Basis Functions Research Articles

Oligonucleotides Containing 8,1′‐Ethano‐2′‐deoxyadenosine: Synthesis and Properties

This article presents the synthesis and properties of oligonucleotides containing 8,1′‐ethano‐2′‐deoxyadenosine (ethano‐dA) in which the adenine base (ethA) is fixed to the syn conformation. Ethano‐dA phosphoramidite was synthesized by using a 1,5‐hydrogen‐atom transfer/radical cyclization process and introduced into oligonucleotides, which were successfully obtained by employing the 4,4′‐dimethoxytrityl‐off synthesis mode. The duplex‐forming ability of the oligonucleotides containing ethano‐dA was evaluated. In the antiparallel Watson–Crick duplex, the ethA formed stable base pairs with thymine and guanine, in which two Hoogsteen‐type hydrogen bonds could be formed. By contrast, the parallel Hoogsteen duplex containing the ethA:thymine base pair showed thermal stability comparable to that containing a natural adenine:thymine base pair because ethA and thymine can form two Watson–Crick‐type hydrogen bonds. These results indicated that ethano‐dA may be helpful for elucidating the function of adenine bases via the syn conformation in DNA.

Event-Triggered Adaptive Neural Impedance Control of Robotic Systems.

This article presents an event-triggered adaptive neural impedance control (ETANIC) scheme for robotic systems, where the combination of impedance control (IC) and event-triggered mechanism can significantly reduce the computational burden and the communication cost under the premise of ensuring the stability and tracking performances of the robotic systems. The IC is used to achieve the compliant behavior of the robotic systems in response to the environment. The uncertainties of the robotic systems are estimated by the radial basis function neural network (RBFNN), and the update laws for RBFNN are derived from the designed Lyapunov function. The stability of the whole closed-loop control system is analyzed by the Lyapunov theory, and the event-triggered conditions are designed to avoid the Zeno behavior. The numerical simulation and experimental tests demonstrate that the proposed ETANIC scheme can achieve better efficiency for controlling the robotic systems to perform the interaction tasks with the environment in comparison to the adaptive neural IC (ANIC).

Predefined Accuracy Adaptive Tracking Control for Nonlinear Multiagent Systems With Unmodeled Dynamics.

This article focuses on an adaptive dynamic surface tracking control issue of nonlinear multiagent systems (MASs) with unmodeled dynamics and input quantization under predefined accuracy. Radial basis function neural networks (RBFNNs) are employed to estimate unknown nonlinear items. A dynamic signal is established to handle the trouble introduced by the unmodeled dynamics. Moreover, the predefined precision control is realized with the aid of two key functions. Unlike the existing works on nonlinear MASs with unmodeled dynamics, to avoid the issue of "explosion of complexity," the dynamic surface control (DSC) method is applied with the nonlinear filter. By using the designed controller, the consensus errors can gather to a precision assigned a priori. Finally, the simulation results are given to demonstrate the effectiveness of the proposed strategy.

Event-Triggered Extended Dissipative FTB for T-S Fuzzy Switched Systems With Mismatched Phenomena and Deception Attacks: A Multidomain Framework.

This article investigates the extended dissipative finite-time boundedness (ED-FTB) problem for fuzzy switched systems under deception attacks. To improve the network resource efficiency, a multidomain probabilistic event-triggered mechanism (MDPETM) is proposed. The mode mismatched phenomenon is modeled based on the switching delay information between the controller mode and the system mode. To extract the true signal generated by the MDPETM, a virtual delay concept is developed. The constraint that the controller and the system must have the same premise variables is removed. Based on the MDPETM, mismatched fuzzy state feedback controllers are first devised which may not share the same modes with the system. Then, by establishing fuzzy basis and controller mode-dependent Lyapunov functionals, sufficient criteria free of nonlinear terms existing in the literature are derived, which ensure the ED-FTB of the closed-loop system under admissible delays and deception attacks. Finally, an application-oriented one-link robotic arm system is utilized to validate the theoretical results.

Distributed Adaptive Output Feedback Consensus for Nonlinear Stochastic Multiagent Systems by Reference Generator Approach.

