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We show that tree-like resolution is not automatable in time no(log n) unless ETH is false. This implies that, under ETH, the algorithm given by Beame and Pitassi (FOCS 1996) that automates tree-like resolution in time no(log n) is optimal. We also provide a simpler proof of the result of Alekhnovich and Razborov (FOCS 2001) that unless the fixed parameter hierarchy collapses, tree-like resolution
Models estimate that up to 80% of all butterfly and moth species host vertically transmitted endosymbiotic microorganisms, which can affect the host fitness, metabolism, reproduction, population dynamics, and genetic diversity, among others. The supporting empirical data are however currently highly biased towards the generally more colourful butterflies, and include less information about moths.
The fragmentation rate function connects the fundamental drop breakup process with the resulting drop size distribution and is central to understanding or modeling emulsification processes. There is a large interest in being able to reliably measure it from an emulsification experiment, both for generating data for validating theoretical fragmentation rate function suggestions and as a tool for st
