A fractional-order Wilson-Cowan formulation of cortical disinhibition.

This work presents a fractional-order Wilson-Cowan model derivation under Caputo's formalism, considering an order of 0 < α ≤ 1 . To that end, we propose memory-dependent response functions and average neuronal excitation functions that permit us to naturally arrive at a fractional-order model that incorporates past dynamics into the description of synaptically coupled neuronal populations' activity. We then shift our focus on a particular example, aiming to analyze the fractional-order dynamics of the disinhibited cortex. This system mimics cortical activity observed during neurological disorders such as epileptic seizures, where an imbalance between excitation and inhibition is present, which allows brain dynamics to transition to a hyperexcited activity state. In the context of the first-order mathematical model, we recover traditional results showing a transition from a low-level activity state to a potentially pathological high-level activity state as an external factor modifies cortical inhibition. On the other hand, under the fractional-order formulation, we establish novel results showing that the system resists such transition as the order is decreased, permitting the possibility of staying in the low-activity state even with increased disinhibition. Furthermore, considering the memory index interpretation of the fractional-order model motivation here developed, our results establish that by increasing the memory index, the system becomes more resistant to transitioning towards the high-level activity state. That is, one possible effect of the memory index is to stabilize neuronal activity. Noticeably, this neuronal stabilizing effect is similar to homeostatic plasticity mechanisms. To summarize our results, we present a two-parameter structural portrait describing the system's dynamics dependent on a proposed disinhibition parameter and the order. We also explore numerical model simulations to validate our results.

New results on bifurcation for fractional-order octonion-valued neural networks involving delays.

This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delayed octonion-valued neural networks exists and is unique. By constructing a fairish function, we confirm that the solution of the involved fractional-order delayed octonion-valued neural networks is bounded. Applying the stability theory and basic bifurcation knowledge of fractional order differential equations, we set up a sufficient condition remaining the stability behaviour and the appearance of Hopf bifurcation for the addressed fractional-order delayed octonion-valued neural networks. To illustrate the justifiability of the derived theoretical results clearly, we give the related simulation results to support these facts. Simultaneously, the bifurcation plots are also displayed. The established theoretical results in this work have important guiding significance in devising and improving neural networks.

Deep Siamese domain adaptation convolutional neural network-based quaternion fractional order Meixner moments fostered big data analytical method for enhancing cloud data security.

In this paper, Quaternion Fractional Order Meixner Moments-based Deep Siamese Domain Adaptation Convolutional Neural Network-based Big Data Analytical Technique is proposed for improving Cloud Data Security (DSDA-CNN-QFOMM-BD-CDS). The proposed methodology comprises six phases: data collection, transmission, pre-processing, storage, analysis, and security of data. Big data analysis methodologies start with the data collection phase. Deep Siamese domain adaptation convolutional Neural Network (DSDA-CNN) is applied to categorize the types of attacks in the cloud database during the data analysis process. During data security phase, Quaternion Fractional Order Meixner Moments (QFOMM) is employed to protect the cloud data for encryption with decryption. The proposed method is implemented in JAVA and assessed using performance metrics, including precision, sensitivity, accuracy, recall, specificity, f-measure, computational complexity information loss, compression ratio, throughput, encryption time, decryption time. The performance of the proposed method offers 23.31%, 15.64%, 18.89% better accuracy and 36.69%, 17.25%, 19.96% less information loss. When compared to existing methods like Fractional order discrete Tchebyshev encryption fostered big data analytical model to maximize the safety of cloud data depend on Enhanced Elman spike neural network (EESNN-FrDTM-BD-CDS), an innovative scheme architecture for safe authentication along data sharing in cloud enabled Big data Environment (LZMA-DBSCAN-BD-CDS).

Hyperspectral Characteristics and SPAD Estimation of Wheat Leaves under CO2 Microleakage Stress.

