The LIL for UU-statistics in Hilbert spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest

High-performance functional renormalization group calculations for interacting fermions

We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the $t$,$t'$ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.Comment: 26 pages, 9 figure

Preliminary report on the first production of the crab stages of alimasag, Portunus pelagicus (Linnaeus)

An experiment was undertaken studying the early life history of Portunus pelagicus in order to obtain information of relevance to rearing techniques for crabs

Exponential and moment inequalities for U-statistics

A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonicalComment: 22 page

What's wrong with this rebuttal?

A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.Comment: 2 page