감동, 마음이 움직이는 것

From the mass conservation, the Fick's law is derived. Hence, for a random walk in inhomogeneous media (diffusion coefficient depends on space), we need an additional term in the diffusion equation. 밀도n의 시간t에 따른 변화는 외부로부터 유입되는 net-flux로 계산된다 (mass conservation).{\displaystyle {\frac {\partial n}{\partial t}}+\nabla \cdot \mathbf {J} =0}따라서, 다음과 같은 식을 얻는다.{\displaystyle {\frac {\partial n}{\parti..

The role of the second largest eigenvalue is determining the equilibration time with the largest eigenvalue:t_{eq} \propto 1/ln(\lambda_1/\lambda_2)In the paper "The space of genotypes is a network of networks: implications for evolutionary and extinction dynamics", at page 4 the first paragraph.

Finding optimum in nonlinear regression (with only one global optimum)gradient descent method (use gradient) --- good to far away from equilibriumGauss-Newton method (use intersection between y=0 and tangential line) --- good to close to equilibriumLevenberg-Marquardt (Combination between method 1. and 2.) --- there is a control parameter which called lambda, limiting values reproduce method 1 o..

https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

The system with a meta-stable state at finite population size always goes to extinct.This is proved in the book "A Kinetic View of Statistical Physics" at the subsection "12.4 Large fluctuations".