On the contribution of D.I. Zaitsev to the Theory of Infinite Groups

We survey the most outstanding contributions due to D.I. Zaitsev in the Theory of Infinite Groups

Magnesium Intake and Depression in U.S. Adults

Research has focused extensively on the negative health effects of inadequate Mg intake, but the extent of the problem of deficiency deserves further exploration. The notion that U.S. adults consume an inadequate amount of magnesium, leading to increased risk for chronic diseases such as depression, is plausible. National Health and Nutrition Examination Surveys (NHANES), which are large, cross-sectional, population-based data sets that assess the health and nutritional status of U.S. adults and children, indicate over half the adult population does not consume adequate amounts of magnesium based on the estimated average requirement (EAR) established by the Institute of Medicine. Using 2007 to 2010 NHANES data we found 54% of adults do not meet the EAR, confirming results from earlier surveys. As a result of this finding, a review exploring the factors impacting magnesium consumption over time and the adequacy of current intake in U.S. adults was conducted. Changes in agricultural processes that reduce magnesium levels in crops combined with the increasing consumption of processed foods containing little to no magnesium have led to a decrease in mean daily intake by 200-300 mg per day over the past century. However, population-based studies show a steady and consistent recovery in magnesium intake in U.S. adults over the past several decades. A simple, rapid, accurate test for whole body Mg status is lacking and, although population-based studies have limitations, continued monitoring of Mg consumption is essential to determine whether this positive trend continues. In the meantime, since the health consequences of inadequate magnesium are well established, there are no reported cases of hypermagnesemia from food alone, and magnesium is found in healthy foods adults should consume more often, there are few reasons not to encourage increased magnesium intake. Cross-sectional and prospective trials in other countries report an association between magnesium intake and symptoms of depression. Depression is a chronic disease affecting a significant portion of the U.S. population. Magnesium plays a role in many of the pathways involved in the pathophysiology of depression and is found in several enzymes, hormones, and neurotransmitters. Depression and magnesium are both associated with systemic inflammation. Current treatment options for depression are limited by efficacy, cost, availability, side effects, and acceptability to patients. As a result of the need for additional treatment options, interest in the role of magnesium in modulating depressive symptoms has grown. We used the NHANES 2007-2010 data to examine this relationship in U.S. adults and found a significant association between very low magnesium intake and symptoms of depression (RR=1.16; 95% confidence interval (CI) 1.06, 1.30; P=0.03). Whether inadequate magnesium leads to increased risk for depression or depression results in poor dietary intake is not known. To test whether supplementation with over-the-counter magnesium chloride improves symptoms of depression, an open-label, blocked, randomized, cross-over trial was carried out in outpatient primary care clinics on 126 adults (mean age 52; 38% male) diagnosed with, and currently experiencing, mild-to-moderate symptoms. Consumption of magnesium chloride tablets for 6 weeks resulted in a clinically significant net improvement in depression (Patient Health Questionnaire-9) scores of -6.0 points (95% CI -7.9, -4.2; P\u3c0.001) and net improvement in anxiety (Generalized Anxiety Disorders-7) scores of -4.5 points (95% CI -6.6, -2.4; P\u3c0.001). Effects were observed regardless of age, gender, baseline magnesium levels, baseline severity of depression, or use of antidepressant treatments. It worked quickly, was well tolerated, and is much safer and less expensive than conventional treatments with medication. Magnesium supplements are effective for mild-to-moderate depression and are an additional treatment option for patients suffering from depression

An investigation into the effects of commencing haemodialysis in the critically ill

<b>Introduction:</b> We have aimed to describe haemodynamic changes when haemodialysis is instituted in the critically ill. 3 hypotheses are tested: 1)The initial session is associated with cardiovascular instability, 2)The initial session is associated with more cardiovascular instability compared to subsequent sessions, and 3)Looking at unstable sessions alone, there will be a greater proportion of potentially harmful changes in the initial sessions compared to subsequent ones. <b>Methods:</b> Data was collected for 209 patients, identifying 1605 dialysis sessions. Analysis was performed on hourly records, classifying sessions as stable/unstable by a cutoff of >+/-20% change in baseline physiology (HR/MAP). Data from 3 hours prior, and 4 hours after dialysis was included, and average and minimum values derived. 3 time comparisons were made (pre-HD:during, during HD:post, pre-HD:post). Initial sessions were analysed separately from subsequent sessions to derive 2 groups. If a session was identified as being unstable, then the nature of instability was examined by recording whether changes crossed defined physiological ranges. The changes seen in unstable sessions could be described as to their effects: being harmful/potentially harmful, or beneficial/potentially beneficial. <b>Results:</b> Discarding incomplete data, 181 initial and 1382 subsequent sessions were analysed. A session was deemed to be stable if there was no significant change (>+/-20%) in the time-averaged or minimum MAP/HR across time comparisons. By this definition 85/181 initial sessions were unstable (47%, 95% CI SEM 39.8-54.2). Therefore Hypothesis 1 is accepted. This compares to 44% of subsequent sessions (95% CI 41.1-46.3). Comparing these proportions and their respective CI gives a 95% CI for the standard error of the difference of -4% to 10%. Therefore Hypothesis 2 is rejected. In initial sessions there were 92/1020 harmful changes. This gives a proportion of 9.0% (95% CI SEM 7.4-10.9). In the subsequent sessions there were 712/7248 harmful changes. This gives a proportion of 9.8% (95% CI SEM 9.1-10.5). Comparing the two unpaired proportions gives a difference of -0.08% with a 95% CI of the SE of the difference of -2.5 to +1.2. Hypothesis 3 is rejected. Fisher’s exact test gives a result of p=0.68, reinforcing the lack of significant variance. <b>Conclusions:</b> Our results reject the claims that using haemodialysis is an inherently unstable choice of therapy. Although proportionally more of the initial sessions are classed as unstable, the majority of MAP and HR changes are beneficial in nature

Direct limits and fixed point sets

For which groups G is it true that whenever we form a direct limit of G-sets, dirlim_{i\in I} X_i, the set of its fixed points, (dirlim_I X_i)^G, can be obtained as the direct limit dirlim_I(X_i^G) of the fixed point sets of the given G-sets? An easy argument shows that this holds if and only if G is finitely generated. If we replace ``group G'' by ``monoid M'', the answer is the less familiar condition that the improper left congruence on M be finitely generated. Replacing our group or monoid with a small category E, the concept of set on which G or M acts with that of a functor E --> Set, and the concept of fixed point set with that of the limit of a functor, a criterion of a similar nature is obtained. The case where E is a partially ordered set leads to a condition on partially ordered sets which I have not seen before (pp.23-24, Def. 12 and Lemma 13). If one allows the {\em codomain} category Set to be replaced with other categories, and/or allows direct limits to be replaced with other kinds of colimits, one gets a vast area for further investigation.Comment: 28 pages. Notes on 1 Aug.'05 revision: Introduction added; Cor.s 9 and 10 strengthened and Cor.10 added; section 9 removed and section 8 rewritten; source file re-formatted for Elsevier macros. To appear, J.Al