To non-destructively and rapidly monitor the chlorophyll content of winter wheat leaves under CO2 microleakage stress, and to establish the quantitative relationship between chlorophyll content and sensitive bands in the winter wheat growing season from 2023 to 2024, the leakage rate was set to 1 L/min, 3 L/min, 5 L/min, and 0 L/min through field experiments. The dimensional reduction was realized, fractional differential processing of a wheat canopy spectrum was carried out, a multiple linear regression (MLR) and partial least squares regression (PLSR) estimation model was constructed using a SPA selection band, and the model's accuracy was evaluated. The optimal model for hyperspectral estimation of wheat SPAD under CO2 microleakage stress was screened. The results show that the spectral curves of winter wheat leaves under CO2 microleakage stress showed a "red shift" of the green peak and a "blue shift" of the red edge. Compared with 1 L/min and 3 L/min, wheat leaves were more affected by CO2 at 5 L/min. Evaluation of the accuracy of the MLR and PLSR models shows that the MLR model is better, where the MLR estimation model based on 1.1, 1.8, 0.4, and 1.7 differential SPAD is the best for leakage rates of 1 L/min, 3 L/min, 5 L/min, and 0 L/min, with validation set R2 of 0.832, 0.760, 0.928, and 0.773, which are 11.528, 14.2, 17.048, and 37.3% higher than the raw spectra, respectively. This method can be used to estimate the chlorophyll content of winter wheat leaves under CO2 trace-leakage stress and to dynamically monitor CO2 trace-leakage stress in crops.

Recognition of 3D Images by Fusing Fractional-Order Chebyshev Moments and Deep Neural Networks.

In order to achieve efficient recognition of 3D images and reduce the complexity of network parameters, we proposed a novel 3D image recognition method combining deep neural networks with fractional-order Chebyshev moments. Firstly, the fractional-order Chebyshev moment (FrCM) unit, consisting of Chebyshev moments and the three-term recurrence relation method, is calculated separately using successive integrals. Next, moment invariants based on fractional order and Chebyshev moments are utilized to achieve invariants for image scaling, rotation, and translation. This design aims to enhance computational efficiency. Finally, the fused network embedding the FrCM unit (FrCMs-DNNs) extracts depth features to analyze the effectiveness from the aspects of parameter quantity, computing resources, and identification capability. Meanwhile, the Princeton Shape Benchmark dataset and medical images dataset are used for experimental validation. Compared with other deep neural networks, FrCMs-DNNs has the highest accuracy in image recognition and classification. We used two evaluation indices, mean square error (MSE) and peak signal-to-noise ratio (PSNR), to measure the reconstruction quality of FrCMs after 3D image reconstruction. The accuracy of the FrCMs-DNNs model in 3D object recognition was assessed through an ablation experiment, considering the four evaluation indices of accuracy, precision, recall rate, and F1-score.

Research on SPAD Estimation Model for Spring Wheat Booting Stage Based on Hyperspectral Analysis.

With the rapid progression of agricultural informatization technology, the methodologies of crop monitoring based on spectral technology are constantly upgraded. In order to carry out the efficient, precise and nondestructive detection of relative chlorophyll (SPAD) during the booting stage, we acquired hyperspectral reflectance data about spring wheat vertical distribution and adopted the fractional-order differential to transform the raw spectral data. After that, based on correlation analysis, fractional differential spectra and fractional differential spectral indices with strong correlation with SPAD were screened and fused. Then, the least-squares support vector machine (LSSSVM) and the least-squares support vector machine (SMA-LSSSVM) optimized on the slime mold algorithm were applied to construct the estimation models of SPAD, and the model accuracy was assessed to screen the optimal estimation models. The results showed that the 0.4 order fractional-order differential spectra had the highest correlation with SPAD, which was 9.3% higher than the maximum correlation coefficient of the original spectra; the constructed two-band differential spectral indices were more sensitive to SPAD than the single differential spectra, in which the correlation reached the highest level of 0.724. The SMA-LSSSVM model constructed based on the two-band fractional-order differential spectral indices was better than the single differential spectra and the integration of both, which realized the assessment of wheat SPAD.

