Approximation and complexity of multi-target graph search and the Canadian traveler problem

In the Canadian traveler problem, we are given an edge weighted graph with two specified vertices s and t and a probability distribution over the edges that tells which edges are present. The goal is to minimize the expected length of a walk from s to t. However, we only get to know whether an edge is active the moment we visit one of its incident vertices. Under the assumption that the edges are active independently, we show NP-hardness on series-parallel graphs and give results on the adaptivity gap. We further show that this problem is NP-hard on disjoint-path graphs and cactus graphs when the distribution is given by a list of scenarios. We also consider a special case called the multi-target graph search problem. In this problem, we are given a probability distribution over subsets of vertices. The distribution specifies which set of vertices has targets. The goal is to minimize the expected length of the walk until finding a target. For the

Approximation algorithms for replenishment problems with fixed turnover times

We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with

Approximation algorithms for replenishment problems with fixed turnover times

We introduce and study a class of optimization problems we call replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Clients with capacity for storing a certain commodity are located at various places; at each client the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Clients should never run empty. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a client becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each client and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min–avg minimizes the average tour cost and min–max minimizes the maximum tour cost over all days. For min–max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min–avg we present a logarithmic factor approximation on general metrics, a 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open

The Nuclear Protein Sge1 of Fusarium oxysporum Is Required for Parasitic Growth

Dimorphism or morphogenic conversion is exploited by several pathogenic fungi and is required for tissue invasion and/or survival in the host. We have identified a homolog of a master regulator of this morphological switch in the plant pathogenic fungus Fusarium oxysporum f. sp. lycopersici. This non-dimorphic fungus causes vascular wilt disease in tomato by penetrating the plant roots and colonizing the vascular tissue. Gene knock-out and complementation studies established that the gene for this putative regulator, SGE1 (SIX Gene Expression 1), is essential for pathogenicity. In addition, microscopic analysis using fluorescent proteins revealed that Sge1 is localized in the nucleus, is not required for root colonization and penetration, but is required for parasitic growth. Furthermore, Sge1 is required for expression of genes encoding effectors that are secreted during infection. We propose that Sge1 is required in F. oxysporum and other non-dimorphic (plant) pathogenic fungi for parasitic growth

Unrequested Findings on Cardiac Computed Tomography: Looking Beyond the Heart

Objectives: To determine the prevalence of clinically relevant unrequested extra-cardiac imaging findings on cardiac Computed Tomography (CT) and explanatory factors thereof. Methods: A systematic review of studies drawn from online electronic databases followed by meta-analysis with metaregression was performed. The prevalence of clinically relevant unrequested findings and potentially explanatory variables were extracted (proportion of smokers, mean age of patients, use of full FOV, proportion of men, years since publication). Results: Nineteen radiological studies comprising 12922 patients met the inclusion criteria. The pooled prevalence of clinically relevant unrequested findings was 13 % (95 % confidence interval 9–18, range: 3–39%). The large differences in prevalence observed were not explained by the predefined (potentially explanatory) variables. Conclusions: Clinically relevant extra-cardiac findings are common in patients undergoing routine cardiac CT, and their prevalence differs substantially between studies. These differences may be due to unreported factors such as different definitions of clinical relevance and differences between populations. We present suggestions for basic reporting whic

Citrulline a More Suitable Substrate than Arginine to Restore NO Production and the Microcirculation during Endotoxemia

BACKGROUND: Impaired microcirculation during endotoxemia correlates with a disturbed arginine-nitric oxide (NO) metabolism and is associated with deteriorating organ function. Improving the organ perfusion in endotoxemia, as often seen in patients with severe infection or systemic inflammatory response syndrome (SIRS) is, therefore, an important therapeutic target. We hypothesized that supplementation of the arginine precursor citrulline rather than arginine would specifically increase eNOS-induced intracellular NO production and thereby improve the microcirculation during endotoxemia. METHODOLOGY/PRINCIPAL FINDINGS: To study the effects of L-Citrulline and L-Arginine supplementation on jejunal microcirculation, intracellular arginine availability and NO production in a non-lethal prolonged endotoxemia model in mice. C57/Bl6 mice received an 18 hrs intravenous infusion of endotoxin (LPS, 0.4 µg • g bodyweight(-1) • h(-1)), combined with either L-Citrulline (6.25 mg • h-1), L-Arginine (6.25 mg • h(-1)), or L-Alanine (isonitrogenous control; 12.5 mg • h(-1)) during the last 6 hrs. The control group received an 18 hrs sterile saline infusion combined with L-Alanine or L-Citrulline during the last 6 hrs. The microcirculation was evaluated at the end of the infusion period using sidestream dark-field imaging of jejunal villi. Plasma and jejunal tissue amino-acid concentrations were measured by HPLC, NO tissue concentrations by electron-spin resonance spectroscopy and NOS protein concentrations using Western blot. CONCLUSION/SIGNIFICANCE: L-Citrulline supplementation during endotoxemia positively influenced the intestinal microvascular perfusion compared to L-Arginine-supplemented and control endotoxemic mice. L-Citrulline supplementation increased plasma and tissue concentrations of arginine and citrulline, and restored intracellular NO production in the intestine. L-Arginine supplementation did not increase the intracellular arginine availability. Jejunal tissues in the L-Citrulline-supplemented group showed, compared to the endotoxemic and L-Arginine-supplemented endotoxemic group, an increase in degree of phosphorylation of eNOS (Ser 1177) and a decrease in iNOS protein level. In conclusion, L-Citrulline supplementation during endotoxemia and not L-Arginine reduced intestinal microcirculatory dysfunction and increased intracellular NO production, likely via increased intracellular citrulline and arginine availability