7 problems

The paper considers second-order particle-swarm-optimization dynamics and a kinetic BGK model obtained in a mean-field limit. In the setting of non-degenerate Gaussian noise and a…

Let $f(t,A,w)$ be the population distribution, let $f_\ell(z)$ be the leaders' opinion distribution, and define the population's average opinion and the leaders' average opinion by…

Let $f$ solve the time-continuous kinetic equation for the genetic algorithm, and consider the same objective-function assumptions and Boltzmann--Gibbs selection framework used for…

Let $(x_k^1,\dots,x_k^N)$ be the GA particle system, and let $(\overline{x}_k^1,\dots,\overline{x}_k^N)$ be $N$ independent copies of the mono-particle process. Coupling conjecture…

Let ${\bf p}(t)$ be the wealth distribution at time $t$, and let $\delta_0$ denote the Dirac distribution concentrated at zero wealth. The total amount of money is preserved, so if…

Conjecture. The functions $q_N$ have unique positive zeroes $M_N$, the sequence $(M_N)$ is increasing and tends to infinity, and the $N^{th}$-order linear system is stable if and o…

Let $e(t)=\left\lVert f(t)-f^\infty\right\rVert_2$ denote the distance from the stable equilibrium $f^\infty$ at time $t$, and let $r=\Delta v/\delta v$ be the ratio of the velocit…