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19 pages, 3282 KB  
Article
A Transformer-Based Framework for DDoS Attack Detection via Temporal Dependency and Behavioral Pattern Modeling
by Yi Li, Xingzhou Deng, Ang Yang and Jing Gao
Algorithms 2025, 18(10), 628; https://doi.org/10.3390/a18100628 (registering DOI) - 4 Oct 2025
Abstract
With the escalating global cyber threats, Distributed Denial of Service (DDoS) attacks have become one of the most disruptive and prevalent network attacks. Traditional DDoS detection systems face significant challenges due to the unpredictable nature, diverse protocols, and coupled behavioral patterns of attack [...] Read more.
With the escalating global cyber threats, Distributed Denial of Service (DDoS) attacks have become one of the most disruptive and prevalent network attacks. Traditional DDoS detection systems face significant challenges due to the unpredictable nature, diverse protocols, and coupled behavioral patterns of attack traffic. To address this issue, this paper proposes a novel approach for DDoS attack detection by leveraging the Transformer architecture to model both temporal dependencies and behavioral patterns, significantly improving detection accuracy. We utilize the global attention mechanism of the Transformer to effectively capture long-range temporal correlations in network traffic, and the model’s ability to process multiple traffic features simultaneously enables it to identify nonlinear interactions. By reconstructing the CIC-DDoS2019 dataset, we strengthen the representation of attack behaviors, enabling the model to capture dynamic attack patterns and subtle traffic anomalies. This approach represents a key contribution by applying Transformer-based self-attention mechanisms to accurately model DDoS attack traffic, particularly in handling complex and dynamic attack patterns. Experimental results demonstrate that the proposed method achieves 99.9% accuracy, with 100% precision, recall, and F1 score, showcasing its potential for high-precision, low-false-alarm automated DDoS attack detection. This study provides a new solution for real-time DDoS detection and holds significant practical implications for cybersecurity systems. Full article
16 pages, 3995 KB  
Article
An Explicit Positivity-Preserving Method for Nonlinear Aït-Sahalia Model Driven by Fractional Brownian Motion
by Zhuoqi Liu
Symmetry 2025, 17(10), 1649; https://doi.org/10.3390/sym17101649 (registering DOI) - 4 Oct 2025
Abstract
This paper develops an explicit positivity-preserving method for the nonlinear Aït-Sahalia interest rate model driven by fractional Brownian motion. To overcome the difficulties in obtaining the convergence rate of this positivity-preserving method, the Lamperti transformation is utilized, which gives an auxiliary equation. And [...] Read more.
This paper develops an explicit positivity-preserving method for the nonlinear Aït-Sahalia interest rate model driven by fractional Brownian motion. To overcome the difficulties in obtaining the convergence rate of this positivity-preserving method, the Lamperti transformation is utilized, which gives an auxiliary equation. And the convergence rate of the numerical method for this auxiliary equation is obtained by virtue of Malliavin calculus. Naturally, the target follows from the inverse of the Lamperti transformation. As a byproduct, the convergence rate of the explicit positivity-preserving method for stochastic differential equations driven by fractional Brownian motion with symmetric coefficients is obtained. Finally, several numerical experiments are performed to verify the theoretical results and demonstrate the advantage of the explicit method. Full article
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13 pages, 1556 KB  
Article
Prediction of Plate End Debonding of FRP-Strengthened RC Beams Based on Explainable Machine Learning
by Sheng Zheng and Woubishet Zewdu Taffese
Buildings 2025, 15(19), 3576; https://doi.org/10.3390/buildings15193576 (registering DOI) - 4 Oct 2025
Abstract
This research explores the phenomenon of plate-end (PE) debonding in reinforced concrete (RC) beams strengthened with fiber-reinforced polymer (FRP) composites. This type of failure represents a key mechanism that undermines the structural performance and efficiency of FRP reinforcement systems. Despite the widespread use [...] Read more.
