A new framework is introduced for constructing interpretable and truly reliable reduced models for multi-scale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is use...
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Fusion frames are an emerging topic of frame theory, with applications to communications and distributed processing. However, until recently, little was known about the existence of tight fusion frames, much less how ...
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It is shown that sigma-delta (/spl Sigma//spl Delta/) algorithms can be used effectively to quantize finite frame expansions for R/sup d/. Error estimates for various quantized frame expansions are derived, and, in pa...
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It is shown that sigma-delta (/spl Sigma//spl Delta/) algorithms can be used effectively to quantize finite frame expansions for R/sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantizers outperform the standard PCM schemes.
A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable...
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A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i¿f . For transition probabilities 0 < P i¿f < 1, a first order diffeomorphic modulation observable response preserving homotopy (D-MORPH) algorithm is utilized to investigate level sets. At the top of the control landscape, P i¿f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse fluence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members.
Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimen...
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Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.
An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular...
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The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that acquire large amounts of very high-dimensional data. To cope with such a data deluge, manifold...
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An axially symmetric perturbed isotropic harmonic oscillator undergoes several bifurcations as the parameter λ adjusting the relative strength of the two terms in the cubic potential is varied. We show that three of ...
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