Search Results (1,800)

Accurate prediction of contaminant transport and self-purification processes in rivers remains challenging because pollutant dispersion, biochemical reactions, and hydrodynamic conditions interact across multiple spatial scales. This study aims to develop and compare mathematical models for soluble contaminant transport and biodegradable organic matter removal in channels and rivers. Unsteady advection–diffusion–reaction equations were formulated for one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) transport scenarios and solved through numerical techniques based on the transformation of partial differential equations into systems of ordinary differential or algebraic equations. In parallel, the classical Streeter–Phelps model and an extended formulation incorporating turbulent diffusion were implemented to evaluate organic load degradation and oxygen deficit dynamics. Simulations were performed using a Matlab R2019a-based computational framework under representative hydraulic and reaction conditions obtained from literature data and empirical correlations. The results showed that, under specific conditions, the 3D model reproduced trends comparable to those predicted by the 2D model, while the latter approached the behavior of the 1D formulation. The Streeter–Phelps model predicted an organic load removal efficiency of 97.74%, a purification index of 1.9564, a critical time of 18.43 h, and a critical distance of 6.93 km. These findings provide a useful framework for river water-quality assessment and support future applications involving complex hydrodynamic and pollutant-loading scenarios. Full article

Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and machine learning (ML), TDA provides multiscale descriptions through persistent homology, Mapper (a graph-based method that summarizes the shape of high-dimensional data), and related topological signatures that are often inaccessible to standard linear and metric methods. In recent years, and especially during 2024–2025, TDA has expanded rapidly across science, engineering, biomedical research, and socio-economic studies, while also being integrated with modern learning paradigms such as deep learning (DL) and graph learning. This survey summarizes recent developments in TDA using a carefully selected set of articles, with emphasis on 2024–2025. We first present the mathematical and computational foundations of TDA, covering simplicial complexes, filtrations, persistent homology, the Mapper algorithm, and computational advances such as data simplification, stability, and efficiency. We then review applications in time series and dynamical systems, biomedical imaging and precision medicine, engineering and physical sciences, finance and risk analysis, DL and interpretability, and security and critical infrastructure systems. Throughout, we highlight how TDA can extract informative features, function as a model component, and provide a conceptual lens for studying complex systems. However, the survey also emphasizes recurrent failure patterns: TDA performance is highly sensitive to filtration, embedding, and vectorization choices; aggressive simplification can dilute or remove informative topological signals; and integration into standard ML workflows still lacks uniform validation and reporting protocols. We conclude by outlining key challenges—including scalability, statistical foundations, interpretability, and compatibility with rapidly evolving artificial intelligence (AI) paradigms—and by identifying directions for future research. The survey also provides a unifying design perspective for TDA systems, highlighting methodological trade-offs and emerging research directions for integrating topology with modern ML. Full article

Petri nets represent a highly versatile mathematical formalism for modeling discrete event and hybrid systems. For the development of modern complex production processes for Industry 4.0, integrating these formal models with industrial communication standards is an appropriate and effective option. The main aim of the proposed article is to design a new web-based software tool for the modeling, simulation, and control of mechatronic systems with OPC Unified Architecture support. To accomplish this task, an original software solution called PetriLink is proposed. This platform leverages an intuitive graphical interface and significantly expands the formalism by combining hybrid Petri nets with Colored Petri Nets (CPN) data extensions and a reactive OPC UA subscription model. These new features greatly expand the area of systems that can be modeled and controlled, bridging the gap between theoretical academic tools and practical industrial automation. Furthermore, the structural flexibility of the implemented Petri net models enables the explicit representation of symmetric cyber-physical architectures, as well as the design of asymmetric, event-driven control strategies (e.g., using inhibitor and reset arcs) for enhanced system robustness. The platform was evaluated on a reference net of 5000 places and 2500 transitions, where an incremental dirty-flag evaluation mechanism keeps the per-step engine cost below 1 ms for sparse industrial markings and at about 350 µs for a moderate workload of one hundred concurrent tokens, yielding a speed-up of up to roughly three orders of magnitude over naive full re-evaluation and confirming consistent soft real-time behavior on commodity hardware. Offering a graphical environment for the design of discrete event and hybrid system control algorithms, it can be used for education, research and practice in cyber-physical systems (Industry 4.0). Full article