This article investigates the distributed leader-following consensus for a class of nonlinear stochastic multiagent systems (MASs) under directed communication topology. In order to estimate unmeasured system states, a dynamic gain filter is designed for each control input with reduced filtering variables. Then, a novel reference generator is proposed, which plays a key role in relaxing the restriction on communication topology. Based on the reference generators and filters, a distributed output feedback consensus protocol is proposed by a recursive control design approach, which incorporates adaptive radial basis function (RBF) neural networks to approximate the unknown parameters and functions. Compared with existing works on stochastic MASs, the proposed approach can significantly reduce the number of dynamic variables in filters. Furthermore, the agents considered in this article are quite general with multiple uncertain/unmatched inputs and stochastic disturbance. Finally, a simulation example is given to demonstrate the effectiveness of our results.

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length.

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

Neural Network-Based Adaptive Tracking Control for Denitrification and Aeration Processes With Time Delays.

Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov-Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.

Adaptive Decentralized Control for Constrained Strong Interconnected Nonlinear Systems and Its Application to Inverted Pendulum.

This work is dedicated to adaptive decentralized tracking control for a class of strong interconnected nonlinear systems with asymmetric constraints. Currently, there are few related studies on unknown strongly interconnected nonlinear systems with asymmetric time-varying constraints. To deal with the assumptions of the interconnection terms in the design process, which include upper functions and structural restrictions, the properties of Gaussian function in radial basis function (RBF) neural networks are applied to overcome this difficulty. By constructing the nonlinear state-dependent function (NSDF) and using a new coordinate transformation, the conservative step that the original state constraint converts into a new boundary of the tracking error is removed. Meanwhile, the virtual controller's feasibility condition is removed. It is proven that all the signals are bounded, especially the original tracking error and the new tracking error, which are both bounded. In the end, simulation studies are carried out to verify the effectiveness and benefits of the proposed control scheme.

Event-Based Nonsingular Fixed-Time Tracking Control of an Uncertain Manipulator System Subject to Full-State Static Constraints.

This article centers around investigating the event-triggered nonsingular fixed-time tracking issue for an n -link rigid robot manipulator with full-state constraints, external disturbances, and model uncertainties. We propose the definition of the constrainedly practically fixed-time stability (CPFTS) and provide a sufficient condition for CPFTS. A novel auxiliary function is developed to address the singularity issue caused by repeated differentiation in achieving the fixed-time tracking control. The uncertain parameters are approximated using the radial basis function neural network (RBFNN). This study proposes the model-based and the neutral network-based tracking control approaches, designed using the scaling function technique and the barrier Lyapunov function, respectively, to ensure that the tracking error systems are CPFTS and the full-state constraints comply. Moreover, the communication transmission load is reduced using the relative threshold event-triggered control strategy. Simulation results demonstrate the effectiveness of the proposed tracking control algorithms.

Accuracy of using the axial length of the fellow eye for IOL calculation in retinal detachment eyes undergoing silicone oil removal

PurposeEvaluate whether the axial length of the fellow eye can be used to calculate the intraocular lens (IOL) in eyes with retinal detachment.DesignRetrospective, consecutive case series.MethodsOur study was conducted at...

Geodesic Basis Function Neural Network.

In the learning of existing radial basis function neural networks-based methods, it is difficult to propagate errors back. This leads to an inconsistency between the learning and recognition task. This article proposes a geodesic basis function neural network with subclass extension learning (GBFNN-ScE). The geodesic basis function (GBF), which is defined here for the first time, uses the geodetic distance in the manifold as a measure to obtain the response of the sample with respect to the local center. To learn network parameters by back-propagating errors for the purpose of correct classification, a specific GBF based on a pruned gamma encoding cosine function is constructed. This function has a concise and explicit expression on the hyperspherical manifold, which is conducive to the realization of error back propagation. In the preprocessing layer, a sample unitization method with no loss of information, nonnegative unit hyperspherical crown (NUHC) mapping, is proposed. The sample can be mapped to the support set of the GBF. To alleviate the problem that one-hot encoding is not effective enough in the differential expression of data labels within a class, a subclass extension (ScE) learning strategy is proposed. The ScE learning strategy can help the learned network be more robust. For the working of GBFNN-ScE, the original sample is projected onto the support set of GBF through the NUHC mapping. Then the mapped samples are sent to the nonlinear computation units composed of GBFs in the hidden layer. Finally, the response obtained in the hidden layer is weighted by the learned weight to obtain the network output. This article theoretically proves that the separability of the data with ScE learning is stronger. The experimental results show that the proposed GBFNN-ScE has a better performance in recognition tasks than existing methods. The ablation experiments show that the ideas of the GBFNN-ScE contribute to the algorithm performance.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Command Filtered Neuroadaptive Fault-Tolerant Control for Nonlinear Systems With Input Saturation and Unknown Control Direction.

