Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics. In a recent paper Bauschke, Luke, Phan and Wang (2014) showed that, locally, the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint. In this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications. These analytical tools can also be applied to other algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem.Comment: 29 pages, 2 figures, 37 references. Much expanded version from last submission. Title changed to reflect new development

The role of aggregate preferences for labor supply - evidence from low-paid employment

Labor supply in the market for low-paid jobs in Germany is strongly influenced by tax exemptions - even for individuals to whom these exemptions do not apply. We present compelling evidence that an individual's choice set depends on other workers' preferences because firms cater their job offers to aggregate preferences in the market. We estimate an equilibrium job search model which rationalizes the strong earnings bunching at the tax exemption threshold using German administrative data. We then simulate modifications to the tax schedule that remove the discontinuity and thus the bunching at the threshold. Results highlight the indirect costs of (discontinuous) tax policies which are shown to be reinforced by firm responses: Workers who would work anyway are hurt by subsidies benefiting groups who enter the market as a result of tax incentives

Referenced Kendrick Mass Defect Annotation and Class-Based Filtering of Imaging MS Lipidomics Experiments.

Because of their diverse functionalities in cells, lipids are of primary importance when characterizing molecular profiles of physiological and disease states. Imaging mass spectrometry (IMS) provides the spatial distributions of lipid populations in tissues. Referenced Kendrick mass defect (RKMD) analysis is an effective mass spectrometry (MS) data analysis tool for classification and annotation of lipids. Herein, we extend the capabilities of RKMD analysis and demonstrate an integrated method for lipid annotation and chemical structure-based filtering for IMS datasets. Annotation of lipid features with lipid molecular class, radyl carbon chain length, and degree of unsaturation allows image reconstruction and visualization based on each structural characteristic. We show a proof-of-concept application of the method to a computationally generated IMS dataset and validate that the RKMD method is highly specific for lipid components in the presence of confounding background ions. Moreover, we demonstrate an application of the RKMD-based annotation and filtering to matrix-assisted laser desorption/ionization (MALDI) IMS lipidomic data from human kidney tissue analysis

Lymphocytes Are the Major Reservoir for Foamy Viruses in Peripheral Blood

AbstractSimian and human foamy virus (FV) DNA can be readily detected in peripheral blood leukocytes. However, it is unknown which leukocyte populations harbor the virusin vivo.We, therefore, analyzed blood samples from nine African green monkeys, four chimpanzees, and two humans for the presence of foamy virus proviral DNA in different FACS-purified leukocyte populations, using a highly sensitive nested polymerase chain reaction (PCR). The CD8+lymphocytes were PCR positive in all 15 samples and the average viral burden was highest in this population. FV DNA was detected in 10 of 15 cell samples enriched for B lymphocytes, and 4 of 9 CD4+lymphocyte, 3 of 13 CD14+monocyte, and 4 of 13 polymorphonuclear leukocyte samples. A highly sensitive reverse transcriptase PCR was performed to detect viral transcripts in peripheral blood leukocytes. All samples were negative. In conclusion, lymphocytes, and especially CD8+T lymphocytes, were found to be a major target for foamy virus in the peripheral blood, but viral gene expression was not detected

Visualization of the growth and production of grapes through analysis of sensory data

Grapes used in the wine industry have been one of the highest value crops in the United States. However, with unpredictable weather changes and recent drought in the Western United States, vineyard owners and grape growers have faced difficulties on producing good quality grapes suited for wine making. Therefore, a technology that would keep record of environmental data and incorporate the data to support agricultural decisions will help the growers to produce quality grapes even in extreme conditions. As such, this research focuses on developing an interactive system that uses sensory data and visual analytics to facilitate vineyard management and agricultural decisions (such as choosing irrigation strategy and deciding harvesting date) through predictive analysis and historical comparisons. The system visualizes the data gathered by data loggers at vineyard sites to aid growers in decision making. The current system incorporates a stack zooming graph of historical temperature data from different sites and depths with annotation of important dates like bud break and harvest. This stack zooming graph can also be used to check for any erroneous data and implement database cleaning to fix these errors. Some analysis of agricultural characteristics such as soil type and moisture relationship and collective effects of different weather components are currently being done. As this is an ongoing project, integrating new features with better predictive analysis and more visuals will be necessary for the growers to rely on this system