This research explores the phenomenon of plate-end (PE) debonding in reinforced concrete (RC) beams strengthened with fiber-reinforced polymer (FRP) composites. This type of failure represents a key mechanism that undermines the structural performance and efficiency of FRP reinforcement systems. Despite the widespread use of FRP in structural repair due to its high strength and corrosion resistance, PE debonding—often triggered by shear or inclined cracks—remains a major challenge. Traditional computational models for predicting PE debonding suffer from low accuracy due to the nonlinear relationship between influencing parameters. To address this, the research employs machine learning techniques and SHapley Additive exPlanations (SHAP), to develop more accurate and explainable predictive models. A comprehensive database is constructed using key parameters affecting PE debonding. Machine learning algorithms are trained and evaluated, and their performance is compared with existing normative models. The study also includes parameter importance and sensitivity analyses to enhance model interpretability and guide future design practices in FRP-based structural reinforcement. Full article
(This article belongs to the Special Issue AI-Powered Structural Health Monitoring: Innovations and Applications)
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23 pages, 5798 KB  
Article
Application of Generative AI in Financial Risk Prediction: Enhancing Model Accuracy and Interpretability
by Kai-Chao Yao, Hsiu-Chu Hung, Ching-Hsin Wang, Wei-Lun Huang, Hui-Ting Liang, Tzu-Hsin Chu, Bo-Siang Chen and Wei-Sho Ho
Information 2025, 16(10), 857; https://doi.org/10.3390/info16100857 - 3 Oct 2025
Abstract
This study explores the application of generative artificial intelligence (AI) in financial risk forecasting, aiming to assess its potential in enhancing both the accuracy and interpretability of predictive models. Traditional methods often struggle with the complexity and nonlinearity of financial data, whereas generative [...] Read more.
This study explores the application of generative artificial intelligence (AI) in financial risk forecasting, aiming to assess its potential in enhancing both the accuracy and interpretability of predictive models. Traditional methods often struggle with the complexity and nonlinearity of financial data, whereas generative AI—such as large language models and generative adversarial networks (GANs)—offers novel solutions to these challenges. The study begins with a comprehensive review of current research on generative AI in financial risk prediction, with a focus on its roles in data augmentation and feature extraction. It then investigates techniques such as Generative Adversarial Explanation (GAX) to evaluate their effectiveness in improving model interpretability. Case studies demonstrate the practical value of generative AI in real-world financial forecasting and quantify its contribution to predictive accuracy. Furthermore, the study identifies key challenges—including data quality, model training costs, and regulatory compliance—and proposes corresponding mitigation strategies. The findings suggest that generative AI can significantly improve the accuracy and interpretability of financial risk models, though its adoption must be carefully managed to address associated risks. This study offers insights and guidance for future research in applying generative AI to financial risk forecasting. Full article
(This article belongs to the Special Issue Modeling in the Era of Generative AI)
11 pages, 2360 KB  
Article
Temperature Hysteresis Calibration Method of MEMS Accelerometer
by Hak Ju Kim and Hyoung Kyoon Jung
Sensors 2025, 25(19), 6131; https://doi.org/10.3390/s25196131 - 3 Oct 2025
Abstract
Micro-electromechanical system (MEMS) sensors are widely used in various navigation applications because of their cost-effectiveness, low power consumption, and compact size. However, their performance is often degraded by temperature hysteresis, which arises from internal temperature gradients. This paper presents a calibration method that [...] Read more.
Micro-electromechanical system (MEMS) sensors are widely used in various navigation applications because of their cost-effectiveness, low power consumption, and compact size. However, their performance is often degraded by temperature hysteresis, which arises from internal temperature gradients. This paper presents a calibration method that corrects temperature hysteresis without requiring any additional hardware or modifications to the existing MEMS sensor design. By analyzing the correlation between the external temperature change rate and hysteresis errors, a mathematical calibration model is derived. The method is experimentally validated on MEMS accelerometers, with results showing an up to 63% reduction in hysteresis errors. We further evaluate bias repeatability, scale factor repeatability, nonlinearity, and Allan variance to assess the broader impacts of the calibration. Although minor trade-offs in noise characteristics are observed, the overall hysteresis performance is substantially improved. The proposed approach offers a practical and efficient solution for enhancing MEMS sensor accuracy in dynamic thermal environments. Full article
(This article belongs to the Section Navigation and Positioning)
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24 pages, 1419 KB  
Article
Food Security Under Energy Shock: Research on the Transmission Mechanism of the Effect of International Crude Oil Prices on Chinese and U.S. Grain Prices
by Xiaowen Zhuang, Sikai Wang, Zhenpeng Tang, Zhenhan Fu and Baihua Dong
Systems 2025, 13(10), 870; https://doi.org/10.3390/systems13100870 - 3 Oct 2025
Abstract
Crude oil and grain, as two pivotal global commodities, exhibit significant price co-movement that profoundly affects national economic stability and food security. From the perspective of systems theory, the energy and grain markets do not exist in isolation but rather form a highly [...] Read more.
