A Jacobi-Davidson type method with a correction equation tailored for integral operators

The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9656-9We propose two iterative numerical methods for eigenvalue computations of large dimensional problems arising from finite approximations of integral operators, and describe their parallel implementation. A matrix representation of the problem on a space of moderate dimension, defined from an infinite dimensional one, is computed along with its eigenpairs. These are taken as initial approximations and iteratively refined, by means of a correction equation based on the reduced resolvent operator and performed on the moderate size space, to enhance their quality. Each refinement step requires the prolongation of the correction equation solution back to a higher dimensional space, defined from the infinite dimensional one. This approach is particularly adapted for the computation of eigenpair approximations of integral operators, where prolongation and restriction matrices can be easily built making a bridge between coarser and finer discretizations. We propose two methods that apply a Jacobi–Davidson like correction: Multipower Defect-Correction (MPDC), which uses a single-vector scheme, if the eigenvalues to refine are simple, and Rayleigh–Ritz Defect-Correction (RRDC), which is based on a projection onto an expanding subspace. Their main advantage lies in the fact that the correction equation is performed on a smaller space while for general solvers it is done on the higher dimensional one. We discuss implementation and parallelization details, using the PETSc and SLEPc packages. Also, numerical results on an astrophysics application, whose mathematical model involves a weakly singular integral operator, are presented.This work was partially supported by European Regional Development Fund through COMPETE, FCT-Fundacao para a Ciencia e a Tecnologia through CMUP-Centro de Matematica da Universidade do Porto and Spanish Ministerio de Ciencia e Innovacion under projects TIN2009-07519 and AIC10-D-000600.Vasconcelos, PB.; D'almeida, FD.; Román Moltó, JE. (2013). A Jacobi-Davidson type method with a correction equation tailored for integral operators. Numerical Algorithms. 64(1):85-103. doi:10.1007/s11075-012-9656-9S85103641Absil, P.A., Mahony, R., Sepulchre, R., Dooren, P.V.: A Grassmann–Rayleigh quotient iteration for computing invariant subspaces. SIAM Rev. 44(1), 57–73 (2002)Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations with Bounded Operators. 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Effects of monoamines and antidepressants on astrocyte physiology: implications for monoamine hypothesis of depression

Major depressive disorder (MDD) is one of the most common neuropsychiatric disorders affecting over one-fifth of the population worldwide. Owing to our limited understanding of the pathophysiology of MDD, the quest for finding novel antidepressant drug targets is severely impeded. Monoamine hypothesis of MDD provides a robust theoretical framework, forming the core of a large jigsaw puzzle, around which we must look for the vital missing pieces. Growing evidence suggests that the glial loss observed in key regions of the limbic system in depressed patients, at least partly, accounts for the structural and cognitive manifestations of MDD. Studies in animal models have subsequently hinted at the possibility that the glial atrophy may play a causative role in the precipitation of depressive symptoms. Antidepressants as well as monoamine neurotransmitters exert profound effects on the gene expression and metabolism in astrocytes. This raises an intriguing possibility that the astrocytes may play a central role alongside neurons in the behavioral effects of antidepressant drugs. In this article, we discuss the gene expression and metabolic changes brought about by antidepressants in astrocytes, which could be of relevance to synaptic plasticity and behavioral effects of antidepressant treatments

Cathepsin B-associated Activation of Amyloidogenic Pathway in Murine Mucopolysaccharidosis Type I Brain Cortex

Mucopolysaccharidosis type I (MPS I) is caused by genetic deficiency of alpha-l-iduronidase and impairment of lysosomal catabolism of heparan sulfate and dermatan sulfate. In the brain, these substrates accumulate in the lysosomes of neurons and glial cells, leading to neuroinflammation and neurodegeneration. Their storage also affects lysosomal homeostasis-inducing activity of several lysosomal proteases including cathepsin B (CATB). In the central nervous system, increased CATB activity has been associated with the deposition of amyloid plaques due to an alternative pro-amyloidogenic processing of the amyloid precursor protein (APP), suggesting a potential role of this enzyme in the neuropathology of MPS I. In this study, we report elevated levels of protein expression and activity of CATB in cortex tissues of 6-month-old MPS I (Idua -/- mice. Besides, increased CATB leakage from lysosomes to the cytoplasm of Idua -/- cortical pyramidal neurons was indicative of damaged lysosomal membranes. The increased CATB activity coincided with an elevated level of the 16-kDa C-terminal APP fragment, which together with unchanged levels of beta-secretase 1 was suggestive for the role of this enzyme in the amyloidogenic APP processing. Neuronal accumulation of Thioflavin-S-positive misfolded protein aggregates and drastically increased levels of neuroinflammatory glial fibrillary acidic protein (GFAP)-positive astrocytes and CD11b-positive activated microglia were observed in Idua -/- cortex by confocal fluorescent microscopy. Together, our results point to the existence of a novel CATB-associated alternative amyloidogenic pathway in MPS I brain induced by lysosomal storage and potentially leading to neurodegeneration

