ABSTRACT This paper studies quasi‐projective synchronization (QPS) of heterogeneous fractional‐order Clifford‐valued neural networks (FO‐CVNNs) under periodic intermittent pinning control. The drive and response networks may have different self‐feedback coefficients, synaptic weights, activation functions, and external inputs. Their states lie in , so the formulation includes real‐, complex‐, quaternion‐, and higher‐dimensional Clifford‐valued networks. A nonzero real projection factor defines the target manifold . The controller reduces actuation in two independent ways: it is applied only to a pinning set and only during periodic ON‐windows with duty cycle . A multivector Lyapunov analysis and a switched fractional comparison argument yield sufficient conditions, in linear‐matrix‐inequality (LMI)‐compatible form, for full and sparse pinning. The heterogeneous error residual is derived explicitly. In particular, the previously implicit nonhomogeneity is retained and bounded rigorously by when . The results distinguish exact Mittag–Leffler convergence in the residual‐free case from practical QPS with a computable ultimate bound under persistent mismatch. Two examples in and , sensitivity studies, 500 Monte Carlo trials, and an image‐encryption illustration support the analysis. For a nominal actuation‐occupancy index , the two examples use and , respectively, compared with for continuous full‐network control. Direct comparison with recent fractional QPS, intermittent‐control, and Clifford‐network studies clarifies that the proposed framework uniquely combines heterogeneity, Clifford states, temporal intermittency, and spatial pinning.

The objective of this paper is to establish verifiable synchronization criteria for fractional-order Clifford-valued neural networks with mixed time-varying delays when the response system is controlled through finite-resolution communication channels. The model contains discrete and distributed delays, non-commutative Clifford-valued connection weights, and Caputo fractional dynamics. Instead of decomposing the Clifford-valued system into 2^m real-valued subnetworks, the analysis is carried out directly in the multivector space by using operator-norm bounds for Clifford left multiplication, a fractional Halanay-type comparison inequality, and a sector representation of the logarithmic quantizer. An adaptive quantized pinning controller is designed, and a quantization-weighted adaptive Lyapunov functional is introduced to show that the adaptive term contributes a positive effective attenuation margin. The main theorem gives an explicit LMI-free algebraic condition for global Mittag–Leffler synchronization. A robustness theorem further provides a practical residual bound under bounded disturbances. The revised numerical section includes step-refinement evidence for the predictor–corrector Adams–Bashforth–Moulton implementation, comparisons with non-quantized and non-adaptive controllers, sensitivity tests for the initial adaptive gains, a discussion of the conservatism caused by Clifford operator-norm estimates, and an additional larger-scale simulation. These results clarify the range, advantages, and limitations of the proposed direct Clifford-valued approach.

In many real-world environments, data samples arrive as continuous streams, and they often contain noise. In this study, we aim to undertake noisy data classification in an online learning setting using a hybrid supervised Adaptive Resonance Theory (ART) neural network model. Specifically, Fuzzy ARTMAP (FAM) is a neural network that is capable of learning new categories incrementally by creating or updating prototype patterns whenever an input is similar enough, subject to a threshold to decide when to form a new category. In view of FAM’s ability in tackling the stability-plasticity dilemma, it is utilised as a baseline model for developing a robust classifier with online learning capability for noisy data classification. We equip FAM with pre-processing and post-processing modules to improve its robustness in combating noise in data samples and enhance its online classification performance. On the one hand, the pre-processing feature extraction module exploits the capability of a feedforward neural network to enhance feature representation capabilities. On the other hand, the post-processing module leverages an ensemble structure with majority voting for minimizing classification errors in the presence of noisy data. Evaluated on benchmark noisy datasets, the hybrid FAM model outperforms the base FAM and other variants, offering a robust online learning model for solving noisy classification problems in data streaming environments. The source code can be obtained from https://github.com/Michael-cyber123/eNeuralFAM .

Synthetic Minority Over-sampling Technique (SMOTE) is a popular over-sampling method to tackle imbalanced class problem. However, SMOTE could produce noisy samples during over-sampling. To overcome the shortcoming of SMOTE, this paper presents a combination of SMOTE, Stacked Sparse Autoencoder (SSAE), and Fuzzy ARTMAP (FAM), namely SMOTE-SSAE-FAM. In the proposed method, SMOTE is applied to over-sample the minority-class samples. Next, all the generated synthetic samples are transformed by SSAE in order to deal with the noises. FAM that performs incremental learning is then applied to learn information from the balanced data sets. The performance of SMOTE-SSAE-FAM is evaluated using 40 benchmark data sets from public portals. The experimental results show that the proposed SMOTE-SSAE-FAM has achieved an excellent performance as compared with other state-of-art SMOTE methods in classifying imbalanced data.

