Semi-Finite Forms of Bilateral Basic Hypergeometric Series

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's $_1\psi_1$ summation, Bailey's $_2\psi_2$ transformations, and Bailey's $_6\psi_6$ summation.Comment: 8 pages. accepted by Proc. Amer. Math. So

Faulhaber's Theorem on Power Sums

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic

The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials

We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unified perspective to investigate several combinatorial objects in connection with the bivariate Eulerian polynomials. We call this approach the Dumont ansatz. As applications, we provide grammatical treatments, in the spirit of the symbolic method, of relations on the Springer numbers, the Euler numbers, the three kinds of peak polynomials, an identity of Petersen, and the two kinds of derivative polynomials, introduced by Knuth-Buckholtz and Carlitz-Scoville, and later by Hoffman in a broader context. We obtain a convolution formula on the left peak polynomials, leading to the Gessel formula. In this framework, we are led to the combinatorial interpretations of the derivative polynomials due to Josuat-Verg\`es.Comment: 30 pages, 5 figure

Temporal order of bipolar cell genesis in the neural retina

NEURAL DEVELOPMENT www.neuraldevelopment.com Temporal order of bipolar cell genesis in the neural retina Eric M Morrow et al

Acetaldehyde-Mediated Neurotoxicity: Relevance to Fetal Alcohol Spectrum Disorders

Ethanol-induced neuro-developmental abnormalities are associated with impaired insulin and IGF signaling, and increased oxidative stress in CNS neurons. We examined the roles of ethanol and its principal toxic metabolite, acetaldehyde, as mediators of impaired insulin/IGF signaling and oxidative injury in immature cerebellar neurons. Cultures were exposed to 3.5 mM acetaldehyde or 50 mM ethanol ± 4-methylpyrazole (4-MP), an inhibitor of ethanol metabolism, and viability, mitochondrial function, oxidative stress, DNA damage, and insulin responsiveness were measured 48 hours later. Acetaldehyde or ethanol increased neuronal death and levels of 8-OHdG and 4-HNE, and reduced mitochondrial function. Ethanol inhibited insulin responsiveness, whereas acetaldehyde did not. 4-MP abated ethanol-induced oxidative stress and mitochondrial dysfunction, but failed to restore insulin responsiveness. Furthermore, alcohol and aldehyde metabolizing enzyme genes were inhibited by prenatal ethanol exposure; this effect was mediated by acetaldehyde and not ethanol + 4MP. These findings suggest that brain insulin resistance in prenatal alcohol exposure is caused by direct effects of ethanol, whereas oxidative stress induced neuronal injury is likely mediated by ethanol and its toxic metabolites. Moreover, the adverse effects of prenatal ethanol exposure on brain development may be exacerbated by down-regulation of genes needed for metabolism and detoxification of alcohol in the brain

Islet Adaptations in Fetal Sheep Persist Following Chronic Exposure to High Norepinephrine

Complications in pregnancy elevate fetal norepinephrine (NE) concentrations. Previous studies in NE-infused sheep fetuses revealed that sustained exposure to high NE resulted in lower expression of α2-adrenergic receptors in islets and increased insulin secretion responsiveness after acutely terminating the NE infusion. In this study, we determined if the compensatory increase in insulin secretion following chronic elevation of NE is independent of hyperglycemia in sheep fetuses and whether it is persistent in conjunction with islet desensitization to NE. Following an initial assessment of glucose-stimulated insulin secretion (GSIS) at 129±1 days of gestation, fetuses were continuously infused for seven days with NE and maintained at euglycemia with a maternal insulin infusion. Fetal GSIS studies were again performed on days 8 and 12. Adrenergic sensitivity was determined in pancreatic islets collected at day 12. NE infusion increased (P\u3c0.01) fetal plasma NE concentrations and lowered (P\u3c0.01) basal insulin concentrations compared to vehicle-infused controls. GSIS was 1.8-fold greater (P\u3c0.05) in NE-infused fetuses compared to controls at both one and five days after discontinuing the infusion. Glucose-potentiated arginine-induced insulin secretion was also enhanced (P\u3c0.01) in NE-infused fetuses. Maximum GSIS in islets isolated from NE-infused fetuses was 1.6-fold greater (P\u3c0.05) than controls, but islet insulin content and intracellular calcium signaling were not different between treatments. The half-maximal inhibitory concentration for NE was 2.6-fold greater (P\u3c0.05) in NE-infused islets compared to controls. These findings show that chronic NE exposure and not hyperglycemia produce persistent adaptations in pancreatic islets that augment β-cell responsiveness in part through decreased adrenergic sensitivity

