Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products

In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or ϵ-type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition.

Reality checks on microbial food web interactions in dilution experiments: responses to the comments of Dolan and McKeon

Dolan and McKeon (2005) have recently criticized microzooplankton grazing rate estimates by the dilution approach as being systematically biased and significantly overestimated. Their argument is based on observed mortality responses of ciliated protozoa to reduced food in several coastal experiments and a global extrapolation which assumes that all grazing in all ocean systems scales to the abundance of ciliates. We suggest that these conclusions are unrealistic on several counts: they do not account for community differences between open ocean and coastal systems; they ignore direct experimental evidence supporting dilution rate estimates in the open oceans, and they discount dilution effects on mortality rate as well as growth in multi-layered, open-ocean food webs. High microzooplankton grazing rates in open-ocean systems are consistent with current views on export fluxes and trophic transfers. More importantly, significantly lower rates would fail to account for the efficient nutrient recycling requirements of these resource-limited and rapid-turnover communities.

Reality checks on microbial food web interactions in dilution experiments: Responses to the comments of Dolan and McKeon

Microzooplankton grazing rate estimates by the dilution approach have recently been criticized as systematically biased in the direction of being overestimates of actual rates in nature, and particularly in the open oceans. This argument is based on observed mortality responses of ciliated protozoa to reduced food in several coastal experiments and a global extrapolation which assumes that all grazing in all ocean systems scales to the abundance of ciliates. We suggest that these conclusions are unrealistic on several counts: they do not account for community differences in open ocean and coastal systems; they ignore experimental direct evidence supporting dilution rate estimates in the open oceans, and they discount dilution effects on mortality as well as growth in multi-layered, open-ocean food webs. High microzooplankton grazing rates in open-ocean systems are consistent with current views on export fluxes and trophic transfers. More importantly, significantly lower rates would fail to account for the efficient nutrient recycling requirements of these resource-limited and rapid-turnover communities.