Fractional partial differential equations (FPDEs) have become essential in modeling complex systems that exhibit memory and non-local effects, commonly encountered in physics, engineering, and applied sciences. In this study, we present an analytical approach that combines a modified integral transform with an iterative technique to solve both linear and nonlinear FPDEs. The proposed framework effectively addresses the challenges posed by the non-local nature of fractional derivatives, offering accurate and convergent series solutions. Several benchmark problems are considered to demonstrate the applicability and reliability of the method. Graphical comparisons with existing analytical techniques further confirm its improved performance. These results highlight the potential of the proposed approach in advancing solution strategies for complex fractional models in mathematical physics and engineering.

For a class of Lur’e multiagent systems (MASs), this article investigates the issue of dynamic event-triggered fixed-time consensus (EFC). First, a new distributed fixed-time controller with a dynamic event-triggered mechanism is proposed by using the local states of both the agent itself and its neighbors. This ensures that the closed-loop MAS has a fixed-time consensus performance. Second, the variables determining the dynamic triggering thresholds are introduced, and their dynamics are constructed by the state estimation errors and consensus errors. Then, a dynamic event-triggered strategy is developed such that the consensus controllers can be dynamically updated according to the triggering conditions, which avoids the continuous transmission of neighbor states and significantly reduces the consumption of communication resources. Third, the stability of the closed-loop MAS and the Zeno phenomenon are analyzed, and the proposed strategy can effectively exclude Zeno behavior. Finally, the effectiveness of the proposed EFC protocol is verified by Lur’e MAS with Chua’s circuit dynamics.

Accurately classifying cognitive load from functional near-infrared spectroscopy (fNIRS) signals remains a significant challenge due to temporal variability, inter-subject differences, and sensitivity to preprocessing choices. This study provides a comprehensive evaluation of EEGNet for fNIRS-based cognitive load classification by systematically examining the effects of temporal segmentation strategies (overlapping vs. non-overlapping), window lengths (10s, 20s, 30s), feature extraction methods (Analysis of Variance (ANOVA), Principal Component Analysis (PCA), Fast Independent Component Analysis (FastICA)), learning rate configurations (fixed and adaptive), and evaluation protocols (random split vs. subject-independent (SI)). Results from random-split experiments show that overlapping segmentation, combined with smaller fixed learning rates (0.01-0.001), yields the highest accuracies, due to temporal redundancy and dense sampling of hemodynamic transitions. However, SI evaluation reveals a substantial drop in accuracy, demonstrating limited generalization to unseen participants. Under SI evaluation, non-overlapping segmentation outperformed overlapping windows, with the best accuracy of 56.11% achieved using PCA features with a 20-second window and a 0.1 learning rate. These findings indicate that eliminating temporal redundancy helps the model learn more robust and generalizable representations of cognitive load across individuals. Although adaptive learning rate strategy improved training stability, it did not surpass the performance of optimally selected fixed learning rates. The study highlights the critical role of segmentation strategy and learning rate selection in improving model generalization and identifies methodological considerations essential for developing reliable, real-time, and SI cognitive load classification systems using fNIRS.

Driver distraction is a major cause of road accidents globally. To address this, there has been significant research into using machine learning to monitor driver behavior. However, many existing reviews are limited in scope. They often focus only on specific algorithms or overlook the critical role of different data types. This paper fills that gap by providing an in-depth systematic review of both the data and the algorithms in machine learning-based driver distraction detection. By providing a clear overview of the current state of the field, this paper aims to improve the understanding of driver distraction detection and guide future research. To ensure a rigorous and unbiased selection process, the PRISMA methodology was used to select studies. To provide a fine-grained view, both topics (data and algorithms) are systematically categorized into specific subdomains. For each category, key concepts are explained, significant contributions are summarized, and their respective strengths and weaknesses are critically analyzed. In addition, this article provides a comparative and critical analysis of widely used driving-related datasets. Finally, challenges, research gaps, and possible directions for future research are analyzed and discussed. The main results of this review show that deep learning methods outperform older models, although they require more computational power. Issues such as model interpretability and monitoring systems with driving automation have received less attention. Also, systems that use multimodal data (end to end multimodal systems) have great potential for the future.