The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order compartmental model is formulated by dividing the population into potential smokers, light smokers, heavy smokers, and quit smokers. The smoking reproduction number is derived to characterize the transmission and persistence of smoking behavior within the population. To determine the impact of model parameters on smoking dynamics, both normalized forward sensitivity analysis and global sensitivity analysis based on Latin Hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC) are performed. The obtained results identify the most sensitive transmission and progression parameters and demonstrate their important role in shaping smoking prevalence within the community. Furthermore, the classical integer-order model is compared with the fractional-order formulation, where the fractional model provides a more realistic description due to its ability to incorporate memory and hereditary effects associated with smoking behavior. An optimal control framework involving awareness and treatment strategies is further introduced to investigate effective smoking reduction policies. The numerical results demonstrate that awareness campaigns reduce smoking initiation, while treatment interventions increase smoking cessation, and the combined implementation of both strategies produces the most significant reduction in smoking prevalence. The consistency between the sensitivity analysis and optimal control results further supports the reliability of the proposed framework. Numerical simulations are carried out to analyze the qualitative and quantitative behavior of the system under different epidemiological scenarios. In addition, an ANN-based computational framework is employed as an efficient numerical tool to accurately approximate the complex dynamics of the proposed fractional-order smoking model with very low prediction error. Overall, the present study provides a comprehensive mathematical and computational framework for understanding, analyzing, and controlling smoking behavior within a population. Full article

Against the backdrop of rapid urbanization, urban sewer networks face increasing challenges, including infrastructure deterioration and imbalanced resource allocation. Conventional single-dimensional risk assessment methods fail to capture the coordinated development of such complex systems. This study proposes a comprehensive HFM framework integrating Health (H), Failure (F), and Management (M), coupled with a Coupling Coordination Degree (CCD) model and an obstacle degree model to evaluate system interactions and identify key constraints. A game theory-based weighting approach combining AHP and CRITIC is applied to integrate subjective and objective weights, while fuzzy mathematics is used for multidimensional evaluation. CCD spatial analysis is conducted at the drainage unit scale. Results show that: (1) The system is in a transitional stage from disorder to coordination, with CCD values mainly ranging from 0.4 to 0.8 and exhibiting significant spatial heterogeneity. (2) High-risk areas tend to have better health conditions and stronger management inputs, whereas low-risk areas may still face latent risks due to insufficient management. (3) Key obstacles are concentrated in Failure and Management systems, particularly pipeline functionality and management capacity. Overall, system risk arises from mismatches between risk sources and management allocation rather than purely structural deficiencies. The proposed framework effectively identifies imbalance areas and priority interventions, supporting the transition toward proactive risk regulation. Full article

