Detecting Local Deflection Patterns of Ultra-high Energy Cosmic Rays using the Principal Axes of the Directional Energy Distribution

From deflections in galactic and extragalactic magnetic fields energy dependent structures in the arrival directions of ultra-high energy cosmic rays (UHECR) are expected. We propose to characterize these structures by the strength of collimation of energy along the principal axes in selected regions in the sky. While the strength of collimation are indicators of anisotropy in the arrival distribution of UHECR, the orientation of the principal system holds information about the direction of the deflections of UHECR. We discuss the method and present expected limits on the strength of deflection and density of sources using simulated scenarios of UHECR proton propagation.Comment: Contribution no. 1063 to the 33rd International Cosmic Ray Conference, Rio de Janeiro, Brazil, July 201

Completed power operations for Morava E-theory

We construct and study an algebraic theory which closely approximates the theory of power operations for Morava E-theory, extending previous work of Charles Rezk in a way that takes completions into account. These algebraic structures are made explicit in the case of K-theory. Methodologically, we emphasize the utility of flat modules in this context, and prove a general version of Lazard's flatness criterion for module spectra over associative ring spectra.Comment: Version 3: Minor corrections. Journal version, up to small cosmetic change

Theory of electronic and spin-orbit proximity effects in graphene on Cu(111)

We study orbital and spin-orbit proximity effects in graphene adsorbed to the Cu(111) surface by means of density functional theory (DFT). The proximity effects are caused mainly by the hybridization of graphene $\pi$ and copper d orbitals. Our electronic structure calculations agree well with the experimentally observed features. We carry out a graphene-Cu(111) distance dependent study to obtain proximity orbital and spin-orbit coupling parameters, by fitting the DFT results to a robust low energy model Hamiltonian. We find a strong distance dependence of the Rashba and intrinsic proximity induced spin-orbit coupling parameters, which are in the meV and hundreds of $\mu$eV range, respectively, for experimentally relevant distances. The Dirac spectrum of graphene also exhibits a proximity orbital gap, of about 20 meV. Furthermore, we find a band inversion within the graphene states accompanied by a reordering of spin and pseudospin states, when graphene is pressed towards copper

Complexity and Approximation of the Continuous Network Design Problem

We revisit a classical problem in transportation, known as the continuous (bilevel) network design problem, CNDP for short. We are given a graph for which the latency of each edge depends on the ratio of the edge flow and the capacity installed. The goal is to find an optimal investment in edge capacities so as to minimize the sum of the routing cost of the induced Wardrop equilibrium and the investment cost. While this problem is considered as challenging in the literature, its complexity status was still unknown. We close this gap showing that CNDP is strongly NP-complete and APX-hard, both on directed and undirected networks and even for instances with affine latencies. As for the approximation of the problem, we first provide a detailed analysis for a heuristic studied by Marcotte for the special case of monomial latency functions (Mathematical Programming, Vol.~34, 1986). Specifically, we derive a closed form expression of its approximation guarantee for arbitrary sets S of allowed latency functions. Second, we propose a different approximation algorithm and show that it has the same approximation guarantee. As our final -- and arguably most interesting -- result regarding approximation, we show that using the better of the two approximation algorithms results in a strictly improved approximation guarantee for which we give a closed form expression. For affine latencies, e.g., this algorithm achieves a 1.195-approximation which improves on the 5/4 that has been shown before by Marcotte. We finally discuss the case of hard budget constraints on the capacity investment.Comment: 27 page

Comment on "A test-tube model for rainfall" by Wilkinson M., EPL 106 (2014) 40001

This paper is a comment to M Wilkinson, EPL 106 (2014) 40001, arXiv:1401.4620 [physics.ao-ph,cond-mat.soft], which draws conclusion from our data that are at variance with our observations

Wiring a periscope--ocelli, retinula axons, visual neuropils and the ancestrality of sea spiders.

The Pycnogonida or sea spiders are cryptic, eight-legged arthropods with four median ocelli in a 'periscope' or eye tubercle. In older attempts at reconstructing phylogeny they were Arthropoda incertae sedis, but recent molecular trees placed them as the sister group either to all other euchelicerates or even to all euarthropods. Thus, pycnogonids are among the oldest extant arthropods and hold a key position for the understanding of arthropod evolution. This has stimulated studies of new sets of characters conductive to cladistic analyses, e.g. of the chelifores and of the hox gene expression pattern. In contrast knowledge of the architecture of the visual system is cursory. A few studies have analysed the ocelli and the uncommon "pseudoinverted" retinula cells. Moreover, analyses of visual neuropils are still at the stage of Hanström's early comprehensive works. We have therefore used various techniques to analyse the visual fibre pathways and the structure of their interrelated neuropils in several species. We found that pycnogonid ocelli are innervated to first and second visual neuropils in close vicinity to an unpaired midline neuropil, i.e. possibly the arcuate body, in a way very similar to ancestral euarthropods like Euperipatoides rowelli (Onychophora) and Limulus polyphemus (Xiphosura). This supports the ancestrality of pycnogonids and sheds light on what eyes in the pycnogonid ground plan might have 'looked' like. Recently it was suggested that arthropod eyes originated from simple ocelli similar to larval eyes. Hence, pycnogonid eyes would be one of the early offshoots among the wealth of more sophisticated arthropod eyes