Crude oil and grain, as two pivotal global commodities, exhibit significant price co-movement that profoundly affects national economic stability and food security. From the perspective of systems theory, the energy and grain markets do not exist in isolation but rather form a highly coupled complex system, characterized by nonlinear feedback, cross-market risk contagion, and cascading effects. This study systematically investigates the transmission mechanisms from international crude oil prices to the domestic prices of Chinese four major grains, employing the DY spillover index, Vector Error Correction Model (VECM), and a mediation effect framework. The empirical findings reveal three key insights. First, rising international crude oil prices significantly strengthen the pass-through of global grain prices to domestic markets, while simultaneously weakening the effectiveness of domestic price stabilization policies. Second, higher crude oil prices amplify international-to-domestic price spillovers by increasing maritime freight costs, a key channel in global grain trade logistics. Third, elevated oil prices stimulate demand for renewable biofuels, including biodiesel and ethanol, thereby boosting international demand for corn and soybeans and intensifying the transmission of price fluctuations in these commodities to the domestic market. These findings reveal the key pathways through which shocks in the energy market affect food security and highlight the necessity of studying the “energy–food” coupling mechanism within a systems framework, enabling a more comprehensive understanding of cross-market risk transmission. Full article
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14 pages, 5634 KB  
Article
Validation of Analytical Models for the Development of Non-Invasive Glucose Measurement Devices
by Bruna Gabriela Pedro, Fernanda Maltauro de Cordova, Yana Picinin Sandri Lissarassa, Fabricio Noveletto and Pedro Bertemes-Filho
Biosensors 2025, 15(10), 669; https://doi.org/10.3390/bios15100669 - 3 Oct 2025
Abstract
Non-invasive glucose monitoring remains a persistent challenge in the scientific literature due to the complexity of biological samples and the limitations of traditional optical methods. Although advances have been made in the use of near-infrared (NIR) spectrophotometry, the direct application of the Lambert–Beer [...] Read more.
Non-invasive glucose monitoring remains a persistent challenge in the scientific literature due to the complexity of biological samples and the limitations of traditional optical methods. Although advances have been made in the use of near-infrared (NIR) spectrophotometry, the direct application of the Lambert–Beer Law (LBL) to such systems has proven problematic, particularly due to the non-linear behavior observed in complex organic solutions. In this context, the objective of this work is to propose and validate a methodology for the determination of the extinction coefficient of glucose in blood, taking into account the limitations of the LBL and the specificities of molecular interactions. The method was optimized through an iterative process to provide consistent results over multiple replicates. Whole blood and plasma samples from two individuals were analyzed using spectrophotometry in the 700 nm to 1400 nm. The results showed that glucose has a high spectral sensitivity close to 975 nm.The extinction coefficients obtained for glucose (αg) ranged from −0.0045 to −0.0053, and for insulin (αi) from 0.000075 to 0.000078, with small inter-individual variations, indicating strong stability of these parameters. The non-linear behaviour observed in the relationship between absorbance, glucose and insulin concentrations might be explained by the changes imposed by both s and p orbitals of organic molecules. In order to make the LBL valid in this context, the extinction coefficients must be functions of the analyte concentrations, and the insulin concentration must also be a function of glucose. A regression model was found which allows to differentiate glucose from insulin concentration, by considering the cuvette thickness and sample absorbance at 965, 975, and 985 nm. It can also be concluded from experiments that wavelength of approximately 975 nm is more suitable for blood glucose calculation by using photometry. The final spectra are consistent with those reported in mid-infrared validation studies, suggesting that the proposed model encompasses the key aspects of glucose behavior in biological media. Full article
(This article belongs to the Special Issue Recent Advances in Glucose Biosensors)
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21 pages, 406 KB  
Article
DRBoost: A Learning-Based Method for Steel Quality Prediction
by Yang Song, Shuaida He and Qiyu Wu
Symmetry 2025, 17(10), 1644; https://doi.org/10.3390/sym17101644 - 3 Oct 2025
Abstract
Steel products play an important role in daily production and life as a common production material. Currently, the quality of steel products is judged by manual experience. However, various inspection criteria employed by human operators and complex factors and mechanisms in the steelmaking [...] Read more.
