We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

Ready-to-use modified-texture food (rMTF) products are commercially available and may have greater appeal than conventional in-house or commercial bulk modified-texture food (cMTF) products. A nine-month pilot study using a prospective interrupted time-series design where participants (n = 42) served as their own controls investigated the impact of cMTF + rMTF on weight goals, weight, food intake, and co-morbidity. Seventy-four per cent of participants achieved their weight goals at the end of six months on rMTF and, although insignificant, participants did have a trend towards weight gain while on rMTF (OR 3.5 p = .16). Main-plate food intake (grams) was not significantly different over time, but a downwards trajectory suggests decreased consumption that was compensated for by a significantly higher fat intake during the intervention period (p = .01). Increased co-morbidity and a decreasing volume of food consumed are common in older adults with dysphagia, and enhanced food products are needed to meet nutrient needs. Methodological issues encountered in this study can provide guidance for future work.

Let $p$ be a prime and $F$ a field containing a primitive $p$ -th root of unity. Then for $n\,\in \,\mathbb{N}$ , the cohomological dimension of the maximal pro- $p$ -quotient $G$ of the absolute Galois group of $F$ is at most $n$ if and only if the corestriction maps ${{H}^{n}}\left( H,\ {{\mathbb{F}}_{p}} \right)\,\to \,{{H}^{n}}\left( G,\ {{\mathbb{F}}_{p}} \right)$ are surjective for all open subgroups $H$ of index $p$ . Using this result, we generalize Schreier's formula for ${{\dim}_{{{\mathbb{F}}_{p}}}}\,{{H}^{1}}\,\left( H,\ {{\mathbb{F}}_{p}} \right)$ to ${{\dim}_{{{\mathbb{F}}_{p}}}}{{H}^{n}}\left( H,\ {{\mathbb{F}}_{p}} \right)$ .