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

A framework for deriving semantic web services

Web service-based development represents an emerging approach for the development of distributed information systems. Web services have been mainly applied by software practitioners as a means to modularize system functionality that can be offered across a network (e.g., intranet and/or the Internet). Although web services have been predominantly developed as a technical solution for integrating software systems, there is a more business-oriented aspect that developers and enterprises need to deal with in order to benefit from the full potential of web services in an electronic market. This ‘ignored’ aspect is the representation of the semantics underlying the services themselves as well as the ‘things’ that the services manage. Currently languages like the Web Services Description Language (WSDL) provide the syntactic means to describe web services, but lack in providing a semantic underpinning. In order to harvest all the benefits of web services technology, a framework has been developed for deriving business semantics from syntactic descriptions of web services. The benefits of such a framework are two-fold. Firstly, the framework provides a way to gradually construct domain ontologies from previously defined technical services. Secondly, the framework enables the migration of syntactically defined web services toward semantic web services. The study follows a design research approach which (1) identifies the problem area and its relevance from an industrial case study and previous research, (2) develops the framework as a design artifact and (3) evaluates the application of the framework through a relevant scenario

Gatekeeper of pluripotency: a common Oct4 transcriptional network operates in mouse eggs and embryonic stem cells

BACKGROUND: Oct4 is a key factor of an expanded transcriptional network (Oct4-TN) that governs pluripotency and self-renewal in embryonic stem cells (ESCs) and in the inner cell mass from which ESCs are derived. A pending question is whether the establishment of the Oct4-TN initiates during oogenesis or after fertilisation. To this regard, recent evidence has shown that Oct4 controls a poorly known Oct4-TN central to the acquisition of the mouse egg developmental competence. The aim of this study was to investigate the identity and extension of this maternal Oct4-TN, as much as whether its presence is circumscribed to the egg or maintained beyond fertilisation. RESULTS: By comparing the genome-wide transcriptional profile of developmentally competent eggs that express the OCT4 protein to that of developmentally incompetent eggs in which OCT4 is down-regulated, we unveiled a maternal Oct4-TN of 182 genes. Eighty of these transcripts escape post-fertilisation degradation and represent the maternal Oct4-TN inheritance that is passed on to the 2-cell embryo. Most of these 80 genes are expressed in cancer cells and 37 are notable companions of the Oct4 transcriptome in ESCs. CONCLUSIONS: These results provide, for the first time, a developmental link between eggs, early preimplantation embryos and ESCs, indicating that the molecular signature that characterises the ESCs identity is rooted in oogenesis. Also, they contribute a useful resource to further study the mechanisms of Oct4 function and regulation during the maternal-to-embryo transition and to explore the link between the regulation of pluripotency and the acquisition of de-differentiation in cancer cells

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/