The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

Extremal Optimization at the Phase Transition of the 3-Coloring Problem

We investigate the phase transition of the 3-coloring problem on random graphs, using the extremal optimization heuristic. 3-coloring is among the hardest combinatorial optimization problems and is closely related to a 3-state anti-ferromagnetic Potts model. Like many other such optimization problems, it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter: the graph's mean vertex degree. This phase transition is often associated with the instances of highest complexity. We use extremal optimization to measure the ground state cost and the ``backbone'', an order parameter related to ground state overlap, averaged over a large number of instances near the transition for random graphs of size $n$ up to 512. For graphs up to this size, benchmarks show that extremal optimization reaches ground states and explores a sufficient number of them to give the correct backbone value after about $O(n^{3.5})$ update steps. Finite size scaling gives a critical mean degree value $\alpha_{\rm c}=4.703(28)$. Furthermore, the exploration of the degenerate ground states indicates that the backbone order parameter, measuring the constrainedness of the problem, exhibits a first-order phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available at http://www.physics.emory.edu/faculty/boettcher

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Enhanced thermoelectric performance of a chalcopyrite compound CuIn3Se5-xTex (x=0~0.5) through crystal structure engineering

In this work the chalcopyrite CuIn3Se5−xTex (x = 0~0.5) with space group through isoelectronic substitution of Te for Se have been prepared, and the crystal structure dilation has been observed with increasing Te content. This substitution allows the anion position displacement ∆u = 0.25-u to be zero at x ≈ 0.15. However, the material at x = 0.1 (∆u = 0.15 × 10−3), which is the critical Te content, presents the best thermoelectric (TE) performance with dimensionless figure of merit ZT = 0.4 at 930 K. As x value increases from 0.1, the quality factor B, which informs about how large a ZT can be expected for any given material, decreases, and the TE performance degrades gradually due to the reduction in nH and enhancement in κL. Combining with the ZTs from several chalcopyrite compounds, it is believable that the best thermoelectric performance can be achieved at a certain ∆u value (∆u ≠ 0) for a specific space group if their crystal structures can be engineered

Chronic kidney disease and arrhythmias: conclusions from a Kidney Disease: Improving Global Outcomes (KDIGO) Controversies Conference.

Patients with chronic kidney disease (CKD) are predisposed to heart rhythm disorders, including atrial fibrillation (AF)/atrial flutter, supraventricular tachycardias, ventricular arrhythmias, and sudden cardiac death (SCD). While treatment options, including drug, device, and procedural therapies, are available, their use in the setting of CKD is complex and limited. Patients with CKD and end-stage kidney disease (ESKD) have historically been under-represented or excluded from randomized trials of arrhythmia treatment strategies,1 although this situation is changing.2 Cardiovascular society consensus documents have recently identified evidence gaps for treating patients with CKD and heart rhythm disorders [...

Domestic Water Demand During Droughts in Temperate Climates: Synthesising Evidence for an Integrated Framework

In the upcoming years, as the population is growing and ageing, as lifestyle changes create the need for more water and as fewer people live in each household, the UK water sector will have to deal with challenges in the provision of adequate water services. Unless critical action is taken, every area in the UK may face a supply-demand gap by the 2080s. Extreme weather events and variations that alter drought and flood frequency add to these pressures. However, little evidence is available about householders’ response to drought and there are few if any studies incorporating this evidence into models of demand forecasting. The present work lays the groundwork for modelling domestic water demand response under drought conditions in temperate climates. After discussing the current literature on estimating and forecasting domestic water consumption under both ‘normal’ and drought conditions, this paper identifies the limited ability of current domestic demand forecasting techniques to include the many different and evolving factors affecting domestic consumption and it stresses the need for the inclusion of inter and intra household factors as well as water use practices in future demand forecasting models

Bismuth coating of non-tunneled haemodialysis catheters reduces bacterial colonization: a randomized controlled trial

Background. Haemodialysis (HD) catheter-related blood stream infections are a major cause of morbidity and mortality in patients with acute and chronic renal failure

Clinical, Genetic, Imaging and Electrophysiological Findings in a Cohort of Patients With GUCA1A-Associated Retinopathy

PURPOSE: To report findings in GUCA1A-associated retinopathy, a rare autosomal-dominant retinopathy. METHODS: Clinical features and investigations from molecularly confirmed patients at a large referral center were analyzed (retrospective cohort study). RESULTS: Nineteen patients (14 families), with five different variants, were included: p.(Tyr99Cys) in 10 families and p.(Leu84Phe), p.(Ile107Thr), p.(Glu111Ala), and p.(leu176Phe) in 1 family each. Mean (SD) ages at first and last visits were 38 (17) and 48 (15) years, respectively. Mean (SD) logMAR visual acuities at the first and last visits were 0.67 (0.61) and 0.94 (0.58) for right eyes and 0.63 (0.63) and 0.95 (0.74) for left eyes. Acuities ranged from 0.00 logMAR to no light perception. Most described progressive problems with central and color vision. Across 144 patient visits, logMAR acuity correlated with age (Spearman coefficients of 0.43 and 0.54 for right and left eyes, P < 0.001), with a high interocular correlation (coefficient 0.90, P < 0.001). Optical coherence tomography showed irregularity and then loss of the central ellipsoid zone. Ultra-widefield imaging showed peripheral degeneration in some patients. Electrophysiology (n = 13) was consistent with cone dystrophy (n = 11) or macular dystrophy (n = 2). Compared with the common p.(Tyr99Cys) variant, patients with p.(Glu111Ala) (n = 2) had worse vision; those with p.(Leu84Phe) (n = 3) were younger with earlier-onset visual loss. Patients with p.(Ile107Thr) (n = 2) showed later presentation, with milder acuity reduction. CONCLUSIONS: We present genotypic and phenotypic findings from the largest cohort with GUCA1A retinopathy. Most had progressive visual loss and electrophysiologic evidence of cone dystrophy. Possible genotype-phenotype correlations emerged, but subgroups were small for four of five variants