Research on Human-Robot Collaboration Method for Parallel Robots Oriented to Segment Docking.

In the field of aerospace, large and heavy cabin segments present a significant challenge in assembling space engines. The substantial inertial force of cabin segments' mass often leads to unexpected motion during docking, resulting in segment collisions, making it challenging to ensure the accuracy and quality of engine segment docking. While traditional manual docking leverages workers' expertise, the intensity of the labor and low productivity are impractical for real-world applications. Human-robot collaboration can effectively integrate the advantages of humans and robots. Parallel robots, known for their high precision and load-bearing capacity, are extensively used in precision assembly under heavy load conditions. Therefore, human-parallel-robot collaboration is an excellent solution for such problems. In this paper, a framework is proposed that is easy to realize in production, using human-parallel-robot collaboration technology for cabin segment docking. A fractional-order variable damping admittance control and an inverse dynamics robust controller are proposed to enhance the robot's compliance, responsiveness, and trajectory tracking accuracy during collaborative assembly. This allows operators to dynamically adjust the robot's motion in real-time, counterbalancing inertial forces and preventing collisions between segments. Segment docking assembly experiments are performed using the Stewart platform in this study. The results show that the proposed method allows the robot to swiftly respond to interaction forces, maintaining compliance and stable motion accuracy even under unknown interaction forces.

Research on Electric Oil-Pneumatic Active Suspension Based on Fractional-Order PID Position Control.

In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. An FOPID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. It is worth noting that, compared to traditional PID control circuits, the FOPID control circuit designed for motors has an improved control performance. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

Development and Experiment of Semi-Physical Simulation Platform for Space Manipulator.

To address the extended development cycle, high costs, and maintenance difficulties associated with existing microgravity simulation methods, this study has developed a semi-physical simulation platform for robotic arms tailored to different gravity environments and loading conditions. The platform represents difficult-to-model joints as physical objects, while the easily modeled components are simulated based on principles of similarity. In response to the strong coupling, nonlinearity, and excess force disturbance issues in the electric variable load loading system, a fractional-order linear active disturbance rejection control algorithm was employed. The controller parameters were tuned using an improved particle swarm algorithm with modified weight coefficients, and experimental results demonstrate that a fractional-order linear active disturbance rejection control improves response speed and disturbance rejection performance compared to linear sliding mode control. The study investigated the differences in the drive force of joint motors in space robotic arms under varying gravity environments and loading conditions. Experimental results indicate that load torque is the primary influencing factor on joint motor drive force, while radial force serves as a secondary influencing factor. Additionally, when the axis of the joint motor is perpendicular to the ground, it can, to some extent, simulate microgravity conditions on the ground.

Fractional-Order Electrical Modeling of Aluminum Coated via Plasma Electro-Oxidation and Thermal Spray Methods to Optimize Radiofrequency Medical Devices.

Active medical devices rely on a source of energy that is applied to the human body for specific purposes such as electrosurgery, ultrasounds for breaking up kidney stones (lithotripsy), laser irradiation, and other medical techniques and procedures that are extensively used. These systems must provide adequate working power with a commitment not to produce side effects on patients. Therefore, the materials used in these devices must effectively transmit energy, allow for security control, sense real-time variations in case of any issues, and ensure the implementation of closed-loop systems for control. This work extends to the experimental data adjustment of some different coating techniques based on plasma electro-oxidation (PEO) and thermal spray (TS) using fractional-order models. According to the physical structure of the coating in different coating techniques, Cole family models were selected. The experimental data were obtained by means of a vector network analyzer (VNA) in the frequency spectrum from 0.3 MHz to 5 MHz. The results show that some models from the Cole family (the single-dispersion model and inductive model) offered a goodness of fit to the experimental impedance in terms of RMSE error and a squared error R2 close to unity. The use of this type of fractional-order electrical model allows an adjustment with a very small number of elements compared to integer-order models, facilitating its use and a consequent reduction in instrumentation cost and the development of control devices that are more robust and easily miniaturized for embedded applications. Additionally, fractional-order models allow for more accurate assessment in industrial and medical applications.

