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

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

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

Emergence of the erythroid lineage from multipotent hematopoiesis [preprint]

Red cell formation begins with the hematopoietic stem cell, but the manner by which it gives rise to erythroid progenitors, and their subsequent developmental path, remain unclear. Here we combined single-cell transcriptomics of murine hematopoietic tissues with fate potential assays to infer a continuous yet hierarchical structure for the hematopoietic network. We define the erythroid differentiation trajectory as it emerges from multipotency and diverges from 6 other blood lineages. With the aid of a new flow-cytometric sorting strategy, we validated predicted cell fate potentials at the single cell level, revealing a coupling between erythroid and basophil/mast cell fates. We uncovered novel growth factor receptor regulators of the erythroid trajectory, including the proinflammatory IL- 17RA, found to be a strong erythroid stimulator; and identified a global hematopoietic response to stress erythropoiesis. We further identified transcriptional and high-purity FACS gates for the complete isolation of all classically-defined erythroid burst-forming (BFU-e) and colony-forming progenitors (CFU-e), finding that they express a dedicated transcriptional program, distinct from that of terminally-differentiating erythroblasts. Intriguingly, profound remodeling of the cell cycle is intimately entwined with CFU-e developmental progression and with a sharp transcriptional switch that extinguishes the CFU-e stage and activates terminal differentiation. Underlying these results, our work showcases the utility of theoretic approaches linking transcriptomic data to predictive fate models, providing key insights into lineage development in vivo

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

Obesity, inflammatory and thrombotic markers, and major clinical outcomes in critically ill patients with COVID‐19 in the US

OBJECTIVE: This study aimed to determine whether obesity is independently associated with major adverse clinical outcomes and inflammatory and thrombotic markers in critically ill patients with COVID-19. METHODS: The primary outcome was in-hospital mortality in adults with COVID-19 admitted to intensive care units across the US. Secondary outcomes were acute respiratory distress syndrome (ARDS), acute kidney injury requiring renal replacement therapy (AKI-RRT), thrombotic events, and seven blood markers of inflammation and thrombosis. Unadjusted and multivariable-adjusted models were used. RESULTS: Among the 4,908 study patients, mean (SD) age was 60.9 (14.7) years, 3,095 (62.8%) were male, and 2,552 (52.0%) had obesity. In multivariable models, BMI was not associated with mortality. Higher BMI beginning at 25 kg/m2 was associated with a greater risk of ARDS and AKI-RRT but not thrombosis. There was no clinically significant association between BMI and inflammatory or thrombotic markers. CONCLUSIONS: In critically ill patients with COVID-19, higher BMI was not associated with death or thrombotic events but was associated with a greater risk of ARDS and AKI-RRT. The lack of an association between BMI and circulating biomarkers calls into question the paradigm that obesity contributes to poor outcomes in critically ill patients with COVID-19 by upregulating systemic inflammatory and prothrombotic pathways

Bayesian Learning of Gas Transport in Three-Dimensional Fracture Networks

Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for predicting gas particle breakthrough times at the surface, but are computationally demanding. We propose a Bayesian machine learning method that serves as an efficient surrogate model, or emulator, for these three-dimensional DFN simulations. Our model trains on a small quantity of simulation data and, using a graph/path-based decomposition of the fracture network, rapidly predicts quantiles of the breakthrough time distribution. The approach, based on Gaussian Process Regression (GPR), outputs predictions that are within 20-30% of high-fidelity DFN simulation results. Unlike previously proposed methods, it also provides uncertainty quantification, outputting confidence intervals that are essential given the uncertainty inherent in subsurface modeling. Our trained model runs within a fraction of a second, which is considerably faster than other methods with comparable accuracy and multiple orders of magnitude faster than high-fidelity simulations

Microbial inactivation properties of a new antimicrobial/antithrombotic catheter lock solution (citrate/methylene blue/parabens)

Background. Microbial infections are the most serious complications associated with indwelling central venous catheters. A catheter lock solution that is both antibacterial and antithrombotic is needed. The goal of this study was to determine whether a new catheter lock solution containing citrate, methylene blue and parabens has antimicrobial properties against planktonic bacteria and against sessile bacteria within a biofilm. These effects were compared to the antimicrobial properties of heparin at 2500 units/ml

Duration of temporary catheter use for hemodialysis: an observational, prospective evaluation of renal units in Brazil

<p>Abstract</p> <p>Background</p> <p>For chronic hemodialysis, the ideal permanent vascular access is the arteriovenous fistula (AVF). Temporary catheters should be reserved for acute dialysis needs. The AVF is associated with lower infection rates, better clinical results, and a higher quality of life and survival when compared to temporary catheters. In Brazil, the proportion of patients with temporary catheters for more than 3 months from the beginning of therapy is used as an evaluation of the quality of renal units. The aim of this study is to evaluate factors associated with the time between the beginning of hemodialysis with temporary catheters and the placement of the first arteriovenous fistula in Brazil.</p> <p>Methods</p> <p>This is an observational, prospective non-concurrent study using national administrative registries of all patients financed by the public health system who began renal replacement therapy (RRT) between 2000 and 2004 in Brazil. Incident patients were eligible who had hemodialysis for the first time. Patients were excluded who: had hemodialysis reportedly started after the date of death (inconsistent database); were younger than 18 years old; had HIV; had no record of the first dialysis unit; and were dialyzed in units with less than twenty patients. To evaluate individual and renal unit factors associated with the event of interest, the frailty model was used (N = 55,589).</p> <p>Results</p> <p>Among the 23,824 patients (42.9%) who underwent fistula placement in the period of the study, 18.2% maintained the temporary catheter for more than three months until the fistula creation. The analysis identified five statistically significant factors associated with longer time until first fistula: higher age (Hazard-risk - HR 0.99, 95% CI 0.99-1.00); having hypertension and cardiovascular diseases (HR 0.94, 95% CI 0.9-0.98) as the cause of chronic renal disease; residing in capitals cities (HR 0.92, 95% CI 0.9-0.95) and certain regions in Brazil - South (HR 0.83, 95% CI 0.8-0.87), Midwest (HR 0.88, 95% CI 0.83-0.94), Northeast (HR 0.91, 95% CI 0.88-0.94), or North (HR 0.88, 95% CI 0.83-0.94) and the type of renal unit (public or private).</p> <p>Conclusion</p> <p>Monitoring the provision of arteriovenous fistulas in renal units could improve the care given to patients with end stage renal disease.</p