A mean value theorem for systems of integrals

More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a,b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a,b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary interval. The proof relies on a version of Caratheodory's convex hull theorem for a continuous curve, that we also prove in the paper. As applications, we give a representation of the covariance for two continuous functions of a random variable, and a most general version of Gruess' inequality.Comment: 7 page

Critical Buckling Load for Lattice Column Elements with Variable Dimensions

Lattice structures are used in a variety of high-value engineering applications; for example, in automobile, aerospace and biomedical applications, due to their light weight, high specific strength, stiffness, heat transfer control and energy absorption. Additive Manufacturing (AM) technologies, such as Selective Laser Melting (SLM), offer radical net-shape manufacturing solutions for metallic structures directly from digital data. The prediction of AM lattice structure mechanical properties prior to manufacture is both cost and time-consuming; particularly as existing models do not readily accommodate the effects of manufacturing defects and lattice node geometry on column buckling. The critical buckling load of columns was algebraically and numerically simulated for a full Design of Experiments (DOE) of independent variables, including column length, column radius, node radius and material type. This simulation data quantifies the effect of independent variables on critical buckling load and demonstrates the limitations of algebraically prediction. This research can be extended to allow the simulation of the load carrying capacity of entire lattice structures; and to accommodate the effect of manufacturing variation on the associated load carrying capacity of AM lattice structures

Flavonoid intake and the risk of age-related cataract in China’s Heilongjiang Province

Background/Objectives: Epidemiological evidence suggests that diets rich in flavonoids may reduce the risk of developing age-related cataract (ARC). Flavonoids are widely distributed in foods of plant origin and the objective of this study was to evaluate retrospectively the association between the intakes of the five flavonoid subclasses and the risk of ARC.  Subjects/Methods: A population-based case-control study (249 cases and 66 controls) was carried out in Heilongjiang province, which is located in the Northeast of China, and where intakes and availability of fresh vegetables and fruits can be limited. Dietary data gathered by food-frequency questionnaire (FFQ) were used to calculate flavonoid intake. Adjusted odds ratio (OR) and 95% confidence interval (CI) were estimated by logistic regression.  Results: No linear associations between risk of developing ARC and intakes of total dietary flavonoids, anthocyanidins, flavon-3-ol, flavanone, total flavones or total flavonols were found, but quercetin and isorhamnetin intake was inversely associated with ARC risk (OR 11.78, 95% CI: 1.62-85.84, P<0.05, and OR 6.99, 95% CI:1.12-43.44, P<0.05, quartile 4 vs quartile 1, respectively).  Conclusion: As quercetin is contained in many plant foods and isorhamnetin is only contained in very few foods, we concluded that higher quercetin intake may be an important dietary factor in the reduction of risk of age-related cataract

Drought, Heat, and the Carbon Cycle: a Review

Purpose of the Review Weather and climate extremes substantially affect global- and regional-scale carbon (C) cycling, and thus spatially or temporally extended climatic extreme events jeopardize terrestrial ecosystem carbon sequestration. We illustrate the relevance of drought and/or heat events (“DHE”) for the carbon cycle and highlight underlying concepts and complex impact mechanisms. We review recent results, discuss current research needs and emerging research topics. Recent Findings Our review covers topics critical to understanding, attributing and predicting the effects of DHE on the terrestrial carbon cycle: (1) ecophysiological impact mechanisms and mediating factors, (2) the role of timing, duration and dynamical effects through which DHE impacts on regional-scale carbon cycling are either attenuated or enhanced, and (3) large-scale atmospheric conditions under which DHE are likely to unfold and to affect the terrestrial carbon cycle. Recent research thus shows the need to view these events in a broader spatial and temporal perspective that extends assessments beyond local and concurrent C cycle impacts of DHE. Summary Novel data streams, model (ensemble) simulations, and analyses allow to better understand carbon cycle impacts not only in response to their proximate drivers (drought, heat, etc.) but also attributing them to underlying changes in drivers and large-scale atmospheric conditions. These attribution-type analyses increasingly address and disentangle various sequences or dynamical interactions of events and their impacts, including compensating or amplifying effects on terrestrial carbon cycling.publishedVersio

Recombinational landscape of porcine X chromosome and individual variation in female meiotic recombination associated with haplotypes of Chinese pigs

