We propose two analytical relationships between affinity and opinion change. The first one focuses on value homophily, while the second one incorporates affinity in opinion dynamics. Three analytical test models are derived based on these relationships: the value homophily model, the temporal evolution of opinion summation, and the evolution of opinion difference between two individuals. We test these models using data from a previous experiment, and the results demonstrate their validity.

Political polarization has attracted many studies in recent years. We developed an opinion dynamics model with affective homophily effect and national social norm effect to describe this phenomenon. The time evolution of the polarization between the two parties and the spread of opinions within each party are affected by three factors: the repulsive effect between the two parties, the attractive and repulsive effects between the members in each party, and the national social norm effect that pulls the opinions of all members towards a common norm. The model is internally consistent and is applied to the simulation of the symmetric patterns of polarization and spread of the opinion distributions in the U.S. Congress, and the results align well with 154 years of recorded data. The time evolution of the strength of the national social norm effect is obtained and is consistent with the important historical events that occurred during the past 150 years.

This research employs a Caputo fractional-derivative model to investigate the effects of magnetic field inclination and thermal radiation on the unsteady flow of a Casson fluid over an inclined plate in a porous medium. The model incorporates memory effects to generalize the classical formulation, while also accounting for internal heat generation and a chemical reaction. The governing equations are solved analytically using the Laplace transform, yielding power-series solutions in the time domain. Convergence analysis and benchmarking confirm the reliability and accuracy of the derived solutions. Key physical parameters are analyzed, and their impacts on the system are presented both graphically and in tabular form. The results indicate that increasing the inclination of the plate and magnetic field significantly suppresses the velocity distribution and reduces the associated boundary-layer thickness. Conversely, a higher fractional-order parameter enhances the velocity, temperature, and species concentration profiles by reducing memory effects. This study makes a significant contribution to the fractional modeling of unsteady heat and mass transfer in complex non-Newtonian fluids and provides valuable insights for the precise control of transport processes in industrial, chemical, and biomedical applications.

Recent research advances on fabric dyeing have focused on modeling the relationship between dye concentrations and the final color on fabrics. The emerging techniques in related studies have great potential to evolve the traditional dyeing industry to manufacture much more smartly. Given that dyeing is a complex process regulated by many factors, one of the challenging problems in the aforementioned techniques is to maintain the modeling accuracy at acceptable level. Other than developing high-performance algorithms and model architectures, it is also important to include effective data pre-processing techniques in modeling. In this paper, we show that conducting log-transform to the industrial dyeing data can greatly improve the performance of industrial dyeing recipe models. Such observations are confirmed on modeling tasks using different formats of color as input and different types of loss function in the model training. These findings may provide useful implications for related studies for the dyeing industry.

During the global pandemic of COVID-19, the term ‘N95’ is frequently encountered in our daily life. ‘N95’ is the abbreviation of facepiece respirators that meet the class 95 standard of US National Institute for Occupational Safety and Health (NIOSH). The number ‘95’ means that the N95 respirator can filter >95% of airborne particles. Numerically, 95% or 0.95 is very close to the function value of $f(x)=1-e^{-x},$ when $x=3.$ Intuitively, there might be some underlying relationship between $f(3)$ and the filtering rate 0.95. In this paper, a constant-law model is presented, giving clear physical picture for the filtering rate of non-woven fabrics. The derived physical model may also be used as a standard for particulate-filtering non-woven fabric products such as facepiece respirators.

Nonlinear filtering can be formulated as the propagation and update of conditional probability densities, but direct numerical propagation of the associated Forward Kolmogorov equation (FKE) over a large fixed domain is computationally expensive. This paper proposes a Recentered-Domain Yau–Yau Filter (RD-YYF) with reduced-order FKE propagation for nonlinear state estimation. The method solves the FKE on a fixed-size local computational window centered at the latest state estimate, thereby concentrating numerical resolution near the dominant posterior density. In the offline stage, physics-informed neural networks (PINNs) generate FKE solution snapshots, principal component analysis constructs a low-dimensional representation of density evolution, and a lightweight residual surrogate maps initial-condition coefficients and the domain center to terminal-solution coefficients. In the online stage, the pretrained surrogate performs per-timestep density prediction within the recentered window, followed by observation update and state estimation. Numerical experiments on two geometrically constrained target-tracking models show that RD-YYF achieves lower tracking errors than the extended Kalman filter and particle filter under matched online evaluation conditions. A fixed-domain ablation further shows that recentering improves density approximation in high-probability regions and reduces offline PINN training epochs. These results indicate that recentered-domain reduced-order FKE propagation is a practical computational strategy for nonlinear density-based filtering.