Complexity最新文献

{"title":"Mechanisms Not Magic: Case-Based and Computational Complexity Methods for Societal Crises and Transitions","authors":"Corinna Elsenbroich","doi":"10.1155/cplx/2893400","DOIUrl":"https://doi.org/10.1155/cplx/2893400","url":null,"abstract":"<p>The global challenges we are facing, environmental, economic and health crises, are complex problems that need a methodological approach that honours this complexity. Current approaches, extrapolating the future from past data, will not be able to tackle the profound changes that are to come. Instead, we need complexity methods that uncover mechanisms and processes underlying social phenomena and that let us extrapolate counterfactual future narratives. This paper discusses how the integration of qualitative and computational complexity methods can help with this endeavour.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/2893400","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural Ordinary Differential Equation With Grünwald–Letnikov Fractional Momentum","authors":"Wei Yang","doi":"10.1155/cplx/9182285","DOIUrl":"https://doi.org/10.1155/cplx/9182285","url":null,"abstract":"<p>Forecasting short annual time series is challenging because limited observations increase the risks of unstable optimization, overfitting, and information leakage. This study proposes a standard first-order neural ordinary differential equation trained with finite-memory Grünwald–Letnikov fractional momentum. The fractional operator acts on the parameter update sequence rather than on the latent-state dynamics. The empirical evaluation combines a descriptive comparison on medium-length regional annual energy-consumption series with a 12-year holdout and a reproducible experiment on five extremely short provincial annual series, with the final two observations reserved for strictly recursive testing. The fractional order is selected by particle swarm optimization using only the training data. GLFNODE is compared with a NODE of the same architecture trained using Adam, together with MLP, ARIMA, SARIMA, ETS, and LSTM baselines. Across the five reported series, GLFNODE achieves test MAPE values ranging from 1.848% to 6.300%. Compared with the Adam-trained NODE, GLFNODE reduces the mean MAPE, MAE, and RMSE by 17.56%, 17.14%, and 15.91%, respectively. These results provide reproducible evidence that fractional-memory optimization can improve a compact neural ODE under extremely short-record conditions, particularly relative to the same architecture trained with Adam.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/9182285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized Projective Riccati Equation Method for Exact Solutions in Fractional Gas Dynamics and Nonlinear Wave Propagation","authors":"Fatemah Mofarreh,&nbsp;Reham Alahmadi,&nbsp;Gulagha Jan Assar,&nbsp;Mohammed Alquraish,&nbsp;Naveed Iqbal","doi":"10.1155/cplx/3190708","DOIUrl":"https://doi.org/10.1155/cplx/3190708","url":null,"abstract":"<p>In this work, the exact solutions of nonlinear wave equations are studied in the framework of fractional gas dynamics. Two powerful methods, such as the generalized projective Riccati equation method (GPREM) and modified extended simple equation method (MESM), are applied to solve the fractional gas dynamics equations, which are used to model complex wave phenomena, exactly and analytically. A central role in this approach is played by the Riccati equation, which we can use to obtain the soliton solutions, periodic waves, and other nonlinear wave patterns. We show that both GPREM and MESM give a systematic way to find exact and soliton solutions that are essential to understanding the dynamics of fractional systems and facilitate the introduction of a novel order of the gas dynamics equations, which poses a unique set of challenges. The physical interpretation of these solutions is discussed in terms of wave propagation, stability, and interaction of nonlinear waves. The findings demonstrate the applicability of the Riccati-based techniques to the solution of fractional nonlinear evolution equations and will help in the development of theoretical models in fractional dynamics. This paper sets the groundwork for additional research into the use of fractional calculus in the study of fluid dynamics and wave propagation and could prove useful in other branches of physics and engineering.