On the Lagrange and Hermite Quadrature Formula

This paper builds on the error analysis method for Newton-Cotes quadrature formulas developed by D. R. Hayes and L. Rubin in 1970, which utilizes Lagrange interpolation polynomials. By adopting and extending their approach, this work derives the error estimate for Hermite interpolation quadrature. Specifically, we construct a polynomial P(x) analogous to the scaling function A(x) used by Hayes and Rubin, and prove its non-negativity over the interval. This allows us to establish a precise error formula for Hermite interpolation quadrature. The results provide a novel application of Hayes and Rubin\u27s methodology, offering new insights into error analysis for high-order interpolation quadrature formulas

Probabilistic analysis of data structures for locality-sensitive hashing functions

For the nearest neighbor search problem in high-dimensional spaces, Locality-Sensitive Hashing (LSH)has shown excellent performance in terms of query cost and disk space utilization. Under the traditional analysis model, LSH is considered a randomized algorithm, with the only uncertainty being the choice of the hash function. In this research, the collision probability obtained under this model is referred to as the hash-function-based collision probability. In this paper, a different analysis model is used to conduct a theoretical analysis of LSH. The motivation for this work is twofold:1) Under the existing analysis model, users must generate random data structures for each query point to achieve the theoretical effect, which is impractical in real applications.2) The performance metric that users are concerned with is the expected collision probability of a random query point in a single data structure. Based on this, this paper derives the collision probability of random point pairs under the Hamming distance for any single hash function. The collision probability derived under this model is referred to as the query-based collision probability. It is also proven that in the Hamming space, the two types of collision probabilities are identical

Genetic and Environmental Basis in Phenotype Correlation Between Physical Function and Cognition in Aging Chinese Twins

Although the correlation between cognition and physical function has been well studied in the general population, the genetic and environmental nature of the correlation has been rarely investigated. We conducted a classical twin analysis on cognitive and physical function, including forced expiratory volume in one second (FEV1), forced vital capacity (FVC), handgrip strength, five-times-sit-to-stand test (FTSST), near visual acuity, and number of teeth lost in 379 complete twin pairs. Bivariate twin models were fitted to estimate the genetic and environmental correlation between physical and cognitive function. Bivariate analysis showed mildly positively genetic correlations between cognition and FEV1, rG = 0.23 [95% CI: 0.03, 0.62], as well as FVC, rG = 0.35 [95% CI: 0.06, 1.00]. We found that FTSST and cognition presented very high common environmental correlation, rC = -1.00 [95% CI: -1.00, -0.57], and low but significant unique environmental correlation, rE = -0.11 [95% CI: -0.22, -0.01], all in the negative direction. Meanwhile, near visual acuity and cognition also showed unique environmental correlation, rE = 0.16 [95% CI: 0.03, 0.27]. We found no significantly genetic correlation for cognition with handgrip strength, FTSST, near visual acuity, and number of teeth lost. Cognitive function was genetically related to pulmonary function. The FTSST and cognition shared almost the same common environmental factors but only part of the unique environmental factors, both with negative correlation. In contrast, near visual acuity and cognition may positively share part of the unique environmental factors.</jats:p

Heritability and whole genome linkage of pulse pressure in Chinese twin pairs

Elevated pulse pressure is associated with cardiovascular disorders and mortality in various populations. The genetic influence on pulse pressure has been confirmed by heritability estimates using related individuals. Recently, efforts have been made in mapping genes that are linked to the phenotype. We report results on our heritability and linkage study conducted on the Chinese population in mainland China where cardiovascular and cerebrovascular diseases are becoming the leading cause of death. A total of 630 pairs of middle-aged Chinese twins were collected for heritability analysis, from which 63 dizygotic twin pairs were randomly selected for genome-wide linkage analysis using Affymetrix 6.0 SNP array. Regression analysis reconfirmed the significant effects of age, sex, and BMI on pulse pressure. Comparison of twin models suggested the parsimonious AE model as the best model with a heritability estimate of 0.45. Genome-wide non-parametric linkage analysis identified three significant linkage peaks on chromosome 11 (lod score 4.06 at 30.5 cM), chromosome 12 (lod score 3.97 at 100.7 cM), and chromosome 18 (lod score 4.01 at 70.7 cM) with the last two peaks closely overlapping with linkage peaks reported by two American studies. In addition, multiple regions with suggestive linkage were identified with many of them overlapping with published linkage regions. Our results provide both epidemiological and molecular genetic evidence for the genetic dissection of pulse pressure in the Chinese population, which could help in fine mapping and in characterizing genes that are involved in the regulation of pulse pressure.</jats:p

Study on the genus Rhopobota Lederer from China (Lepidoptera: Tortricidae: Olethreutinae)

This paper deals with seventeen species of the genus Rhopobota from China. Five species (R. furcata sp. n., R. orbiculata sp. n., R. fanjingensis sp. n., R. floccosa sp. n. and R. bucera sp. n.) are described as new to science and four species [R. blanditana (Kuznetsov), R. falcata Nasu, R. okui Nasu and R. symbolias (Meyrick)] are new for China. The male of Rhopobota eclipticodes (Meyrick) is described for the first time. Photographs of the adults and genitalia of the species mentioned are provided. A key to the known Chinese species is given based on adults and male genitalia