Underdiagnosis of mild cognitive impairment: A consequence of ignoring practice effects

INTRODUCTION: Longitudinal testing is necessary to accurately measure cognitive change. However, repeated testing is susceptible to practice effects, which may obscure true cognitive decline and delay detection of mild cognitive impairment (MCI). METHODS: We retested 995 late-middle-aged men in a ∼6-year follow-up of the Vietnam Era Twin Study of Aging. In addition, 170 age-matched replacements were tested for the first time at study wave 2. Group differences were used to calculate practice effects after controlling for attrition effects. MCI diagnoses were generated from practice-adjusted scores. RESULTS: There were significant practice effects on most cognitive domains. Conversion to MCI doubled after correcting for practice effects, from 4.5% to 9%. Importantly, practice effects were present although there were declines in uncorrected scores. DISCUSSION: Accounting for practice effects is critical to early detection of MCI. Declines, when lower than expected, can still indicate practice effects. Replacement participants are needed for accurately assessing disease progression.Published versio

Gestational Exposure to Endocrine-Disrupting Chemicals and Reciprocal Social, Repetitive, and Stereotypic Behaviors in 4- and 5-Year-Old Children: The HOME Study

Background: Endocrine-disrupting chemicals (EDCs) may be involved in the etiology of autism spectrum disorders, but identifying relevant chemicals within mixtures of EDCs is difficult. Objective: Our goal was to identify gestational EDC exposures associated with autistic behaviors. Methods: We measured the concentrations of 8 phthalate metabolites, bisphenol A, 25 polychlorinated biphenyls (PCBs), 6 organochlorine pesticides, 8 brominated flame retardants, and 4 perfluoroalkyl substances in blood or urine samples from 175 pregnant women in the HOME (Health Outcomes and Measures of the Environment) Study (Cincinnati, OH). When children were 4 and 5 years old, mothers completed the Social Responsiveness Scale (SRS), a measure of autistic behaviors. We examined confounder-adjusted associations between 52 EDCs and SRS scores using a two-stage hierarchical analysis to account for repeated measures and confounding by correlated EDCs. Results: Most of the EDCs were associated with negligible absolute differences in SRS scores (≤ 1.5). Each 2-SD increase in serum concentrations of polybrominated diphenyl ether-28 (PBDE-28) (β = 2.5; 95% CI: –0.6, 5.6) or trans-nonachlor (β = 4.1; 95% CI: 0.8–7.3) was associated with more autistic behaviors. In contrast, fewer autistic behaviors were observed among children born to women with detectable versus nondetectable concentrations of PCB-178 (β = –3.0; 95% CI: –6.3, 0.2), β-hexachlorocyclohexane (β = –3.3; 95% CI: –6.1, –0.5), or PBDE-85 (β = –3.2; 95% CI: –5.9, –0.5). Increasing perfluorooctanoate (PFOA) concentrations were also associated with fewer autistic behaviors (β = –2.0; 95% CI: –4.4, 0.4). Conclusions: Some EDCs were associated with autistic behaviors in this cohort, but our modest sample size precludes us from dismissing chemicals with null associations. PFOA, β-hexachlorocyclohexane, PCB-178, PBDE-28, PBDE-85, and trans-nonachlor deserve additional scrutiny as factors that may be associated with childhood autistic behaviors. Citation: Braun JM, Kalkbrenner AE, Just AC, Yolton K, Calafat AM, Sjödin A, Hauser R, Webster GM, Chen A, Lanphear BP. 2014. Gestational exposure to endocrine-disrupting chemicals and reciprocal social, repetitive, and stereotypic behaviors in 4- and 5-year-old children: the HOME Study. Environ Health Perspect 122:513–520; http://dx.doi.org/10.1289/ehp.130726