Integrating multi-omics data to understand biological processes in human diseases is a complex bioinformatic task. Machine learning (ML), particularly deep learning (DL) models, offers a promising approach to multi-omics data integration and analysis. However, existing DL models generally integrate multi-omics data by concatenating the input data space or learned feature space, which is a sub-optimal approach. In addition, single classifiers are commonly used in DL-based methods, which can compromise the performance. Furthermore, the gradient descent optimization technique in DL suffers from a high computational cost and local sub-optimal solutions. To address these challenges, this article presents a novel cancer subtype classification framework using multi-omics integration and an ensemble-based parallel DL/ML architecture. Specifically, a multimodal autoencoder is used for effective feature learning across omics types, overcoming the limitations of naïve concatenation. A hybrid ensemble model comprising DL and ML learners with a meta-learner enhances classification robustness beyond single models. To improve optimization and computation, we incorporate a hybrid Back-Propagation and Particle Swarm Optimization (PSO) strategy and execute the entire framework on a parallel processing platform, reducing computation time while enhancing global search capability. The proposed framework is evaluated empirically with two benchmark data sets from The Cancer Genome Atlas (TCGA), namely the TCGA Pan-cancer and TCGA Breast Invasive Carcinoma (BRCA) data sets. The results indicate a high performance with accuracy rates of 89.51% and 90.9% for TCGA Pan-cancer and TCGA BRCA, respectively. The parallel implementation of the proposed framework reduces the computation time, resulting in a speed-up of 3 times and 2.5 times for TCGA Pan-cancer and TCGA BRCA, respectively. The findings ascertain the efficacy of the proposed framework for the classification of cancer subtypes, offering a promising solution for implementation in real-world environments.

Non-stationary sequences may exhibit changing effective memory. We study the Learnable-Order Fractional Recurrent Network (LOFT-RNN), a recurrent block in which the order αt ∈ (0, 1) of a type-I Caputo derivative is generated from the evolving state and input. The hidden trajectory follows 0CDtα(t)h(t)=fθ(h(t),x(t)), with α(t)=αmin+(αmax-αmin)σ(gϕ(h(t),x(t))). The theoretical scope is deliberately limited. We give (i) a represented-class approximation proposition, conditional on a finite-dimensional fractional-state realization and uniform continuous dependence of its solution map; (ii) a uniform consistency estimate for the exact-weight L1 formula, together with a separate interpolation-error term for the order grid; (iii) a variable-order bounded-input bounded-state estimate under dissipativity, with a Mittag-Leffler refinement only for constant order; and (iv) a regret result for an auxiliary one-dimensional reset-OGD tracker under convex surrogate losses and explicit detection assumptions. The auxiliary tracker is not identified with end-to-end neural-gate training. We also state the boundary assumptions at t=0, explain the choice of the Caputo derivative, and show that the untruncated history convolution costs O(N2d) over a length-N trajectory. The archived aggregate experiments cover a delimited-copy task, regime-switching ARFIMA sequences, Bonn EEG segment classification, and S&P 500 volatility forecasting. Because seed-level outputs, split manifests, executable code, and some requested baselines are absent from the supplied archive, the empirical comparisons are reported descriptively and no statistical-significance or state-of-the-art claim is made.

Post-hoc explainable AI (XAI) methods typically produce deterministic attribution maps, whereas Bayesian neural networks (BNNs) induce a distribution over explanations. Capturing the variability of this distribution is important for uncertainty-aware decision-making. This paper formalises the explanation distribution as the push-forward measure of the BNN posterior through any Lipschitz-continuous attribution operator. It further proposes the uncertainty-aware relevance attribution operator (UA-RAO), a general family of operators that summarises the explanation distribution using the mean, variance, coefficient of variation, quantiles, and set-theoretic aggregation measures. Theoretical support is provided through Monte Carlo accessibility and Wasserstein approximation bounds. The framework is evaluated on a 15-class power quality disturbance (PQD) classification benchmark, comparing three BNN approximations paired with three attribution operators using relevance mass accuracy and intersection-over-union as localisation metrics. Results show that deep ensembles with the mean UA-RAO improve localisation over the deterministic baseline, while other UA-RAO summaries reveal uncertainty patterns absent from point-estimate attributions. Qualitative results on measured signals further suggest that these patterns generalise beyond the synthetic training distribution. The framework is domain-agnostic and can be applied to any BNN paired with a Lipschitz-continuous attribution operator.

