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Michael Nsikan John

Academic / Lecturer · Edo State University, Iyamho

Pure Mathematics, Algebra and Computational MathematicsDepartment of Mathematics · Nigeria

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Dr. Michael Nsikan John is a pure mathematician specialising in algebra, with research interests in group theory, semigroup theory, computational algebra, algebraic cryptography and algebraic artificial intelligence.

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9 research works linked to this profile

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Stone duality; spectral reconstruction; X-top lattices; dynamic spectra; categorical classification; temporal topology · 2026 · African Journal of Mathematics, Statistics and Computer Science

Dynamic Stone Duality, Spectral Reconstruction, and Categorical Classification of Evolving X-Top Lattices

Michael Nsikan John

This paper develops a comprehensive categorical and spectral framework for the analysis of evolving X-top lattices. An X-top lattice is modeled as a bounded distributive lattice endowed with an interior-type operator, while an evolving X-top lattice is formulated as a time-indexed family of such structures connected through compatible evolution morphisms. To capture their temporal behavior, we introduce dynamic spectra constructed from prime X-top ideals and organize them into dynamic spectral spaces. A contravariant dynamic spectrum functor is established alongside a reconstruction functor derived from compact-open spectral data. Within a coherent subcategory in which classical prime-spectrum representations exist at every temporal stage, we prove a Dynamic Stone Duality theorem that extends classical Stone representation theory to evolving algebraic-topological systems. Furthermore, we establish a spectral reconstruction theorem demonstrating that evolving X-top lattices can be recovered from their associated dynamic spectra. The dynamic spectral dimension may be expressed as $$ d_s(X)=\sup_{t\in T}\dim(\mathrm{Spec}(X_t)). $$ The dynamic spectral rank is similarly represented by $$ r_s(X)=\max_{t\in T} r(X_t). $$ Several illustrative examples are presented, including growing Boolean systems, finite chain systems, stable evolutionary systems, and refining topological lattices. The framework extends classical duality and representation theories from static settings to temporally evolving structures and provides a foundational basis for temporal spectral topology.

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Research · 2026 · Ktrend - International Journal of Physical Sciences (IJPS)

Numerical Analysis of Quantum State Evolution on Finite Group Symmetry Spaces: A Conjugacy-Class Approach to Discrete Quantum Dynamics

Michael Nsikan John

The study of symmetry remains one of the most important themes in modern mathematical physics, providing a rigorous framework for understanding conservation laws, quantum state transitions, and dynamical invariants. Finite groups offer natural algebraic representations of discrete symmetry systems and have found applications in quantum mechanics, cryptography, coding theory, and computational physics. This paper develops a mathematical and numerical framework for quantum state evolution on finite group symmetry spaces using conjugacy-class dynamics. A finite-dimensional state space is constructed from the elements of a finite group, while a conjugacy-class transition matrix is introduced to model interactions among discrete quantum states. The associated conjugacy-class Laplacian generates a system of ordinary differential equations governing the evolution of the state vector. The model is analyzed using spectral theory, energy methods, and numerical approximation. The Forward Euler method and the classical fourth-order Runge–Kutta method are formulated for the proposed dynamical system. Stability and convergence properties are established theoretically, and a spectral stability theorem is proved for the conjugacy-class Laplacian. Numerical experiments based on the symmetric group S3 illustrate the computational behaviour of the model and confirm the superior accuracy of the Runge–Kutta scheme compared with the Euler approximation. The study establishes a direct connection between finite group theory, mathematical physics, and numerical analysis, thereby providing a structured approach to discrete quantum dynamics generated by algebraic symmetry.

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Research · 2026 · Ktrend - International Journal of Data Science and Machine Learning (IJDSML)

A Hybrid Algebraic Cryptographic Strength Index and Machine Learning Model for Predicting the Security of Algebraic Structures

