Journal of Statistics and Mathematical Engineering

Discrete Lattice Cryptosystem based on q-ary Lattice Polynomial

Shivani Sharma — 2026-06-25

In this paper, a new post-quantum lattice cryptosystem is proposed based on the discrete structure of the lattice referred to as the discrete lattice cryptosystem (DLC). There are three concepts in DLC, i.e. polynomial algebra, reduction modulo and probability. The proposed DLC is secure and practical, both due to the hardness of the discrete structure of the lattice defined over the q-ary matrix transformation. The q-ary lattice problems are the extended lattice problems over the field; thus these are advanced lattice problems with more hardness than the lattice problems due to its extension possibilities in finite-dimensional vector spaces over the field. The flexibility and extendibility of the hardness of q-ary lattice problems interact with standard cryptographic protocols. This paper deals with q-ary lattice problems and their application in a cryptosystem with computational complexity and flow algorithms. The hardness of q-ary lattice problems interacts with the field characteristics and its extension through finite-dimensional vector spaces, linear transformations, and probabilistic distributions.

Machine Learning Models for Climate Prediction: A Comparative Study with Classical Statistical Methods

Md. Tanvin Mahfuz Tuhin — 2026-05-22

This work investigates the role of advanced modeling techniques in improving the accuracy of climate prediction, which is vital for understanding environmental change and guiding mitigation efforts. Conventional statistical models, including Autoregressive Integrated Moving Average (ARIMA) and Seasonal ARIMA (SARIMA), have been extensively used due to their clarity, efficiency, and effectiveness in handling linear and stationary time series data. However, the growing complexity of climate systems has encouraged the adoption of machine learning approaches that can better capture nonlinear relationships and long-term dependencies. Techniques such as Long Short-Term Memory (LSTM) networks, Convolutional Neural Networks (CNN), and ensemble learning models have shown strong potential in extracting meaningful patterns from large and complex climate datasets. In this study, a detailed comparison is conducted between traditional statistical methods and modern machine learning models for forecasting key variables such as temperature, rainfall, and atmospheric CO₂ concentration. Performance is assessed using widely accepted evaluation metrics, including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²), along with considerations of computational requirements and model interpretability. The findings suggest that machine learning models, especially LSTM and hybrid approaches, generally provide more accurate predictions for nonlinear and large-scale data. Nevertheless, statistical models remain reliable for short-term forecasts and relatively stable datasets, highlighting the value of combining both approaches for enhanced climate prediction.

Mathematical Modeling and Analysis of Channel Capacity in Shannon Information Theory

Md. Nurul Islam — 2026-05-02

This work investigates channel capacity as a fundamental concept in information theory, representing the maximum achievable data transmission rate over a communication channel with an arbitrarily low probability of error. The study develops a comprehensive mathematical and analytical framework, based on Shannon’s theory, to evaluate channel capacity across different communication models. Both discrete memory-less channels and continuous channel models are examined to provide a broad and systematic understanding of theoretical capacity limits. Particular attention is given to the Additive White Gaussian Noise (AWGN) channel, which serves as a standard model for practical communication systems due to its ability to accurately represent thermal noise and other random disturbances. The analysis incorporates key information-theoretic measures such as entropy and mutual information to derive channel capacity expressions. The Shannon–Hartley theorem is explored in detail to establish the relationship between channel capacity, bandwidth, and signal-to-noise ratio (SNR). To validate the theoretical findings, numerical simulations are performed to analyze the variation of channel capacity with respect to SNR under different bandwidth conditions. The results demonstrate that channel capacity increases logarithmically with SNR, highlighting the phenomenon of diminishing returns at higher signal power levels. Furthermore, the study examines the effects of noise characteristics, power constraints, and signal design on achievable data rates. The outcomes of this research provide important insights for the design and optimization of modern communication systems, including wireless and optical networks. By linking theoretical principles with practical considerations, this work contributes to a deeper understanding of efficient data transmission and the fundamental limits imposed by noise and bandwidth in real-world channels.

Application of Numerical Methods in 3D Surface Modelling

Kartika Choudhary — 2026-06-18

Three-dimensional surface modelling is a fundamental challenge in engineering and applied mathematics, underpinning applications ranging from computer-aided design (CAD) and finite element analysis to medical imaging and terrain reconstruction. Classical parametric representations, such as NURBS and implicit surfaces, require known analytical forms and therefore fail when surfaces are defined purely by sampled measurement data. This paper presents a systematic comparative evaluation of four numerical methods for continuous surface reconstruction from point clouds: bilinear interpolation, bicubic spline fitting, finite difference methods, and Radial Basis Function (RBF) interpolation. All methods are benchmarked on a common trigonometric test surface f(x,y) = sin(√(x²+y²))·e^(−0.15(x²+y²)) at grid resolutions N {4, 8, 16, 32, 64, 128}, with error measured as maximum absolute deviation on a 512×512 evaluation grid. Results demonstrate that bicubic splines achieve O(h) convergence (RMSE: 0.0048) versus O(h²) for bilinear interpolation (RMSE: 0.0245), at moderate computational overhead (3.4 ms vs. 0.8 ms per query). RBF interpolation with a Gaussian kernel achieves the lowest RMSE of 0.0031 on unstructured scattered data but requires O(n³) matrix precomputation. Laplacian mesh smoothing is quantified for the first time: 20 iterations reduce surface noise by 97% while preserving macro-scale geometry. Findings provide practitioners with evidence-based method selection guidance, with direct applications to terrain modelling, dental prosthetic design, and automotive CAD workflows.

Factor Analytic Modelling of Empowerment and Financial Inclusion

Madhusmita Tripathy — 2026-05-16

The study uses factor analysis to explain the effect of financial inclusion on the lives of women and how it influences their ability to advance socially, economically and politically. A dataset of twelve variables is used to establish the underlying factors, and find out the interrelations between different measures of women empowerment. Before performing factor analysis, supplementary methods like the principal component analysis, Bartlett test of sphericity and the Kaiser Meyer Olkins measure had been used to verify the suitability of the analysis. Three main factors consider in this study like, economic empowerment, social empowerment, and political empowerment, followed by regression analysis to understand the influence of various aspects of empowerment on the degree of financial inclusion in a community; the results show that women who feel more in control of their economic, social and political lives are much more inclined to use the financial system. In turn, women empowerment is a key mechanism in promoting an inclusive community building, which has heavy implications on policy makers who strive to make a positive impact in the societies they operate.