Cognitive load is a critical factor that influences learning and performance. In recent years, eye-tracking technologies have emerged as a promising method for detecting and measuring cognitive load in real-time during learning activities. This paper presents a comprehensive review of the state-of-the-art machine learning (ML) and deep learning (DL) methods utilizing eye-tracking technology for cognitive load assessment. We systematically selected and analyzed 27 studies using the PRISMA protocol, focusing on the methodologies, data, and tasks employed. The reviewed studies leverage a variety of eye-tracking features, such as pupil size, fixations, saccades, blink rate, and eye gaze, to classify cognitive load. Key contributions of this review include identifying specific eye movement patterns associated with cognitive load and exploring multimodal approaches that combine eye-tracking data with other physiological measures to enhance model accuracy and generalizability. By tracking changes in eye movements, researchers can gain insights into the cognitive processes underlying learning activities and identify strategies for improving instructional designs. ML and DL models have become increasingly popular for cognitive load classification based on eye-tracking metrics. These algorithms are capable of learning complex patterns in data and identifying subtle changes in eye movements that are indicative of changes in cognitive load. Therefore, this review focuses on how ML/DL models are used to study cognitive processes using eye-tracking technology, along with relevant variables. The review involved an extensive examination of electronic repositories and a thorough exploration of references from papers that met the inclusion criteria. After removing duplicates and irrelevant papers, the analysis focused on journal articles that presented well-executed studies involving eye-tracking and physiological signals. Specifically, the studies needed to analyze healthy individuals both at rest and during cognitive load. Eye-tracking offers a rich source of data, including fixations, pupil size, saccades, blinks, and eye-gaze, which can provide valuable insights into attentional processes during cognitive tasks. Several studies focus on the use of DL algorithms for automated detection and classification of cognitive load levels using eye-tracking features. While the potential of Artificial Neural Networks (ANNs) and Convolutional Neural Networks (CNNs) in accurately classifying cognitive load levels is emphasized, it is crucial to acknowledge their limitations. These models heavily rely on the quality and quantity of training data, as well as the generalizability of the learned patterns to different populations and learning contexts. We discuss the challenges posed by these gaps and emphasize the need for privacy-preserving technologies and robust legal frameworks to protect individuals' privacy as the adoption of eye-tracking technology grows. Additionally, the interpretability of DL models poses challenges, as their decision-making processes are often perceived as black boxes. Thus, it is important for future research to address these limitations and develop more robust and interpretable ML/DL models for cognitive load classification. It is worth noting that eye-tracking data are subject to potential bias as the related experiments are often conducted under controlled conditions with a small number of participants. Although eye-tracking technology has been the primary focus of analysis in many studies, researchers are increasingly exploring the benefits of combining eye-tracking data with other physiological signals. By integrating eye-tracking data with other physiological signals, effective classification models can be established to enhance the understanding of human cognitive processes. However, further research is needed to understand the generalizability and effectiveness of these approaches in different contexts and larger datasets.

For many unmanned aerial vehicle (UAV)-based applications, especially those that need to operate with resource-limited edge networked devices in real-time, it is crucial to have a lightweight computing model for data processing and analysis. In this study, we focus on UAV-based forest fire imagery detection using a lightweight convolution neural network (CNN). The task is challenging owing to complex image backgrounds and insufficient training samples. Specifically, we enhance the MobileNetV2 model with an attention mechanism for UAV-based image classification. The proposed model first employs a transfer learning strategy that leverages the pre-trained weights from ImageNet to expedite learning. Then, the model incorporates randomly initialised weights and dropout mechanisms to mitigate over-fitting during training. In addition, an ensemble framework with a majority voting scheme is adopted to improve the classification performance. A case study on forest fire scenes classification with benchmark and real-world images is demonstrated. The results on a publicly available UAV-based image data set reveal the competitiveness of our proposed model as compared with those from existing methods. In addition, based on a set of self-collected images with complex backgrounds, the proposed model illustrates its generalisation capability to undertake forest fire classification tasks with aerial images.

This special issue contains 84 articles that explore challenges in understanding and controlling nonlinear physical systems. The contributions cover a wide range of modern topics, including stability and stabilization issues, fluid dynamics, complex dynamical systems, fractional and partial differential equations, numerical analysis, mathematical modelling, fuzzy set theory and its applications, as well as multidisciplinary applications in machine learning, complexity analysis, and graph theory. This collection highlights innovative mathematical approaches, computational strategies, and experimental results pertaining to dynamical behaviour of complex systems and their applicability to undertake real-world problems in science and engineering. Overall, this special issue presents a collection of papers related to nonlinear physical systems, aiming to inspire researchers and practitioners to further drive research into understanding, modelling, and controlling the intricate dynamics of nonlinear systems across diverse domains.