Steel products play an important role in daily production and life as a common production material. Currently, the quality of steel products is judged by manual experience. However, various inspection criteria employed by human operators and complex factors and mechanisms in the steelmaking process may lead to inaccuracies. To address these issues, we propose a learning-based method for steel quality prediction, which is named DRBoost,based on multiple machine learning techniques, including Decision tree, Random forest, and the LSBoost algorithm. In our method, the decision tree clearly captures the nonlinear relationships between features and serves as a solid baseline for making preliminary predictions. Random forest enhances the model’s robustness and avoids overfitting by aggregating multiple decision trees. LSBoost uses gradient descent training to assign contribution coefficients to different kinds of raw materials to obtain more accurate predictions. Five key chemical elements, including carbon, silicon, manganese, phosphorus, and sulfur, which significantly influence the major performance characteristics of steel products, are selected. Steel quality prediction is conducted by predicting the contents of these chemical elements. Multiple models are constructed to predict the contents of five key chemical elements in steel products. These models are symmetrically complementary, meeting the requirements of different production scenarios and forming a more accurate and universal method for predicting the steel product’s quality. In addition, the prediction method provides a symmetric quality control system for steel product production. Experimental evaluations are conducted based on a dataset of 2012 samples from a steel plant in Liaoning Province, China. The input variables include various raw material usages, while the outputs are the content of five key chemical elements that influence the quality of steel products. The experimental results show that the models demonstrate their advantages in different performance metrics and are applicable to practical steelmaking scenarios. Full article
(This article belongs to the Section Computer)
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17 pages, 5087 KB  
Article
Study on the Strength Characteristics of Ion-Adsorbed Rare Earth Ore Under Chemical Leaching and the Duncan–Chang Model Parameters
by Zhongqun Guo, Xiaoming Lin, Haoxuan Wang, Qiqi Liu and Jianqi Wu
Metals 2025, 15(10), 1104; https://doi.org/10.3390/met15101104 - 3 Oct 2025
Abstract
Ionic rare earths are extracted from primary sources by the in situ chemical leaching method, where the type and concentration of leaching agents significantly affect the mechanical properties and microstructure of the ore body. In this study, MgSO4 and Al2(SO [...] Read more.
Ionic rare earths are extracted from primary sources by the in situ chemical leaching method, where the type and concentration of leaching agents significantly affect the mechanical properties and microstructure of the ore body. In this study, MgSO4 and Al2(SO4)3 solutions of varying concentrations were used as leaching agents to investigate the evolution of shear strength, the characteristics of Duncan–Chang hyperbolic model parameters, and the changes in microstructural pore characteristics of rare earth samples under different leaching conditions. The results show that the stress–strain curves of all samples consistently exhibit strain-hardening behavior under all leaching conditions, and shear strength is jointly influenced by confining pressure and the chemical interaction between the leaching solution and the soil. The samples leached with MgSO4 exhibited higher shear strength than those treated with water. The samples leached with 3% and 6% Al2(SO4)3 showed increased strength, while 9% Al2(SO4)3 caused a slight decrease. With increasing leaching agent concentration, the cohesion of the samples significantly declined, whereas the internal friction angle remained relatively stable. The Duncan–Chang model accurately described the nonlinear deformation behavior of the rare earth samples, with the model parameter b markedly decreasing as confining pressure increased, indicating that confining stress plays a dominant role in governing the nonlinear response. Under the coupled effects of chemical leaching and mechanical stress, the number and size distribution of pores of the rare earth samples underwent a complex multiscale co-evolution. These results provide theoretical support for the green, efficient, and safe exploitation of ionic rare earth ores. Full article
(This article belongs to the Special Issue Metal Leaching and Recovery)
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24 pages, 3808 KB  
Article
Study of Soliton Solutions, Bifurcation, Quasi-Periodic, and Chaotic Behaviour in the Fractional Coupled Schrödinger Equation
by Manal Alharbi, Adel Elmandouh and Mamdouh Elbrolosy
Mathematics 2025, 13(19), 3174; https://doi.org/10.3390/math13193174 - 3 Oct 2025
Abstract
This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical system. Due to its non-Hamiltonian nature, this system [...] Read more.
