Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the $k$-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

Does self-monitoring of blood glucose improve outcome in type 2 diabetes? The Fremantle Diabetes Study

AIMS/HYPOTHESIS: To assess whether self-monitoring of blood glucose (SMBG) is an independent predictor of improved outcome in a community-based cohort of type 2 diabetic patients. MATERIALS AND METHODS: We used longitudinal data from (1) 1,280 type 2 diabetic participants in the observational Fremantle Diabetes Study (FDS) who reported SMBG and diabetes treatment status at study entry (1993–1996), and (2) a subset of 531 participants who attended six or more annual assessments (referred to as the 5-year cohort). Diabetes-related morbidity, cardiac death and all-cause mortality were ascertained at each assessment, supplemented by linkage to the Western Australian Data Linkage System. RESULTS: At baseline, 70.2% (898 out of 1,280) of type 2 patients used SMBG. During 12,491 patient-years of follow-up (mean 9.8 ± 3.5 years), 486 (38.0%) type 2 participants died (196 [15.3%] from cardiac causes). SMBG was significantly less prevalent in those who died during follow-up than in those who were still alive at the end of June 2006 (65.4 vs 73.0%, p = 0.005). In Cox proportional hazards modelling, after adjustment for confounding and explanatory variables, SMBG was not independently associated with all-cause mortality, but was associated with a 79% increased risk of cardiovascular mortality in patients not treated with insulin. For the 5-year cohort, time-dependent SMBG was independently associated with a 48% reduced risk of retinopathy. CONCLUSIONS/INTERPRETATION: SMBG was not independently associated with improved survival. Inconsistent findings relating to the association of SMBG with cardiac death and retinopathy may be due to confounding, incomplete covariate adjustment or chance

Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

A note on the use of sensitivity analysis to explore the potential impact of declining institutional care utilisation on disability prevalence

Many health and disability surveys are conducted using the non-institutionalised population as a sampling frame. Consequently, it is possible that changes in the utilisation of institutional care could account for all or part of any change in the observed prevalence of functional limitation, disability or other health state, based on samples from the non-institutionalised population. Using conditional probability arguments, I present an adjustment formula for computing health state prevalences for the non-institutionalised population under a scenario in which health state prevalences are held constant except for movement into the non-institutionalised population of individuals who would formerly have been in institutional care. By comparing the adjusted prevalence with observed non-institutionalised health state prevalences the contribution of changes in institutionalisation to observed changes in the non-institutionalised health state prevalence can be assessed

Moving from evidence-based medicine to evidence-based health.

While evidence-based medicine (EBM) has advanced medical practice, the health care system has been inconsistent in translating EBM into improvements in health. Disparities in health and health care play out through patients' limited ability to incorporate the advances of EBM into their daily lives. Assisting patients to self-manage their chronic conditions and paying attention to unhealthy community factors could be added to EBM to create a broader paradigm of evidence-based health. A perspective of evidence-based health may encourage physicians to consider their role in upstream efforts to combat socially patterned chronic disease

The characteristic blue spectra of accretion disks in quasars as uncovered in the infrared

Quasars are thought to be powered by supermassive black holes accreting surrounding gas. Central to this picture is a putative accretion disk which is believed to be the source of the majority of the radiative output. It is well known, however, that the most extensively studied disk model -- an optically thick disk which is heated locally by the dissipation of gravitational binding energy -- is apparently contradicted by observations in a few major respects. In particular, the model predicts a specific blue spectral shape asymptotically from the visible to the near-infrared, but this is not generally seen in the visible wavelength region where the disk spectrum is observable. A crucial difficulty was that, toward the infrared, the disk spectrum starts to be hidden under strong hot dust emission from much larger but hitherto unresolved scales, and thus has essentially been impossible to observe. Here we report observations of polarized light interior to the dust-emiting region that enable us to uncover this near-infrared disk spectrum in several quasars. The revealed spectra show that the near-infrared disk spectrum is indeed as blue as predicted. This indicates that, at least for the outer near-infrared-emitting radii, the standard picture of the locally heated disk is approximately correct. The model problems at shorter wavelengths should then be directed toward a better understanding of the inner parts of the revealed disk. The newly uncovered disk emission at large radii, with more future measurements, will also shed totally new light on the unanswered critical question of how and where the disk ends.Comment: published in Nature, 24 July 2008 issue. Supplementary Information can be found at http://www.mpifr-bonn.mpg.de/div/ir-interferometry/suppl_info.pdf Published version can be accessed from http://www.nature.com/nature/journal/v454/n7203/pdf/nature07114.pd

Risk-Sensitive Mean-Field Type Control under Partial Observation

We establish a stochastic maximum principle (SMP) for control problems of partially observed diffusions of mean-field type with risk-sensitive performance functionals.Comment: arXiv admin note: text overlap with arXiv:1404.144

An extracellular steric seeding mechanism for Eph-ephrin signaling platform assembly

Erythropoetin-producing hepatoma (Eph) receptors are cell-surface protein tyrosine kinases mediating cell-cell communication. Upon activation, they form signaling clusters. We report crystal structures of the full ectodomain of human EphA2 (eEphA2) both alone and in complex with the receptor-binding domain of the ligand ephrinA5 (ephrinA5 RBD). Unliganded eEphA2 forms linear arrays of staggered parallel receptors involving two patches of residues conserved across A-class Ephs. eEphA2-ephrinA5 RBD forms a more elaborate assembly, whose interfaces include the same conserved regions on eEphA2, but rearranged to accommodate ephrinA5 RBD. Cell-surface expression of mutant EphA2s showed that these interfaces are critical for localization at cell-cell contacts and activation-dependent degradation. Our results suggest a 'nucleation' mechanism whereby a limited number of ligand-receptor interactions 'seed' an arrangement of receptors which can propagate into extended signaling arrays

Punica granatum (Pomegranate) juice provides an HIV-1 entry inhibitor and candidate topical microbicide

BACKGROUND: For ≈ 24 years the AIDS pandemic has claimed ≈ 30 million lives, causing ≈ 14,000 new HIV-1 infections daily worldwide in 2003. About 80% of infections occur by heterosexual transmission. In the absence of vaccines, topical microbicides, expected to block virus transmission, offer hope for controlling the pandemic. Antiretroviral chemotherapeutics have decreased AIDS mortality in industrialized countries, but only minimally in developing countries. To prevent an analogous dichotomy, microbicides should be: acceptable; accessible; affordable; and accelerative in transition from development to marketing. Already marketed pharmaceutical excipients or foods, with established safety records and adequate anti-HIV-1 activity, may provide this option. METHODS: Fruit juices were screened for inhibitory activity against HIV-1 IIIB using CD4 and CXCR4 as cell receptors. The best juice was tested for inhibition of: (1) infection by HIV-1 BaL, utilizing CCR5 as the cellular coreceptor; and (2) binding of gp120 IIIB and gp120 BaL, respectively, to CXCR4 and CCR5. To remove most colored juice components, the adsorption of the effective ingredient(s) to dispersible excipients and other foods was investigated. A selected complex was assayed for inhibition of infection by primary HIV-1 isolates. RESULTS: HIV-1 entry inhibitors from pomegranate juice adsorb onto corn starch. The resulting complex blocks virus binding to CD4 and CXCR4/CCR5 and inhibits infection by primary virus clades A to G and group O. CONCLUSION: These results suggest the possibility of producing an anti-HIV-1 microbicide from inexpensive, widely available sources, whose safety has been established throughout centuries, provided that its quality is adequately standardized and monitored