Spacecraft Attitude Measurement and Control Using VSMSCSG and Fractional-Order Zeroing Neural Network Adaptive Steering Law.

In order to improve the accuracy and convergence speed of the steering law under the conditions of high dynamics, high bandwidth, and a small deflection angle, and in an effort to improve attitude measurement and control accuracy of the spacecraft, a spacecraft attitude measurement and control method based on variable speed magnetically suspended control sensitive gyroscopes (VSMSCSGs) and the fractional-order zeroing neural network (FO-ZNN) steering law is proposed. First, a VSMSCSG configuration is designed to realize attitude measurement and control integration in which the VSMSCSGs are employed as both actuators and attitude-rate sensors. Second, a novel adaptive steering law using FO-ZNN is designed. The matrix pseudoinverses are replaced by FO-ZNN outputs, which solves the problem of accuracy degradation in the traditional pseudoinverse steering laws due to the complexity of matrix pseudoinverse operations under high dynamics conditions. In addition, the convergence and robustness of the FO-ZNN are proven. The results show that the proposed FO-ZNN converges faster than the traditional zeroing neural network under external disturbances. Finally, a new weighting function containing rotor deflection angles is added to the steering law to ensure that the saturation of the rotor deflection angles can be avoided. Semi-physical simulation results demonstrate the correctness and superiority of the proposed method.

Sliding mode tracking control of a class of fractional-order nonstrict-feedback nonlinear systems.

Since the Leibniz rule for integer-order derivatives of the product of functions, which includes a finite number of terms, is not true for fractional-order (FO) derivatives of that, all sliding mode control (SMC) methods introduced in the literature involved a very limited class of FO nonlinear systems. This article presents a solution for the unsolved problem of SMC of a class of FO nonstrict-feedback nonlinear systems with uncertainties. Using the Leibniz rule for the FO derivative of the product of two functions, which includes an infinite number of terms, it is shown that only one of these terms is needed to design a SMC law. Using this point, an algorithm is given to design the controller for reference tracking, that significantly reduces the number of design parameters, compared to the literature. Then, it is proved that the algorithm has a closed-form solution which presents a straightforward tool to the designer to obtain the controller. The solution is applicable to the systems with a mixture of integer-order and FO dynamics. Stability and finite-time convergence of the offered control law are also demonstrated. In the end, the availability of the suggested SMC is illustrated through a numerical example arising from a real system.

A PID controller for synchronization between master-slave neurons in fractional-order of neocortical network model.

Modeling of the biological neurons is a way to understand the architecture of neural networks of the brain. A complex brain network includes the synchronization between some groups of neurons. The dynamic behavior of interactions between groups of slave-master neurons in the neocortical network is unpredictable and challenging. The purpose of synchronizing a neural interaction is to reduce the synchronization error between the chaotic slave-master neurons. This paper uses a proportional-integral-derivative (PID) controller to synchronize master-slave neurons in the fractional-order of the neocortical network model based on dendritic spike frequency adaptation (DSFA) uncertainties and unknown disturbance effects. The purpose of this article is in two parts: First, we implemented the effect of previous states of the neuron conditions by fractional-order of the differential equations in the neocortical network model. Second, by synchronizing the FO neocortical master-slave model by PID controller, we investigated the connection strength of the complex network in chaotic point of view. The optimized PID coefficients and fractional-order were calculated using root mean square error (RMSE) criteria to control the membrane voltage synchronization. The chaotic behavior of the system was evaluated by numerical techniques such as attractor analysis and time series diagrams. The optimal RMSE value for master-slave neurons occurred at fractional-orders 0.89. It is shown that the synchronization of master-slave neurons improves over time, and eventually they are fully synchronized while the controller error is reduced.

Predicting of elderly population structure and density by a novel grey fractional-order model with theta residual optimization: a case study of Shanghai City, China.

