Continuum percolation with steps in an annulus

Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1 and let G_A be the random graph with vertex set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the area of A is large, then G_A almost surely has an infinite component. Moreover, if we fix \epsilon, increase r and let n_c=n_c(\epsilon) be the area of A when this infinite component appears, then n_c\to1 as \epsilon \to 0. This is in contrast to the case of a ``square'' annulus where we show that n_c is bounded away from 1.Comment: Published at http://dx.doi.org/10.1214/105051604000000891 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Planning Rural Water Services in Nicaragua: A Systems-Based Analysis of Impact Factors Using Graphical Modeling

The success or failure of rural water services in the developing world is a result of numerous factors that interact in a complex set of connections that are difficult to separate and identify. This research effort presented a novel means to empirically reveal the systemic interactions of factors that influence rural water service sustainability in the municipalities of Darío and Terrabona, Nicaragua. To accomplish this, the study employed graphical modeling to build and analyze factor networks. Influential factors were first identified by qualitatively and quantitatively analyzing transcribed interviews from community water committee members. Factor influences were then inferred by graphical modeling to create factor network diagrams that revealed the direct and indirect interaction of factors. Finally, network analysis measures were used to identify “impact factors” based on their relative influence within each factor network. Findings from this study elucidated the systematic nature of such factor interactions in both Darío and Terrabona, and highlighted key areas for programmatic impact on water service sustainability for both municipalities. Specifically, in Darío, the impact areas related to the current importance of water service management by community water committees, while in Terrabona, the impact areas related to the current importance of finances, viable water sources, and community capacity building by external support. Overall, this study presents a rigorous and useful means to identify impact factors as a way to facilitate the thoughtful planning and evaluation of sustainable rural water services in Nicaragua and beyond

LES of an Inclined Jet into a Supersonic Turbulent Crossflow

This short article describes flow parameters, numerical method, and animations of the fluid dynamics video "LES of an Inclined Jet into a Supersonic Turbulent Crossflow" (http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg [high-resolution] and http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v [low-resolution] video). We performed large-eddy simulation with the sub-grid scale (LES-SGS) stretched-vortex model of momentum and scalar transport to study the gas-dynamics interactions of a helium inclined round jet into a supersonic ($M=3.6$) turbulent (\Reth$=13\times10^3$) air flow over a flat surface. The video shows the temporal development of Mach-number and magnitude of density-gradient in the mid-span plane, and isosurface of helium mass-fraction and \lam_2 (vortical structures). The identified vortical structures are sheets, tilted tubes, and discontinuous rings. The vortical structures are shown to be well correlated in space and time with helium mass-fraction isosurface ($Y_{\rm He}=0.25$).Comment: 7 pages, 1 figure, 1 table, article describing fluid dynamics video submitted to Gallery of Fluid Motion, APS-DFD 200

Random Geometric Graphs and Isometries of Normed Spaces

Given a countable dense subset $S$ of a finite-dimensional normed space $X$, and $0<p<1$, we form a random graph on $S$ by joining, independently and with probability $p$, each pair of points at distance less than $1$. We say that $S$ is `Rado' if any two such random graphs are (almost surely) isomorphic. Bonato and Janssen showed that in $l_\infty^d$ almost all $S$ are Rado. Our main aim in this paper is to show that $l_\infty^d$ is the unique normed space with this property: indeed, in every other space almost all sets $S$ are non-Rado. We also determine which spaces admit some Rado set: this turns out to be the spaces that have an $l_\infty$ direct summand. These results answer questions of Bonato and Janssen. A key role is played by the determination of which finite-dimensional normed spaces have the property that every bijective step-isometry (meaning that the integer part of distances is preserved) is in fact an isometry. This result may be of independent interest

Constructing realistic Szekeres models from initial and final data

The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution

Depression in primary care patients with coronary heart disease: baseline findings from the UPBEAT UK study

BACKGROUND: An association between depression and coronary heart disease is now accepted but there has been little primary care research on this topic. The UPBEAT-UK studies are centred on a cohort of primary patients with coronary heart disease assessed every six months for up to four years. The aim of this research was to determine the prevalence and associations of depression in this cohort at baseline. METHOD: Participants with coronary heart disease were recruited from general practice registers and assessed for cardiac symptoms, depression, quality of life and social problems. RESULTS: 803 people participated. 42% had a documented history of myocardial infarction, 54% a diagnosis of ischaemic heart disease or angina. 44% still experienced chest pain. 7% had an ICD-10 defined depressive disorder. Factors independently associated with this diagnosis were problems living alone (OR 5.49, 95% CI 2.11-13.30), problems carrying out usual activities (OR 3.71, 95% CI 1.93-7.14), experiencing chest pain (OR 3.27, 95% CI 1.58-6.76), other pains or discomfort (OR 3.39, 95% CI 1.42-8.10), younger age (OR 0.95 per year 95% CI 0.92-0.98). CONCLUSION: Problems living alone, chest pain and disability are important predictors of depression in this population

Government Entrepreneurship: How COP, Direct Supervision, and a Business Plan Helped to Solve Santa Ana\u27s Crime Problems

Much has been written about Community Oriented Policing for police agencies and about the Direct Supervision concept for jail operations. Each strategy is at the cutting edge of its respective discipline. This Commentary describes how the progressive City of Santa Ana implemented both strategies— along with a visionary business plan to operate its jail at minimal cost—to combat crime successfully. The City’s business plan relies on entrepreneurship that is too often lacking in government programs. This approach has led to a number of innovations in law enforcement, corrections, and government service. Pay-to-Stay programs provide yet another example of how Santa Ana’s willingness to innovate helped it build ever more effective and efficient correctional facilities

Government Entrepreneurship: How COP, Direct Supervision, and a Business Plan Helped to Solve Santa Ana\u27s Crime Problems

Much has been written about Community Oriented Policing for police agencies and about the Direct Supervision concept for jail operations. Each strategy is at the cutting edge of its respective discipline. This Commentary describes how the progressive City of Santa Ana implemented both strategies— along with a visionary business plan to operate its jail at minimal cost—to combat crime successfully. The City’s business plan relies on entrepreneurship that is too often lacking in government programs. This approach has led to a number of innovations in law enforcement, corrections, and government service. Pay-to-Stay programs provide yet another example of how Santa Ana’s willingness to innovate helped it build ever more effective and efficient correctional facilities