In heavy-haul railway systems, effective empty railcar distribution (ERD) can optimize composition planning and meet empty railcar requirements (ERRs) at all loading ends, thereby improving the efficiency of train operations. To solve practical challenges such as the imbalanced supply–demand of empty trains, redundant loading and unloading cycles, and prolonged waiting times, this study establishes a multi-objective and 0–1 integer programming model for ERD at the loading end of a heavy-haul railway. The model can simultaneously maximize the fulfilment of all ERRs, minimize the ERD delay time, and reduce the waiting time in the heavy-train combination problem under complex constraints, including the passing capacity of sections, combination capacity of stations, and ERR at the loading end. While traditional optimization methods such as mathematical programming or heuristic algorithms partially address these issues, they are ineffective under dynamic constraints and state-space explosion. Furthermore, traditional reinforcement learning-based methods, such as Q-learning, exhibit limitations in railway scheduling due to the state-space explosion problem and inadequate model generalization. To overcome these limitations, this study proposes an innovative framework; the ERD at the loading end of the heavy-haul railway is formalized as a Markov decision process and optimized using deep Q-network (DQN) reinforcement learning. In addition, this study proposes an experience data fusion mechanism that integrates the empirical rules of the dispatchers through a modular architecture, achieving real-time constraint compliance while maintaining scalability for practical implementation. The NSGA-II genetic algorithm for multi-objective problems is used in this study to evaluate the performance of the DQN algorithm. The experimental results demonstrate that the DQN algorithm can fully meet ERRs with zero delay and produce optimal schemes for train combinations. Meanwhile, NSGA-II presents superior performance in minimizing the combination waiting time and same-destination train combinations. Meanwhile, the DQN algorithm can identify superior ERD strategies in the expanded-action and state spaces, enabling the effective handling of complex constraint-based ERD. Full article

Understanding advanced pre-tertiary mathematics, particularly three-dimensional vectors, demands robust spatial reasoning skills that many students find challenging to develop through traditional pedagogical methods. This study proposes and evaluates an innovative educational tool that leverages large vision models to automate the conversion of handwritten vector equations into accurate 3D graphical representations. By interpreting students’ handwritten input using advanced computer vision, the system provides immediate, interactive visual feedback to bridge the cognitive gap between abstract symbolic notation and tangible geometric concepts. We evaluated the system using a dataset of 1000 handwritten vector equations typical of the Singapore-Cambridge GCE ‘A’ Level H2 Mathematics syllabus. Our findings demonstrate that while GPT-4o serves as a capable baseline, achieving 84.6% accuracy with multi-shot prompting, newer variants such as GPT-4.1-mini offer superior performance, reaching 91.4% accuracy with significantly higher computational efficiency. The results confirm that AI-powered visualisation tools can effectively interpret complex spatial mathematical layouts when guided by optimal prompt engineering. Implementing such technology in educational settings presents a viable, scalable, and cost-effective method to democratise learning support, fostering independent study and enhancing students’ conceptual comprehension of spatial mathematics. Full article

Complex products continue to face low iterative-design efficiency and poor cross-generation data compatibility, while existing product-gene research is still constrained by the predominance of qualitative approaches, ambiguous representations of hierarchical associations, and insufficient standardization. Based on the principles of decomposition and reconstruction and the systems thinking of genetic engineering, this study develops a generic three-level framework for product genes at the platform, assembly, and component levels. Hierarchical mapping functions and parameter-constraint equations are introduced to enable quantitative representation, and a quantitative product-gene information system is established, including a core-parameter quantification model and inter-/intra-level association-strength models. By integrating multiple international standards, the study further constructs a tripartite standardized description system covering metadata, semantics, and format, and proposes a mathematical mapping method from product information to standardized formats. A case study of Company A’s Platform B and Concept Vehicle C shows that the association-strength model achieves the required adaptation threshold, thereby validating the proposed framework. This study provides quantitative theoretical support for the platform-based and intelligent development of complex products and offers an implementable technical solution for product-gene reuse and data sharing, particularly in the new energy vehicle industry. Full article

This study develops a game-theoretic framework to analyze collaborative advertising decisions between manufacturers and retailers in seasonal product supply chains characterized by competitive–cooperative channel relationships. We formulate a mathematical programming model to jointly optimize advertising efforts, the manufacturer’s advertising cost-sharing rate, order quantities, and inventory decisions across distinct channel configurations—including a single manufacturer–retailer dyad and a competitive multi-channel market. Numerical experiments and sensitivity analyses are conducted to investigate how key structural parameters—particularly demand elasticity and channel power asymmetry—influence overall system performance and equilibrium decision outcomes. Results indicate that well-designed collaborative advertising mechanisms enhance total channel profitability and, under specific conditions, yield Pareto-improving outcomes for both parties. This study makes three primary contributions: (i) it integrates inter-firm competition with intra-channel cooperation within a unified strategic framework; (ii) it jointly coordinates advertising and inventory decisions—two critical operational levers—rather than treating them in isolation; and (iii) it embeds financial arrangements (e.g., cost sharing) endogenously into the analytical model, thereby offering a novel, theoretically grounded, and practically implementable decision-support framework for distribution systems operating in complex, dynamic market environments. Full article

