Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration

In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of sqrt{K} for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors

Taxonomic surrogacy in biodiversity assessments, and the meaning of Linnaean ranks

Copyright © 2006 The Natural History MuseumThe majority of biodiversity assessments use species as the base unit. Recently, a series of studies have suggested replacing numbers of species with higher ranked taxa (genera, families, etc.); a method known as taxonomic surrogacy that has an important potential to save time and resources in assesments of biological diversity. We examine the relationships between taxa and ranks, and suggest that species/higher taxon exchanges are founded on misconceptions about the properties of Linnaean classification. Rank allocations in current classifications constitute a heterogeneous mixture of various historical and contemporary views. Even if all taxa were monophyletic, those referred to the same rank would simply denote separate clades without further equivalence. We conclude that they are no more comparable than any other, non-nested taxa, such as, for example, the genus Rattus and the phylum Arthropoda, and that taxonomic surrogacy lacks justification. These problems are also illustrated with data of polychaetous annelid worms from a broad-scale study of benthic biodiversity and species distributions in the Irish Sea. A recent consensus phylogeny for polychaetes is used to provide three different family-level classifications of polychaetes. We use families as a surrogate for species, and present Shannon–Wiener diversity indices for the different sites and the three different classifications, showing how the diversity measures rely on subjective rank allocations.Y. Bertrand, F. Pleijel and G. W. Rous

Evolution of the northern Tethyan Helvetic Platform during the late Berriasian and early Valanginian

The Early Cretaceous period is characterized by widespread carbonate production in tropical and subtropical epicontinental seas, which was modulated by changes in sea-level, detrital and nutrient fluxes, and the global carbon cycle. As a result, carbonate platforms were sensitive recorders of environmental change, which often anticipated global environmental perturbations. A good example is provided by the northern Tethyan carbonate platform, which is presently preserved in the central European Helvetic Alps. There, the latest early to late Valanginian Weissert episode of global change, which is defined by the first important positive shift in δ13C records of the Cretaceous, is expressed by a prolonged, stepwise drowning phase. In this contribution, a detailed reconstruction of palaeoenvironmental change before and during the Weissert episode is provided based on three representative sections of the Helvetic platform. The sections are placed along a deepening transect and correlated by means of ammonite and microfossil biostratigraphy, sequence stratigraphy and δ13C chemostratigraphy. In a first phase of palaeoenvironmental change during the latest Berriasian, photozoan carbonate production was stopped by a major and hitherto undetected drowning episode, which was followed by a phase of renewed carbonate production by heterozoan biota. This phase was linked to major sea-level rise, a change to a more humid climate and strong regional subsidence associated with tectonic block tilting. During the Valanginian, the circulation of nutrient-enriched sea waters prevented a return to oligotrophic conditions and two further drowning episodes occurred, which are both documented by condensed phosphate-rich beds and dated as middle early Valanginian and late Valanginian to early Hauterivian. The exact causes of the three-step deterioration in carbonate production are not established but a link to episodic volcanic activity is likely, eventually related to the formation of the Paranà-Etendeka large igneous province