Percolation Threshold Estimation Via Probabilistic Bounds And Simulation
Authors: Hanumesha S T
Abstract: Percolation theory provides a mathematically elegant and practically powerful framework for modeling connectivity transitions in random media, with applications ranging from porous materials and composite conductivity to epidemics, network robustness, and transport in disordered systems. A central quantity is the percolation threshold p_c, the critical occupation probability at which macroscopic connectivity emerges with nontrivial scaling. Although p_c is known exactly for a few planar cases and lattices, many practical scenarios require estimation under finite-size, boundary, and uncertainty constraints. This paper develops a rigorous and computation-oriented methodology for percolation threshold estimation that couples (i) probabilistic inequalities and bracketing arguments (crossing probabilities, monotonicity, sharp-threshold heuristics, and finite-size scaling), with (ii) simulation-based estimators (spanning probability curves, union-find connectivity, confidence intervals, and extrapolation). We emphasize a "two-engine" approach: bounds that constrain plausible threshold locations and simulation that refines the estimate while quantifying uncertainty. We also introduce an uncertainty-aware parameterization using intuitionistic fuzzy sets and (hyper)graph abstractions to represent ambiguous occupancy mechanisms and heterogeneous coupling patterns; this is motivated by real settings where the effective "open probability" is not a crisp scalar but a range informed by measurement noise or multi-factor criteria. The final manuscript provides a Word-ready, mathematics-forward exposition, with figures and tables embedded to illustrate lattice configurations, spanning curves, scaling collapse, and probabilistic bracketing.
DOI: http://doi.org/10.5281/zenodo.18092138
Graph Analytics For Network Topology Optimization
Authors: Muhammad Hakim
Abstract: The escalating complexity of global digital infrastructures, characterized by the convergence of 5G, massive IoT deployments, and hyperscale cloud-to-edge continuums, has rendered traditional linear network management models obsolete. At the heart of this complexity lies the network topology—the intricate map of nodes and interconnections that dictates the flow, latency, and resilience of data. This review article explores the paradigm shift toward Graph Analytics for Network Topology Optimization. Unlike traditional tabular data analysis, graph analytics treats the network as a native mathematical graph, where routers, switches, and endpoints are vertices, and the communication links are edges. This relational perspective allows for the discovery of structural properties—such as centrality, community clusters, and bottleneck bottlenecks—that are invisible to classical monitoring. We categorize the core methodologies of graph-driven optimization, including the use of Graph Neural Networks (GNNs) for predictive traffic steering and PageRank-inspired algorithms for identifying critical infrastructure vulnerabilities. The article examines how graph analytics enables "Topological Resilience," allowing networks to autonomously reconfigure their structure in response to failures or shifting demand. Furthermore, the review addresses the critical challenges of processing massive-scale dynamic graphs in real-time, the computational overhead of graph embeddings, and the necessity for explainable graph models in network operations. By synthesizing recent breakthroughs in spectral graph theory and combinatorial optimization, this paper provides a strategic roadmap for building "Self-Optimizing Topologies." The findings suggest that graph analytics is the foundational intelligence required to manage the "Relational Complexity" of the 6G era, ensuring that global networks are not just faster, but fundamentally more robust, efficient, and adaptive.
DOI: https://doi.org/10.5281/zenodo.19491714
Behavioural Analytics For Insider Threat Detection Using Machine Learning
Authors: Ahmad Rizal
Abstract: Insider threats represent one of the most challenging cybersecurity risks, as they originate from individuals with legitimate access to organizational systems and data. Traditional security mechanisms often fail to detect such threats due to their reliance on signature-based or rule-based approaches that lack contextual awareness. Behavioral analytics, powered by machine learning (ML), has emerged as a transformative approach for identifying anomalous patterns indicative of insider misuse, fraud, or sabotage. This review explores the integration of behavioral analytics and ML techniques to enhance insider threat detection capabilities. By leveraging user activity logs, network traffic data, and system interactions, ML models can establish baseline behavioral profiles and identify deviations in real time. The study examines supervised, unsupervised, and hybrid learning approaches, highlighting their effectiveness in detecting both known and unknown threats. Additionally, it discusses feature engineering, data preprocessing, and the role of contextual information in improving detection accuracy. Challenges such as data imbalance, privacy concerns, adversarial behavior, and model interpretability are also critically analyzed. The review further explores emerging trends, including deep learning, graph-based analytics, and explainable AI, which are shaping next-generation insider threat detection systems. Ultimately, behavioral analytics
DOI: https://doi.org/10.5281/zenodo.19491716