Agricultural cooperatives in developing economies struggle with capital access and typically depend on subsidized credit with rigid repayment schedules that create vulnerability during low-production cycles. In this paper, we present a mathematical framework implemented through a smart contract to tokenize cooperative capital. Our mathematical framework uses magnified accumulators (scaled accumulator variables) to maintain temporal fairness, allocating dividends proportionally based on token holding periods through correction factors. The dividend distribution model operates with $O\left(1\right)$ computational complexity, regardless of cooperative size. The CooperativeToken smart contract combines ERC20 standards with automated dividend distribution, democratic governance mechanisms, and a hybrid payment architecture supporting both cryptocurrency and fiat transactions. Deployment verification and a gas analysis demonstrate operational viability with consistent performance and minimal transaction costs, enabling scalability from small to large cooperatives. The proposed system offers agricultural cooperatives a debt-free alternative to conventional financing, democratizing access to tokenized capital structures that were previously restricted to large agribusinesses. While the model is validated via Ethereum Sepolia testnet simulation, real-world deployment and field testing in active cooperatives remain necessary to confirm practical feasibility. This study provides the algorithmic and economic foundation for such pilots. Full article

The complexity of a graph, defined as its number of spanning trees, serves as a key measure of network reliability. Stacked graphs constitute a significant and versatile class of graphs, formed by superimposing multiple copies of a base graph upon a shared central vertex set. Their inherent layered symmetry and structural regularity make them compelling models for a wide range of real-world networks, including multi-tier communication systems, hierarchical data networks, and resilient distributed architectures. Moreover, their systematic construction from well-known graph families renders the study of their complexity both mathematically rich and algorithmically meaningful. In this paper, we derive closed-form formulas for the complexity of several stacked graph families based on path- and cycle-based structures with a central vertex, including stacked fan and wheel graphs, stacked double fan and double wheel graphs, and stacked path flower, cycle flower, and gear graphs. The derivations are based on techniques from linear algebra, matrix theory, and Chebyshev polynomials. Full article

Reliable mathematical models are essential for high-performance analysis and optimization of complex power and energy systems. However, inherent nonlinearities pose significant challenges to accurate model identification. The Hammerstein model, a typical block oriented nonlinear system, consists of a static nonlinear block followed by a linear dynamic block. This paper investigates the data-driven modeling method for the Hammerstein model and proposes a hierarchical identification strategy that integrates the correlation analysis with the Levenberg–Marquardt algorithm. Unlike traditional methods, this hierarchical algorithm strategy decouples the linear and nonlinear modules to avoid parameter coupling and reduces computational complexity. Simulations on a solid oxide fuel cell system and a real-world wind power system confirm the effectiveness and feasibility of the proposed method. The results demonstrate that the hierarchical identification strategy achieves accurate parameter estimation with satisfactory convergence performance. Full article

