主题词：Stochastic processes and statistical mechanics; Stochastic processes and financial applications; Markov Chains and Monte Carlo Methods; Random Matrices and Applications; Theoretical and Computational Physics; Mathematical Dynamics and Fractals; Advanced Mathematical Modeling in Engineering; Point processes and geometric inequalities; Bayesian Methods and Mixture Models; Statistical Methods and Inference; Financial Risk and Volatility Modeling; Diffusion and Search Dynamics; Geometry and complex manifolds; Geometric Analysis and Curvature Flows; Probability and Risk Models; advanced mathematical theories; Advanced Thermodynamics and Statistical Mechanics; Advanced Combinatorial Mathematics; Nonlinear Partial Differential Equations; Advanced Algebra and Geometry; Spectral Theory in Mathematical Physics; Mathematical Biology Tumor Growth; Quantum chaos and dynamical systems; Complex Systems and Time Series Analysis; Stability and Controllability of Differential Equations