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.

We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature Ric m f in timelike directions. We prove that they still hold when m is finite, and when m is infinite, they hold under the additional assumption that f is bounded from above.

The emission spectra of 70 bioluminescent marine species were measured with a computer controlled optical multichannel analyzer (OMA). A 350 nm spectral window is simultaneously measured using a linear array of 700 silicon photodiodes, coupled by fiber optics to a microchannel plate image intensifier on which a polychromator generated spectrum is focused. Collection optics include a quartz fiber optic bundle which allows spectra to be measured from single photophores. Since corrections are not required for temporal variations in emissions, it was possible to acquire spectra of transient luminescent events that would be difficult or impossible to record with conventional techniques. Use of this system at sea on freshly trawled material and in the laboratory has permitted acquisition of a large collection of bioluminescence spectra of precision rarely obtained previously with such material. Among unusual spectral features revealed were organisms capable of emitting more than one color, including: Umbellula magniflora and Stachyptilum superbum (Pennatulacea), Parazoanthus lucificum (Zoantharia), and Cleidopus gloria-maris (Pisces). Evidence is presented that the narrow bandwidth of the emission spectrum for Argyropelecus affinis (Pisces) is due to filters in the photophores.

We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C 2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.