The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.htmlComment: Please cite "Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011." (available at arXiv:1109.0367) instead for a more general method called Linearized Alternating Direction Method This manuscript first appeared as University of Illinois at Urbana-Champaign technical report #UILU-ENG-09-2215 in October 2009 Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011. (available at http://arxiv.org/abs/1109.0367

Management of a pregnant woman with fibromuscular dysplasia

No abstract available

The AIMSS Project, III : the stellar populations of compact stellar systems

In recent years, a growing zoo of compact stellar systems (CSSs) have been found whose physical properties (mass, size, velocity dispersion) place them between classical globular clusters (GCs) and true galaxies, leading to debates about their nature. Here we present results using a so far underutilized discriminant, their stellar population properties. Based on new spectroscopy from 8-10m telescopes, we derive ages, metallicities, and [α/Fe] of 29 CSSs. These range from GCs with sizes of merely a few parsec to compact ellipticals (cEs) larger than M32. Together with a literature compilation, this provides a panoramic view of the stellar population characteristics of early-type systems. We find that the CSSs are predominantly more metal rich than typical galaxies at the same stellar mass. At high mass, the cEs depart from the mass-metallicity relation of massive early-type galaxies, which forms a continuous sequence with dwarf galaxies. At lower mass, the metallicity distribution of ultracompact dwarfs (UCDs) changes at a few times 10^7 M⊙, which roughly coincides with the mass where luminosity function arguments previously suggested the GC population ends. The highest metallicities in CSSs are paralleled only by those of dwarf galaxy nuclei and the central parts of massive early types. These findings can be interpreted as CSSs previously being more massive and undergoing tidal interactions to obtain their current mass and compact size. Such an interpretation is supported by CSSs with direct evidence for tidal stripping, and by an examination of the CSS internal escape velocities.Fil: Janz, Joachin. Swinburne University; AustraliaFil: Norris, Mark A.. Gobierno de la Republica Federal de Alemania. Max Planck Institut Fur Astrophysik; AlemaniaFil: Forbes, Duncan A.. Swinburne University; AustraliaFil: Huxor, Avon. Universität Heidelberg; AlemaniaFil: Romanowsky, Aaron. San José State University; Estados UnidosFil: Frank, Matthias. Universität Heidelberg; AlemaniaFil: Escudero, Carlos Gabriel. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica la Plata; ArgentinaFil: Faifer, Favio Raúl. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica la Plata; ArgentinaFil: Forte, Juan Carlos. Gobierno de la Ciudad de Buenos Aires. Secretaria de Cultura. Subsecretaria de Patrimonio Cultural. Planetario ; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kannappan, Sheila J.. University of North Carolina; Estados UnidosFil: Maraston, Claudia. Institute of Cosmology snd Gravitation; Estados UnidosFil: Brodie, Jean. University of California; Estados UnidosFil: Strader, Jay. Michigan State University; Estados UnidosFil: Thompson, Bradley. San José State University; Estados Unido

The Structure and X-ray Recombination Emission of a Centrally Illuminated Accretion Disk Atmosphere and Corona

We model an accretion disk atmosphere and corona photoionized by a central X-ray continuum source. We calculate the opacity and radiation transfer for an array of disk radii, to obtain the two-dimensional structure of the disk and its X-ray recombination emission. The atmospheric structure is insensitive to the viscosity alpha. We find a feedback mechanism between the disk structure and the central illumination, which expands the disk and increases the solid angle subtended by the atmosphere. We model the disk of a neutron star X-ray binary. We map the temperature, density, and ionization structure of the disk, and we simulate the high resolution spectra observable with the Chandra and XMM-Newton grating spectrometers. The X-ray emission lines from the disk atmosphere are detectable, especially for high-inclination binary systems. The grating observations of two classes of X-ray binaries already reveal important spectral similarities with our models. The line spectrum is very sensitive to the structure of each atmospheric layer, and it probes the heating mechanisms in the disk. The model spectrum is dominated by double-peaked lines of H-like and He-like ions, plus weak Fe L. Species with a broad range of ionization levels coexist at each radius: from Fe XXVI in the hot corona, to C VI at the base of the atmosphere. The choice of stable solutions affects the spectrum, since a thermal instability is present in the regime where the X-ray recombination emission is most intense.Comment: 32 pages, incl. 26 figures, accepted for publication in Ap

