Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Minimizing Unsatisfaction in Colourful Neighbourhoods

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional explanatio

Association of antihypertensive monotherapy with serum sodium and potassium levels in Chinese patients

<b>Background</b> International guidelines on management of hypertension recommend any major classes of antihypertensive drugs. However, the low prescribing rate of thiazides has been attributed to concerns about electrolyte disturbances and studies between antihypertensive drug classes and hyponatremia/hypokalemia among Chinese patients were scarce. <p></p> <b>Methods</b> From clinical databases we included 2,759 patients who received their first-ever antihypertensive monotherapy from January 2004 to June 2007 in a large territory of Hong Kong. We studied the plasma sodium and potassium levels 8 weeks after prescriptions and factors associated with hyponatremia and hypokalemia by multivariable regression analyses. <p></p> <b>Results</b> Among major antihypertensive drug classes, thiazide users had the lowest sodium level (139.6 mEq/l, 95% confidence interval (CI) 139.3, 140.0, P < 0.001) and patients-prescribed calcium channel blockers (CCBs; 3.92 mEq/l, 95% CI 3.89, 3.95) or thiazide diuretics (3.99 mEq/l, 95% CI 3.93, 4.04) had the lowest potassium levels (P < 0.001). Multivariate analysis reported that advanced age (>/=70 years, odds ratio (OR) 7.49, 95% CI 2.84, 19.8, P < 0.001), male gender (OR 2.38, 95% CI 1.45, 3.91, P < 0.001), and thiazide users (OR 2.42, 95% CI 1.29, 4.56, P = 0.006) were significantly associated with hyponatremia, while renin-angiotensin system (RAS) (OR 0.31, 95% CI 0.13, 0.73, P = 0.008) and beta-blockers (BBs) (OR 0.35, 95% CI 0.23, 0.54, P < 0.001) users were less likely to present with hypokalemia. However, the proportions having normonatremic (95.1%) and normokalemic (89.4%) levels were high. <p></p> <b>Conclusions</b> In view of the low prevalence of hyponatremia and hypokalemia associated with thiazides, physicians should not be deterred from prescribing thiazide diuretics as first-line antihypertensive agents as recommended by most international guidelines

Measurement of Cosmic-ray Muons and Muon-induced Neutrons in the Aberdeen Tunnel Underground Laboratory

We have measured the muon flux and production rate of muon-induced neutrons at a depth of 611 m water equivalent. Our apparatus comprises three layers of crossed plastic scintillator hodoscopes for tracking the incident cosmic-ray muons and 760 L of gadolinium-doped liquid scintillator for producing and detecting neutrons. The vertical muon intensity was measured to be $I_{\mu} = (5.7 \pm 0.6) \times 10^{-6}$ cm$^{-2}$s$^{-1}$sr$^{-1}$. The yield of muon-induced neutrons in the liquid scintillator was determined to be $Y_{n} = (1.19 \pm 0.08 (stat) \pm 0.21 (syst)) \times 10^{-4}$ neutrons/($\mu\cdot$g$\cdot$cm$^{-2}$). A fit to the recently measured neutron yields at different depths gave a mean muon energy dependence of $\left\langle E_{\mu} \right\rangle^{0.76 \pm 0.03}$ for liquid-scintillator targets.Comment: 14 pages, 17 figures, 3 table