On Complete Convergence for Weighted Sums of Arrays of Dependent Random Variables

A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of φ-mixing and ρ*-mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010)

Complete convergence for sums of arrays of random elements

Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability

On complete convergence for arrays of rowwise independent random elements

A complete convergence theorem for arrays of rowwise independent random variables was proved by Sung, Volodin, and Hu. In this paper, we extend this theorem to the Banach space without any geometric assumptions on the underlying Banach space. Our theorem also improves some known results from the literature.Korea Research Foundation Gran

On Complete Convergence and Strong Law for Weighted Sums of i.i.d. Random Variables

We improve and generalize the result of Stout (1974, Theorem 4.1.3). In particular, the sharp moment conditions are obtained and some well-known results can be obtained as special cases of the main result. The method of the proof is completely different from that in Stout. We also improve and generalize Li et al. (1995) strong law for weighted sums of i.i.d. random variables

On Complete Convergence for Arrays of Random Elements

Abstract: A complete convergence theorem for arrays of rowwise independent random variables was obtained by Kruglov, Volodin, and Hu (Statistics and Probability Letters 2006Letters , 76:1631Letters -1640. In this article, we extend the result to a Banach space without any additional conditions. No assumptions are made concerning the geometry of the underlying Banach space

Insulin Secretion and Incretin Hormone Concentration in Women with Previous Gestational Diabetes Mellitus

BackgroundWe examined the change in the levels of incretin hormone and effects of glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide 1 (GLP-1) on insulin secretion in women with previous gestational diabetes (pGDM).MethodsA 75-g oral glucose tolerance test (OGTT) was conducted on 34 women with pGDM. In addition, 11 women with normal glucose tolerance, matched for age, height and weight, were also tested. The insulin, GIP, GLP-1, and glucagon concentrations were measured, and their anthropometric and biochemical markers were also measured.ResultsAmong 34 women with pGDM, 18 had normal glucose tolerance, 13 had impaired glucose tolerance (IGT) and 1 had diabetes. No significant differences were found in GLP-1 concentration between the pGDM and control group. However, a significantly high level of glucagon was present in the pGDM group at 30 minutes into the OGTT. The GIP concentration was elevated at 30 minutes and 60 minutes in the pGDM group. With the exception of the 30-minute timepoint, women with IGT had significantly high blood glucose from 0 to 120 minutes. However, there was no significant difference in insulin or GLP-1 concentration. The GIP level was significantly high from 0 to 90 minutes in patients diagnosed with IGT.ConclusionGLP-1 secretion does not differ between pGDM patients and normal women. GIP was elevated, but that does not seem to induce in increase in insulin secretion. Therefore, we conclude that other factors such as heredity and environment play important roles in the development of type 2 diabetes

Carotid Intimal-Medial Thickness Is Not Increased in Women with Previous Gestational Diabetes Mellitus

BackgroundGestational diabetes mellitus (GDM) is known to increase the risk of cardiovascular diseases. Measuring the carotid artery intimal-medial thickness (CIMT) is a non-invasive technique used to evaluate early atherosclerosis and to predict future cardiovascular diseases. We examined the association between CIMT and cardiovascular risk factors in young Korean women with previous GDM.MethodsOne hundred one women with previous GDM and 19 women who had normal pregnancies (NP) were recruited between 1999 and 2002. At one year postpartum, CIMT was measured using high-resolution B-mode ultrasonography, and oral glucose tolerance tests were performed. Fasting glucose, glycated hemoglobin A1c (HbA1c), insulin levels and lipid profiles were also measured. CIMTs in the GDM and NP groups were compared, and the associations between CIMT and cardiovascular risk factors were analyzed in the GDM group.ResultsCIMT results of the GDM group were not significantly different from those of the NP group (GDM, 0.435±0.054 mm; NP, 0.460±0.046 mm; P=0.069). In the GDM group, a higher HbA1c was associated with an increase in CIMT after age adjustment (P=0.011). CIMT results in the group with HbA1c >6.0% were higher than those of the normal HbA1c (HbA1c ≤6.0%) (P=0.010). Nine of the patients who are type 2 diabetes mellitus converters within one year postpartum but showed no significant difference in CIMT results compared to NP group.ConclusionHigher HbA1c is associated with an increase in CIMT in women with previous GDM. However, CIMT at one year postpartum was not increased in these women compared to that in NP women

Ammonium Inhibits Chromomethylase 3-Mediated Methylation of the Arabidopsis Nitrate Reductase Gene NIA2

Gene methylation is an important mechanism regulating gene expression and genome stability. Our previous work showed that methylation of the nitrate reductase (NR) gene NIA2 was dependent on chromomethylase 3 (CMT3). Here, we show that CMT3-mediated NIA2 methylation is regulated by ammonium in Arabidopsis thaliana. CHG sequences (where H can be A, T, or C) were methylated in NIA2 but not in NIA1, and ammonium [(NH4)2SO4] treatment completely blocked CHG methylation in NIA2. By contrast, ammonium had no effect on CMT3 methylation, indicating that ammonium negatively regulates CMT3-mediated NIA2 methylation without affecting CMT3 methylation. Ammonium upregulated NIA2 mRNA expression, which was consistent with the repression of NIA2 methylation by ammonium. Ammonium treatment also reduced the overall genome methylation level of wild-type Arabidopsis. Moreover, CMT3 bound to specific promoter and intragenic regions of NIA2. These combined results indicate that ammonium inhibits CMT3-mediated methylation of NIA2 and that of other target genes, and CMT3 selectively binds to target DNA sequences for methylation

The Association of Maximum Body Weight on the Development of Type 2 Diabetes and Microvascular Complications: MAXWEL Study

Background: Obesity precedes the development of type 2 diabetes (T2D). However, the relationship between the magnitude and rate of weight gain to T2D development and complications, especially in non-White populations, has received less attention. Methods and Findings: We determined the association of rate and magnitude of weight gain to age at T2D diagnosis (AgeT2D), HbA1c at T2D diagnosis (HbA1cT2D), microalbuminuria, and diabetic retinopathy after adjusting for sex, BMI at age 20 years, lifestyles, family history of T2D and/or blood pressure and lipids in 2164 Korean subjects aged ≥30 years and newly diagnosed with diabetes. Body weight at age 20 years (Wt20y) was obtained by recall or from participants’ medical, school, or military records. Participants recalled their maximum weight (Wtmax) prior to T2D diagnosis and age at maximum weight (Agemax_wt). The rate of weight gain (Ratemax_wt) was calculated from magnitude of weight gain (ΔWt = Wtmax–Wt20y) divided by ΔTime (Agemax_wt –20 years). The mean Agemax_wt and AgeT2D were 41.5±10.9 years and 50.1±10.5 years, respectively. The Wt20y and Wtmax were 59.9±10.5 kg and 72.9±11.4 kg, respectively. The Ratemax_wt was 0.56±0.50 kg/year. After adjusting for risk factors, greater ΔWt and higher Ratemax_wt were significantly associated with earlier AgeT2D, higher HbA1cT2D after additional adjusting for AgeT2D, and microalbuminuria after further adjusting for HbA1cT2D and lipid profiles. Greater ΔWt and higher Ratemax_wt were also significantly associated with diabetic retinopathy. Conclusions: This finding supports public health recommendations to reduce the risk of T2D and its complications by preventing weight gain from early adulthood