The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research. By using the monomiality principle, new outcomes are produced, thus in line with prior facts, our aim is to introduce the degenerate 2D bivariate Appell polynomials ${\mathbb{R}}_j^m(u,v;h)$. Further, we obtain some well-known main properties and explicit forms satisfied by these polynomials. Also, generating relations corresponding to the degenerate 2D bivariate Bernoulli, Euler, and Genocchi polynomials are established, they will further be helpful in establishing the corresponding results for these polynomials.

Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we derived the AF for the proposed transform. A bunch of important properties, including the reconstruction formula associated with the AF, are studied.

This research presents a model called the ‘Gaussian negative binomial mixture with a latent class choice model’, which serves as a robust and efficient tool for analyzing decisions across different areas. Our innovative model combines elements of mixture models, negative binomial distributions, and latent class choice modeling to create an approach that captures the complexities of decision-making processes. We explain how the model is formulated and estimated, showcasing its effectiveness in analyzing and predicting choices in scenarios. Through the use of a dataset, we demonstrate the performance of this method, marking a significant advancement in choice modeling. Our results highlight the applications of this model and point towards promising directions for future research, especially in exploring symmetrical patterns and structures, within decision-making processes.

This study introduces an enhanced version of the discrete choice model combining embedded neural architecture to enhance predictive accuracy while preserving interpretability in choice modeling across temporal dimensions. Unlike the traditional architectures, which directly utilize raw data without intermediary transformations, this study introduces a modified approach incorporating temporal embeddings for improved predictive performance. Leveraging the Phones Accelerometer dataset, the model excels in predictive accuracy, discrimination capability and robustness, outperforming traditional benchmarks. With intricate parameter estimates capturing spatial orientations and user-specific patterns, the model offers enhanced interpretability. Additionally, the model exhibits remarkable computational efficiency, minimizing training time and memory usage while ensuring competitive inference speed. Domain-specific considerations affirm its predictive accuracy across different datasets. Overall, the subject model emerges as a transparent, comprehensible, and powerful tool for deciphering accelerometer data and predicting user activities in real-world applications.