Bounds for the Rayleigh quotient and the spectrum of self-adjoint operators

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If $x$ is an eigenvector of a self-adjoint bounded operator $A$ in a Hilbert space, then the RQ of the vector $x$, denoted by $\rho(x)$, is an exact eigenvalue of $A$. In this case, the absolute change of the RQ $|\rho(x)-\rho(y)|$ becomes the absolute error in an eigenvalue $\rho(x)$ of $A$ approximated by the RQ $\rho(y)$ on a given vector $y.$ There are three traditional kinds of bounds of the eigenvalue error: a priori bounds via the angle between vectors $x$ and $y$; a posteriori bounds via the norm of the residual $Ay-\rho(y)y$ of vector $y$; mixed type bounds using both the angle and the norm of the residual. We propose a unifying approach to prove known bounds of the spectrum, analyze their sharpness, and derive new sharper bounds. The proof approach is based on novel RQ vector perturbation identities.Comment: 13 page

Convergence of genes and cellular pathways dysregulated in autism spectrum disorders

Rare copy-number variation (CNV) is an important source of risk for autism spectrum disorders (ASDs). We analyzed 2,446 ASD-affected families and confirmed an excess of genic deletions and duplications in affected versus control groups (1.41-fold, p = 1.0 × 10(-5)) and an increase in affected subjects carrying exonic pathogenic CNVs overlapping known loci associated with dominant or X-linked ASD and intellectual disability (odds ratio = 12.62, p = 2.7 × 10(-15), ∼3% of ASD subjects). Pathogenic CNVs, often showing variable expressivity, included rare de novo and inherited events at 36 loci, implicating ASD-associated genes (CHD2, HDAC4, and GDI1) previously linked to other neurodevelopmental disorders, as well as other genes such as SETD5, MIR137, and HDAC9. Consistent with hypothesized gender-specific modulators, females with ASD were more likely to have highly penetrant CNVs (p = 0.017) and were also overrepresented among subjects with fragile X syndrome protein targets (p = 0.02). Genes affected by de novo CNVs and/or loss-of-function single-nucleotide variants converged on networks related to neuronal signaling and development, synapse function, and chromatin regulation

Mechanisms shaping size structure and functional diversity of phytoplankton communities in the ocean

The factors regulating phytoplankton community composition play a crucial role in structuring aquatic food webs. However, consensus is still lacking about the mechanisms underlying the observed biogeographical differences in cell size composition of phytoplankton communities. Here we use a trait-based model to disentangle these mechanisms in two contrasting regions of the Atlantic Ocean. In our model, the phytoplankton community can self-assemble based on a trade-off emerging from relationships between cell size and (1) nutrient uptake, (2) zooplankton grazing, and (3) phytoplankton sinking. Grazing 'pushes' the community towards larger cell sizes, whereas nutrient uptake and sinking 'pull' the community towards smaller cell sizes. We find that the stable environmental conditions of the tropics strongly balance these forces leading to persistently small cell sizes and reduced size diversity. In contrast, the seasonality of the temperate region causes the community to regularly reorganize via shifts in species composition and to exhibit, on average, bigger cell sizes and higher size diversity than in the tropics. Our results raise the importance of environmental variability as a key structuring mechanism of plankton communities in the ocean and call for a reassessment of the current understanding of phytoplankton diversity patterns across latitudinal gradients

Analysis of the gene expression profile of mouse male meiotic germ cells

Wide genome analysis of difference in gene expression between spermatogonial populations from 7-day-old mice and pachytene spermatocytes from 18-day-old mice was performed using Affymetrix gene chips representing approximately 12,500 mouse known genes or EST sequences, spanning approximately 1/3rd of the mouse genome. To delineate differences in the profile of gene expression between mitotic and meiotic stages of male germ cell differentiation, expressed genes were grouped in functional clusters. The analysis confirmed the previously described pre-meiotic or meiotic expression for several genes, in particular for those involved in the regulation of the mitotic and meiotic cell cycle, and for those whose transcripts are accumulated during the meiotic stages to be translated later in post-meiotic stages. Differential expression of several additional genes was discovered. In few cases (pro-apoptotic factors Bak, Bad and Bax), data were in conflict with the previously published stage-dependent expression of genes already known to be expressed in male germ cells. Northern blot analysis of selected genes confirmed the results obtained with the microarray chips. Six of these were novel genes specifically expressed in pachytene spermatocytes: a chromatin remodeling factor (chrac1/YCL1), a homeobox gene (hmx1), a novel G-coupled receptor for an unknown ligand (Gpr19), a glycoprotein of the intestinal epithelium (mucin 3), a novel RAS activator (Ranbp9), and the A630056B21Rik gene (predicted to encode a novel zinc finger protein). These studies will help to delineate the global patterns of gene expression characterizing male germ cell differentiation for a better understanding of regulation of spermatogenesis in mammals

Pollution sources affecting oxidative potential of fine aerosols from a Portuguese urban-industrial area

Trabalho apresentado em European Aerosol Conference 2023 (EAC2023), September 3−8, 2023, Malaga, SpainN/

The long-term legacy of plastic mass production

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordMismanaged plastic waste is transported via rivers or city drains into the ocean where it accumulates in coastal sediments, ocean gyres and the deep ocean. Plastic harms marine biota and may ultimately return to humans via the food chain. Private initiatives proposing to collect plastic from the sea and rivers have gained widespread attention, especially in the media. However, few of these methods are proven concepts and it remains unclear how effective they are. Here we estimate the amount of plastic in the global surface ocean to assess the long-term legacy of plastic mass production, calculate the time required to clean up the oceans with river barriers and clean up devices, and explore the fate of collected plastic waste. We find that the projected impact of both single and multiple clean up devices is very modest. A significant reduction of plastic debris in the ocean can be only achieved with collection at rivers or with a combination of river barriers and clean up devices. We also show that the incineration and production of plastic has a significant long-term effect on the global atmospheric carbon budget. We conclude that a combination of reduced plastic emissions and reinforced collection is the only way to rid the ocean of plastic waste

Extinction and dawn of the modern world in the Carnian (Late Triassic)

The Carnian Pluvial Episode (Late Triassic) was a time of global environmental changes and possibly substantial coeval volcanism. The extent of the biological turnover in marine and terrestrial ecosystems is not well understood. Here, we present a meta-analysis of fossil data that suggests a substantial reduction in generic and species richness and the disappearance of 33% of marine genera. This crisis triggered major radiations. In the sea, the rise of the first scleractinian reefs and rock-forming calcareous nannofossils points to substantial changes in ocean chemistry. On land, there were major diversifications and originations of conifers, insects, dinosaurs, crocodiles, lizards, turtles, and mammals. Although there is uncertainty on the precise age of some of the recorded biological changes, these observations indicate that the Carnian Pluvial Episode was linked to a major extinction event and might have been the trigger of the spectacular radiation of many key groups that dominate modern ecosystems