Preconditioning Newton-Krylov Methods in Non-Convex Large Scale Optimization

We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices products or matrices storage. The set of directions generated by the Krylov subspace method is used, as by product, to provide an approximate inverse preconditioner. Then, we experience our preconditioner within Truncated Newton schemes for large scale unconstrained optimization, where we generalize the truncation rule by Nash–Sofer (Oper. Res. Lett. 9:219–221, 1990) to the indefinite case, too. We use a Krylov subspace method to both approximately solve the Newton equation and to construct the preconditioner to be used at the current outer iteration. An extensive numerical experience shows that the proposed preconditioning strategy, compared with the unpreconditioned strategy and PREQN (Morales and Nocedal in SIAM J. Optim. 10:1079–1096, 2000), may lead to a reduction of the overall inner iterations. Finally, we show that our proposal has some similarities with the Limited Memory Preconditioners (Gratton et al. in SIAM J. Optim. 21:912–935, 2011)

A critical analysis of high-redshift, massive galaxy clusters: I

We critically investigate current statistical tests applied to high redshift clusters of galaxies in order to test the standard cosmological model and describe their range of validity. We carefully compare a sample of high-redshift, massive, galaxy clusters with realistic Poisson sample simulations of the theoretical mass function, which include the effect of Eddington bias. We compare the observations and simulations using the following statistical tests: the distributions of ensemble and individual existence probabilities (in the >M,>z sense), the redshift distributions, and the 2d Kolmogorov-Smirnov test. Using seemingly rare clusters from Hoyle et al. (2011), and Jee et al. (2011) and assuming the same survey geometry as in Jee et al. (2011, which is less conservative than Hoyle et al. 2011), we find that the (>M,>z) existence probabilities of all clusters are fully consistent with LCDM. However assuming the same survey geometry, we use the 2d K-S test probability to show that the observed clusters are not consistent with being the least probable clusters from simulations at >95% confidence, and are also not consistent with being a random selection of clusters, which may be caused by the non-trivial selection function and survey geometry. Tension can be removed if we examine only a X-ray selected sub sample, with simulations performed assuming a modified survey geometry.Comment: 20 pages, 6 figures, 2 tables, modified to match accepted version (JCAP); title changed, main analysis unchanged, additional analysi

Genome-wide Analyses Identify KIF5A as a Novel ALS Gene

To identify novel genes associated with ALS, we undertook two lines of investigation. We carried out a genome-wide association study comparing 20,806 ALS cases and 59,804 controls. Independently, we performed a rare variant burden analysis comparing 1,138 index familial ALS cases and 19,494 controls. Through both approaches, we identified kinesin family member 5A (KIF5A) as a novel gene associated with ALS. Interestingly, mutations predominantly in the N-terminal motor domain of KIF5A are causative for two neurodegenerative diseases: hereditary spastic paraplegia (SPG10) and Charcot-Marie-Tooth type 2 (CMT2). In contrast, ALS-associated mutations are primarily located at the C-terminal cargo-binding tail domain and patients harboring loss-of-function mutations displayed an extended survival relative to typical ALS cases. Taken together, these results broaden the phenotype spectrum resulting from mutations in KIF5A and strengthen the role of cytoskeletal defects in the pathogenesis of ALS.Peer reviewe

On the Geometry Phase in Model-Based Algorithms for Derivative-Free Optimization

A numerical study of model-based methods for derivative-free optimization is presented. These methods typically include a geometry phase whose goal is to ensure the adequacy of the interpolation set. The paper studies the performance of an algorithm that dispenses with the geometry phase altogether (and therefore does not attempt to control the position of the interpolation set). Data are presented describing the evolution of the condition number of the interpolation matrix and the accuracy of the gradient estimate. The experiments are performed on smooth unconstrained optimization problems with dimensions ranging between 2 and 15

Patterns and processes of Chasmagnathus granulata and Cyrtograpsus angulatus (Brachyura: Grapsidae) recruitment in Mar Chiquita coastal lagoon, Argentina

Recruitment patterns of crabs and other benthic invertebrates with planktonic larvae are determined by a combination of pre- and post-settlement factors. Recruitment is considered settlement limited when there is a positive correlation between the postlarvae available in the water column and the number of recruits, and regulated when abundance of individuals is mainly affected by post-settlement factors, such as competence and inter or intraspecific predation. Temperate southwestern Atlantic saltmarshes are inhabited by Cyrtograpsus angulatus and Chasmagnathus granulata, two intertidal grapsid crabs. These crabs are considered key species in the ecosystem in Mar Chiquita coastal lagoon, Buenos Aires, Argentina. In this work, we compare the recruitment pattern of Cyrtograpsus angulatus and Chasmagnathus granulata on the basis of a 3-year sampling programme. Furthermore, we examine experimentally, in laboratory and field, settlement and postsettlement processes that can help explain these patterns: habitat selection, intra- and inter-cohort cannibalism and predator avoidance behaviour. Finally, we integrate our results with the previous knowledge about distribution, growth and reproductive biology of both species, to propose a model of recruitment of each species. Both species had a consistent recruitment pattern through 3 years. Recruitment of both species started at the beginning of summer, and continued to autumn, but recruits were present until the beginning of spring. Densities of recruits and juveniles of C. angulatus were not correlated, whereas, there was a relationship between abundance of recruits and juveniles of C. granulata. In the field, recruits of C. angulatus suffered high mortality caused by intra- and inter-cohort cannibalism. Megalopae of C. angulatus selected a substrate (crevices in Ficopomatus enigmaticus reef) that gave them refuge against cannibals. First crabs of C. granulata selected adult conspecific substrate (mud from adult habitats). Recruits of C. angulatus avoided adults of either species. A qualitative model of recruitment of both species is proposed. Post-settlement processes strongly affects the recruitment pattern and, consequently, both species have regulated recruitment. The degree of such regulation, however, is more intense in C. angulatus than in C. granulata

Thalamic Deep Brain Stimulation for Orthostatic Tremor: A Multicenter International Registry

Neurological Motor Disorder