Effects of exogenous lactase administration on hydrogen breath excretion and intestinal symptoms in patients presenting lactose malabsorption and intolerance

To establish whether supplementation with a standard oral dose of Beta-Galactosidase affects hydrogen breath excretion in patients presenting with lactose malabsorption. METHODS: Ninety-six consecutive patients positive to H2 Lactose Breath Test were enrolled. Mean peak H2 levels, the time to reach the peak H2, the time to reach the cut-off value of 20 ppm, the cumulative breath H2 excretion, the areas under the curve, and a Visual Analogical 10-point Scale for symptoms were calculated. Genotyping of the C/T-13910 variant was carried out. RESULTS: Following the oral administration of Beta-Galactosidase, in 21.88% of the cases, H2 Lactose Breath Test became negative (Group A), while mean peak H2 levels (74.95 ppm versus 7.85), P < 0.0000, in 17.71% (Group B) were still positive, with the H2 level 20 ppm above the baseline, but the peak H2 levels were significantly lower than those observed at the baseline test (186.7 ppm versus 66.64), P < 0.0000, while in 60.41% (Group C) they were still positive with the peak H2 levels similar to those observed at the baseline test (94.43 versus 81.60 ppm). All 96 individuals tested presented the C/C-13910 genotype nonpersistence. CONCLUSIONS: The response to oral administration of Beta-Galactosidase in patients with symptoms of lactose malabsorption presents a significant variability

Post Quantum Cryptography from Mutant Prime Knots

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme combines an asymmetric public key protocol with symmetric private ones and is intrinsecally secure against quantum eavesdropper attacks.Comment: 14 pages, 5 figure

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries