On Resource-bounded versions of the van Lambalgen theorem

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is Martin-L\"of random relative to $B$ if and only if the interleaved sequence $A \uplus B$ is Martin-L\"of random. This implies that $A$ is relative random to $B$ if and only if $B$ is random relative to $A$ \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness

Simulated annealing for generalized Skyrme models

We use a simulated annealing algorithm to find the static field configuration with the lowest energy in a given sector of topological charge for generalized SU(2) Skyrme models. These numerical results suggest that the following conjecture may hold: the symmetries of the soliton solutions of extended Skyrme models are the same as for the Skyrme model. Indeed, this is verified for two effective Lagrangians with terms of order six and order eight in derivatives of the pion fields respectively for topological charges B=1 up to B=4. We also evaluate the energy of these multi-skyrmions using the rational maps ansatz. A comparison with the exact numerical results shows that the reliability of this approximation for extended Skyrme models is almost as good as for the pure Skyrme model. Some details regarding the implementation of the simulated annealing algorithm in one and three spatial dimensions are provided.Comment: 14 pages, 6 figures, added 2 reference

Floating stones off El Hierro, Canary Islands: xenoliths of pre-island sedimentary origin in the early products of the October 2011 eruption

The eruption that started off the south coast of El Hierro, Canary Islands, in October 2011 has emitted intriguing eruption products found floating in the sea. These specimens appeared as floating volcanic "bombs" that have in the meantime been termed "restingolites" (after the close-by village of La Restinga) and exhibit cores of white and porous pumice-like material. Currently the nature and origin of these "floating stones" is vigorously debated among researchers, with important implications for the interpretation of the hazard potential of the ongoing eruption. The "restingolites" have been proposed to be either (i) juvenile high-silica magma (e.g. rhyolite), (ii) remelted magmatic material (trachyte), (iii) altered volcanic rock, or (iv) reheated hyaloclastites or zeolite from the submarine slopes of El Hierro. Here, we provide evidence that supports yet a different conclusion. We have collected and analysed the structure and composition of samples and compared the results to previous work on similar rocks found in the archipelago. Based on their high silica content, the lack of igneous trace element signatures, and the presence of remnant quartz crystals, jasper fragments and carbonate relicts, we conclude that "restingolites" are in fact xenoliths from pre-island sedimentary rocks that were picked up and heated by the ascending magma causing them to partially melt and vesiculate. They hence represent messengers from depth that help us to understand the interaction between ascending magma and crustal lithologies in the Canary Islands as well as in similar Atlantic islands that rest on sediment/covered ocean crust (e.g. Cape Verdes, Azores). The occurrence of these "restingolites" does therefore not indicate the presence of an explosive high-silica magma that is involved in the ongoing eruption

Corrigendum to "Floating stones off El Hierro, Canary Islands: xenoliths of pre-island sedimentary origin in the early products of the October 2011 eruption" published in Solid Earth, 3, 97–110, 2012

No abstract available