Visualization and Analysis of Sensory Data

Recently, California has suffered a severe drought, making water a scarce resource to its population. Many viticulturists are based in this area who rely on heavy irrigation to produce a better grape and a better wine. Not just in California, but throughout the nation, irrigation must be applied intelligently for efficient use of water and funding. By taking measurements of physical characteristics of a vineyard over time, one may be able to visualize trends in the data which lend itself to describing preferred growing methods. Wireless sensors can be used to take measurements including moisture, temperature, sunlight, and more. Sensors have been installed at multiple locations about a vineyard. A framework has been put in place to capture, adjust, and calibrate the data as well as store it for future retrieval. The data are visualized over time to see the effects of techniques in the long term. These are helpful for suggesting irrigation strategy that will lead to the best yield. Sensors are cheap and effective, but are prone to malfunction and transmission errors. When these problems occur, the faulty time-series data can be cleaned by correlating with similar time-series data in the same time span. The data system will be a necessity for competitive viticulturists, reducing cost of irrigation and improving quality of wine. In the future, the tool could be applied to other crops. Also, if any new important values must be derived or measured, the system can be extended to include them

Local Linear Convergence of Approximate Projections onto Regularized Sets

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von Neumann has been shown to converge locally at a linear rate dependent on the regularity modulus of the intersection. In many applications, however, the sets in question come from inexact measurements that are matched to idealized models. It is unlikely that any such problems in applications will enjoy metrically regular intersection, let alone set intersection. We explore a regularization strategy that generates an intersection with the desired regularity properties. The regularization, however, can lead to a significant increase in computational complexity. In a further refinement, we investigate and prove linear convergence of an approximate alternating projection algorithm. The analysis provides a regularization strategy that fits naturally with many ill-posed inverse problems, and a mathematically sound stopping criterion for extrapolated, approximate algorithms. The theory is demonstrated on the phase retrieval problem with experimental data. The conventional early termination applied in practice to unregularized, consistent problems in diffraction imaging can be justified fully in the framework of this analysis providing, for the first time, proof of convergence of alternating approximate projections for finite dimensional, consistent phase retrieval problems.Comment: 23 pages, 5 figure

Deep contextualized word representations

We introduce a new type of deep contextualized word representation that models both (1) complex characteristics of word use (e.g., syntax and semantics), and (2) how these uses vary across linguistic contexts (i.e., to model polysemy). Our word vectors are learned functions of the internal states of a deep bidirectional language model (biLM), which is pre-trained on a large text corpus. We show that these representations can be easily added to existing models and significantly improve the state of the art across six challenging NLP problems, including question answering, textual entailment and sentiment analysis. We also present an analysis showing that exposing the deep internals of the pre-trained network is crucial, allowing downstream models to mix different types of semi-supervision signals.Comment: NAACL 2018. Originally posted to openreview 27 Oct 2017. v2 updated for NAACL camera read

Plasmonic Gadolinium Oxide Nanomatryoshkas: Bifunctional Magnetic Resonance Imaging Enhancers for Photothermal Cancer Therapy

Nanoparticle-assisted laser-induced photothermal therapy (PTT) is a promising method for cancer treatment; yet, visualization of nanoparticle uptake and photothermal response remain a critical challenge. Here, we report a magnetic resonance imaging-active nanomatryoshka (Gd2O3-NM), a multilayered (Au core/Gd2O3 shell/Au shell) sub-100 nm nanoparticle capable of combining T1 MRI contrast with PTT. This bifunctional nanoparticle demonstrates an r1 of 1.28 × 108 mM-1 s-1, an MRI contrast enhancement per nanoparticle sufficient for T1 imaging in addition to tumor ablation. Gd2O3-NM also shows excellent stability in an acidic environment, retaining 99% of the internal Gd(3). This report details the synthesis and characterization of a promising system for combined theranostic nanoparticle tracking and PTT