BACKGROUND: Accurately predicting the future development trend of population aging is conducive to accelerating the development of the elderly care industry. This study constructed a combined optimization grey prediction model to predict the structure and density of elderly population. METHODS: In this paper, a GT-FGM model is proposed, which combines Theta residual optimization with fractional-order accumulation operator. Fractional-order accumulation can effectively weaken the randomness of the original data sequence. Meanwhile, Theta residual optimization can adjust parameter by minimizing the mean absolute error. And the population statistics of Shanghai city from 2006 to 2020 were selected for prediction analysis. By comparing with the other traditional grey prediction methods, three representative error indexes (MAE, MAPE, RMSE) were conducting for error analysis. RESULTS: Compared with the FGM model, GM (1,1) model, Verhulst model, Logistic model, SES and other classical prediction methods, the GT-FGM model shows significant forecasting advantages, and its multi-step rolling prediction accuracy is superior to other prediction methods. The results show that the elderly population density in nine districts in Shanghai will exceed 0.5 by 2030, among which Huangpu District has the highest elderly population density, reaching 0.6825. There has been a steady increase in the elderly population over the age of 60. CONCLUSIONS: The GT-FGM model can improve the prediction accuracy effectively. The elderly population in Shanghai shows a steady growth trend on the whole, and the differences between districts are obvious. The government should build a modern pension industry system according to the aging degree of the population in each region, and promote the balanced development of each region.

Grading of clear cell renal cell carcinoma using diffusion MRI with a fractional order calculus model.

BACKGROUND: The fractional order calculus (FROC) model has been developed to describe restrained motion of water molecules as well as microstructural heterogeneity, providing a novel tool for non-invasive tumor grading. PURPOSE: To evaluate the role of the FROC model in characterizing clear cell renal cell carcinoma (ccRCC) grades. MATERIAL AND METHODS: A total of 59 patients diagnosed with ccRCC were included in this prospective study. The diffusion metrics derived from the mono-exponential model (apparent diffusion coefficient [ADC]), intra-voxel incoherent motion [IVIM] model [D, D*, f], and FROC model [Dfroc, ß, µ]) were calculated and compared between low- and high-grade ccRCCs. Binary logistic regression analysis was performed to establish the diagnostic models. Receiver operating characteristic (ROC) analysis and DeLong test were performed to evaluate and compare the diagnostic performance of metrics in grading ccRCC. RESULTS: All the metrics except D* and f exhibited statistical differences between low- and high-grade ccRCCs. ROC analysis showed individual FROC parameters, µ, Dfroc, and ß, outperformed ADC and IVIM parameters in grading ccRCC. For single parameter, µ demonstrated the highest AUC value, sensitivity, and diagnostic accuracy in discriminating the two ccRCC groups while ß exhibited the optimal specificity. Importantly, the combination of Dfroc, µ, and ß could further improve the diagnostic performance. CONCLUSION: The FROC parameters were superior to ADC and IVIM parameters in grading ccRCC, indicating the great potential of the FROC model in distinguishing low- and high-grade ccRCCs.

Effect of Load on Quartz Crystal Microbalance Sensor Response Addressed Using Fractional Order Calculus.

To accurately model the effect of the load caused by a liquid medium as a function of its viscosity, the fractional order Butterworth-Van Dyke (BVD) model of the QCM sensor is proposed in this study. A comprehensive understanding of the fractional order BVD model followed by a simulation of situations commonly encountered in experimental investigations underpins the new QCM sensor approach. The Levenberg-Marquardt (LM) algorithm is used in two fitting steps to extract all parameters of the fractional order BVD model. The integer-order electrical parameters were determined in the first step and the fractional order parameters were extracted in the second step. A parametric investigation was performed in air, water, and glycerol-water solutions in ten-percent steps for the fractional order BVD model. This indicated a change in the behavior of the QCM sensor when it swapped from air to water, modeled by the fractional order BVD model, followed by a specific dependence with increasing viscosity of the glycerol-water solution. The effect of the liquid medium on the reactive motional circuit elements of the BVD model in terms of fractional order calculus (FOC) was experimentally demonstrated. The experimental results demonstrated the value of the fractional order BVD model for a better understanding of the interactions occurring at the QCM sensor surface.

