A note on best approximation and invertibility of operators on uniformly convex Banach spaces

It is shown that if X is a uniformly convex Banach space and S a bounded linear operator on X for which ‖I−S‖=1, then S is invertible if and only if ‖I−12S‖<1. From this it follows that if S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation to I from [S], a natural (partial) converse to the well-known sufficient condition for invertibility that dist(I,[S])<1

Restriction associated DNA-genotyping at multiple spatial scales in Arabidopsis lyrata reveals signatures of pathogen-mediated selection

Background: Genome scans based on outlier analyses have revolutionized detection of genes involved in adaptive processes, but reports of some forms of selection, such as balancing selection, are still limited. It is unclear whether high throughput genotyping approaches for identification of single nucleotide polymorphisms have sufficient power to detect modes of selection expected to result in reduced genetic differentiation among populations. In this study, we used Arabidopsis lyrata to investigate whether signatures of balancing selection can be detected based on genomic smoothing of Restriction Associated DNA sequencing (RAD-seq) data. We compared how different sampling approaches (both within and between subspecies) and different background levels of polymorphism (inbreeding or outcrossing populations) affected the ability to detect genomic regions showing key signatures of balancing selection, specifically elevated polymorphism, reduced differentiation and shifts towards intermediate allele frequencies. We then tested whether candidate genes associated with disease resistance (R-gene analogs) were detected more frequently in these regions compared to other regions of the genome. Results: We found that genomic regions showing elevated polymorphism contained a significantly higher density of R-gene analogs predicted to be under pathogen-mediated selection than regions of non-elevated polymorphism, and that many of these also showed evidence for an intermediate site-frequency spectrum based on Tajima’s D. However, we found few genomic regions that showed both elevated polymorphism and reduced FST among populations, despite strong background levels of genetic differentiation among populations. This suggests either insufficient power to detect the reduced population structure predicted for genes under balancing selection using sparsely distributed RAD markers, or that other forms of diversifying selection are more common for the R-gene analogs tested. Conclusions: Genome scans based on a small number of individuals sampled from a wide range of populations were sufficient to confirm the relative scarcity of signatures of balancing selection across the genome, but also identified new potential disease resistance candidates within genomic regions showing signatures of balancing selection that would be strong candidates for further sequencing efforts

Toward a common standard for data and specimen provenance in life sciences

Open and practical exchange, dissemination, and reuse of specimens and data have become a fundamental requirement for life sciences research. The quality of the data obtained and thus the findings and knowledge derived is thus significantly influenced by the quality of the samples, the experimental methods, and the data analysis. Therefore, a comprehensive and precise documentation of the pre-analytical conditions, the analytical procedures, and the data processing are essential to be able to assess the validity of the research results. With the increasing importance of the exchange, reuse, and sharing of data and samples, procedures are required that enable cross-organizational documentation, traceability, and non-repudiation. At present, this information on the provenance of samples and data is mostly either sparse, incomplete, or incoherent. Since there is no uniform framework, this information is usually only provided within the organization and not interoperably. At the same time, the collection and sharing of biological and environmental specimens increasingly require definition and documentation of benefit sharing and compliance to regulatory requirements rather than consideration of pure scientific needs. In this publication, we present an ongoing standardization effort to provide trustworthy machine-actionable documentation of the data lineage and specimens. We would like to invite experts from the biotechnology and biomedical fields to further contribute to the standard.</p

R-gene variation across Arabidopsis lyrata subspecies: effects of population structure, selection and mating system.

BACKGROUND: Examining allelic variation of R-genes in closely related perennial species of Arabidopsis thaliana is critical to understanding how population structure and ecology interact with selection to shape the evolution of innate immunity in plants. We finely sampled natural populations of Arabidopsis lyrata from the Great Lakes region of North America (A. l. lyrata) and broadly sampled six European countries (A. l. petraea) to investigate allelic variation of two R-genes (RPM1 and WRR4) and neutral genetic markers (Restriction Associated DNA sequences and microsatellites) in relation to mating system, phylogeographic structure and subspecies divergence. RESULTS: Fine-scale sampling of populations revealed strong effects of mating system and population structure on patterns of polymorphism for both neutral loci and R-genes, with no strong evidence for selection. Broad geographic sampling revealed evidence of balancing selection maintaining polymorphism in R-genes, with elevated heterozygosity and diversity compared to neutral expectations and sharing of alleles among diverged subspecies. Codon-based tests detected both positive and purifying selection for both R-genes, as commonly found for animal immune genes. CONCLUSIONS: Our results highlight that combining fine and broad-scale sampling strategies can reveal the multiple factors influencing polymorphism and divergence at potentially adaptive genes such as R-genes

EnGraft: a multicentre, open-label, randomised, two-arm, superiority study protocol to assess bioavailability and practicability of Envarsus® versus Advagraf™ in liver transplant recipients

