Coloured peak algebras and Hopf algebras

For $G$ a finite abelian group, we study the properties of general equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of $G$ with the symmetric group \SG_n, also known as the $G$-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of \k G_n as well as graded connected Hopf subalgebras of \bigoplus_{n\ge o} \k G_n. In particular we construct a $G$-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra). We show that the direct sum of the $G$-coloured peak algebras is a Hopf algebra. We also have similar results for a $G$-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the $G$-coloured descent Hopf algebra whose image is the $G$-coloured peak Hopf algebra. We outline a theory of combinatorial $G$-coloured Hopf algebra for which the $G$-coloured quasi-symmetric Hopf algebra and the graded dual to the $G$-coloured peak Hopf algebra are central objects.Comment: 26 pages latex2

Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal subalgebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added connections with Masuoka's families KA and KB, description of K3 in KD(n), lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for KD(6), misc improvements, accepted for publication in Journal of Algebra and Its Application

Combinatorial Hopf algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.Comment: 7 page

Modal Gating of Human CaV2.1 (P/Q-type) Calcium Channels: I. The Slow and the Fast Gating Modes and their Modulation by β Subunits

The single channel gating properties of human CaV2.1 (P/Q-type) calcium channels and their modulation by the auxiliary β1b, β2e, β3a, and β4a subunits were investigated with cell-attached patch-clamp recordings on HEK293 cells stably expressing human CaV2.1 channels. These calcium channels showed a complex modal gating, which is described in this and the following paper (Fellin, T., S. Luvisetto, M. Spagnolo, and D. Pietrobon. 2004. J. Gen. Physiol. 124:463–474). Here, we report the characterization of two modes of gating of human CaV2.1 channels, the slow mode and the fast mode. A channel in the two gating modes differs in mean closed times and latency to first opening (both longer in the slow mode), in voltage dependence of the open probability (larger depolarizations are necessary to open the channel in the slow mode), in kinetics of inactivation (slower in the slow mode), and voltage dependence of steady-state inactivation (occurring at less negative voltages in the slow mode). CaV2.1 channels containing any of the four β subtypes can gate in either the slow or the fast mode, with only minor differences in the rate constants of the transitions between closed and open states within each mode. In both modes, CaV2.1 channels display different rates of inactivation and different steady-state inactivation depending on the β subtype. The type of β subunit also modulates the relative occurrence of the slow and the fast gating mode of CaV2.1 channels; β3a promotes the fast mode, whereas β4a promotes the slow mode. The prevailing mode of gating of CaV2.1 channels lacking a β subunit is a gating mode in which the channel shows shorter mean open times, longer mean closed times, longer first latency, a much larger fraction of nulls, and activates at more positive voltages than in either the fast or slow mode

Pregnancy per- and polyfluoroalkyl substance concentrations and postpartum health in Project Viva, a prospective cohort

CONTEXT: Per- and polyfluoroalkyl substances (PFAS) are environmental chemicals linked to weight gain and type 2 diabetes. OBJECTIVE: We examined the extent to which PFAS plasma concentrations during pregnancy were associated with postpartum anthropometry and biomarkers. DESIGN, PATIENTS, MEASURES: We studied women recruited between 1999-2002 in the Project Viva prospective cohort with pregnancy plasma concentrations of PFAS, including perfluorooctanesulfonic acid (PFOS), perfluorooctanoic acid (PFOA), and 2-(N-ethyl-perfluorooctane sulfonamide) acetic acid (EtFOSAA). Three-year postpartum anthropometry measurements were available from 786-801 women, blood pressure from 761 women, and blood biomarkers from 450-454 women. We used multivariable regression to evaluate the association of log2-transformed PFAS with postpartum anthropometry, blood pressure, and blood biomarkers (leptin, adiponectin, sex hormone binding globulin [SHBG], hemoglobin A1c [HbA1c], interleukin-6 [IL-6], C-reactive protein [CRP]), adjusting for age, pre-pregnancy BMI, marital status, race/ethnicity, education, income, smoking, parity, and breastfeeding history. RESULTS: Pregnancy concentrations of certain PFAS were associated with greater adiposity (e.g., 0.4 cm [95%CI: -0.1, 0.9] greater waist circumference per doubling in EtFOSAA; 0.2 cm [95%CI: -0.1, 0.5] greater mid-upper arm circumference per doubling in PFOA; 1.2 mm [95%CI: 0.1, 2.2] thicker sum of subscapular and triceps skinfolds per doubling in PFOS) and higher systolic blood pressure (e.g., 1.2 mm Hg [95%CI: 0.3, 2.2] per doubling in PFOS) at three years postpartum. Higher EtFOSAA concentrations were also associated with 10.8% higher IL-6 (95%CI: 3.3, 18.9) and 6.1% lower SHBG (95%CI: 0.7, 11.2) per doubling. CONCLUSIONS: Pregnancy concentrations of EtFOSAA, PFOS, and PFOA were associated with adverse postpartum cardiometabolic markers

Diabetes Risk Perception and Intention to Adopt Healthy Lifest yles Among Primary Care Patients