Human Developmental Chondrogenesis as a Basis for Engineering Chondrocytes from Pluripotent Stem Cells

Joint injury and osteoarthritis affect millions of people worldwide, but attempts to generate articular cartilage using adult stem/progenitor cells have been unsuccessful. We hypothesized that recapitulation of the human developmental chondrogenic program using pluripotent stem cells (PSCs) may represent a superior approach for cartilage restoration. Using laser-capture microdissection followed by microarray analysis, we first defined a surface phenotype (CD166(low/neg)CD146(low/neg)CD73(+)CD44(low)BMPR1B(+)) distinguishing the earliest cartilage committed cells (prechondrocytes) at 5-6 weeks of development. Functional studies confirmed these cells are chondrocyte progenitors. From 12 weeks, only the superficial layers of articular cartilage were enriched in cells with this progenitor phenotype. Isolation of cells with a similar immunophenotype from differentiating human PSCs revealed a population of CD166(low/neg)BMPR1B(+) putative cartilage-committed progenitors. Taken as a whole, these data define a developmental approach for the generation of highly purified functional human chondrocytes from PSCs that could enable substantial progress in cartilage tissue engineering.Fil: Wu, Ling. University of California at Los Angeles; Estados UnidosFil: Bluguermann, Carolina. Fundación para la Lucha contra las Enfermedades Neurológicas de la Infancia. Laboratorio de Biología del Desarrollo Celular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of California at Los Angeles; Estados UnidosFil: Kyupelyan, Levon. University of California at Los Angeles; Estados UnidosFil: Latour, Brooke. University of California at Los Angeles; Estados UnidosFil: Gonzalez, Stephanie. University of California at Los Angeles; Estados UnidosFil: Shah, Saumya. University of California at Los Angeles; Estados UnidosFil: Galic, Zoran. University of California at Los Angeles; Estados UnidosFil: Ge, Sundi. University of California at Los Angeles; Estados UnidosFil: Zhu, Yuhua. University of California at Los Angeles; Estados UnidosFil: Petrigliano, Frank A.. University of California at Los Angeles; Estados UnidosFil: Nsair, Ali. University of California at Los Angeles; Estados UnidosFil: Miriuka, Santiago Gabriel. Fundación para la Lucha contra las Enfermedades Neurológicas de la Infancia. Laboratorio de Biología del Desarrollo Celular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Li, Xinmin. University of California at Los Angeles; Estados UnidosFil: Lyons, Karen M.. University of California at Los Angeles; Estados UnidosFil: Crooks, Gay M.. University of California at Los Angeles; Estados UnidosFil: McAllister, David R.. University of California at Los Angeles; Estados UnidosFil: Van Handel, Ben. Novogenix Laboratories; Estados UnidosFil: Adams, John S.. University of California at Los Angeles; Estados UnidosFil: Evseenko, Denis. University of California at Los Angeles; Estados Unido

Limbal BCAM expression identifies a proliferative progenitor population capable of holoclone formation and corneal differentiation

The corneal epithelium is renowned for high regenerative potential, which is dependent on the coordinated function of its diverse progenitor subpopulations. However, the molecular pathways governing corneal epithelial progenitor differentiation are incompletely understood. Here, we identify a highly proliferative limbal epithelial progenitor subpopulation characterized by expression of basal cell adhesion molecule (BCAM) that is capable of holocone formation and corneal epithelial sheet generation. BCAM-positive cells can be found among ABCB5-positive limbal stem cells (LSCs) as well as among ABCB5-negative limbal epithelial cell populations. Mechanistically, we show that BCAM is functionally required for cellular migration and differentiation and that its expression is regulated by the transcription factor p63. In aggregate, our study identifies limbal BCAM expression as a marker of highly proliferative corneal epithelial progenitor cells and defines the role of BCAM as a critical molecular mediator of corneal epithelial differentiation