Abtract： Machine learning using neural networks is a very powerful methodology which has demonstrated utility in many different situations. In this talk I will show how work in the mathematical discipline called topological data analysis can be used to (1) lessen the amount of data needed in order to be able to learn and (2) make the computations more transparent. We will work primarily w...
Abtract：We consider on arbitrary Riemannian manifolds the Leibenson equation:$\partial _{t}u=\Delta _{p}u^{q}.$This equation comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. Here $u(x,t)$ is the fraction of the volume that the liquid takes in porous medium at time $t$ at point $x$. The parameter $p$ characterizes the turbulence of a...
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