Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics of projections of the residuals on a given set of sub-spaces in the image-space of the operator. We prove general consistency and convergence rate results in the framework of Bregman-divergences which allows for a vast range of penalty functionals. Various examples that indicate the applicability of our approach will be discussed. We will illustrate in the context of signal and image processing that the presented method constitutes a locally adaptive reconstruction method

Constant-time connectivity tests

We present implementations of constant-time algorithms for connectivity tests and related problems. Some are implementations of slightly improved variants of previously known algorithms; for other problems we present new algorithms that have substantially better runtime than previously known algorithms (estimates of the distance to and tolerant testers for connectivity, 2-edge-connectivity, 3-edge-connectivity, eulerianity)

Strong magnetic fields and large rotation measures in protogalaxies by supernova seeding

We present a model for the seeding and evolution of magnetic fields in protogalaxies. Supernova (SN) explosions during the assembly of a protogalaxy provide magnetic seed fields, which are subsequently amplified by compression, shear flows and random motions. We implement the model into the MHD version of the cosmological N-body / SPH simulation code GADGET and we couple the magnetic seeding directly to the underlying multi-phase description of star formation. We perform simulations of Milky Way-like galactic halo formation using a standard LCDM cosmology and analyse the strength and distribution of the subsequent evolving magnetic field. A dipole-shape divergence-free magnetic field is injected at a rate of 10^{-9}G / Gyr within starforming regions, given typical dimensions and magnetic field strengths in canonical SN remnants. Subsequently, the magnetic field strength increases exponentially on timescales of a few ten million years. At redshift z=0, the entire galactic halo is magnetized and the field amplitude is of the order of a few $\mu$G in the center of the halo, and 10^{-9} G at the virial radius. Additionally, we analyse the intrinsic rotation measure (RM) of the forming galactic halo over redshift. The mean halo intrinsic RM peaks between redshifts z=4 and z=2 and reaches absolute values around 1000 rad m^{-2}. While the halo virializes towards redshift z=0, the intrinsic RM values decline to a mean value below 10 rad m^{-2}. At high redshifts, the distribution of individual starforming, and thus magnetized regions is widespread. In our model for the evolution of galactic magnetic fields, the seed magnetic field amplitude and distribution is no longer a free parameter, but determined self-consistently by the star formation process occuring during the formation of cosmic structures.Comment: 13 pages, 14 figures, accepted to MNRAS after moderate revisio

Maximal cocliques and the chromatic number of the Kneser graph on chambers of PG(3,q)(3,q)

Let $\Gamma$ be the graph whose vertices are the chambers of the finite projective $3$-space PG$(3,q)$, with two vertices being adjacent if and only if the corresponding chambers are in general position. We show that a maximal independent set of vertices of $\Gamma$ contains $q^4+3q^3+4q^2+3q+1$, or $3q^3+5q^2+3q+1$, or at most $3q^3+4q^2+3q+2$ elements. For $q\geq 4$ the structure of the largest maximal independent sets is described. For $q\geq 7$ the structure of the maximal independent sets of the three largest cardinalities is described. Using the cardinality of the second largest maximal independent sets, we show that the chromatic number of $\Gamma$ is $q^2+q$

Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice

We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-1/2 $XY$-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin liquid phases predicted recently [Schmied et al., New J. Phys. {\bf 10}, 045017 (2008)].Comment: 6 pages, as published in EP

Does Telemedical Support of First Responders Improve Guideline Adherence in an Offshore Emergency Scenario? A Simulator-Based Prospective Study

OBJECTIVE: To investigate, in a simulator-based prospective study, whether telemedical support improves quality of emergency first response (performance) by medical non-professionals to being non-inferior to medical professionals. SETTING: In a simulated offshore wind power plant, duos (teams) of offshore engineers and teams of paramedics conducted the primary survey of a simulated patient. PARTICIPANTS: 38 offshore engineers and 34 paramedics were recruited by the general email invitation. INTERVENTION: Teams (randomised by lot) were supported by transmission technology and a remote emergency physician in Berlin. OUTCOME MEASURES: From video recordings, performance (17 item checklist) and required time (up to 15 min) were quantified by expert rating for analysis. Differences were analysed using two-sided exact Mann-Whitney U tests for independent measures, non-inferiority was analysed using Schuirmann one-sided test. The significance level of 5 % was Holm-Bonferroni adjusted in each family of pairwise comparisons. RESULTS: Nine teams of engineers with, nine without, nine teams of paramedics with and eight without support completed the task. Two experts quantified endpoints, insights into rater dependence were gained. Supported engineers outperformed unsupported engineers (p<0.01), insufficient evidence was found for paramedics (p=0.11). Without support, paramedics outperformed engineers (p<0.01). Supported engineers' performance was non-inferior (at one item margin) to that by unsupported paramedics (p=0.03). Supported groups were slower than unsupported groups (p<0.01). CONCLUSIONS: First response to medical emergencies in offshore wind farms with substantially delayed professional care may be improved by telemedical support. Future work should test our result during additional scenarios and explore interdisciplinary and ecosystem aspects of this support. TRIAL REGISTRATION NUMBER: DRKS0001437