Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is a optimization problem in the nondeterministic polynomial-complete complexity class, therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Er\"odos-Renyi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.Comment: 6 page

Variants of the low oxygen sensors EGLN1 and HIF-1AN associated with acute mountain sickness.

Two low oxygen sensors, Egl nine homolog 1 (EGLN1) and hypoxia-inducible factor 1-α inhibitor (HIF-1AN), play pivotal roles in the regulation of HIF-1α, and high altitude adaption may be involved in the pathology of acute mountain sickness (AMS). Here, we aimed to analyze single nucleotide polymorphisms (SNPs) in the untranslated regions of the EGLN1 and HIF-1AN genes and SNPs chosen from a genome-wide adaptation study of the Han Chinese population. To assess the association between EGLN1 and HIF-1AN SNPs and AMS in a Han Chinese population, a case-control study was performed including 190 patients and 190 controls. In total, thirteen SNPs were genotyped using the MassARRAY® MALDI-TOF system. Multiple genetic models were tested; The Akaike's information criterion (AIC) and Bayesian information criterion (BIC) values indicated that the dominant model may serve as the best-fit model for rs12406290 and rs2153364 of significant difference. However, these data were not significant after Bonferroni correction. No significant association was noted between AMS and rs12757362, rs1339894, rs1361384, rs2009873, rs2739513 or rs2486729 before and after Bonferroni correction. Further haplotype analyses indicated the presence of two blocks in EGLN1; one block consists of rs12406290-rs2153364, located upstream of the EGLN1 gene. Carriers of the "GG" haplotype of rs12406290-rs2153364 exhibited an increased risk of AMS after adjustments for age and smoking status. However, no significant association was observed among HIF-1AN 3'-untranslated region (3'-UTR) polymorphisms, haplotype and AMS. Our study indicates that variants in the EGLN1 5'-UTR influence the susceptibility to AMS in a Han Chinese population

Numerical Analysis of Bubble Dynamics in Electrohydraulic and Electromagnetic Shock Wave Lithotripsy

This study numerically investigated the bubble dynamics in electrohydraulic (EH) and electromagnetic (EM) shock wave lithotripsy (SWL). The acoustic pressure generated by a typical EH (i.e., Dornier HM-3) and EM (i.e., Siemens Modularis) lithotripters has been measured. The dynamics of cavitation bubbles in SWL has been numerically simulated using the Gilemore formulation coupled with zero-order gas diffusion. The pressure measurement results showed that both the peak positive and negative pressure of the Modularis at E4.0 are slightly higher than the corresponding values of the HM-3 at 20 kV. However, the pressure waveforms generated by an EH lithotripter is different from these of an EM lithotripter. The EM shock wave has a remarkable 2nd compressive pulse, which might suppress the cavitation activities in the EM lithotripter. In addition, the numerical simulation showed the EH lithotripter could produce stronger cavitation activities than the EM lithotripter