Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach

In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\ell_1$-norm are given in [3]. When the unknown vector is not conventionally sparse but is "group sparse" instead, a variety of alternatives to the $\ell_1$-norm have been proposed in the literature, including the group LASSO, sparse group LASSO, and group LASSO with tree structured overlapping groups. However, no error bounds are available for any of these modified objective functions. In the present paper, a unified approach is presented for deriving upper bounds on the error between the true vector and its approximation, based on the notion of decomposable and $\gamma$-decomposable norms. The bounds presented cover all of the norms mentioned above, and also provide a guideline for choosing norms in future to accommodate alternate forms of sparsity.Comment: 28 pages, final version of 1401.6623, accepted for publication. arXiv admin note: substantial text overlap with arXiv:1401.662

Predicting Surface Clustering at Ambient Conditions from Thermodynamic Data

Scanning tunneling microscopy (STM) has proved to be a prime tool to characterize the atomic structure of crystal surfaces under UHV conditions. With the development of high-pressure scanning tunneling microscopy (HP-STM), the scope of this technique has been largely extended, as new structures were found to occur under gas phase chemical potentials achieved under ambient conditions. Particularly interesting is the substantial restructuring of initially flat and stable surfaces into new orientations by formation of nanoclusters. Here we discuss the possible generality of this phenomenon by analyzing cases where atomically flat surfaces of certain transition metals undergo such changes in the presence of CO at room temperature (RT) while some remain unchanged. From our analysis we argue that such changes can be predicted from thermodynamic data published in the literature, particularly from the difference in adsorption energy on low-and high-coordination sites, like terrace and step sites, which can be obtained from thermal desorption spectroscopy (TDS) measurements, and possibly also from theoretical calculations. For the vicinal surfaces with high Miller indices, changes in the repulsive elastic interactions between the ordered steps due to adsorbates may also play an important role

Optimal Haplotype Assembly from High-Throughput Mate-Pair Reads

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.Comment: 10 pages, 4 figures, Submitted to ISIT 201

Data Augmentation in Training CNNs: Injecting Noise to Images

Noise injection is a fundamental tool for data augmentation, and yet there is no widely accepted procedure to incorporate it with learning frameworks. This study analyzes the effects of adding or applying different noise models of varying magnitudes to Convolutional Neural Network (CNN) architectures. Noise models that are distributed with different density functions are given common magnitude levels via Structural Similarity (SSIM) metric in order to create an appropriate ground for comparison. The basic results are conforming with the most of the common notions in machine learning, and also introduce some novel heuristics and recommendations on noise injection. The new approaches will provide better understanding on optimal learning procedures for image classification.Comment: 12 pages, 9 figures, 2 tables, old paper just submitted to arXi

Geometric explanation of anomalous finite-size scaling in high dimensions

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behaviour for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.Comment: 5 pages, 4 figure

Pure hydrogen low-temperature plasma exposure of HOPG and graphene: Graphane formation?

Single- and multilayer graphene and highly ordered pyrolytic graphite (HOPG) were exposed to a pure hydrogen low-temperature plasma (LTP). Characterizations include various experimental techniques such as photoelectron spectroscopy, Raman spectroscopy and scanning probe microscopy. Our photoemission measurement shows that hydrogen LTP exposed HOPG has a diamond-like valence-band structure, which suggests double-sided hydrogenation. With the scanning tunneling microscopy technique, various atomic-scale charge-density patterns were observed, which may be associated with different C-H conformers. Hydrogen-LTP-exposed graphene on SiO₂ has a Raman spectrum in which the D peak to G peak ratio is over 4, associated with hydrogenation on both sides. A very low defect density was observed in the scanning probe microscopy measurements, which enables a reverse transformation to graphene. Hydrogen-LTP-exposed HOPG possesses a high thermal stability, and therefore, this transformation requires annealing at over 1000 °C

Lifted Worm Algorithm for the Ising Model

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energy estimator on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energy estimator on the complete graph, and leads to a significant constant improvement on toroidal grids.Comment: 9 pages, 6 figure

Operando STM study of the interaction of imidazolium-based ionic liquid with graphite

Understanding interactions at the interfaces of carbon with ionic liquids (ILs) is crucially beneficial for the diagnostics and performance improvement of electrochemical devices containing carbon as active materials or conductive additives in electrodes and ILs as solvents or additives in electrolytes. The interfacial interactions of three typical imidazolium-based ILs, 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (AMImTFSI) ILs having ethyl (C2), butyl (C4) and octyl (C8) chains in their cations, with highly oriented pyrolytic graphite (HOPG) were studied in-situ by electrochemical scanning tunneling microscopy (EC-STM). The etching of HOPG surface and the exfoliation of graphite/graphene flakes as well as cation intercalation were observed at the HOPG/C2MImTFSI interface. The etching also takes place in C4MImTFSI at −1.5 V vs Pt but only at step edges with a much slower rate, whereas C8MIm+ cations adsorbs strongly on the HOPG surface under similar conditions with no observable etching or intercalation. The EC-STM observations can be explained by the increase in van der Waals interaction between the cations and the graphite surface with increasing length of alkyl chains

Intensity-modulated radiation therapy (IMRT) with couch rotation in right unilateral breast cancer

Background: In this study, intensity-modulated radiation therapy plans were made with and without couch rotation in patients with right unilateral breast cancer, and a dosimetry analysis was carried out to compare the radiation doses received by target and normal tissues. Materials and Methods: The radiotherapy planning tomography sets of 10 patients who underwent right unilateral mastectomies were retrospectively selected. Target volumes and normal at-risk organs were recontoured, two radiotherapy plans were created for each patient, and these plans were compared by dosimetry analyses. Results: Doses in the target volume (D2%, D98, D50, HI, VRI, and T -PTV-V95) were similar between the plans. In terms of organs at-risk doses, the maximum doses in the contralateral breast were similar between the plans, while the differences in all other organs at-risk dose parameters between the plans were statistically significant. All dosimetry parameters of the heart were significantly lower in the plans with couch rotation. Ipsilateral lung doses were higher in the plans with couch rotation. Contralateral lung and mean breast doses were significantly lower in the plans with couch rotation. Conclusion: In this study, organs at-risk doses were reduced, especially for the heart and the contralateral breast, in patients who were subjected to postmastectomy radiotherapy with right thoracic wall and regional nodal irradiation without compromising radiotherapy dose coverage for the target volumes by rotating the treatment couch by 270°