Functional central limit theorems for vicious walkers

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publicatio

Population density, water supply, and the risk of dengue fever in Vietnam: cohort study and spatial analysis.

BACKGROUND: Aedes aegypti, the major vector of dengue viruses, often breeds in water storage containers used by households without tap water supply, and occurs in high numbers even in dense urban areas. We analysed the interaction between human population density and lack of tap water as a cause of dengue fever outbreaks with the aim of identifying geographic areas at highest risk. METHODS AND FINDINGS: We conducted an individual-level cohort study in a population of 75,000 geo-referenced households in Vietnam over the course of two epidemics, on the basis of dengue hospital admissions (n = 3,013). We applied space-time scan statistics and mathematical models to confirm the findings. We identified a surprisingly narrow range of critical human population densities between around 3,000 to 7,000 people/km² prone to dengue outbreaks. In the study area, this population density was typical of villages and some peri-urban areas. Scan statistics showed that areas with a high population density or adequate water supply did not experience severe outbreaks. The risk of dengue was higher in rural than in urban areas, largely explained by lack of piped water supply, and in human population densities more often falling within the critical range. Mathematical modeling suggests that simple assumptions regarding area-level vector/host ratios may explain the occurrence of outbreaks. CONCLUSIONS: Rural areas may contribute at least as much to the dissemination of dengue fever as cities. Improving water supply and vector control in areas with a human population density critical for dengue transmission could increase the efficiency of control efforts. Please see later in the article for the Editors' Summary

Multicolour correlative imaging using phosphor probes

Correlative light and electron microscopy exploits the advantages of optical methods, such as multicolour probes and their use in hydrated live biological samples, to locate functional units, which are then correlated with structural details that can be revealed by the superior resolution of electron microscopes. One difficulty is locating the area imaged by the electron beam in the much larger optical field of view. Multifunctional probes that can be imaged in both modalities and thus register the two images are required. Phosphor materials give cathodoluminescence (CL) optical emissions under electron excitation. Lanthanum phosphate containing thulium or terbium or europium emits narrow bands in the blue, green and red regions of the CL spectrum; they may be synthesised with very uniform-sized crystals in the 10- to 50-nm range. Such crystals can be imaged by CL in the electron microscope, at resolutions limited by the particle size, and with colour discrimination to identify different probes. These materials also give emissions in the optical microscope, by multiphoton excitation. They have been deposited on the surface of glioblastoma cells and imaged by CL. Gadolinium oxysulphide doped with terbium emits green photons by either ultraviolet or electron excitation. Sixty-nanometre crystals of this phosphor have been imaged in the atmospheric scanning electron microscope (JEOL ClairScope). This probe and microscope combination allow correlative imaging in hydrated samples. Phosphor probes should prove to be very useful in correlative light and electron microscopy, as fiducial markers to assist in image registration, and in high/super resolution imaging studies

In-situ fluorescence spectroscopy indicates total bacterial abundance and dissolved organic carbon

We explore in-situ fluorescence spectroscopy as an instantaneous indicator of total bacterial abundance and faecal contamination in drinking water. Eighty-four samples were collected outside of the recharge season from groundwater-derived water sources in Dakar, Senegal. Samples were analysed for tryptophan-like (TLF) and humic-like (HLF) fluorescence in-situ, total bacterial cells by flow cytometry, and potential indicators of faecal contamination such as thermotolerant coliforms (TTCs), nitrate, and in a subset of 22 samples, dissolved organic carbon (DOC). Significant single-predictor linear regression models demonstrated that total bacterial cells were the most effective predictor of TLF, followed by on-site sanitation density; TTCs were not a significant predictor. An optimum multiple-predictor model of TLF incorporated total bacterial cells, nitrate, nitrite, on-site sanitation density, and sulphate (r2 0.68). HLF was similarly related to the same parameters as TLF, with total bacterial cells being the best correlated (ρs 0.64). In the subset of 22 sources, DOC clustered with TLF, HLF, and total bacterial cells, and a linear regression model demonstrated HLF was the best predictor of DOC (r2 0.84). The intergranular nature of the aquifer, timing of the study, and/or non-uniqueness of the signal to TTCs can explain the significant associations between TLF/HLF and indicators of faecal contamination such as on-site sanitation density and nutrients but not TTCs. The bacterial population that relates to TLF/HLF is likely to be a subsurface community that develops in-situ based on the availability of organic matter originating from faecal sources. In-situ fluorescence spectroscopy instantly indicates a drinking water source is impacted by faecal contamination but it remains unclear how that relates specifically to microbial risk in this setting

Do residents’ perceptions of being well-placed and objective presence of local amenities match? A case study in West Central Scotland, UK

Background:<p></p> Recently there has been growing interest in how neighbourhood features, such as the provision of local facilities and amenities, influence residents’ health and well-being. Prior research has measured amenity provision through subjective measures (surveying residents’ perceptions) or objective (GIS mapping of distance) methods. The latter may provide a more accurate measure of physical access, but residents may not use local amenities if they do not perceive them as ‘local’. We believe both subjective and objective measures should be explored, and use West Central Scotland data to investigate correspondence between residents’ subjective assessments of how well-placed they are for everyday amenities (food stores, primary and secondary schools, libraries, pharmacies, public recreation), and objective GIS-modelled measures, and examine correspondence by various sub-groups.<p></p> Methods:<p></p> ArcMap was used to map the postal locations of ‘Transport, Health and Well-being 2010 Study’ respondents (n = 1760), and the six amenities, and the presence/absence of each of them within various straight-line and network buffers around respondents’ homes was recorded. SPSS was used to investigate whether objective presence of an amenity within a specified buffer was perceived by a respondent as being well-placed for that amenity. Kappa statistics were used to test agreement between measures for all respondents, and by sex, age, social class, area deprivation, car ownership, dog ownership, walking in the local area, and years lived in current home.<p></p> Results:<p></p> In general, there was poor agreement (Kappa <0.20) between perceptions of being well-placed for each facility and objective presence, within 800 m and 1000 m straight-line and network buffers, with the exception of pharmacies (at 1000 m straight-line) (Kappa: 0.21). Results varied between respondent sub-groups, with some showing better agreement than others. Amongst sub-groups, at 800 m straight-line buffers, the highest correspondence between subjective and objective measures was for pharmacies and primary schools, and at 1000 m, for pharmacies, primary schools and libraries. For road network buffers under 1000 m, agreement was generally poor.<p></p> Conclusion:<p></p> Respondents did not necessarily regard themselves as well-placed for specific amenities when these amenities were present within specified boundaries around their homes, with some exceptions; the picture is not clear-cut with varying findings between different amenities, buffers, and sub-groups

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

The Link between Dengue Incidence and El Niño Southern Oscillation

Pejman Rohani discusses a new study that examined the dynamic relationship between climate variables and dengue incidence in Thailand, Mexico, and Puerto Rico