On the Convergence of Adaptive Iterative Linearized Galerkin Methods

A wide variety of different (fixed-point) iterative methods for the solution of nonlinear equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from our previous work that covers some prominent procedures (including the Zarantonello, Ka\v{c}anov and Newton iteration methods). In combination with appropriate discretization methods so-called (adaptive) iterative linearized Galerkin (ILG) schemes are obtained. The main purpose of this paper is the derivation of an abstract convergence theory for the unified ILG approach (based on general adaptive Galerkin discretization methods) proposed in our previous work. The theoretical results will be tested and compared for the aforementioned three iterative linearization schemes in the context of adaptive finite element discretizations of strongly monotone stationary conservation laws

Computational neuroanatomy and co-expression of genes in the adult mouse brain, analysis tools for the Allen Brain Atlas

We review quantitative methods and software developed to analyze genome-scale, brain-wide spatially-mapped gene-expression data. We expose new methods based on the underlying high-dimensional geometry of voxel space and gene space, and on simulations of the distribution of co-expression networks of a given size. We apply them to the Allen Atlas of the adult mouse brain, and to the co-expression network of a set of genes related to nicotine addiction retrieved from the NicSNP database. The computational methods are implemented in {\ttfamily{BrainGeneExpressionAnalysis}}, a Matlab toolbox available for download.Comment: 25 pages, 8 figures, accepted in Quantitative Biology (2012) 000

Very accurate Distances and Radii of Open Cluster Cepheids from a Near-Infrared Surface Brightness Technique

We have obtained the radii and distances of 16 galactic Cepheids supposed to be members in open clusters or associations using the new optical and near-infrared calibrations of the surface brightness (Barnes-Evans) method given by Fouque & Gieren (1997). We discuss in detail possible systematic errors in our infrared solutions and conclude that the typical total uncertainty of the infrared distance and radius of a Cepheid is about 3 percent in both infrared solutions, provided that the data are of excellent quality and that the amplitude of the color curve used in the solution is larger than ~0.3 mag. We compare the adopted infrared distances of the Cepheid variables to the ZAMS-fitting distances of their supposed host clusters and associations and find an unweighted mean value of the distance ratio of 1.02 +- 0.04. A detailed discussion of the individual Cepheids shows that the uncertainty of the ZAMS-fitting distances varies considerably from cluster to cluster. We find clear evidence that four Cepheids are not cluster members (SZ Tau, T Mon, U Car and SV Vul) while we confirm cluster membership for V Cen and BB Sgr for which the former evidence for cluster membership was only weak. After rejection of non-members, we find a weighted mean distance ratio of 0.969 +- 0.014, with a standard deviation of 0.05, which demonstrates that both distance indicators are accurate to better than 5%, including systematic errors, and that there is excellent agreement between both distance scales.Comment: LaTeX, 11 Figures, 5 Tables, to be published in The Astrophysical Journal, Oct. 10, 1997 issu

Can Big Media do "Big Society"?: A Critical Case Study of Commercial, Convergent Hyperlocal News

The UK Government is committed to helping ‘nurture a new generation of local media companies’. Changes to local media ownership rules allowing companies to follow their customers from platform to platform are supposed to assist in this by encouraging economies of scale. This paper provides a timely case study examining a UK-based commercial local news network owned by Daily Mail & General Trust that leverages economies of scale: Northcliffe Media’s network of 154 Local People websites. The study evaluates the level of audience engagement with the Local People sites through a user survey, and by looking at the numbers of active users, their contributions and their connections with other users. Interviews with ten of the ‘community publishers’ who oversee each site on the ground were conducted, along with a content survey. Although the study reveals a demand for community content, particularly of a practical nature, the results question the extent to which this type of ‘big media’ local news website can succeed as a local social network, reinvigorate political engagement, or encourage citizen reporting. The Government hopes that communities, especially rural ones, will increasingly use the Internet to access local news and information, thereby supporting new, profitable local media companies, who will nurture a sense of local identity and hold locally-elected politicians to account. This case study highlights the difficulties inherent in achieving such outcomes, even using the Government’s preferred convergent, commercial model