Sleep deprivation increases oleoylethanolamide in human cerebrospinal fluid

This study investigated the role of two fatty acid ethanolamides, the endogenous cannabinoid anandamide and its structural analog oleoylethanolamide in sleep deprivation of human volunteers. Serum and cerebrospinal fluid (CSF) samples were obtained from 20 healthy volunteers before and after a night of sleep deprivation with an interval of about 12 months. We found increased levels of oleoylethanolamide in CSF (P = 0.011) but not in serum (P = 0.068) after 24 h of sleep deprivation. Oleoylethanolamide is an endogenous lipid messenger that is released after neural injury and activates peroxisome proliferator-activated receptor-α (PPAR-α) with nanomolar potency. Exogenous PPAR-α agonists, such as hypolipidemic fibrates and oleoylethanolamide, exert both neuroprotective and neurotrophic effects. Thus, our results suggest that oleoylethanolamide release may represent an endogenous neuroprotective signal during sleep deprivation

Diagnosing mucopolysaccharidosis IVA

Mucopolysaccharidosis IVA (MPS IVA; Morquio A syndrome) is an autosomal recessive lysosomal storage disorder resulting from a deficiency of N-acetylgalactosamine-6-sulfate sulfatase (GALNS) activity. Diagnosis can be challenging and requires agreement of clinical, radiographic, and laboratory findings. A group of biochemical genetics laboratory directors and clinicians involved in the diagnosis of MPS IVA, convened by BioMarin Pharmaceutical Inc., met to develop recommendations for diagnosis. The following conclusions were reached. Due to the wide variation and subtleties of radiographic findings, imaging of multiple body regions is recommended. Urinary glycosaminoglycan analysis is particularly problematic for MPS IVA and it is strongly recommended to proceed to enzyme activity testing even if urine appears normal when there is clinical suspicion of MPS IVA. Enzyme activity testing of GALNS is essential in diagnosing MPS IVA. Additional analyses to confirm sample integrity and rule out MPS IVB, multiple sulfatase deficiency, and mucolipidoses types II/III are critical as part of enzyme activity testing. Leukocytes or cultured dermal fibroblasts are strongly recommended for enzyme activity testing to confirm screening results. Molecular testing may also be used to confirm the diagnosis in many patients. However, two known or probable causative mutations may not be identified in all cases of MPS IVA. A diagnostic testing algorithm is presented which attempts to streamline this complex testing process

Worldwide trends in population-based survival for children, adolescents, and young adults diagnosed with leukaemia, by subtype, during 2000–14 (CONCORD-3) : analysis of individual data from 258 cancer registries in 61 countries

Background Leukaemias comprise a heterogenous group of haematological malignancies. In CONCORD-3, we analysed data for children (aged 0–14 years) and adults (aged 15–99 years) diagnosed with a haematological malignancy during 2000–14 in 61 countries. Here, we aimed to examine worldwide trends in survival from leukaemia, by age and morphology, in young patients (aged 0–24 years). Methods We analysed data from 258 population-based cancer registries in 61 countries participating in CONCORD-3 that submitted data on patients diagnosed with leukaemia. We grouped patients by age as children (0–14 years), adolescents (15–19 years), and young adults (20–24 years). We categorised leukaemia subtypes according to the International Classification of Childhood Cancer (ICCC-3), updated with International Classification of Diseases for Oncology, third edition (ICD-O-3) codes. We estimated 5-year net survival by age and morphology, with 95% CIs, using the non-parametric Pohar-Perme estimator. To control for background mortality, we used life tables by country or region, single year of age, single calendar year and sex, and, where possible, by race or ethnicity. All-age survival estimates were standardised to the marginal distribution of young people with leukaemia included in the analysis. Findings 164563 young people were included in this analysis: 121328 (73·7%) children, 22963 (14·0%) adolescents, and 20272 (12·3%) young adults. In 2010–14, the most common subtypes were lymphoid leukaemia (28205 [68·2%] patients) and acute myeloid leukaemia (7863 [19·0%] patients). Age-standardised 5-year net survival in children, adolescents, and young adults for all leukaemias combined during 2010–14 varied widely, ranging from 46% in Mexico to more than 85% in Canada, Cyprus, Belgium, Denmark, Finland, and Australia. Individuals with lymphoid leukaemia had better age-standardised survival (from 43% in Ecuador to ≥80% in parts of Europe, North America, Oceania, and Asia) than those with acute myeloid leukaemia (from 32% in Peru to ≥70% in most high-income countries in Europe, North America, and Oceania). Throughout 2000–14, survival from all leukaemias combined remained consistently higher for children than adolescents and young adults, and minimal improvement was seen for adolescents and young adults in most countries. Interpretation This study offers the first worldwide picture of population-based survival from leukaemia in children, adolescents, and young adults. Adolescents and young adults diagnosed with leukaemia continue to have lower survival than children. Trends in survival from leukaemia for adolescents and young adults are important indicators of the quality of cancer management in this age group.peer-reviewe