Nonlinear dynamical systems underpin phenomena across fluid mechanics, epidemiology, climate science, and engineering, yet their inherent complexity renders classical analytical methods insufficient for real-world applications. This paper proposes and evaluates a Hybrid AI-Mathematical Modelling (HAIMM) framework that synergistically integrates physics-informed neural networks (PINNs), symbolic regression, and reservoir computing with traditional mathematical constructs such as ordinary and partial differential equations. The framework preserves the interpretability and physical consistency of mathematical models while harnessing the pattern-learning capacity of modern machine learning. Through four representative case studies Lorenz attractor forecasting, epidemic compartmental modelling, fluid boundary-layer prediction, and structural vibration identification we demonstrate that HAIMM achieves up to 94.3% prediction accuracy with a 40% reduction in computational overhead compared to purely numerical baselines. A structured comparison across model families is presented via tabular benchmarks, and key dynamical behaviors are illustrated through system-generated flow diagrams. The results suggest that hybrid approaches represent a principled, scalable pathway for taming the complexity of nonlinear dynamics in science and engineering.
Brain tumor diagnosis from magnetic resonance imaging (MRI) remains a challenging task due to the presence of noise, complex tumor structures, and high-dimensional image features. Accurate detection and classification are essential for effective clinical decision-making and treatment planning. To address these challenges, this study proposes a novel RGCS-NCGNN-AAM framework for automated brain tumor analysis. The proposed approach integrates advanced preprocessing, dimensionality reduction, segmentation, classification, and optimization techniques into a unified pipeline. Initially, MRI images are enhanced using a LABF-based preprocessing method to suppress noise while preserving important structural information. Subsequently, Spatially Driven Principal Component Analysis (SD-PCA) is employed to reduce feature dimensionality and retain discriminative tumor-related characteristics. For precise tumor localization, a LA-ST segmentation technique is introduced to accurately delineate tumor boundaries and improve region extraction. The segmented features are then processed through a Robust Graph Convolution Structure-based Neural Context Graph Neural Network (RGCS-NCGNN), which effectively captures both topological and semantic relationships among data samples. Furthermore, an Adaptive Altruistic Mutualism (AAM) optimization strategy is incorporated to dynamically adjust model parameters and enhance learning performance. The proposed framework was evaluated using benchmark brain tumor MRI datasets and demonstrated superior performance in terms of classification accuracy, segmentation quality, and model robustness. Experimental results indicate that the integration of graph-based learning and adaptive optimization significantly improves diagnostic reliability compared with conventional machine learning and deep learning approaches. In addition, the framework preserves critical spatial information, enabling more accurate tumor characterization and boundary identification. The proposed method also exhibits strong scalability and generalization capabilities across diverse MRI samples. These findings suggest that the RGCS-NCGNN-AAM framework can serve as an effective computer-aided diagnostic tool for supporting radiologists and healthcare professionals in brain tumor assessment. Future research will focus on incorporating quantum graph neural networks and self-supervised learning techniques to further enhance computational efficiency and diagnostic performance in real-world clinical environments.
The validity of certain documents, such as the Registration Certificate (RC), Pollution Under Control (PUC) certificate, and motor insurance, is necessary for vehicle regulatory compliance. This study suggests a multivariate statistical methodology that uses Multiple Correspondence Analysis (MCA) to profile vehicle-document validity. A structured dataset with recorded years and vehicle-document expiration dates is used in the analysis. A uniformly specified reference-date rule is used to convert the expiration dates into categorical validity indicators. MCA is used to find dominating dimensions of variation, investigate the relative placement of compliance categories in a low-dimensional space, and investigate relationships between document-validity categories and temporal groups. The multivariate interpretation is supplemented by descriptive statistics and contingency-table analyzes. Instead of establishing causal linkages or forecasting future non-compliance, the study's goal is to find patterns of co-occurrence. Its contribution is to show how multivariate profiling can help with compliance monitoring and prioritization by using a clear categorical-data analytic approach to vehicle-document records. Following independent verification of the final validity classification and MCA outputs, numerical results will be presented.
Organizations that run collaboration on SharePoint Online accumulate content faster than they dispose of it. Storage quotas fill with files that nobody has opened in years, retention obligations are applied unevenly, and the native safety nets (recycle bins, version history and the Preservation Hold library) are widely misunderstood, which leaves recovery windows shorter than administrators assume. This paper proposes the PSRR framework (Policy-Based Stubbing, Retention and Recoverability), a lifecycle management approach that treats the three concerns as one coordinated policy set instead of three separate administrative tasks. Content is classified into lifecycle classes. Each class receives an inactivity threshold for stubbing (replacing cold content with a lightweight placeholder that keeps its location, metadata and permissions while the payload moves to a cheaper tier), a retention and disposition rule, and a recoverability tier that states how long and by which mechanism a deleted or damaged item can be restored. The framework is described against the platform behavior documented by Microsoft as of October 2023, including the two-stage recycle bin, the Preservation Hold library and Microsoft 365 Archive. To examine the design trade-offs we built a synthetic tenant of 60,000 files and ran 200 simulated replications. At a 180-day inactivity threshold, stubbing moved about 81% of stored volume to the cold tier while 24.5% of annual file accesses touched a stub, and a naive stubbing design lowered the share of accidentally deleted items that could be recovered from 82.5% to 62.3%. Coordinating payload retention with recovery windows restored this to 83.8%, and adding an independent backup layer raised it to 97.2%. These results are synthetic and show the logic of the design, not measurements from a production tenant. The paper closes with a governance model, an implementation roadmap and a research agenda.
Any relational hypersubstitution for algebraic systems of type (τ, τ ′ ) = ((m i ) i∈I , (n j ) j∈J ) is a mapping which maps any m i -ary operation symbol to an m i -ary term and maps any n j -ary relational symbol to an n j -ary relational term preserving arities, where I, J are indexed sets.The set of all relational hypersubstitutions for algebraic systems of type (τ, τ ′ ) together with a binary operation defined on the set and its identity forms a monoid.The properties of this structure are expressed by terms and formulas.Some algebraic properties of the monoid of a special type, especially the set of all unit-regular elements, were studied.In this paper, we determine all maximal unit-regular submonoids of this monoid of type ((m), (n)) for arbitrary natural numbers m, n ≥ 2.