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/3190708","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling Fractional-Order Tuberculosis Epidemics Using SL-BRNN","authors":"Zulqurnain Sabir,&nbsp;Zafar Duman Abbasov,&nbsp;Nabila Brahmi Chendouh,&nbsp;A. M. Shloof","doi":"10.1155/cplx/9424770","DOIUrl":"https://doi.org/10.1155/cplx/9424770","url":null,"abstract":"<p>The present research provides the solutions of the fractional order (FO) tuberculosis (TB) epidemics model by applying the supervised learning Bayesian regularization neural network (SL-BRNN). The Caputo fractional derivative is executed to solve the TB epidemic model, which is essential to perform the intricate systems with nonlinear relations and delivers a powerful mathematical structure for relating systems with FO dynamics. The model is described into six population groups: susceptible, latent, treatment of Type 1 and 2, infected, and recovered. A construction of network is performed by taking sigmoid activation function and 21 neurons in the hidden layer, 1000 epochs, and optimization through BR. The dataset of the FO-TB epidemics model is calculated using the Adams–Bashforth–Moulton technique in intervals 0 and 1, with a 0.01 step size, which reduces the mean square error by data splitting into training (73%), testing (14%), and validation (13%). Moreover, the data training is performed using the designed construction of the solver based on SL-BRNN. The solutions of three FO-TB epidemics models are presented in three cases by taking the FO derivative values 0.7, 0.8, and 0.9. In addition, the solutions of the proposed SL-RNN are compared with the Levenberg–Marquardt backpropagation algorithm in order to check the accuracy of the scheme. Moreover, the best training values, error histogram, fitness performances, absolute error, and state transition further provide the accuracy and reliability of the designed SL-BRNN.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/9424770","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PNAR Models for Population Dynamics in Complex Networks: A High-Dimensional Approach","authors":"Oscar Luis Alonso-Cienfuegos,&nbsp;Ana Isabel Otero-Sanchez","doi":"10.1155/cplx/7676109","DOIUrl":"https://doi.org/10.1155/cplx/7676109","url":null,"abstract":"<p>This paper analyzes population dynamics in Asturias (Spain) using a network-based time series framework. This setting constitutes a complex system where interactions between settlements shape aggregate population outcomes. We model interdependencies between settlements through a complex network derived from the provision of secondary education services. We compare two approaches: the generalized network autoregressive (GNAR) model and the Poisson network autoregressive (PNAR) model. While GNAR provides a flexible representation of network dependencies, it faces limitations in high-dimensional settings with short time series. PNAR, by contrast, offers a more suitable framework for count data and improves model stability and interpretability. Using empirical estimation and simulation, we show that population dynamics are primarily driven by temporal persistence, but also influenced by network interactions. Moreover, counterfactual simulations based on alternative network structures suggest that more balanced connectivity patterns may enhance local population outcomes. Our results highlight the importance of model choice in network time series and demonstrate that PNAR models provide a robust computational framework for high-dimensional network count data, with potential applications to other complex systems.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/7676109","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advanced Neurocomputational Framework for Assessing Memory-Driven COVID-19 Transmission Dynamics: Integrating Fractional Modeling With Deep Neural Networks","authors":"Muhammad Farhan,&nbsp;Zhi Ling,&nbsp;Saif Ullah,&nbsp;Abdul Baseer Saqib,&nbsp;Mabrook S. Al-Rakhami,&nbsp;Atif M. Alamri","doi":"10.1155/cplx/4545491","DOIUrl":"https://doi.org/10.1155/cplx/4545491","url":null,"abstract":"<p>COVID-19 remains a critical global health challenge, necessitating advanced computational methods to accurately predict its transmission dynamics. This study aims to develop a novel neurocomputing procedure based on the Levenberg–Marquardt back propagation neural network for the transmission dynamics of COVID-19 with vaccination and isolation. We investigate the model’s mathematical properties, including global stability, and identify key parameters influencing disease incidence through normalized sensitivity analysis. The numerical solutions of the transmission dynamics of COVID-19 with vaccination are obtained through the reliable stochastic intelligent approach based on the deep neural network (DNN). The model’s accuracy is validated via comparative analysis across all compartments, with performance evaluated through convergence