Recent Trends in Mathematics

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• Published Subscription Original Research 28 Aug 2026

  Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting

  By Chethana N S, Markala Karthik, S. Vairachilai

  Abstract: A fractional Riemannian fuzzy c-means framework is proposed for uncertain economic forecasting on non-Euclidean data domains. Observations are represented on a Riemannian manifold, cluster centres are intrinsic prototypes, and a latent fuzzy regime signal is regularised by both autoregressive and fractional-memory penalties. The resulting objective couples geometric clustering with time-series consistency, thereby discouraging partitions that are locally plausible but temporally incoherent. Closed-form membership updates, exponential-map centre updates, normal equations for …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 49–55 Read article →

• Published Subscription Review Article 28 Aug 2026

  Matrix Factorization and Tensor Decomposition at Scale: Mathematical Foundations and Computational Approaches

  By Mayank Garg

  Abstract: Matrix factorization and tensor decomposition techniques have emerged as fundamental tools in machine learning and data science for handling high dimensional data efficiently. This paper presents a comprehensive analysis of scalable matrix factorization and tensor decomposition methods, focusing on their mathematical foundations, computational complexity, and practical applications. We examine key algorithms including Singular Value Decomposition (SVD), Non-negative Matrix Factorization (NMF), CP decomposition, and Tucker decomposition, with particular emphasis on their …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 56–59 Read article →

• Published Subscription Original Research 10 Aug 2026

  Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design

  By Chethana N S, Markala Karthik, S. Vairachilai

  Abstract: A new discrete-mathematical framework is developed for resilient network design on intuitionistic fuzzy hypergraphs, where uncertainty is explicitly represented through membership, non-membership, and hesitation degrees associated with both vertices and hyperedges. These three components are systematically integrated into an effective incidence operator that captures the underlying uncertain relationships within complex hypergraph structures. Based on this operator, both un-normalised and normalized Laplacian matrices are formulated to characterize the spectral properties and …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 41–48 Read article →

• Published Subscription Original Research 10 Aug 2026

  A Mathematical Perspective on Recent Cloud-Computing Trends for Scalable and Secure Social-Media Platforms

  By Vaibhav Nandakishor Anasane

  Abstract: Cloud computing underpins modern social-media platforms by providing elastic compute, storage, and data-processing pipelines capable of absorbing highly bursty workloads. This paper surveys recent cloud-native trends—serverless and event-driven design, container orchestration, edge/CDN offload, streaming analytics, and privacy-enhancing security controls—and formalizes their impact through a compact mathematical model. We express workload volatility using arrival-rate functions, use queueing-based capacity sizing to derive auto-scaling rules, and formulate an optimization objective that balances cost …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 35–40 Read article →

• Published Subscription Original Research 10 Aug 2026

  A Comprehensive Investigation of Bagging-Based Ensemble Methods for Improving Machine Learning Model Robustness

  By Navneet Shukla, Aadil Siddiqui, Padma Mishra

  Abstract: Machine learning models such as Decision Trees, Logistic Regression, and K-Nearest Neighbors are widely used for classification tasks due to their simplicity and interpretability. However, these models often suffer from high variance, overfitting, and poor generalization when applied to real-world datasets, particularly those that are small, noisy, or imbalanced, as commonly encountered in healthcare, finance, and cybersecurity applications. To address these limitations, this research proposes a Bagging (Bootstrap Aggregating)-based ensemble …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 24–34 Read article →

• Published Subscription Review Article 30 Jul 2026

  Agentic AI: Architectures, Types, Capabilities, Mathematical Equations and Governance in the Era of Autonomous Intelligence

  By Dr. Nitin S. Shrirao, Mr. Dnyaneshwar S. Jadhav, Mrs. Sarita B Patil

  Abstract: Agentic Artificial Intelligence (Agentic AI) represents a major advancement in the evolution of intelligent systems by enabling autonomous planning, decision-making, and action execution. Unlike traditional AI models, which are primarily reactive and designed to respond to predefined inputs, Agentic AI systems possess capabilities such as memory, reasoning, goal-oriented planning, tool integration, and dynamic adaptation to changing environments. These characteristics allow them to perform complex, multi-step tasks with minimal human intervention, …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 01–14 Read article →

• Published Subscription Original Research 28 Jul 2026

  Automated Machine Learning System for Model Selection and Hyperparameter Optimization

  By Ankit Maurya, Shiraj Ahmad

  Abstract: The proliferation of machine learning applications in various scientific and industrial domains has given rise to an urgent need for developing principled, automated techniques for optimal architecture selection and hyperparameter tuning for machine learning models without human expert intervention. In this paper, we introduce the Automated Machine Learning System for Model selection and hyperparameter Optimization (AMLSMO)—a state-of-the-art, all-encompassing AutoML system that combines the power of meta-learning-based warm-starting, Bayesian Optimization with …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 15–23 Read article →

• Published Subscription Review Article 10 Mar 2026

  Complex Space-Time and the Structure of Relativistic Quantum Theory

  By Abhishek Ranjan Singh

  Abstract: Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 22–27 Read article →

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