This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical system. Due to its non-Hamiltonian nature, this system poses significant analytical challenges. To overcome this complexity, the dynamical behavior is examined within a specific phase–space subspace, where the system simplifies to a two-dimensional, single-degree-of-freedom Hamiltonian system. The qualitative theory of planar dynamical systems is then employed to characterize the corresponding phase portraits. Bifurcation analysis identifies the physical parameter conditions that give rise to super-periodic, periodic, and solitary wave solutions. These solutions are derived analytically and illustrated graphically to highlight the influence of the fractional derivative order on their spatial and temporal evolution. Furthermore, when an external generalized periodic force is introduced, the model exhibits quasi-periodic behavior followed by chaotic dynamics. Both configurations are depicted through 3D and 2D phase portraits in addition to the time-series graphs. The presence of chaos is quantitatively verified by calculating the Lyapunov exponents. Numerical simulations demonstrate that the system’s behavior is highly sensitive to variations in the frequency and amplitude of the external force. Full article
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87 pages, 2494 KB  
Systematic Review
A Systematic Review of Models for Fire Spread in Wildfires by Spotting
by Edna Cardoso, Domingos Xavier Viegas and António Gameiro Lopes
Fire 2025, 8(10), 392; https://doi.org/10.3390/fire8100392 - 3 Oct 2025
Abstract
Fire spotting (FS), the process by which firebrands are lofted, transported, and ignite new fires ahead of the main flame front, plays a critical role in escalating extreme wildfire events. This systematic literature review (SLR) analyzes peer-reviewed articles and book chapters published in [...] Read more.
Fire spotting (FS), the process by which firebrands are lofted, transported, and ignite new fires ahead of the main flame front, plays a critical role in escalating extreme wildfire events. This systematic literature review (SLR) analyzes peer-reviewed articles and book chapters published in English from 2000 to 2023 to assess the evolution of FS models, identify prevailing methodologies, and highlight existing gaps. Following a PRISMA-guided approach, 102 studies were selected from Scopus, Web of Science, and Google Scholar, with searches conducted up to December 2023. The results indicate a marked increase in scientific interest after 2010. Thematic and bibliometric analyses reveal a dominant research focus on integrating the FS model within existing and new fire spread models, as well as empirical research and individual FS phases, particularly firebrand transport and ignition. However, generation and ignition FS phases, physics-based FS models (encompassing all FS phases), and integrated operational models remain underexplored. Modeling strategies have advanced from empirical and semi-empirical approaches to machine learning and physical-mechanistic simulations. Despite advancements, most models still struggle to replicate the stochastic and nonlinear nature of spotting. Geographically, research is concentrated in the United States, Australia, and parts of Europe, with notable gaps in representation across the Global South. This review underscores the need for interdisciplinary, data-driven, and regionally inclusive approaches to improve the predictive accuracy and operational applicability of FS models under future climate scenarios. Full article
29 pages, 886 KB  
Article
The Value Enhancement Path of ESG Practices from a Resource Dependence Perspective: A Research Model with Mediating and Moderating Effects
by Sheng Xu, Zhao Chen and Yuhao Liu
Sustainability 2025, 17(19), 8856; https://doi.org/10.3390/su17198856 - 3 Oct 2025
Abstract
This study constructs a research model with regulation and mediation based on the resource dependence theory to explore the nonlinear relationship between ESG responsibility fulfillment and firm value. This study uses a sample of Chinese A-share listed manufacturing firms from 2015 to 2022 [...] Read more.
This study constructs a research model with regulation and mediation based on the resource dependence theory to explore the nonlinear relationship between ESG responsibility fulfillment and firm value. This study uses a sample of Chinese A-share listed manufacturing firms from 2015 to 2022 and conducts empirical analysis using STATA version 18.0. The results indicate a U-shaped relationship between ESG responsibility fulfillment and firm value. Stakeholders’ interests play a partial mediating role in the above relationship. Moreover, institutional investors’ shareholding further strengthens the positive association between ESG responsibility fulfillment and stakeholder interests. The firm life cycle has a heterogeneous effect on the relationship between ESG responsibility fulfillment and stakeholder interests. Specifically, firms in the maturity stage exhibit the most pronounced protection of stakeholder interests, whereas firms in the decline stage show relatively weaker protection effects. Additionally, there is a complementary interaction between the firm life cycle and institutional investors’ shareholding. This combination significantly enhances the positive moderating effect of institutional investors’ shareholding on the relationship between ESG responsibility fulfillment and stakeholder interests only when firms are in the growth or decline stages. This study not only expands the boundaries of resource dependence theory, but also provides management insights for sustainable practices in the real economy. Full article
(This article belongs to the Section Economic and Business Aspects of Sustainability)
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34 pages, 2710 KB  
Review
The Role of Fractional Calculus in Modern Optimization: A Survey of Algorithms, Applications, and Open Challenges
by Edson Fernandez, Victor Huilcapi, Isabela Birs and Ricardo Cajo
Mathematics 2025, 13(19), 3172; https://doi.org/10.3390/math13193172 - 3 Oct 2025
Abstract
This paper provides a comprehensive overview of the application of fractional calculus in modern optimization methods, with a focus on its impact in artificial intelligence (AI) and computational science. We examine how fractional-order derivatives have been integrated into traditional methodologies, including gradient descent, [...] Read more.
