We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system models, which do not, at present, incorporate all of the competitive strategies that a population might adopt. The second is a simplification of the first, in which competition is only supposed to act within lattice sites and the total population size within each lattice point is a constant. In a special case, this second model is dual to a branching annihilating random walk. For each model, using a comparison with oriented percolation, we show that for certain parameter values, both populations will coexist for all time with positive probability. As a corollary, we deduce survival for all time of branching annihilating random walk for sufficiently large branching rates. We also present a number of conjectures relating to the rôle of space in the survival probabilities for the two populations.

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Reliable cerebral rSO2 readings before, during, and after shunt tap were demonstrated. Left cerebral rSO2 changes from before to after shunt tap were more predictive for shunt malfunction location than right cerebral rSO2 changes. Observing cerebral rSO2 changes in relationship to shunt tap represents a potential surrogate in measuring cerebral pressures and blood flow changes after cerebral spinal fluid drainage. Significantly greater cerebral rSO2 changes occur for distal malfunction versus proximal malfunction after shunt tap, indicating its potential as an adjunct tool for detecting shunt malfunction type.

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The 5-year incidence of SCA in Tennessee high schools is 1 in 12, but increases to 1 in 7 for schools with more than 1000 students. Compliance with AHA guidelines for MERPs is poor, but improved in schools with recent SCA. Future recommendations should encourage the inclusion of AED placement in schools with more than 1000 students.