Genetic and Environmental Influences on Pulmonary Function and Muscle Strength: The Chinese Twin Study of Aging

Genetic and environmental influences on predictors of decline in daily functioning, including forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), handgrip, and five-times-sit-to-stand test (FTSST), have not been addressed in the aging Chinese population. We performed classical twin modeling on FEV1, FVC, handgrip, and FTSST in 379 twin pairs (240 MZ and 139 DZ) with median age of 50 years (40–80 years). Data were analyzed by fitting univariate and bivariate twin models to estimate the genetic and environmental influences on these measures of physical function. Heritability was moderate for FEV1, handgrip, and FTSST (55–60%) but insignificant for FVC. Only FVC showed moderate control, with shared environmental factors accounting for about 50% of the total variance. In contrast, all measures of pulmonary function and muscle strength showed modest influences from the unique environment (40–50%). Bivariate analysis showed highly positive genetic correlations between FEV1 and FVC (rG = 1.00), and moderately negative genetic correlations between FTSST and FEV1 (rG = −0.33) and FVC (rG = −0.42). FEV1 and FVC, as well as FEV1 and handgrip, displayed high common environmental correlations (rC = 1.00), and there were moderate correlations between FVC and handgrip (rC = 0.44). FEV1 and FVC showed high unique environmental correlations (rE = 0.76) and low correlations between handgrip and FEV1 (rE = 0.17), FVC (rE = 0.14), and FTSST (rE = −0.13) with positive or negative direction. We conclude that genetic factors contribute significantly to the individual differences in common indicators of daily functioning (FEV1, handgrip, and FTSST). FEV1 and FVC were genetically and environmentally correlated. Pulmonary function and FTSST may share similar sets of genes but in the negative direction. Pulmonary function and muscle strength may have a shared environmental background.</jats:p

Thrombospondin1 Deficiency Reduces Obesity-Associated Inflammation and Improves Insulin Sensitivity in a Diet-Induced Obese Mouse Model

BACKGROUND: Obesity is prevalent worldwide and is associated with insulin resistance. Advanced studies suggest that obesity-associated low-grade chronic inflammation contributes to the development of insulin resistance and other metabolic complications. Thrombospondin 1 (TSP1) is a multifunctional extracellular matrix protein that is up-regulated in inflamed adipose tissue. A recent study suggests a positive correlation of TSP1 with obesity, adipose inflammation, and insulin resistance. However, the direct effect of TSP1 on obesity and insulin resistance is not known. Therefore, we investigated the role of TSP1 in mediating obesity-associated inflammation and insulin resistance by using TSP1 knockout mice. METHODOLOGY/PRINCIPAL FINDINGS: Male TSP1-/- mice and wild type littermate controls were fed a low-fat (LF) or a high-fat (HF) diet for 16 weeks. Throughout the study, body weight and fat mass increased similarly between the TSP1-/- mice and WT mice under HF feeding conditions, suggesting that TSP1 deficiency does not affect the development of obesity. However, obese TSP1-/- mice had improved glucose tolerance and increased insulin sensitivity compared to the obese wild type mice. Macrophage accumulation and inflammatory cytokine expression in adipose tissue were reduced in obese TSP1-/- mice. Consistent with the local decrease in pro-inflammatory cytokine levels, systemic inflammation was also decreased in the obese TSP1-/- mice. Furthermore, in vitro data demonstrated that TSP1 deficient macrophages had decreased mobility and a reduced inflammatory phenotype. CONCLUSION: TSP1 deficiency did not affect the development of high-fat diet induced obesity. However, TSP1 deficiency reduced macrophage accumulation in adipose tissue and protected against obesity related inflammation and insulin resistance. Our data demonstrate that TSP1 may play an important role in regulating macrophage function and mediating obesity-induced inflammation and insulin resistance. These data suggest that TSP1 may serve as a potential therapeutic target to improve the inflammatory and metabolic complications of obesity

CD47 Differentially Regulates White and Brown Fat Function

Mechanisms that enhance energy expenditure are attractive therapeutic targets for obesity. Previously we have demonstrated that mice lacking cd47 are leaner, exhibit increased energy expenditure, and are protected against diet-induced obesity. In this study, we further defined the physiological role of cd47 deficiency in regulating mitochondrial function and energy expenditure in both white and brown adipose tissue. We observed that cd47 deficient mice (under normal chow diet) had comparable amount of white fat mass but reduced white adipocyte size as compared to wild-type mice. Subsequent ex vivo and in vitro studies suggest enhanced lipolysis, and not impaired lipogenesis or energy utilization, contributes to this phenotype. In contrast to white adipose tissue, there were no obvious morphological differences in brown adipose tissue between wild-type and knockout mice. However, mitochondria isolated from brown fat of cd47 deficient mice had significantly higher rates of free fatty acid-mediated uncoupling. This suggests that enhanced fuel availability via white adipose tissue lipolysis may perpetuate elevated brown adipose tissue energy expenditure and contributes to the lean phenotype observed in cd47 deficient mice