<p>Abstract</p> <p>Background</p> <p>Variations in recombination fraction (θ) among chromosomal regions, individuals and families have been observed and have an important impact on quantitative trait loci (QTL) mapping studies. Such variations on porcine chromosome X (SSC-X) and on other mammalian chromosome X are rarely explored. The emerging assembly of pig sequence provides exact physical location of many markers, facilitating the study of a fine-scale recombination landscape of the pig genome by comparing a clone-based physical map to a genetic map. Using large offspring of F₁females from two large-scale resource populations (Large White ♂ × Chinese Meishan ♀, and White Duroc ♂ × Chinese Erhualian ♀), we were able to evaluate the heterogeneity in θ for a specific interval among individual F₁females.</p> <p>Results</p> <p>Alignments between the cytogenetic map, radiation hybrid (RH) map, genetic maps and clone map of SSC-X with the physical map of human chromosome X (HSA-X) are presented. The most likely order of 60 markers on SSC-X is inferred. The average recombination rate across SSC-X is of ~1.27 cM/Mb. However, almost no recombination occurred in a large region of ~31 Mb extending from the centromere to Xq21, whereas in the surrounding regions and in the Xq telomeric region a recombination rate of 2.8-3.3 cM/Mb was observed, more than twice the chromosome-wide average rate. Significant differences in θ among F₁females within each population were observed for several chromosomal intervals. The largest variation was observed in both populations in the interval <it>UMNP71-SW1943</it>, or more precisely in the subinterval <it>UMNP891-UMNP93</it>. The individual variation in θ over this subinterval was found associated with F₁females' maternal haplotypes (Chinese pig haplotypes) and independent of paternal haplotype (European pig haplotypes). The θ between <it>UMNP891 </it>and <it>UMNP93 </it>for haplotype 1122 and 4311 differed by more than fourteen-fold (10.3% vs. 0.7%).</p> <p>Conclusions</p> <p>This study reveals marked regional, individual and haplotype-specific differences in recombination rate on SSC-X. Lack of recombination in such a large region makes it impossible to narrow QTL interval using traditional fine-mapping approaches. The relationship between recombination variation and haplotype polymorphism is shown for the first time in pigs.</p

Wolbachia and DNA barcoding insects: patterns, potential and problems

Wolbachia is a genus of bacterial endosymbionts that impacts the breeding systems of their hosts. Wolbachia can confuse the patterns of mitochondrial variation, including DNA barcodes, because it influences the pathways through which mitochondria are inherited. We examined the extent to which these endosymbionts are detected in routine DNA barcoding, assessed their impact upon the insect sequence divergence and identification accuracy, and considered the variation present in Wolbachia COI. Using both standard PCR assays (Wolbachia surface coding protein – wsp), and bacterial COI fragments we found evidence of Wolbachia in insect total genomic extracts created for DNA barcoding library construction. When >2 million insect COI trace files were examined on the Barcode of Life Datasystem (BOLD) Wolbachia COI was present in 0.16% of the cases. It is possible to generate Wolbachia COI using standard insect primers; however, that amplicon was never confused with the COI of the host. Wolbachia alleles recovered were predominantly Supergroup A and were broadly distributed geographically and phylogenetically. We conclude that the presence of the Wolbachia DNA in total genomic extracts made from insects is unlikely to compromise the accuracy of the DNA barcode library; in fact, the ability to query this DNA library (the database and the extracts) for endosymbionts is one of the ancillary benefits of such a large scale endeavor – for which we provide several examples. It is our conclusion that regular assays for Wolbachia presence and type can, and should, be adopted by large scale insect barcoding initiatives. While COI is one of the five multi-locus sequence typing (MLST) genes used for categorizing Wolbachia, there is limited overlap with the eukaryotic DNA barcode region

Predictors of lung adenocarcinoma with leptomeningeal metastases: A 2022 targeted-therapy-assisted molGPA model

Objective: To explore prognostic indicators of lung adenocarcinoma with leptomeningeal metastases (LM) and provide an updated graded prognostic assessment model integrated with molecular alterations (molGPA). Methods: A cohort of 162 patients was enrolled from 202 patients with lung adenocarcinoma and LM. By randomly splitting data into the training (80%) and validation (20%) sets, the Cox regression and random survival forest methods were used on the training set to identify statistically significant variables and construct a prognostic model. The C-index of the model was calculated and compared with that of previous molGPA models. Results: The Cox regression and random forest models both identified four variables, which included KPS, LANO neurological assessment, TKI therapy line, and controlled primary tumor, as statistically significant predictors. A novel targeted-therapy-assisted molGPA model (2022) using the above four prognostic factors was developed to predict LM of lung adenocarcinoma. The C-indices of this prognostic model in the training and validation sets were higher than those of the lung-molGPA (2017) and molGPA (2019) models. Conclusions: The 2022 molGPA model, a substantial update of previous molGPA models with better prediction performance, may be useful in clinical decision making and stratification of future clinical trials