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

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

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

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

Infektionsabwehr und lymphatischer Rachenring

Foraging behaviours used by two female Australian fur seals (Arctocephalus pusillus doriferus) were documented during controlled feeding trials. During these trials the seals were presented with prey either free-floating in open water or concealed within a mobile ball or a static box feeding device. When targeting free-floating prey both subjects primarily used raptorial biting in combination with suction, which was used to draw prey to within range of the teeth. When targeting prey concealed within either the mobile or static feeding device, the seals were able to use suction to draw out prey items that could not be reached by biting. Suction was followed by lateral water expulsion, where water drawn into the mouth along with the prey item was purged via the sides of the mouth. Vibrissae were used to explore the surface of the feeding devices, especially when locating the openings in which the prey items had been hidden. The mobile ball device was also manipulated by pushing it with the muzzle to knock out concealed prey, which was not possible when using the static feeding device. To knock prey out of this static device one seal used targeted bubble blowing, where a focused stream of bubbles was blown out of the nose into the openings in the device. Once captured in the jaws, prey items were manipulated and re-oriented using further mouth movements or chews so that they could be swallowed head first. While most items were swallowed whole underwater, some were instead taken to the surface and held in the teeth, while being vigorously shaken to break them into smaller pieces before swallowing. The behavioural flexibility displayed by Australian fur seals likely assists in capturing and consuming the extremely wide range of prey types that are targeted in the wild, during both benthic and epipelagic foraging

Using interpretative phenomenological analysis to inform physiotherapy practice: An introduction with reference to the lived experience of cerebellar ataxia

The attached file is a pre-published version of the full and final paper which can be found at the link below.This article has been made available through the Brunel Open Access Publishing Fund.Qualitative research methods that focus on the lived experience of people with health conditions are relatively underutilised in physiotherapy research. This article aims to introduce interpretative phenomenological analysis (IPA), a research methodology oriented toward exploring and understanding the experience of a particular phenomenon (e.g., living with spinal cord injury or chronic pain, or being the carer of someone with a particular health condition). Researchers using IPA try to find out how people make sense of their experiences and the meanings they attach to them. The findings from IPA research are highly nuanced and offer a fine grained understanding that can be used to contextualise existing quantitative research, to inform understanding of novel or underresearched topics or, in their own right, to provoke a reappraisal of what is considered known about a specified phenomenon. We advocate IPA as a useful and accessible approach to qualitative research that can be used in the clinical setting to inform physiotherapy practice and the development of services from the perspective of individuals with particular health conditions.This article is available through the Brunel Open Access Publishing Fund

Family coordination in families who have a child with autism spectrum disorder

Little is known about the interactions of families where there is a child with autism spectrum disorder (ASD). The present study applies the Lausanne Trilogue Play (LTP) to explore both its applicability to this population as well as to assess resources and areas of deficit in these families. The sample consisted of 68 families with a child with ASD, and 43 families with a typically developing (TD) child. With respect to the global score for family coordination there were several negative correlations: the more severe the symptoms (based on the child’s ADOS score), the more family coordination was dysfunctional. This correlation was particularly high when parents had to play together with the child. In the parts in which only one of the parents played actively with the child, while the other was simply present, some families did achieve scores in the functional range, despite the child’s symptom severity. The outcomes are discussed in terms of their clinical implications both for assessment and for interventio

Niche as a determinant of word fate in online groups

Patterns of word use both reflect and influence a myriad of human activities and interactions. Like other entities that are reproduced and evolve, words rise or decline depending upon a complex interplay between {their intrinsic properties and the environments in which they function}. Using Internet discussion communities as model systems, we define the concept of a word niche as the relationship between the word and the characteristic features of the environments in which it is used. We develop a method to quantify two important aspects of the size of the word niche: the range of individuals using the word and the range of topics it is used to discuss. Controlling for word frequency, we show that these aspects of the word niche are strong determinants of changes in word frequency. Previous studies have already indicated that word frequency itself is a correlate of word success at historical time scales. Our analysis of changes in word frequencies over time reveals that the relative sizes of word niches are far more important than word frequencies in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings. We also distinguish endogenous versus exogenous factors as additional contributors to the fates of words, and demonstrate the force of this distinction in the rise of novel words. Our results indicate that short-term nonstationarity in word statistics is strongly driven by individual proclivities, including inclinations to provide novel information and to project a distinctive social identity.Comment: Supporting Information is available here: http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0019009.s00