Background Graft rejection and chronic CNI toxicity remain obstacles to organ transplant success. Current formulations of tacrolimus, such as Prograf® and Advagraf™, exhibit limitations in terms of pharmacokinetics and tolerability, related in part to suboptimal bioavailability. As dosing non-compliance can result in graft rejection, the once daily formulation of tacrolimus, Advagraf™, was developed (vs 2x/day Prograf®). Benefits of Advagraf™ are counterbalanced by delayed achievement of therapeutic trough levels and need for up to 50% higher doses to maintain Prograf®-equivalent troughs. Envarsus® is also a prolonged-release once-daily tacrolimus formulation, developed using MeltDose™ drug-delivery technology to increase drug bioavailability; improved bioavailability results in low patient drug absorption variability and less pronounced peak-to-trough fluctuations. In phase III de novo kidney transplant studies, Envarsus® proved non-inferior to twice-daily tacrolimus; however, no phase IV studies show superiority of Envarsus® vs Advagraf™ in de novo liver transplant (LTx) recipients. Methods The EnGraft compares bioavailability and tests superiority of Envarsus® (test arm) versus Advagraf™ (comparator arm) in de novo LTx recipients. A total of 268 patients from 15 German transplant centres will be randomised 1:1 within 14 days post-LTx. The primary endpoint is dose-normalised trough level (C/D ratio) measured 12 weeks after randomisation. Secondary endpoints include the number of dose adjustments, time to reach first defined trough level and incidence of graft rejections. Additionally, clinical and laboratory parameters will be assessed over a 3-year period. Discussion C/D ratio is an estimate for tacrolimus bioavailability. Improving bioavailability and increasing C/D ratio using Envarsus could reduce renal dysfunction and other tacrolimus-related toxicities; previous trials have shown that a higher C/D ratio (i.e. slower tacrolimus metabolism) is not only associated with improved renal function but also linked to reduced neurotoxic side effects. A higher C/D ratio could improve clinical outcomes for LTx recipients; EnGraft has begun, with one third of patients recruited by January 2022

Consumption of pasteurized human lysozyme transgenic goats’ milk alters serum metabolite profile in young pigs

Nutrition, bacterial composition of the gastrointestinal tract, and general health status can all influence the metabolic profile of an organism. We previously demonstrated that feeding pasteurized transgenic goats’ milk expressing human lysozyme (hLZ) can positively impact intestinal morphology and modulate intestinal microbiota composition in young pigs. The objective of this study was to further examine the effect of consuming hLZ-containing milk on young pigs by profiling serum metabolites. Pigs were placed into two groups and fed a diet of solid food and either control (non-transgenic) goats’ milk or milk from hLZ-transgenic goats for 6 weeks. Serum samples were collected at the end of the feeding period and global metabolite profiling was performed. For a total of 225 metabolites (160 known, 65 unknown) semi-quantitative data was obtained. Levels of 18 known and 4 unknown metabolites differed significantly between the two groups with the direction of change in 13 of the 18 known metabolites being almost entirely congruent with improved health status, particularly in terms of the gastrointestinal tract health and immune response, with the effects of the other five being neutral or unknown. These results further support our hypothesis that consumption of hLZ-containing milk is beneficial to health

GA4GH: International policies and standards for data sharing across genomic research and healthcare.

The Global Alliance for Genomics and Health (GA4GH) aims to accelerate biomedical advances by enabling the responsible sharing of clinical and genomic data through both harmonized data aggregation and federated approaches. The decreasing cost of genomic sequencing (along with other genome-wide molecular assays) and increasing evidence of its clinical utility will soon drive the generation of sequence data from tens of millions of humans, with increasing levels of diversity. In this perspective, we present the GA4GH strategies for addressing the major challenges of this data revolution. We describe the GA4GH organization, which is fueled by the development efforts of eight Work Streams and informed by the needs of 24 Driver Projects and other key stakeholders. We present the GA4GH suite of secure, interoperable technical standards and policy frameworks and review the current status of standards, their relevance to key domains of research and clinical care, and future plans of GA4GH. Broad international participation in building, adopting, and deploying GA4GH standards and frameworks will catalyze an unprecedented effort in data sharing that will be critical to advancing genomic medicine and ensuring that all populations can access its benefits

The handbook for standardized field and laboratory measurements in terrestrial climate change experiments and observational studies (ClimEx)

1. Climate change is a world‐wide threat to biodiversity and ecosystem structure, functioning and services. To understand the underlying drivers and mechanisms, and to predict the consequences for nature and people, we urgently need better understanding of the direction and magnitude of climate change impacts across the soil–plant–atmosphere continuum. An increasing number of climate change studies are creating new opportunities for meaningful and high‐quality generalizations and improved process understanding. However, significant challenges exist related to data availability and/or compatibility across studies, compromising opportunities for data re‐use, synthesis and upscaling. Many of these challenges relate to a lack of an established ‘best practice’ for measuring key impacts and responses. This restrains our current understanding of complex processes and mechanisms in terrestrial ecosystems related to climate change. 2. To overcome these challenges, we collected best‐practice methods emerging from major ecological research networks and experiments, as synthesized by 115 experts from across a wide range of scientific disciplines. Our handbook contains guidance on the selection of response variables for different purposes, protocols for standardized measurements of 66 such response variables and advice on data management. Specifically, we recommend a minimum subset of variables that should be collected in all climate change studies to allow data re‐use and synthesis, and give guidance on additional variables critical for different types of synthesis and upscaling. The goal of this community effort is to facilitate awareness of the importance and broader application of standardized methods to promote data re‐use, availability, compatibility and transparency. We envision improved research practices that will increase returns on investments in individual research projects, facilitate second‐order research outputs and create opportunities for collaboration across scientific communities. Ultimately, this should significantly improve the quality and impact of the science, which is required to fulfil society's needs in a changing world

Riesz bases and positive operators on Hilbert space

It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product on H in which it is an orthonormal basis, thereby extending the sense in which Riesz bases and orthonormal bases are thought of as being the same. A consequence of the method of proof of this result yields a series representation for all positive isomorphisms on a Hilbert space