, etc. Therefore, it is imperative to discover, through promising mathematical methods and physical modules, some novel mechanisms to overcome the aforementioned weaknesses of the PUFs. Motivated by this need, in this paper, we propose applying the FHNNs to defend against chip cloning attacks. At first, we implement the arbitrary-order fractor of a FHNN. Secondly, we describe the implementation cost of the FHNNs. Thirdly, we propose the achievement of the constant-order performance of a FHNN when ambient temperature varies. Fourthly, we analyze the electrical performance stability of the FHNNs under electromagnetic disturbance conditions. Fifthly, we study the amount of entropy of the FHNNs. Lastly, we perform experiments to analyze the pass-band width of the fractor of an arbitrary-order FHNN and the defense against chip cloning attacks capability of the FHNNs. In particular, the capabilities of defense against chip cloning attacks, anti-electromagnetic interference, and anti-temperature variation of a FHNN are illustrated experimentally in detail. Some significant advantages of the FHNNs are that their implementation cost is considerably lower than that of the PUFs, their electrical performance is much more stable than that of the PUFs under different temperature conditions, their electrical performance stability of the FHNNs under electromagnetic disturbance conditions is much more robust than that of the PUFs, and their amount of entropy is significantly higher than that of the PUFs with the same rank circuit scale. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the order-frequency characteristics of a promising circuit element: fractor. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator or integrator in an analog circuit. In this paper, we studied some electrical properties of a fractor. In particular, the order-frequency characteristics of a fractor are introduced. First, the order-sensitivity characteristics of a fractor are proposed. Second, the order-frequency characteristics of a fractor are studied. Third, the time constant of a fractor is analyzed. Last, through mathematical analysis and simulation results, we discussed in detail some issues of the electrical properties of a fractor, especially its time constant. [ABSTRACT FROM AUTHOR]