This article studies the tracking control of a class of nonlinear systems with input saturation, subject to nonaffine faults and unknown control direction. A fault-tolerant command filtered control (CFC) method based on adaptive neural networks (NNs) is proposed for this kind of nonlinear system. First, the combination of CFC and error compensation overcomes the "explosion of complexity" issue and alleviates the impact of filter errors. Then, a set of radial basis function NNs is constructed to approximate the unknown nonlinear items containing the nonaffine fault function. Additionally, the issue of unknown control direction in the system is effectively resolved by using Nussbaum gain technology. It is proven that the designed controller can ensure that all signals in the closed-loop system are bounded and convergent, and the upper bound of the absolute value of system tracking error is given. Finally, three comparative simulation results are illustrated to show the effectiveness of the proposed method.

The error term of the sum of digital sum functions in arbitrary bases

Let $k$ be a non-negative integer and $q > 1$ be a positive integer. Let $s_q(k)$ be the sum of digits of $k$ written in base $q.$ In 1940, Bush proved that $A_q(x)=\sum_{k \leq x} s_q (k)$ is asymptotic to $\frac{q-1}{2}x \log_q x.$ In 1968, Trollope proved an explicit formula for the error term of $A_2(n-1),$ labeled by $-E_2(n),$ where $n$ is a positive integer. In 1975, Delange extended Trollope's result to an arbitrary base $q$ by another method and labeled the error term $nF_q(\log_q n).$ When $q=2,$ the two formulas of the error term are supposed to be equal, but they look quite different. We proved directly that those two formulas are equal. More interestingly, Cooper and Kennedy in 1999 applied Trollope's method to extend $-E_2(n)$ to $-E_q(n)$ with a general base $q,$ and we also proved directly that $nF_q(\log_q n)$ and $-E_q(n)$ are equal for any $q.$

Analyzing physical activity impact based on ubiquitous nonlinear dynamics and electroencephalography data.

Understanding complex systems is made easier with the tools provided by the theory of nonlinear dynamic systems. It provides novel ideas, algorithms, and techniques for signal processing, analysis, and classification. Presently, these ideas are being applied to the investigation of how physiological signals evolve. The study applies nonlinear dynamics theory to electroencephalogram (EEG) signals to better comprehend the range of alcoholic mental states. One of the main contributions of this paper is an algorithm for automatically distinguishing between sober and drunken EEG signals based on their salient features. The study utilized various entropy-based features, including ApEn, SampEn, Shannon and Renyi entropies, PE, TS, FE, WE, and KSE, to extract information from EEG signals. To identify the most relevant features, the study employed ranking methods like T-test, Wilcoxon, and Bhattacharyya, and trained SVM classifiers with the selected features. The Bhattacharyya ranking method was found to be the most effective in achieving high classification accuracy, sensitivity, and specificity. Classification accuracy of 95.89%, the sensitivity of 94.43%, and specificity of 96.67% are achieved by the SVM classifier with radial basis function (RBF) for polynomial Kernel using the Bhattacharyya ranking method. From the result, it is clear that the model serves as a cost-effective and accurate decision-support tool for doctors in diagnosing alcoholism and for rehabilitation centres to monitor the effectiveness of interventions aimed at mitigating or reversing brain damage caused by alcoholism.

Knowledge-based Data Processing for Multilingual Natural Language Analysis

Natural Language Processing (NLP) aids the empowerment of intelligent machines by enhancing human language understanding for linguistic-based human-computer communication. Recent developments in processing power, as well as the availability of large volumes of linguistic data, have enhanced the demand for data-driven methods for automatic semantic analysis. This paper proposes multilingual data processing using feature extraction with classification using deep learning architectures. Here, the input text data has been collected based on various languages and processed to remove missing values and null values. The processed data has been extracted using Histogram Equalization based Global Local Entropy (HEGLE) and classified using Kernel-based Radial basis Function (Ker_Rad_BF). These architectures could be utilized to process natural language. We present solutions to the multilingual sentiment analysis issue in this research article by implementing algorithms, and we compare precision factors to discover the optimum option for multilingual sentiment analysis. For the HASOC dataset, the proposed HEGLE_ Ker_Rad_BF achieved an accuracy of 98%, a precision of 97%, a recall of 90.5%, an f-1 score of 85%, RMSE of 55.6%, and a loss curve analysis attained 44%. For the TRAC dataset, the accuracy of 98%, the precision attained is 97%, the Recall is 91%, the F-1 score is 87%, and the RMSE of the proposed neural network is 55%.

