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Diophantine approximation with restricted numerators and denominators on semisimple groups
Diophantine approximation restricted numerators and denominators semisimple groups Dynamical Systems
2012/5/25
We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numera- tors and denominators and establish a quantitative approximation result f...
Convergence and Rate Analysis of Neural Networks for Sparse Approximation
Locally Competitive Algorithm sparse approximation global stability exponential convergence non-smooth objective
2011/9/23
Abstract: We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that solves sparse approximation problems (e.g., approximating a vector from a dictionary u...
A simple linear response closure approximation for slow dynamics of a multiscale system with linear coupling
closure approximation slow dynamics multiscale system linear coupling
2011/9/14
Abstract: Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolv...