Combinatorial algorithms for distributed graph coloring

Numerous problems in Theoretical Computer Science can be solved very efficiently using powerful algebraic constructions. Computing shortest paths, constructing expanders, and proving the PCP Theorem, are just few examples of this phenomenon. The quest for combinatorial algorithms that do not use heavy algebraic machinery, but are roughly as efficient, has become a central field of study in this area. Combinatorial algorithms are often simpler than their algebraic counterparts. Moreover, in many cases, combinatorial algorithms and proofs provide additional understanding of studied problems. In this paper we initiate the study of combinatorial algorithms for Distributed Graph Coloring problems. In a distributed setting a communication network is modeled by a graph $G=(V,E)$ of maximum degree $\varDelta $ . The vertices of $G$ host the processors, and communication is performed over the edges of $G$ . The goal of distributed vertex coloring is to color $V$ with $(\varDelta + 1)$ colors such that any two neighbors are colored with distinct colors. Currently, efficient algorithms for vertex coloring that require $O(\varDelta + \log ^* n)$ time are based on the algebraic algorithm of Linial (SIAM J Comput 21(1):193–201, 1992) that employs set-systems. The best currently-known combinatorial set-system free algorithm, due to Goldberg et al. (SIAM J Discret Math 1(4):434–446, 1988), requires $O(\varDelta ^2+\log ^*n)$ time. We significantly improve over this by devising a combinatorial $(\varDelta + 1)$ -coloring algorithm that runs in $O(\varDelta + \log ^* n)$ time. This exactly matches the running time of the best-known algebraic algorithm. In addition, we devise a tradeoff for computing $O(\varDelta \cdot t)$ -coloring in $O(\varDelta /t + \log ^* n)$ time, for almost the entire range $1 < t < \varDelta $ . We also compute a Maximal Independent Set in $O(\varDelta + \log ^* n)$ time on general graphs, and in $O(\log n/ \log \log n)$ time on graphs of bounded arboricity. Prior to our work, these results could be only achieved using algebraic techniques. We believe that our algorithms are more suitable for real-life networks with limited resources, such as sensor networks.     

Predictors of mortality and the provision of dialysis in patients with acute tubular necrosis. The Auriculin Anaritide Acute Renal Failure Study Group

BACKGROUND: Improvement of angina pectoris symptoms after cholesterol lowering has raised questions as to the underlying mechanisms. METHODS: Rabbit experiment: We compared arterial blood samples from New Zealand White cholesterol-supplemented rabbits (n = 6) with nonsupplemented rabbit samples (n = 4) in a closed-loop circulation diffusion system. The pH and partial pressures of oxygen (pO2) and carbon dioxide (pCO2) were measured continuously. The samples were first oxygen (O2) saturated (pO2, 160 mm Hg; pCO2, 4 mm Hg) and then desaturated in 100% nitrogen. Cholesterol levels were determined in whole blood, plasma (P Chol), red blood cells (RBCs), and RBC membranes. Human experiment: We exposed quadruple desaturated venous blood samples (n = 4) with P Chol levels of 87 to 400 mg/dL in a gas exchanger to capillary gas conditions (pO2, 23 mm Hg; pCO2, 46 mm Hg). After 15 minutes we performed blood gas analyses and compared our results to baseline values. RESULTS: In the rabbit experiment the cholesterol-supplemented group as compared to the control group showed higher plasma pO2 levels during the saturation phase and lower plasma pO2 levels during the desaturation phase. It also had a markedly increased RBC membrane cholesterol content: 121 +/- 3 (standard error of the mean [SEM]) mg/dL versus 22 +/- 1.7 mg/dL in the control group (P < .05). This barrier to RBC membrane O2 diffusion caused delayed O2 entry into the RBCs during saturation, with a higher plasma pO2, and delayed O2 release from the RBCs during desaturation, with a lower plasma pO2. In the human experiment the P Chol level was inversely correlated with the percentage change of O2 content in milliliters of O2 per deciliter of blood (P < .05). CONCLUSIONS: Increased RBC membrane cholesterol in hypercholesterolemia appears to decrease the transmembrane O2 diffusion rate.     

Right and left ventricular dysfunction in patients with severe pulmonary disease

AIM OF STUDY: To measure the effect of specific preoperative information on postoperative anxiety, satisfaction with information, and demand for analgesia, of Chinese males having transurethral resection of the prostate (TURP). DESIGN: A controlled experimental design. The researchers allocated all patients (n = 30) undergoing TURP in a general hospital in Hong Kong, during a 3-month period, to one of two groups. The experimental group (n = 15) received a specific information pamphlet and a general preoperative counselling video. The control group (n = 15) received a video alone. PROCEDURE AND MEASURES: Following ethical approval, a researcher took baseline measures of state and trait anxiety using the Chinese State-Trait Anxiety Inventory (C -STAI). Five days after surgery the researcher administered the C-STAI (A-State), a patients' satisfaction questionnaire, and, recorded requests for analgesia during the first 5 postoperative days. RESULTS: Experimental subjects reported significantly lower anxiety levels post-operatively and a significantly higher level of satisfaction with the preoperative information, than controls. Postoperative demand for analgesia did not significantly differ between groups. CONCLUSIONS: The findings support the importance of providing patients with specific, written preoperative information about their surgery and its effects to minimize their postoperative anxiety levels, and improve their satisfaction with the care provided.     

Indirect mitogenic effect of transforming growth factor-beta on cell proliferation of subconjunctival fibroblasts

Single amino acid replacement analogs of Manduca adipokinetic hormone (M-AKH) pGlu-Leu-Thr-Phe-Thr-Ser-Ser-Trp-GlyNH2 were tested for activity in bioassays as well as receptor binding assays. Amino acids were replaced by Ala and by D-analogs. In addition an extended M-AKH and analogs containing photo affinity labels were tested. All analogs had reduced activity. All the peptides which had enough activity to allow a full dose response curve reached the same maximal activity as native M-AKH. The use of analogs, in which L-Phe4 was replaced by Ala or by D-Phe and of L-Thr3 replaced by D-Thr, as competitors led to improved binding of M-AKH in our competitive receptor binding assay. In the bioassay an inactive concentration of Ala4 M-AKH increased the activity of a half optimal concentration of native M-AKH.