As health management increasingly gains importance, the demand for personalized systems is on the rise. Although wearable devices and smartphones generate substantial amounts of data, the effective integration and utilization of this information pose significant challenges. Traditional health management systems often depend on single-technology methodologies and encounter difficulties in processing complex, multi-modal data. These systems typically lack robust integration frameworks and do not adequately address the requirements for personalized health management. To overcome these shortcomings, we propose the Health Assistant AI Fusion Framework (HAAFF), which aims to provide a comprehensive intelligent, and personalized health management solution. HAAFF is comprised of four primary modules: data acquisition, information processing, scene recognition, and generation and interaction. The data acquisition module is responsible for gathering diverse user data, while the information processing module conducts initial data processing. The scene recognition module utilizes sensor data to ascertain user contexts, and the generation and interaction module offers personalized health recommendations based on the analyzed data. To validate the efficacy of HAAFF, we utilize binaural beats as a practical case study, collecting user datasets through Apple Watch and iPhones. The information processing module facilitates preliminary data handling, while the scene recognition module employs machine learning techniques to identify user contexts. Ultimately, the generation and interaction module leverages large language models to produce personalized binaural beat music and provide real-time feedback. The results demonstrate that HAAFF successfully integrates and analyzes multi-source data, generates tailored binaural beat music, and adapts and optimizes based on user feedback, thereby highlighting its potential applications in personalized health management.

One debatable issue in traffic safety research is that cognitive load from secondary tasks reduces primary task performance, such as driving. Although physiological signals have been extensively used in driving-related research to assess cognitive load, only a few studies have specifically focused on high cognitive load scenarios. Most existing studies tend to examine moderate or low levels of cognitive load In this study, we adopted an auditory version of the n-back task of three levels as a cognitively loading secondary task while driving in a driving simulator. During the simultaneous execution of driving and the n-back task, we recorded fNIRS, eye-tracking, and driving behavior data to predict cognitive load at three different levels. To the best of our knowledge, this combination of data sources has never been used before. Unlike most previous studies that utilize binary classification of cognitive load and driving in conditions without traffic, our study involved three levels of cognitive load, with drivers operating in normal traffic conditions under low visibility, specifically during nighttime and rainy weather. We proposed a neural network combining a 1D Convolutional Neural Network and a Recurrent Neural Network to predict cognitive load. Our experimental results demonstrate that the proposed model, with fewer parameters, increases accuracy from 99.82

While the Vision Transformer (ViT) architecture gains prominence in computer vision and finds growing applications in edge computing, its lack of strong inductive biases regarding shift, scale, and rotational invariance necessitates pre-training on large-scale datasets. Moreover, the increasing depth and parameter counts in ViT models present significant challenges for training, particularly in edge environments where computational resources are constrained. To mitigate these challenges, this paper introduces a novel Horizontally Scalable Vision Transformer (HSViT) architecture. Specifically, a novel image-level feature embedding approach is introduced that incorporates convolutional layers prior to the Transformer blocks. This design helps preserve inductive biases, allowing the model to potentially eliminate the need for pre-training while achieving strong performance on small datasets. Furthermore, a novel horizontally scalable architecture is designed, facilitating collaborative model training and inference across multiple edge devices. The experimental results show that, without pre-training, HSViT achieves up to 10% higher top-1 accuracy than state-of-the-art methods on several small datasets, while improving the top-1 accuracy of existing CNN backbones by up to 3.1% on ImageNet-1k. The code is available at https://github.com/xuchenhao001/HSViT.

While deep learning models have seen significant success across various domains, their black-box learning nature and lack of interpretability affect their reliability in safety-critical applications like medical diagnostics and autonomous vehicles. In an attempt to address these limitations, Bayesian neural networks (BNNs) offer a promising alternative by incorporating uncertainty estimation into model predictions, enhancing transparency and decision-making. However, BNN development has primarily focused on efficient, high-fidelity approximate inference and guaranteed convergence in asymptotic settings. These are unsuitable for modern high-dimensional, multi-modal, and non-asymptotic deep learning applications, undermining their theoretical advantages. To bridge this gap, this paper provides in-depth reviews on how approximate Bayesian inference leverages deep learning optimization to achieve high efficiency and fidelity in high-dimensional spaces and multi-modal loss landscapes. It also reconciles Bayesian consistency with generalization objectives in non-asymptotic settings and investigates the generalization capabilities of BNNs. Additionally, this survey examines the often-overlooked expressiveness of BNNs, emphasizing how weight uncertainty and the absence of in-between uncertainty affect their performance. This survey aims to inspire BNN practitioners to adopt a deep learning perspective and offer valuable insights to propel further advancements in the field.