Sparse Representation Classification Beyond L1 Minimization and the Subspace Assumption

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency under a latent subspace model and contamination. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance and significantly faster.

The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models

We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized (exactly flat band, non-zero Chern number, local hopping), it is not possible to simultaneously satisfy all three. Our theorem covers both the case of a single flat band, for which we give a rather elementary proof, as well as the case of multiple degenerate flat bands. In the latter case, our result is obtained as an application of $K$-theory. We also introduce a class of models on the Lieb lattice with nearest and next-nearest neighbor hopping parameters, which have an isolated exactly flat band of zero Chern number but, in general, non-zero Berry curvature.

Unsupervised deconvolution of dynamic imaging reveals intratumor vascular heterogeneity

Intratumor heterogeneity is often manifested by vascular compartments with distinct pharmacokinetics that cannot be resolved directly by in vivo dynamic imaging. We developed tissue-specific compartment modeling (TSCM), an unsupervised computational method of deconvolving dynamic imaging series from heterogeneous tumors that can improve vascular phenotyping in many biological contexts. Applying TSCM to dynamic contrast-enhanced MRI of breast cancers revealed characteristic intratumor vascular heterogeneity and therapeutic responses that were otherwise undetectable.

High spatial resolution X-ray spectroscopy of SNR Cassiopeia A with {sl Chandra}

We present high spatial resolution X-ray spectroscopy of supernova remnant Cassiopeia A with the {sl Chandra} observations. The X-ray emitting region of this remnant was divided into 38 $times$ 34 pixels with a scale of 10$arcsec$ $times$ 10$arcsec$ each. Spectra of 960 pixels were created and fitted with an absorbed two component non-equilibrium ionization model. With the spectral analysis results we obtained maps of absorbing column density, temperatures, ionization ages, and the abundances for Ne, Mg, Si, S, Ca and Fe. The Si, S and possibly Ca abundance maps show obviously jet structures, while Fe doesnt follow the jet but seems to be distributed perpendicular to it. In the range of about two orders of magnitude, the abundances of Si, S and Ca show tight correlations between each other, suggesting them to be ejecta from explosive O-burning and incomplete Si-burning. Meanwhile, Ne abundance is well correlated with that of Mg, indicating them to be the ashes of explosive C/Ne burning. The Fe abundance is positively correlated with that of Si when Si abundance is lower than 3 solar abundances, but a negative correlation appears when the Si abundance is higher. We suggest that such a two phase correlation is the results of different ways in which Fe is synthesized.