1,764 research outputs found
On the Phase Transition of Corrupted Sensing
In \cite{FOY2014}, a sharp phase transition has been numerically observed
when a constrained convex procedure is used to solve the corrupted sensing
problem. In this paper, we present a theoretical analysis for this phenomenon.
Specifically, we establish the threshold below which this convex procedure
fails to recover signal and corruption with high probability. Together with the
work in \cite{FOY2014}, we prove that a sharp phase transition occurs around
the sum of the squares of spherical Gaussian widths of two tangent cones.
Numerical experiments are provided to demonstrate the correctness and sharpness
of our results.Comment: To appear in Proceedings of IEEE International Symposium on
Information Theory 201
Data-driven parameterization of the generalized Langevin equation
We present a data-driven approach to determine the memory kernel and random
noise in generalized Langevin equations. To facilitate practical
implementations, we parameterize the kernel function in the Laplace domain by a
rational function, with coefficients directly linked to the equilibrium
statistics of the coarse-grain variables. We show that such an approximation
can be constructed to arbitrarily high order and the resulting generalized
Langevin dynamics can be embedded in an extended stochastic model without
explicit memory. We demonstrate how to introduce the stochastic noise so that
the second fluctuation-dissipation theorem is exactly satisfied. Results from
several numerical tests are presented to demonstrate the effectiveness of the
proposed method
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