The Performance Investigation of Smart Diagnosis for Bearings Using Mixed Chaotic Features with Fractional Order.

This article presents a performance investigation of a fault detection approach for bearings using different chaotic features with fractional order, where the five different chaotic features and three combinations are clearly described, and the detection achievement is organized. In the architecture of the method, a fractional order chaotic system is first applied to produce a chaotic map of the original vibration signal in the chaotic domain, where small changes in the signal with different bearing statuses might be present; then, a 3D feature map can be obtained. Second, five different features, combination methods, and corresponding extraction functions are introduced. In the third action, the correlation functions of extension theory used to construct the classical domain and joint fields are applied to further define the ranges belonging to different bearing statuses. Finally, testing data are fed into the detection system to verify the performance. The experimental results show that the proposed different chaotic features perform well in the detection of bearings with 7 and 21 mil diameters, and an average accuracy rate of 94.4% was achieved in all cases.

A Novel Fractional Accumulative Grey Model with GA-PSO Optimizer and Its Application.

The prediction of cyber security situation plays an important role in early warning against cyber security attacks. The first-order accumulative grey model has achieved remarkable results in many prediction scenarios. Since recent events have a greater impact on future decisions, new information should be given more weight. The disadvantage of first-order accumulative grey models is that with the first-order accumulative method, equal weight is given to the original data. In this paper, a fractional-order cumulative grey model (FAGM) is used to establish the prediction model, and an intelligent optimization algorithm known as particle swarm optimization (PSO) combined with a genetic algorithm (GA) is used to determine the optimal order. The model discussed in this paper is used for the prediction of Internet cyber security situations. The results of a comparison with the traditional grey model GM(1,1), the grey model GM(1,n), and the fractional discrete grey seasonal model FDGSM(1,1) show that our model is suitable for cases with insufficient data and irregular sample sizes, and the prediction accuracy and stability of the model are better than those of the other three models.

Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus.

The operational status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying the real-time acquisition of accurate inspection data of important parts of weak-motion units and comparing them with their motion status evaluation criteria. A differential data fusion model based on the fractional-order differential operator is established through the study of the application characteristics of fractional-order calculus theory. The advantages of Internet of Things (IoT) technology and a fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of the operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by applying the method to the machining center operation status assessment.

A Novel Hybrid Harris Hawk-Arithmetic Optimization Algorithm for Industrial Wireless Mesh Networks.

A novel hybrid Harris Hawk-Arithmetic Optimization Algorithm (HHAOA) for optimizing the Industrial Wireless Mesh Networks (WMNs) and real-time pressure process control was proposed in this research article. The proposed algorithm uses inspiration from Harris Hawk Optimization and the Arithmetic Optimization Algorithm to improve position relocation problems, premature convergence, and the poor accuracy the existing techniques face. The HHAOA algorithm was evaluated on various benchmark functions and compared with other optimization algorithms, namely Arithmetic Optimization Algorithm, Moth Flame Optimization, Sine Cosine Algorithm, Grey Wolf Optimization, and Harris Hawk Optimization. The proposed algorithm was also applied to a real-world industrial wireless mesh network simulation and experimentation on the real-time pressure process control system. All the results demonstrate that the HHAOA algorithm outperforms different algorithms regarding mean, standard deviation, convergence speed, accuracy, and robustness and improves client router connectivity and network congestion with a 31.7% reduction in Wireless Mesh Network routers. In the real-time pressure process, the HHAOA optimized Fractional-order Predictive PI (FOPPI) Controller produced a robust and smoother control signal leading to minimal peak overshoot and an average of a 53.244% faster settling. Based on the results, the algorithm enhanced the efficiency and reliability of industrial wireless networks and real-time pressure process control systems, which are critical for industrial automation and control applications.