This paper provides a comprehensive overview of the application of fractional calculus in modern optimization methods, with a focus on its impact in artificial intelligence (AI) and computational science. We examine how fractional-order derivatives have been integrated into traditional methodologies, including gradient descent, least mean squares algorithms, particle swarm optimization, and evolutionary methods. These modifications leverage the intrinsic memory and nonlocal features of fractional operators to enhance convergence, increase resilience in high-dimensional and non-linear environments, and achieve a better trade-off between exploration and exploitation. A systematic and chronological analysis of algorithmic developments from 2017 to 2025 is presented, together with representative pseudocode formulations and application cases spanning neural networks, adaptive filtering, control, and computer vision. Special attention is given to advances in variable- and adaptive-order formulations, hybrid models, and distributed optimization frameworks, which highlight the versatility of fractional-order methods in addressing complex optimization challenges in AI-driven and computational settings. Despite these benefits, persistent issues remain regarding computational overhead, parameter selection, and rigorous convergence analysis. This review aims to establish both a conceptual foundation and a practical reference for researchers seeking to apply fractional calculus in the development of next-generation optimization algorithms. Full article
(This article belongs to the Special Issue Fractional Order Systems and Its Applications)
26 pages, 1838 KB  
Article
Modeling the Emergence of Insight via Quantum Interference on Semantic Graphs
by Arianna Pavone and Simone Faro
Mathematics 2025, 13(19), 3171; https://doi.org/10.3390/math13193171 - 3 Oct 2025
Abstract
Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this [...] Read more.
Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this work, we propose a computational model of insight generation grounded in continuous-time quantum walks over weighted semantic graphs, where nodes represent conceptual units and edges encode associative relationships. By exploiting the principles of quantum superposition and interference, the model enables the probabilistic amplification of semantically distant but contextually relevant concepts, providing a plausible account of non-local transitions in thought. The model is implemented using standard Python 3.10 libraries and is available both as an interactive fully reproducible Google Colab notebook and a public repository with code and derived datasets. Comparative experiments on ConceptNet-derived subgraphs, including the Candle Problem, 20 Remote Associates Test triads, and Alternative Uses, show that, relative to classical diffusion, quantum walks concentrate more probability on correct targets (higher AUC and peaks reached earlier) and, in open-ended settings, explore more broadly and deeply (higher entropy and coverage, larger expected radius, and faster access to distant regions). These findings are robust under normalized generators and a common time normalization, align with our formal conditions for transient interference-driven amplification, and support quantum-like dynamics as a principled process model for key features of insight. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
13 pages, 322 KB  
Article
Observer-Based Exponential Stabilization for Time Delay Takagi–Sugeno–Lipschitz Models
by Omar Kahouli, Hamdi Gassara, Lilia El Amraoui and Mohamed Ayari
Mathematics 2025, 13(19), 3170; https://doi.org/10.3390/math13193170 - 3 Oct 2025
Abstract
This paper addresses the problem of observer-based control (OBC) for nonlinear systems with time delay (TD). A novel hybrid modeling framework for nonlinear TD systems is first introduced by synergistically combining TD Takagi–Sugeno (TDTS) fuzzy and Lipschitz approaches. The proposed methodology broadens the [...] Read more.
This paper addresses the problem of observer-based control (OBC) for nonlinear systems with time delay (TD). A novel hybrid modeling framework for nonlinear TD systems is first introduced by synergistically combining TD Takagi–Sugeno (TDTS) fuzzy and Lipschitz approaches. The proposed methodology broadens the range of representable systems by enabling Lipschitz nonlinearities to fulfill dual functions: they may describe essential dynamic behaviors of the system or represent aggregated uncertainties, depending on the specific application. The proposed TDTS–Lipschitz (TDTSL) model class features measurable premise variables while accommodating Lipschitz nonlinearities that may depend on unmeasurable system states. Then, through the construction of an appropriate Lyapunov–Krasovskii (L-K) functional, we derive sufficient conditions to ensure exponential stability of the augmented closed-loop model. Subsequently, through a decoupling methodology, these stability conditions are reformulated as a set of linear matrix inequalities (LMIs). Finally, the proposed OBC design is validated through application to a continuous stirred tank reactor (CSTR) with lumped uncertainties. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis: Theory, Methods and Applications)
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