Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees' comment

Glycolaldehyde, methyl formate and acetic acid adsorption and thermal desorption from interstellar ices

We have undertaken a detailed investigation of the adsorption, desorption and thermal processing of the astrobiologically significant isomers glycolaldehyde, acetic acid and methyl formate. Here, we present the results of laboratory infrared and temperature programmed desorption (TPD) studies of the three isomers from model interstellar ices adsorbed on a carbonaceous dust grain analogue surface. Laboratory infrared data show that the isomers can be clearly distinguished on the basis of their infrared spectra, which has implications for observations of interstellar ice spectra. Laboratory TPD data also show that the three isomers can be distinguished on the basis of their thermal desorption behaviour. In particular, TPD data show that the isomers cannot be treated the same way in astrophysical models of desorption. The desorption of glycolaldehyde and acetic acid from water-dominated ices is very similar, with desorption being mainly dictated by water ice. However, methyl formate also desorbs from the surface of the ice, as a pure desorption feature, and therefore desorbs at a lower temperature than the other two isomers. This is more clearly indicated by models of the desorption on astrophysical time-scales corresponding to the heating rate of 25 and 5 M⊙ stars. For a 25 M⊙ star, our model shows that a proportion of the methyl formate can be found in the gas phase at earlier times compared to glycolaldehyde and acetic acid. This has implications for the observation and detection of these molecules, and potentially explains why methyl formate has been observed in a wider range of astrophysical environments than the other two isomers

Trapping and desorption of complex organic molecules in water at 20 K

The formation, chemical and thermal processing of complex organic molecules (COMs) is currently a topic of much interest in interstellar chemistry. The isomers glycolaldehyde, methyl formate and acetic acid are particularly important because of their role as pre-biotic species. It is becoming increasingly clear that many COMs are formed within interstellar ices which are dominated by water. Hence the interaction of these species with water ice is crucially important in dictating their behaviour. Here we present the first detailed comparative study of the adsorption and thermal processing of glycolaldehyde, methyl formate and acetic acid adsorbed on and in water ices at astrophysically relevant temperatures (20 K). We show that the functional group of the isomer dictates the strength of interaction with water ice, and hence the resulting desorption and trapping behaviour. Furthermore, the strength of this interaction directly affects the crystallization of water, which in turn affects the desorption behaviour. Our detailed coverage and composition dependent data allow us to categorize the desorption behaviour of the three isomers on the basis of the strength of intermolecular and intramolecular interactions, as well as the natural sublimation temperature of the molecule. This categorization is extended to other C, H and O containing molecules in order to predict and describe the desorption behaviour of COMs from interstellar ices

Preliminary indications of the effect of a brief yoga intervention on markers of inflammation and DNA methylation in chronically stressed women

© The Author(s) 2016. This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if thematerial is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material.Yoga is associated with reduced stress and increased well-being, although the molecular basis for these benefits is not clear. Mounting evidence implicates the immune response, with current studies focused on protein immune markers (such as cytokines) in clinical populations. To explore the molecular impact, this pilot study uses a subsample (n = 28) from a randomised waitlist control trial Investigating the impact of an 8-week yoga intervention in a community population of women reporting psychological distress (N = 116). We measured interleukin-6 (IL-6), tumour necrosis factor (TNF) and C-reactive protein (CRP) protein levels, and the DNA methylation of these genes and the global indicator, LINE-1. Correlations between these and psychological variables were explored, identifying moderate correlations with CRP protein levels, and methylation of IL-6, CRP and LINE-1. Many cytokine samples were below detection, however a Mann–Whitney U demonstrated a trend of moderate between-group effect for elevated IL-6 in the yoga group. Methylation analyses applied cross-sectional and non-controlled longitudinal analyses. Waist-to-height ratio and age were covaried. We demonstrated reduced methylation of the TNF region in the yoga group relative to the waitlist control group. No other genes demonstrated a significant difference. Longitudinal analysis further supported these results. This study is one of the first to explore yoga and immunological markers in a non-clinical population, and is the first study to explore DNA methylation. These findings indicate that further research into molecular impact of yoga on markers of immune function is warranted, with larger studies required

Glycolaldehyde formation via the dimerization of the formyl radical

Glycolaldehyde, the simplest monosaccharide sugar, has recently been detected in low- and high-mass star-forming cores. Following our previous investigation into glycolaldehyde formation, we now consider a further mechanism for the formation of glycolaldehyde that involves the dimerization of the formyl radical, HCO. Quantum mechanical investigation of the HCO dimerization process upon an ice surface is predicted to be barrierless and therefore fast. In an astrophysical context, we show that this mechanism can be very efficient in star-forming cores. It is limited by the availability of the formyl radical, but models suggest that only very small amounts of CO are required to be converted to HCO to meet the observational constraints

Fibroblast growth factors 1 and 2 in cerebrospinal fluid are associated with HIV disease, methamphetamine use, and neurocognitive functioning.

