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Neighborliness of Randomly-Projected Simplices in High Dimensions
Neighborly Polytopes Convex Hull of Gaussian Sample
2015/8/21
Let A be a d by n matrix, d < n. Let T = T
n−1 be the standard regular simplex in R
n
.
We count the faces of the projected simplex AT in the case where the projection is random,
the dimens...
Some standard numerical problems become intractable in high dimensions.
Yet successes are often achieved in practice. This may be explained in terms
of the underlying target function being somehow s...
Continuous dependence for $H^{2}$ critical nonlinear Schr鰀inger equations in high dimensions
Nonlinear Schrodinger equation Continuous dependence Cauchy problem Strichartz抯 estimates
2012/4/17
The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the soluti...