Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex objective functions with $L$-Lipschitz continuous gradient. In the framework of Nesterov both $\mu$ and $L$ are assumed known -- an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient $\mu$ and $L$ during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. The results show that for ill-conditioned problems solved to high accuracy, the proposed method significantly outperforms state-of-the-art first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Charged particle densities from Au+Au collisions at sqrt{s_{NN}}=130 GeV

We present charged particle densities as a function of pseudorapidity and collision centrality for the 197Au+197Au reaction at sqrt{s_{NN}}=130 GeV. An integral charged particle multiplicity of 3860+/-300 is found for the 5% most central events within the pseudorapidity range -4.7 <= eta <= 4.7. At mid-rapidity an enhancement in the particle yields per participant nucleon pair is observed for central events. Near to the beam rapidity, a scaling of the particle yields consistent with the ``limiting fragmentation'' picture is observed. Our results are compared to other recent experimental and theoretical discussions of charged particle densities in ultra-relativistic heavy-ion collisions.Comment: 14 pages, 4 figures; to be published in Phys. Lett.

Some Consequences of Thermosolutal Convection: The Grain Structure of Castings

The essential principles of thermosolutal convection are outlined, and how convection provides a transport mechanism between the mushy region of a casting and the open bulk liquid is illustrated. The convective flow patterns which develop assist in heat exchange and macroscopic solute segregation during solidification; they also provide a mechanism for the transport of dendritic fragments from the mushy region into the bulk liquid. Surviving fragments become nuclei for equiaxed grains and so lead to blocking of the parental columnar, dendritic growth front from which they originated. The physical steps in such a sequence are considered and some experimental data are provided to support the argument

Modeling body size evolution in Felidae under alternative phylogenetic hypotheses

The use of phylogenetic comparative methods in ecological research has advanced during the last twenty years, mainly due to accurate phylogenetic reconstructions based on molecular data and computational and statistical advances. We used phylogenetic correlograms and phylogenetic eigenvector regression (PVR) to model body size evolution in 35 worldwide Felidae (Mammalia, Carnivora) species using two alternative phylogenies and published body size data. The purpose was not to contrast the phylogenetic hypotheses but to evaluate how analyses of body size evolution patterns can be affected by the phylogeny used for comparative analyses (CA). Both phylogenies produced a strong phylogenetic pattern, with closely related species having similar body sizes and the similarity decreasing with increasing distances in time. The PVR explained 65% to 67% of body size variation and all Moran's I values for the PVR residuals were non-significant, indicating that both these models explained phylogenetic structures in trait variation. Even though our results did not suggest that any phylogeny can be used for CA with the same power, or that “good” phylogenies are unnecessary for the correct interpretation of the evolutionary dynamics of ecological, biogeographical, physiological or behavioral patterns, it does suggest that developments in CA can, and indeed should, proceed without waiting for perfect and fully resolved phylogenies

Eine Bilanzierung der Verschiebungen der Lebensverlauf-Beschäftigungsprofile von verheirateten Frauen der Jahrgänge zwischen 1940 und 1960

Life-cycle employment profiles of married women born between 1940 and 1960 shifted upwards and became flatter. We calibrate a dynamic life-cycle model of employment decisions of married women to assess the quantitative importance of three competing explanations of the change in employment profiles: the decrease and delay in fertility, the increase in relative wages of women to men, and the decline in child-care costs. We find that the decrease and delay in fertility and the decline in child-care cost affect employment very early in life, while increases in relative wages affect employment increasingly with age. Changes in relative wages, in particular returns to experience, account for the bulk (67 percent) of changes in life-cycle employment of married women

Genome-wide interaction study of a proxy for stress-sensitivity and its prediction of major depressive disorder

Individual response to stress is correlated with neuroticism and is an important predictor of both neuroticism and the onset of major depressive disorder (MDD). Identification of the genetics underpinning individual differences in response to negative events (stress-sensitivity) may improve our understanding of the molecular pathways involved, and its association with stress-related illnesses. We sought to generate a proxy for stress-sensitivity through modelling the interaction between SNP allele and MDD status on neuroticism score in order to identify genetic variants that contribute to the higher neuroticism seen in individuals with a lifetime diagnosis of depression compared to unaffected individuals. Meta-analysis of genome-wide interaction studies (GWIS) in UK Biobank (N = 23,092) and Generation Scotland: Scottish Family Health Study (N = 7,155) identified no genome-wide significance SNP interactions. However, gene-based tests identified a genome-wide significant gene, ZNF366, a negative regulator of glucocorticoid receptor function implicated in alcohol dependence (p = 1.48x10-7; Bonferroni-corrected significance threshold p < 2.79x10-6). Using summary statistics from the stress-sensitivity term of the GWIS, SNP heritability for stress-sensitivity was estimated at 5.0%. In models fitting polygenic risk scores of both MDD and neuroticism derived from independent GWAS, we show that polygenic risk scores derived from the UK Biobank stress-sensitivity GWIS significantly improved the prediction of MDD in Generation Scotland. This study may improve interpretation of larger genome-wide association studies of MDD and other stress-related illnesses, and the understanding of the etiological mechanisms underpinning stress-sensitivity

Genome-wide meta-analysis associates HLA-DQA1/DRB1 and LPA and lifestyle factors with human longevity

Genomic analysis of longevity offers the potential to illuminate the biology of human aging. Here, using genome-wide association meta-analysis of 606,059 parents' survival, we discover two regions associated with longevity (HLA-DQA1/DRB1 and LPA). We also validate previous suggestions that APOE, CHRNA3/5, CDKN2A/B, SH2B3 and FOXO3A influence longevity. Next we show that giving up smoking, educational attainment, openness to new experience and high-density lipoprotein (HDL) cholesterol levels are most positively genetically correlated with lifespan while susceptibility to coronary artery disease (CAD), cigarettes smoked per day, lung cancer, insulin resistance and body fat are most negatively correlated. We suggest that the effect of education on lifespan is principally mediated through smoking while the effect of obesity appears to act via CAD. Using instrumental variables, we suggest that an increase of one body mass index unit reduces lifespan by 7 months while 1 year of education adds 11 months to expected lifespan