A sharp adaptive confidence ball for self-similar functions

In the nonparametric Gaussian sequence space model an $\ell^2$-confidence ball $C_n$ is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and honest asymptotic coverage over appropriately defined `self-similar' parameter spaces. It is shown by information-theoretic methods that this `self-similarity' condition is weakest possible.Comment: To appear in Stochastic Processes and Applications (memorial issue for E. Gin\'e

Exterior depth and exterior generic annihilator numbers

We study the exterior depth of an $E$-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree $E$-module we show how it relates to the symmetric depth of the corresponding $S$-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior shifting. We define exterior annihilator numbers analogously to the annihilator numbers over the polynomial ring introduced by Trung and Conca, Herzog and Hibi. In addition to a combinatorial interpretation of the annihilator numbers we show how they are related to the symmetric Betti numbers and the Cartan-Betti numbers, respectively. We finally conclude with an example which shows that neither the symmetric nor the exterior generic annihilator numbers are minimal among the annihilator numbers with respect to a sequence.Comment: 22 pages; added proof of Thm. 4.6, extended Ex. 2.11

Radiocarbon Chronologies and Extinction Dynamics of the Late Quaternary Mammalian Megafauna of the Taimyr Peninsula, Russian Federation

This paper presents 75 new radiocarbon dates based on late Quaternary mammal remains recovered from eastern Taimyr Peninsula and adjacent parts of the northern Siberian lowlands, Russian Federation, including specimens of woolly mammoth (Mammuthus primigenius), steppe bison (Bison priscus), muskox (Ovibos moschatus), moose (Alces alces), reindeer (Rangifer tarandus), horse (Equus caballus) and wolf (Canis lupus). New evidence permits reanalysis of megafaunal extinction dynamics in the Asian high Arctic periphery. Increasingly, radiometric records of individual species show evidence of a gap at or near the Pleistocene/Holocene boundary (PHB). In the past, the PHB gap was regarded as significant only when actually terminal, i.e., when it marked the apparent ‘‘last’’ occurrence of a species (e.g., current ‘‘last’’ occurrence date for woolly mammoth in mainland Eurasia is 9600 yr BP). However, for high Arctic populations of horses and muskoxen the gap marks an interruption rather than extinction, because their radiocarbon records resume, nearly simultaneously, much later in the Holocene. Taphonomic effects, ΔC14 flux, and biased sampling are unlikely explanations for these hiatuses. A possible explanation is that the gap is the signature of an event, of unknown nature, that prompted the nearly simultaneous crash of many megafaunal populations in the high Arctic and possibly elsewhere in Eurasia.

Invariant Measures for a Stochastic Fokker-Planck Equation

We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when the noise intensity is sufficiently small, the system with prescribed mass admits a unique invariant measure which is exponentially mixing. The proof uses hypocoercive decay estimates and hypoelliptic gains of regularity. At last we also exhibit an explicit example showing that some restriction on the noise intensity is indeed required.Comment: Extended versio