Michael Nsikan John

The choice of algebraic structure is a central problem in modern cryptography, especially in the transition from classical public-key schemes to quantum-resistant security models. Classical cryptographic systems such as RSA and elliptic curve cryptography are strongly connected to number theory, finite groups, conjugacy behavior, bilinear maps, and discrete logarithm assumptions; however, there is still no generally accepted data-driven framework for predicting the cryptographic strength of algebraic structures before deployment. This paper proposes a new hybrid modelling framework called the Algebraic Cryptographic Strength Index (ACSI), combined with supervised machine learning, for predicting whether a finite or computationally represented algebraic structure is suitable for cryptographic use. The framework transforms group-theoretic, character theoretic, elliptic-curve, bilinear, lattice, and number-theoretic invariants into a structured feature space. A simulated dataset of 12,000 algebraic structures was generated using mathematically motivated constraints derived from conjugacy classes, centralizer ratios, derived length, monomial character indices, elliptic curve security margins, RSA modulus complexity, bilinear pairing depth, and lattice hardness. Four models were trained and evaluated: Random Forest, Gradient Boosting, Support Vector Machine, and Neural Network. The Neural Network achieved the best overall accuracy of 78.86% and ROC-AUC of 87.49%, while Gradient Boosting and Random Forest provided more interpretable feature-importance patterns. The results suggest that lattice hardness, elliptic curve security margin, small cancellation score, conjugacy density, and character-codegree entropy are among the most influential predictors. The study contributes a reproducible mathematical-data-science framework for algebraic cryptographic suitability prediction and opens a pathway for explainable machine learning in post-quantum cryptographic structure selection.

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Research · 2026 · Ktrend - International Journal of Computer Science and Artificial Intelligence (IJCSAI)

Machine Learning Assisted Selection of Algebraic Structures for Post-Quantum Cryptographic Systems

Michael Nsikan John

The migration from classical public-key cryptography to post-quantum cryptography requires systematic methods for identifying algebraic structures whose computational properties remain secure against both classical and quantum adversaries. Traditional selection is largely based on theoretical hardness assumptions, implementation cost, parameter constraints, and expert judgement. This paper develops a Machine Learning Assisted Algebraic Structure Selection Framework (MLASSF) for classifying candidate algebraic structures as suitable or unsuitable for post-quantum cryptographic use. The framework combines finite group invariants, conjugacy class statistics, character-theoretic indicators, elliptic-curve descriptors, lattice parameters, implementation efficiency, and estimated security categories into a supervised learning pipeline. A reproducible simulated dataset of 5,000 candidate structures was generated to model algebraic and computational features relevant to post quantum design. Five classifiers were trained and evaluated: logistic regression, support vector machine, random forest, gradient boosting, and artificial neural network. The best-performing model was gradient boosting, with an accuracy of 93.80%, precision of 95.04%, recall of 96.21%, F1-score of 95.62%, and ROCAUC of 95.29%. Random forest followed closely with 93.60% accuracy and also provided interpretable feature importance, showing that lattice dimension, implementation efficiency, character-degree variance, elliptic-curve rank, and derived length were influential predictors. The results show that machine learning can serve as a decision-support layer for algebraic selection in post-quantum cryptographic research, especially when combined with rigorous mathematical analysis rather than used as a substitute for proof-based security.

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Research · 2026 · Ktrend - International Journal of Mathematics and Statistics (IJMS)

A Deterministic Mathematical Model for the Transmission Dynamics of Typhoid Fever Incorporating Asymptomatic Carriers

Robert Folorunsho Akerejola, Michael Nsikan John, ALHASSAN, C.J.

Typhoid fever is a highly infectious disease, and remains a major public health problem, especially in low- and middle-income countries, despite several interventions such as environmental sanitation, personal hygiene, vaccination, and treatment with antibiotic drugs. Evidently, asymptomatic typhoid carriers play a critical role in the transmission dynamics of typhoid fever. Therefore, this research work presents a deterministic mathematical model on the dynamics and spread of typhoid fever incorporating asymptomatic carriers. The basic reproduction number, R0 of the proposed model is computed using the next generation matrix approach, and the stability analyses of the disease-free equilibrium were investigated. Results show that the disease-free equilibrium is locally asymptotically stable when R0 < 1, and globally asymptotically stable when R0 ? 1.

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Algebra · 2026 · International Journal of Mathematics and Statistics

Differential Semigroups of Automaton Perturbations and Incremental Syntactic Reconstruction

Michael Nsikan John, Okeke Ikenna Stephen, Robert Akerejola F., Alhassan, C. J.

This paper investigates the enumeration of elements in three classes of signed partial transformation semigroups: partial signed order-preserving, partial signed order-decreasing, and partial signed order-preserving-or-order-reversing transformations. It examines the reported PSPD₄ numerical inconsistency and develops a domain-rank framework for extending the finite enumerations, while distinguishing interpolated computational conjectures from exact counting formulae.

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