Bioluminescence spans all oceanic dimensions and has evolved many times--from bacteria to fish--to powerfully influence behavioral and ecosystem dynamics. New methods and technology have brought great advances in understanding of the molecular basis of bioluminescence, its physiological control, and its significance in marine communities. Novel tools derived from understanding the chemistry of natural light-producing molecules have led to countless valuable applications, culminating recently in a related Nobel Prize. Marine organisms utilize bioluminescence for vital functions ranging from defense to reproduction. To understand these interactions and the distributions of luminous organisms, new instruments and platforms allow observations on individual to oceanographic scales. This review explores recent advances, including the chemical and molecular, phylogenetic and functional, community and oceanographic aspects of bioluminescence.

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We call a metric quasi-Einstein if the m-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics. We study properties of quasi-Einstein metrics and prove several rigidity results. We also give a splitting theorem for some Kähler quasi-Einstein metrics.

The biological and physical processes contributing to planktonic thin layer dynamics were examined in a multidisciplinary study conducted in East Sound, Washington, USA between June 10 and June 25, 1998. The temporal and spatial scales characteristic of thin layers were determined using a nested sampling strategy utilizing 4 major types of platforms: (1) an array of 3 moored acoustical instrument packages and 2 moored optical instrument packages that recorded distributions and intensities of thin layers; (2) additional stationary instrumentation deployed outside the array comprised of meteorological stations, wave-tide gauges, and thermistor chains; (3) a research vessel anchored 150 m outside the western edge of the array; (4) 2 mobile vessels performing basin-wide surveys to define the spatial extent of thin layers and the physical hydrography of the Sound. We observed numerous occurrences of thin layers that contained locally enhanced concentrations of material; many of the layers persisted for intervals of several hours to a few days. More than one persistent thin layer may be present at any one time, and these spatially distinct thin layers often contain distinct plankton assemblages. The results suggest that the species or populations comprising each distinct thin layer have responded to different sets of biological and/or physical processes. The existence and persistence of planktonic thin layers generates extensive biological heterogeneity in the water column and may be important in maintaining species diversity and overall community structure.

Abstract. We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli-Silvestre extension for (−∆) γ when γ ∈ (0, 1), and both a geometric interpretation and a curved analogue of the higher order extension found by R. Yang for (−∆) γ when γ > 1. We give three applications of this correspondence. First, we exhibit some energy identities for the fractional GJMS operators in terms of energies in the compactified Poincaré-Einstein manifold, including an interpretation as a renormalized energy. Second, for γ ∈ (1, 2), we show that if the scalar curvature and the fractional Q-curvature Q 2γ of the boundary are nonnegative, then the fractional GJMS operator P 2γ is nonnegative. Third, by assuming additionally that Q 2γ is not identically zero, we show that P 2γ satisfies a strong maximum principle.