19,670 research outputs found
Signal reconstruction via operator guiding
Signal reconstruction from a sample using an orthogonal projector onto a
guiding subspace is theoretically well justified, but may be difficult to
practically implement. We propose more general guiding operators, which
increase signal components in the guiding subspace relative to those in a
complementary subspace, e.g., iterative low-pass edge-preserving filters for
super-resolution of images. Two examples of super-resolution illustrate our
technology: a no-flash RGB photo guided using a high resolution flash RGB
photo, and a depth image guided using a high resolution RGB photo.Comment: 5 pages, 8 figures. To appear in Proceedings of SampTA 2017: Sampling
Theory and Applications, 12th International Conference, July 3-7, 2017,
Tallinn, Estoni
Sparse preconditioning for model predictive control
We propose fast O(N) preconditioning, where N is the number of gridpoints on
the prediction horizon, for iterative solution of (non)-linear systems
appearing in model predictive control methods such as forward-difference
Newton-Krylov methods. The Continuation/GMRES method for nonlinear model
predictive control, suggested by T. Ohtsuka in 2004, is a specific application
of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve
a forward difference approximation of the optimality equations on every time
step.Comment: 6 pages, 5 figures, to appear in proceedings of the American Control
Conference 2016, July 6-8, Boston, MA, USA. arXiv admin note: text overlap
with arXiv:1509.0286
Accelerated graph-based spectral polynomial filters
Graph-based spectral denoising is a low-pass filtering using the
eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial
filtering avoids costly computation of the eigendecomposition by projections
onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the
bilateral and guided filters. We propose constructing accelerated polynomial
filters by running flexible Krylov subspace based linear and eigenvalue solvers
such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG)
method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop
on Machine Learning for Signal Processin
Preconditioned warm-started Newton-Krylov methods for MPC with discontinuous control
We present Newton-Krylov methods for efficient numerical solution of optimal
control problems arising in model predictive control, where the optimal control
is discontinuous. As in our earlier work, preconditioned GMRES practically
results in an optimal complexity, where is a discrete horizon
length. Effects of a warm-start, shifting along the predictive horizon, are
numerically investigated. The~method is tested on a classical double integrator
example of a minimum-time problem with a known bang-bang optimal control.Comment: 8 pages, 10 figures, to appear in Proceedings SIAM Conference on
Control and Its Applications, July 10-12, 2017, Pittsburgh, PA, US
Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension one
or larger, self-interacting via the mean field mechanism. We analyze the
long-time asymptotics of finite energy solutions and prove that, under certain
generic assumptions, each solution converges (as time goes to infinity) to the
two-dimensional set of all ``nonlinear eigenfunctions'' of the form
\phi(x)e\sp{-i\omega t}. This global attraction is caused by the nonlinear
energy transfer from lower harmonics to the continuous spectrum and subsequent
dispersive radiation
Recent advances in the synthesis and application of fluorescent α-amino acids
Fluorescence spectroscopy has become a powerful technique for probing a range of complex biological processes including enzyme mechanisms and protein-protein interactions. While the application of this technique uses a number of strategies, many of these rely on the use of fluorescent α-amino acids. This review highlights the recent synthetic methods developed for the incorporation of highly conjugated chromophores into the side-chain of α-amino acids and the application of these compounds as probes for imaging in medicine and biology. In particular, the design and synthesis of α-amino acids bearing coumarin, flavone and polyaromatic derived chromophores is described
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