studies, error distribution assessments, and regression analysis. A dataset generated by the modified fractional Adams–Bashforth iterative scheme is used to develop a DNN-based numerical scheme. The DNN architecture consists of an input layer, two hidden layers with 50 and 5 neurons, respectively, and an output layer corresponding to the model state variables. The proposed scheme is then used to minimize the mean square error by dividing the data 15% for both validation and testing, while 70% is applied for training. Seven cases based on the initial conditions with <i>α</i> = 0.90, 0.92, 0.94, 0.96, 1 are used to analyze the robustness of numerical scheme for the COVID-19 model with different memory effects. The present approach provides solutions that match precisely with benchmark data attaining the best validation results ranging from 10⁻⁰⁸ to 10⁻¹¹, and least absolute error within the range 10⁻⁰⁴ to 10⁻¹⁰ across the model equations. In addition to this, the stability analysis and sensitivity results further validate the model’s reliability for real-world applications. This study pioneers applying the DNN utilizing Tanh and ReLU activation functions in the hidden layers to model the dynamics of COVID-19 with various control measures. The proposed hybrid procedure can be efficiently used to solve more complex infectious disease models beyond COVID-19.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/4545491","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Delayed Parasitism and Population Cycles in Mosquito–Water Mite Systems","authors":"Dipesh,&nbsp;Pankaj Kumar,&nbsp;Zabihullah Movaheedi,&nbsp;Sandeep Malik","doi":"10.1155/cplx/9474425","DOIUrl":"https://doi.org/10.1155/cplx/9474425","url":null,"abstract":"<p>This study uses a delay differential equation (DDE) model that takes into account both parasitism and predation effects to examine the dynamic interactions between water mites and mosquito populations. The proposed DDE model uniquely captures the dual ecological role of water mites as both parasites and predators of mosquitoes through biologically motivated nonlinear interactions. To account for parasitism’s biological lag and its effect on water mite reproduction, the model adds a time delay. In order to ensure biologically meaningful solutions, mathematical analysis verifies the system’s positivity and boundedness. The model performs stability analysis at a variety of delay conditions and locates a biologically viable equilibrium point. At a critical point of delay, a Hopf bifurcation occurs and marks the beginning of long-term oscillations of the population dynamics. Numerical simulations are used to create time-domain plots and phase space diagrams that demonstrate how the system responds without a delay, below the delay threshold, at the critical point and exceeding it. Under the findings, a small delay results in the creation of the asymptotic stability, and a large delay results in the creation of the periodic solutions as well as population cycles. The analysis of the significance of time delays in the establishment of ecological balance between the parasite and host species is brought into the limelight of the study. It further emphasizes that the study establishes the existence and uniqueness of the biologically feasible equilibrium, investigates delay-induced stability switching and Hopf bifurcation, and examines the influence of developmental delay on the long-term population dynamics. The modeling approach also serves as a natural foundation of future ecological studies that incorporate time-dependent interactions by providing an understanding of biological control measures and population management in aquatic ecosystems.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/9474425","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RPriori: A Divide-and-Conquer Frequent Itemset Mining Algorithm With Improved Time-Space Efficiency on Large Transactional Data","authors":"Rahat Ali Shah,&nbsp;Jamal Uddin,&nbsp;Hameed Hussain,&nbsp;Khaistah Khan,&nbsp;Shujaat Ali,&nbsp;Dilawar Shah,&nbsp;Muhammad Tahir","doi":"10.1155/cplx/8830401","DOIUrl":"https://doi.org/10.1155/cplx/8830401","url":null,"abstract":"<p>Frequent itemset mining (FIM) is a fundamental task in data mining with applications ranging from market basket analysis and recommendation systems to fraud detection and bioinformatics. However, mining frequent itemsets from massive datasets remains computationally challenging due to high execution time and memory consumption. Traditional algorithms such as Apriori suffer from exponential candidate generation and repeated database scans, FP-Growth incurs high memory overhead