The good, the bad and the ugly: pandemic priority decisions and triage.

In this analysis we discuss the change in criteria for triage of patients during three different phases of a pandemic like COVID-19, seen from the critical care point of view. Availability of critical care beds has become a hot topic, and in many countries, we have seen a huge increase in the provision of temporary intensive care bed capacity. However, there is a limit where the hospitals may run out of resources to provide critical care, which is heavily dependent on trained staff, just-in-time supply chains for clinical consumables and drugs and advanced equipment. In the first (good) phase, we can still do clinical prioritisation and decision-making as usual, based on the need for intensive care and prognostication: what are the odds for a good result with regard to survival and quality of life. In the next (bad phase), the resources are mostly available, but the system is stressed by many patients arriving over a short time period and auxiliary beds in different places in the hospital being used. We may have to abandon admittance of patients with doubtful prognosis. In the last (ugly) phase, usual medical triage and priority setting may not be sufficient to decrease inflow and there may not be enough intensive care unit beds available. In this phase different criteria must be applied using a utilitarian approach for triage. We argue that this is an important transition where society, and not physicians, must provide guidance to support triage that is no longer based on medical priorities alone

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints

The impact of iodised salt or iodine supplements on iodine status during pregnancy lactation and infancy

Objectives: Monitoring of iodine status during pregnancy, lactation and infancy is difficult as there are no established reference criteria for urinary iodine concentration (UI) for these groups; so it is uncertain whether iodized salt programs meet the needs of these life stages. Design and Subjects: The method used in this paper was: 1) to estimate the median UI concentration that reflects adequate iodine intake during these life stages; and 2) to use these estimates in a review of the literature to assess whether salt iodisation can control iodine deficiency in pregnant and lactating women, and their infants. Results: For pregnancy, recommended mean daily iodine intakes of 220-250 ¿g were estimated to correspond to a median UI concentration of about 150 ¿g l¿ 1, and larger surveys from the iodine sufficient countries have reported a median UI in pregnant women ¿ 140 ¿g l¿ 1. Iodine supplementation in pregnant women who are mild-to-moderately iodine deficient is beneficial, but there is no clear affect on maternal or newborn thyroid hormone levels. In countries where the iodine intake is sufficient, most mothers have median breast milk iodine concentration (BMIC) greater than the concentration (100-120 ¿g l¿ 1) required to meet an infant's needs. The median UI concentration during infancy that indicates optimal iodine nutrition is estimated to be ¿ 100 ¿g l¿ 1. In iodine-sufficient countries, the median UI concentration in infants ranges from 90-170 ¿g l¿ 1, suggesting adequate iodine intake in infancy. Conclusions: These findings suggest pregnant and lactating women and their infants in countries with successful sustained iodised salt programs have adequate iodine status

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Temporal Patterns in Perchlorate, Thiocyanate, and Iodide Excretion in Human Milk

BACKGROUND: Perchlorate and thiocyanate interfere with iodide uptake at the sodium–iodide symporter and are potential disruptors of thyroid hormone synthesis. Perchlorate is a common contaminant of water, food, and human milk. Although it is known that iodide undergoes significant diurnal variations in serum and urinary excretion, less is known about diurnal variations of milk iodide levels. OBJECTIVES: Variability in perchlorate and thiocyanate excretion in human milk has not been examined. Our objective was to determine variability of perchlorate, thiocyanate, and iodide in serially collected samples of human milk. METHODS: Ten lactating women were asked to collect six milk samples on each of 3 days. As an alternative, subjects were asked to collect as many milk samples as comfortably possible over 3 days. Samples were analyzed for perchlorate, iodide, and thiocyanate by ion chromatography coupled with mass spectrometry. RESULTS: Individual perchlorate, iodide, and thiocyanate levels varied significantly over time; there was also considerable variation among individuals. The iodide range, mean ± SD, and median for all samples (n = 108) were 3.1–334 μg/L, 87.9 ± 80.9 μg/L, and 55.2 μg/L, respectively. The range, mean ± SD, and median of perchlorate in all samples (n = 147) were 0.5–39.5 μg/L, 5.8 ± 6.2 μg/L, and 4.0 μg/L. The range, mean ± SD, and median of thiocyanate in all samples (n = 117) were 0.4 –228.3 μg/L, 35.6 ± 57.9 μg/L, and 5.6 μg/L. The data are not symmetrically distributed; the mean is higher than the median in all cases. CONCLUSIONS: Iodine intake may be inadequate in a significant fraction of this study population. Perchlorate and thiocyanate appear to be common in human milk. The role of these chemicals in reducing breast milk iodide is in need of further investigation