The high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals poses a significant challenge for power-limited satellite transponders, leading to power amplifier nonlinearity and reduced system efficiency. This paper proposes a novel joint algorithm named Polar-SLM-CPM for efficient PAPR suppression in satellite coded OFDM (COFDM) systems. The core of this scheme is a deeply integrated design that synergistically combines polar coding, intelligent selective mapping (SLM), and adaptive continuous phase modulation (CPM). Unlike conventional approaches that treat these components separately, our method leverages the constant-envelope property of CPM for inherent PAPR limitation, employs a gradient-learning-optimized intelligent SLM mechanism for efficient low-PAPR sequence search, and utilizes capacity-approaching polar codes to guarantee transmission reliability. The synergistic operation is mathematically modeled and extensively evaluated via MATLAB simulations. Results demonstrate that the proposed algorithm achieves a substantial PAPR reduction of approximately 4.2 dB at a complementary cumulative distribution function (CCDF) of ${10}^{-3}$ while maintaining bit error rate (BER) performance comparable to conventional polar-coded OFDM under additive white Gaussian noise (AWGN) channels. Further analyses on synchronization, computational complexity (Big-O), parameter sensitivity, spectral efficiency trade-offs, and robustness in realistic nonlinear/phase-noise channels are provided, confirming the scheme’s practical viability. This work presents a balanced and effective solution for enhancing the power efficiency and signal integrity of next-generation integrated satellite communication and navigation systems employing COFDM-CPM waveforms. Full article

In complex socio-technical systems, human–AI collaboration is becoming fundamental to the processes of knowledge creation, content generation, and innovation. The existing innovation models typically consider only a single actor, the sole AI system, or a content artifact, and therefore do not capture the dynamics between these heterogeneous actors. This study introduces a Multimodal Graph Neural Network (MM-GNN), for modeling and analyzing innovation dynamics within Human–AI–Content (HAC) networks. The proposed framework is based on HAC networks as dynamic tripartite graphs, where human nodes, AI agent nodes, and content nodes are interconnected by edges representing interactions that evolve over time. Multimodal information, including text, image, code, and structured interaction traces, is merged by attention-based fusion, and multimodal dependency and evolution of interactions are modeled by relation-aware graph message passing and GRU-based temporal propagation. The innovation potential is realized as an upper-bounded composite score based on normalized novelty, entropy change, diffusion contribution, and human-rated creativity if available. The model is assessed as a composition of node-level classification and a regression model for innovation-level classification and estimation of continuous innovation potential. Experiments on synthetic HAC datasets and selected real-world AIGC corpora demonstrate that MM-GNN performs better than the graph learning and index-based baselines, with an average F1 score of 0.87, temporal stability ρ = 0.89, and lower regression error. The ablation and visualization analyses demonstrate that the multimodal fusion and temporal propagation are beneficial for representation quality, diffusion modeling, and interpretation. The results offer a mathematical and computational approach to the study of innovation as an emergent phenomenon of dynamic human, AI, and content interactions and lay the groundwork for additional validation on a more expansive socio-technical scale. Full article

Fractional differential operators provide an effective approach for modeling complex technological processes, particularly physical phenomena in continuum mechanics characterized by memory and non-local effects. Different types of fractional derivatives require different numerical approximation schemes; in this study, the Caputo and Grünwald–Letnikov derivatives are considered. The aim of this work was to develop and validate a fractional differential model of longitudinal oscillations in a suspended monorail system that accounts for nonlinear and memory-dependent effects. In contrast to classical integer-order approaches, the proposed framework incorporates multiscale surface irregularity effects, including rail roughness, friction, and other disturbances influencing system dynamics, through a fractional-order formulation. A fractional differential mathematical model describing the motion of longitudinal oscillations of a large-sized cargo transported along a suspended monorail is proposed. A numerical algorithm based on finite-difference approximation of fractional operators was developed for its implementation. The scientific contribution lies in integrating multiscale surface irregularity effects into a fractional-order modeling framework to improve the accuracy of dynamic response prediction. Numerical experiments demonstrated the effectiveness of the approach, and the results were validated through comparison with existing models of monorail dynamics. Additionally, statistical validation based on correlation analysis confirmed good agreement with the experimental data. The proposed model can be applied to the design and optimization of suspended transport systems, improving vibration control, reliability, and operational safety under real dynamic loading conditions. Full article