from tree construction, and Equivalence Class Transformation (ECLAT) faces expensive tid-list intersections. To address these limitations, we propose RPriori, a novel recursive divide-and-conquer algorithm that operates on the item-space instead of the transaction-space. RPriori recursively partitions the set of items and terminates early when a subset is found frequent, thereby eliminating candidate generation and avoiding global data structures. It performs localized support counting and merges only verified frequent subsets, resulting in O (NMlogM) time complexity and O (M) space complexity. Extensive experiments on six benchmark datasets, namely, Bakery, Chess, Mushroom, Retail, Accident, and T10I4D100K, demonstrate that RPriori consistently outperforms Apriori, FP-Growth, ECLAT, and TL-DIC. At low support thresholds, RPriori achieves up to 91% reduction in runtime and 93% reduction in memory usage, confirming its superior scalability and efficiency for both sparse and dense datasets.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/8830401","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Predicting Physicochemical Properties of Antibiotic Drugs via Neighborhood Degree-Based Topological Indices and QSPR Models","authors":"Fengwei Li,&nbsp;Nazek Alessa,&nbsp;Atef F. Hashem,&nbsp;Muhammad Kamran Siddiqui,&nbsp;Mohamed Abubakar Fiidow","doi":"10.1155/cplx/2363849","DOIUrl":"https://doi.org/10.1155/cplx/2363849","url":null,"abstract":"<p>Quantitative structure–property relationship (QSPR) models generate a mathematical formalism describing the molecular structure with the help of physical and chemical properties of compounds. In the present work, we are reporting an investigation on a set of neighborhood degree-based topological indices for QSPR studies of some antibiotic drugs such as amoxicillin, ampicillin, ciprofloxacin, gemifloxacin, norfloxacin, oxytetracycline, sulfadimidine, sulfamethoxazole, sulfamethoxypyridazine, sulfanilamide, tetracycline, and thiram. For each drug there exists a modeled molecular graph, and some neighborhood degree-based descriptors are calculated. The evaluated topological descriptors are used in QSPR models based on linear regression and logarithmic regression for the relationship between the molecular structure and physicochemical properties. The statistical study confirms that the neighborhood degree-based descriptors have a robust predictive power, indicating an efficient molecular descriptor. We find that descriptors at the level of neighborhood degree are highly correlated with a variety of physicochemical properties of antibiotic molecules. The results underscore the mathematical significance and utility of these indexes in QSPR modeling and shed more light on the structural characterization and theoretical evaluation of biologically active molecules. This study is of use for gaining some insights regarding the structure–property relationship of the antibiotic drugs and justifies using a graph-theoretical descriptor approach in drug property predictions.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/2363849","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical Investigation of Trajectory Evolution and Bifurcation Behavior in the Fractional Perturbed Gerdjikov–Ivanov Equation With External Modulation","authors":"Linda Alzaben,&nbsp;Monia Naghi","doi":"10.1155/cplx/5124873","DOIUrl":"https://doi.org/10.1155/cplx/5124873","url":null,"abstract":"<p>In this work, an efficient Bäcklund-enhanced unified analytical framework is developed to study the fractional perturbed Gerdjikov–Ivanov (pGI) equation that describes the propagation of nonlinear pulses in dispersive optical media. A fractional formulation is developed with Jumarie’s modified Riemann–Liouville derivative to include memory-dependent dynamics. The proposed method involves the unified method and the Bäcklund transformation and is systematically used to obtain a wide class of exact analytical solutions. The spatiotemporal dynamics generated are later investigated in detail by spatiotemporal simulations and nonlinear dynamical diagnostics with maximum Lyapunov exponent and phase portraits, as well as energy landscapes. The results show that the fractional-order parameter can be used as an effective control tool for setting the wave propagation properties and the stability range of the system, which can give valuable insight for the design and optimization of future high-capacity photonic crystal fiber communication systems.</p>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2026 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/5124873","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}