Time Efficient Ultrasound Localization Microscopy Based on A Novel Radial Basis Function 2D Interpolation.

Ultrasound localization microscopy (ULM) allows for the generation of super-resolved (SR) images of the vasculature by precisely localizing intravenously injected microbubbles. Although SR images may be useful for diagnosing and treating patients, their use in the clinical context is limited by the need for prolonged acquisition times and high frame rates. The primary goal of our study is to relax the requirement of high frame rates to obtain SR images. To this end, we propose a new time-efficient ULM (TEULM) pipeline built on a cutting-edge interpolation method. More specifically, we suggest employing Radial Basis Functions (RBFs) as interpolators to estimate the missing values in the 2-dimensional (2D) spatio-temporal structures. To evaluate this strategy, we first mimic the data acquisition at a reduced frame rate by applying a down-sampling (DS = 2, 4, 8, and 10) factor to high frame rate ULM data. Then, we up-sample the data to the original frame rate using the suggested interpolation to reconstruct the missing frames. Finally, using both the original high frame rate data and the interpolated one, we reconstruct SR images using the ULM framework steps. We evaluate the proposed TEULM using four in vivo datasets, a Rat brain (dataset A), a Rat kidney (dataset B), a Rat tumor (dataset C) and a Rat brain bolus (dataset D), interpolating at the in-phase and quadrature (IQ) level. Results demonstrate the effectiveness of TEULM in recovering vascular structures, even at a DS rate of 10 (corresponding to a frame rate of sub-100Hz). In conclusion, the proposed technique is successful in reconstructing accurate SR images while requiring frame rates of one order of magnitude lower than standard ULM.

Codesign of FDI Attacks Detection, Isolation, and Mitigation for Complex Microgrid Systems: An HBF-NN-Based Approach.

The primary purpose of this article is to design an intelligent false data injection (FDI) attacks detection, isolation, and mitigation scheme for a class of complex microgrid systems with electric vehicles (EVs). First, a networked microgrid with an EV model is well established, which takes load disturbance, wind generation fluctuation, and FDI attacks into account so as to truly reflect the operation process of the complex system. Then, an intelligent hyper basis function neural network (HBF-NN) observer is designed to accurately estimate the state of the microgrids, learn, and reconstruct the possible attack signal online. Subsequently, a novel HBF-NN-based H∞ controller is skillfully designed to mitigate the negative impact of FDI attacks online, so as to ensure the normal operation of the complex systems in an unreliable network environment. Finally, a two-stage integrated intelligent detection and maintenance algorithm is summarized and one simulation is presented to provide tangible evidence of the feasibility and superiority of the proposed FDI attacks detection, isolation, and mitigation methodology.

A Hybrid Controller for Musculoskeletal Robots Targeting Lifting Tasks in Industrial Metaverse.

In manufacturing, musculoskeletal robots have gained more attention with the potential advantages of flexibility, robustness, and adaptability over conventional serial-link rigid robots. Focusing on the fundamental lifting tasks, a hybrid controller is proposed to overcome control challenges of such robots for widely applications in industry. The metaverse technology offers an available simulated-reality-based platform to verify the proposed method. The hybrid controller contains two main parts. A muscle-synergy-based radial basis function (RBF) network is proposed as the feedforward controller, which is able to characterize the phasic and the tonic muscle synergies simultaneously. The adaptive dynamic programming (ADP) is applied as the feedback controller to address the optimal control problem. The actor-critic structure is applied in the ADP-based controller, where the critic network is trained to approximate the optimal performance index and the actor network is trained to compute the optimal muscle excitations. Furthermore, the convergence and stability of the ADP algorithm are also analyzed. Finally, experiments have been designed to verify the effectiveness of this hybrid controller on an upper limb musculoskeletal system, and the comparisons with other controllers are also illustrated. The results show that the proposed controller can obtain a satisfactory performance for lifting tasks.