Missing values in rainfall datasets reduce the reliability of statistical inference and undermine decision-making in agriculture, climate studies, and environmental management. This study evaluated the performance of five imputation techniques; Expectation-Maximization (EM), Multiple Imputation (MI), Regression Imputation (RI), Bootstrap Expectation-Maximization (BEM), and Random Forest (RF) using the 2019 Nigerian rainfall dataset obtained from the National Bureau of Statistics. The methods were compared using Raw Bias, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Variance to assess estimation accuracy, predictive performance, and stability. The results revealed that MI produced the lowest bias (-0.003), making it the most suitable method for minimizing systematic estimation error. In contrast, RF achieved the highest predictive accuracy, recording the lowest MSE (0.9530) and RMSE (0.9762). Although BEM exhibited the lowest variance (0.9844), indicating greater stability, it was associated with relatively high bias, limiting its overall effectiveness. The findings demonstrate that no single method is universally optimal; rather, the choice of imputation technique should be guided by the primary analytical objective. RF is recommended for applications requiring high predictive accuracy, whereas MI is preferable when unbiased parameter estimation is essential. The study provides empirical evidence to support the adoption of robust imputation techniques by agencies such as the Nigerian Meteorological Agency (NiMet), thereby improving the quality of national climate databases and strengthening evidence-based agricultural and environmental decision-making.
This paper presents a unified coefficient-recurrence framework for obtaining series solutions of second-order linear ordinary differential equations with variable coefficients. The standard power-series method, applicable at ordinary points, and the Frobenius method, applicable at regular singular points, are treated as special cases of a common series ansatz $y(x)=(x-x_0)^r\sum_{n=0}^{\infty}a_n(x-x_0)^n$, where $r=0$ recovers the ordinary case and $r$ is determined by an indicial equation in the singular case. General recurrence relations for analytic coefficient functions are derived, conditions under which series terminate to yield polynomial solutions are established, and resonance in the integer-difference root case is characterized. Carefully selected examples illustrate the framework, including polynomial solutions, fractional exponents, resonance with logarithmic terms, and the Bessel equation. The analysis provides a systematic structural comparison of the two methods in terms of recurrence order, termination, resonance, and computational complexity.
The transition to post-quantum cryptography creates a mathematical decision problem in which security strength, algebraic structure, key and ciphertext sizes, execution time, memory demand, implementation complexity, and side-channel resilience must be considered simultaneously. This paper develops a machine learning-assisted multi-objective computational framework for ranking candidate algebraic structures and parameter configurations for post-quantum cryptographic deployment. The framework combines a normalized utility model, feasibility constraints, Pareto dominance, and supervised learning. A reproducible simulation study with 2,400 synthetic candidate configurations representing lattice-, code-, hash-, multivariate-, and group-based families is used to demonstrate the methodology without presenting the simulated values as implementation benchmarks. Random Forest, Gradient Boosting, and Support Vector Machine classifiers are compared using a stratified 70:30 train-test split and five-fold cross-validation. On the held-out test set, Gradient Boosting achieved an accuracy of 0.901, F1-score of 0.869, and ROC-AUC of 0.968, while five-fold cross-validation produced a mean ROC-AUC of 0.960. Security strength was the dominant predictor in permutation analysis, but side-channel resilience, algebraic dimension, key size, memory demand, and decapsulation time also contributed to the selection boundary. A Pareto analysis identified 25 non-dominated feasible configurations in the simulated design space. The proposed model provides a transparent mathematical mechanism for combining cryptographic constraints with data-driven classification and can be adapted to measured benchmark datasets as they become available. The principal contribution is therefore methodological: it gives a reproducible bridge between computational algebra, multi-criteria optimization, and machine learning for cryptographic parameter selection.