BackgroundHuman immunodeficiency virus (HIV) and methamphetamine use commonly affect neurocognitive (NC) functioning. We evaluated the relationships between NC functioning and two fibroblast growth factors (FGFs) in volunteers who differed in HIV serostatus and methamphetamine dependence (MAD).MethodsA total of 100 volunteers were categorized into four groups based on HIV serostatus and MAD in the prior year. FGF-1 and FGF-2 were measured in cerebrospinal fluid by enzyme-linked immunosorbent assays along with two reference biomarkers (monocyte chemotactic protein [MCP]-1 and neopterin). Comprehensive NC testing was summarized by global and domain impairment ratings.ResultsSixty-three volunteers were HIV+ and 59 had a history of MAD. FGF-1, FGF-2, and both reference biomarkers differed by HIV and MAD status. For example, FGF-1 levels were lower in subjects who had either HIV or MAD than in HIV- and MAD- controls (P=0.003). Multivariable regression identified that global NC impairment was associated with an interaction between FGF-1 and FGF-2 (model R(2)=0.09, P=0.01): higher FGF-2 levels were only associated with neurocognitive impairment among subjects who had lower FGF-1 levels. Including other covariates in the model (including antidepressant use) strengthened the model (model R(2)=0.18, P=0.004) but did not weaken the association with FGF-1 and FGF-2. Lower FGF-1 levels were associated with impairment in five of seven cognitive domains, more than FGF-2, MCP-1, or neopterin.ConclusionThese findings provide in vivo support that HIV and MAD alter expression of FGFs, which may contribute to the NC abnormalities associated with these conditions. These cross-sectional findings cannot establish causality and the therapeutic benefits of recombinant FGF-1 need to be investigated

Carbon chemistry in Galactic Bulge Planetary Nebulae

Galactic Bulge Planetary Nebulae show evidence of mixed chemistry with emission from both silicate dust and PAHs. This mixed chemistry is unlikely to be related to carbon dredge up, as third dredge-up is not expected to occur in the low mass Bulge stars. We show that the phenomenon is widespread, and is seen in 30 nebulae out of 40 of our sample, selected on the basis of their infrared flux. HST images and UVES spectra show that the mixed chemistry is not related to the presence of emission-line stars, as it is in the Galactic disk population. We also rule out interaction with the ISM as origin of the PAHs. Instead, a strong correlation is found with morphology, and the presence of a dense torus. A chemical model is presented which shows that hydrocarbon chains can form within oxygen-rich gas through gas-phase chemical reactions. The model predicts two layers, one at $A_V\sim 1.5$ where small hydrocarbons form from reactions with C$^+$, and one at $A_V\sim 4$, where larger chains (and by implication, PAHs) form from reactions with neutral, atomic carbon. These reactions take place in a mini-PDR. We conclude that the mixed chemistry phenomenon occurring in the Galactic Bulge Planetary Nebulae is best explained through hydrocarbon chemistry in an UV-irradiated, dense torus.Comment: 13 pages, 10 figue

The Spitzer discovery of a galaxy with infrared emission solely due to AGN activity

We present a galaxy (SAGE1CJ053634.78-722658.5) at a redshift of 0.14 of which the IR is entirely dominated by emission associated with the AGN. We present the 5-37 um Spitzer/IRS spectrum and broad wavelength SED of SAGE1CJ053634, an IR point-source detected by Spitzer/SAGE (Meixner et al 2006). The source was observed in the SAGE-Spec program (Kemper et al., 2010) and was included to determine the nature of sources with deviant IR colours. The spectrum shows a redshifted (z=0.14+-0.005) silicate emission feature with an exceptionally high feature-to-continuum ratio and weak polycyclic aromatic hydrocarbon (PAH) bands. We compare the source with models of emission from dusty tori around AGNs from Nenkova et al. (2008). We present a diagnostic diagram that will help to identify similar sources based on Spitzer/MIPS and Herschel/PACS photometry. The SED of SAGE1CJ053634 is peculiar because it lacks far-IR emission and a clear stellar counterpart. We find that the SED and the IR spectrum can be understood as emission originating from the inner ~10 pc around an accreting black hole. There is no need to invoke emission from the host galaxy, either from the stars or from the interstellar medium, although a possible early-type host galaxy cannot be excluded based on the SED analysis. The hot dust around the accretion disk gives rise to a continuum, which peaks at 4 um, whereas the strong silicate features may arise from optically thin emission of dusty clouds within ~10 pc around the black hole. The weak PAH emission does not appear to be linked to star formation, as star formation templates strongly over-predict the measured far-IR flux levels. The SED of SAGE1CJ053634 is rare in the local universe but may be more common in the more distant universe. The conspicuous absence of host-galaxy IR emission places limits on the far-IR emission arising from the dusty torus alone.Comment: Accepted for publication in A&A, 7 pages, 6 figure

Ariel - Volume 10 Number 1

Executive Editors Madalyn Schaefgen David Reich Business Manager David Reich News Editors Medical College Edward Zurad CAHS John Guardiani World Mark Zwanger Features Editors Meg Trexler Jim O\u27Brien Editorials Editor Jeffrey Banyas Photography and Sports Editor Stuart Singer Commons Editor Brenda Peterso