OBJECTIVE—To examine perceived risk of developing diabetes in primary care patients. RESEARCH DESIGN AND METHODS—We recruited 150 nondiabetic primary care patients. We made standard clinical measurements, collected fasting blood samples, and used the validated Risk Perception Survey for Developing Diabetes questionnaire. RESULTS—Patients with high perceived risk were more likely than those with low perceived risk to have a family history of diabetes (68 vs. 18%; P < 0.0001) and to have metabolic syndrome (53 vs. 35%; P = 0.04). However, patients with high perceived risk were not more likely to have intentions to adopt healthier lifestyle in the coming year (high 26.0% vs. low 29.2%; P = 0.69). CONCLUSIONS—Primary care patients with higher perceived risk of diabetes were at higher actual risk but did not express greater intention to adopt healthier lifestyles. Aspects of health behavior theory other than perceived risk need to be explored to help target efforts in the primary prevention of diabetes

Per- and polyfluoroalkyl substances and kidney function: Follow-up results from the Diabetes Prevention Program trial

Per- and polyfluoroalkyl substances (PFAS) are ubiquitously detected in populations worldwide and may hinder kidney function. The objective of the study was to determine longitudinal associations of plasma PFAS concentrations with estimated glomerular filtration rate (eGFR) and evaluate whether a lifestyle intervention modify the associations. We studied 875 participants initially randomized to the lifestyle or placebo arms in the Diabetes Prevention Program (DPP, 1996–2002) trial and Outcomes Study (DPPOS, 2002–2014). We ran generalized linear mixed models accounting a priori covariates to evaluate the associations between baseline PFAS concentrations and repeated measures of eGFR, separately, for six PFAS (PFOS, PFOA, PFHxS, EtFOSAA, MeFOSAA, PFNA); then used quantile-based g-computation to evaluate the effects of the six PFAS chemicals as a mixture. The cohort was 64.9% female; 73.4% 40–64 years-old; 29.4% with hypertension; 50.5% randomized to lifestyle intervention and 49.5% to placebo and had similar plasma PFAS concentrations as the general U.S. population in 1999–2000. Most participants had normal kidney function (eGFR \u3e 90 mL/min/1.73 m2) over the approximately 14 years of follow-up. We found that plasma PFAS concentrations during DPP were inversely associated with eGFR during DPPOS follow-up. Each quartile increase in baseline plasma concentration of the 6 PFAS as a mixture was associated with 2.26 mL/min/1.73 m2 lower eGFR (95% CI: −4.12, −0.39) at DPPOS Year 5, approximately 9 years since DPP randomization and PFAS measurements. The lifestyle intervention did not modify associations, but inverse associations were stronger among participants with hypertension at baseline. Among prediabetic adults, we found inverse associations between baseline plasma PFAS concentrations and measures of eGFR throughout 14 years of follow-up. The lifestyle intervention of diet, exercise and behavioral changes did not modify the associations, but persons with hypertension may have heightened susceptibility

Plasma metabolite profiles in children with current asthma

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146270/1/cea13183.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146270/2/cea13183_am.pd

Developmental programming: State-of-the-science and future directions-Summary from a Pennington Biomedical symposium.

OBJECTIVE: On December 8-9, 2014, the Pennington Biomedical Research Center convened a scientific symposium to review the state-of-the-science and future directions for the study of developmental programming of obesity and chronic disease. The objectives of the symposium were to discuss: (i) past and current scientific advances in animal models, population-based cohort studies, and human clinical trials, (ii) the state-of-the-science of epigenetic-based research, and (iii) considerations for future studies. RESULTS: This symposium provided a comprehensive assessment of the state of the scientific field and identified research gaps and opportunities for future research in order to understand the mechanisms contributing to the developmental programming of health and disease. CONCLUSIONS: Identifying the mechanisms which cause or contribute to developmental programming of future generations will be invaluable to the scientific and medical community. The ability to intervene during critical periods of prenatal and early postnatal life to promote lifelong health is the ultimate goal. Considerations for future research including the use of animal models, the study design in human cohorts with considerations about the timing of the intrauterine exposure, and the resulting tissue-specific epigenetic signature were extensively discussed and are presented in this meeting summary.The symposium was funded by NORC Center Grant P30DK072476 from the NIDDK. LAG is supported by T32DK064584 from the NIDDK. Work in MS Laboratory was supported by MOP‐42411 from the Canadian Institute of Health Research. Work in JAM Laboratory was supported by the Center for Nutrition Research at the University of Navarra in Pamplona, Spain. RAW is supported by a grant from the U.S. Department of Agriculture (USDA) [CRIS 3092‐5‐001‐059]. Work in BTH Laboratory was supported by the National Institutes of Health (R01AG042190) and the European Union's Seventh Framework Program IDEAL (FP7/2007‐2011; grant agreement No. 259679). Work in CL Laboratory was funded by The Swedish Research Council and The Novo Nordisk Foundation. SEO is a member of the University of Cambridge MRC Metabolic Diseases Unit. MFH is the recipient of an American Diabetes Association (ADA) Pathways To Stop Diabetes Award. Work in ER and LMR Laboratories was partially funded by a NORC grant titled “Nutritional Programming: Environmental and Molecular Interactions” to ER (P30DK072476)