Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings

We study the electronic transport in quasiperiodic separable tight-binding models in one, two, and three dimensions. First, we investigate a one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci chain. The associated d-dimensional quasiperiodic tilings are constructed from the product of d such chains, which yields either the square/cubic Fibonacci tiling or the labyrinth tiling. We study the scaling behavior of the mean square displacement and the return probability of wave packets with respect to time. We also discuss results of renormalization group approaches and lower bounds for the scaling exponent of the width of the wave packet.Comment: 6 pages, 4 figures, conference proceedings Aperiodic 2012 (Cairns

Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group

Let $U_n$ denote the group of $n\times n$ unipotent upper-triangular matrices over a fixed finite field \FF_q, and let U_\cP denote the pattern subgroup of $U_n$ corresponding to the poset \cP. This work examines the superclasses and supercharacters, as defined by Diaconis and Isaacs, of the family of normal pattern subgroups of $U_n$. After classifying all such subgroups, we describe an indexing set for their superclasses and supercharacters given by set partitions with some auxiliary data. We go on to establish a canonical bijection between the supercharacters of U_\cP and certain \FF_q-labeled subposets of \cP. This bijection generalizes the correspondence identified by Andr\'e and Yan between the supercharacters of $U_n$ and the \FF_q-labeled set partitions of $\{1,2,...,n\}$. At present, few explicit descriptions appear in the literature of the superclasses and supercharacters of infinite families of algebra groups other than \{U_n : n \in \NN\}. This work signficantly expands the known set of examples in this regard.Comment: 28 page

Quality measurement of out-patient neuropsychological therapy after stroke in Germany: definition of indicators and retrospective pilot study

Background: In contrast to the hospital setting, today little work has been directed to the definition, measurement, and improvement of the quality of out-patient medical and therapeutic care. We developed a set of indicators to measure the quality of out-patient neuropsychological therapy after stroke. Methods: The indicators cover core and interdisciplinary aspects of out-patient neuropsychological work such as mediation of patients into social care in case of need. Selection of the quality-indicators was done together with a consensus group of out-patient therapists and supported by evidence, validity, reliability as well as estimated relevance and variability with the quality of care. The set of indicators was further tested in a retrospective cohort study. Anonymous data of 104 patients were collected from out-patient clinical records of five clinics between November 2017 and April 2018. Associations between process and outcome quality were estimated exploitatively. Results: Results allowed for the identification of areas with greater variability in the quality of process care and indicated that attention training as recommended by current guidelines had the lowest overall rate for meeting the quality-aim (met in 44% of the cases). This was followed by time<1month until the start of therapy (63% met) and mediation into social care in case of need (65% met). We further observed that overall quality and involving relatives in the therapy was associated with higher rates of professional reintegration (p-value=0.03). However, the need for mediation into social care was associated with a reduced chance for successful professional reintegration (p-value=0.009). Conclusion: In conclusion, we describe a first set of quality indicators which cover different aspects of out-patient neuropsychological therapy and sufficient variability with care. First data further suggests that meeting the specified quality aims may indeed have relevant effects on outcomes

Genetic partitioning of interleukin-6 signalling in mice dissociates Stat3 from Smad3-mediated lung fibrosis

Idiopathic pulmonary fibrosis (IPF) is a fatal disease that is unresponsive to current therapies and characterized by excessive collagen deposition and subsequent fibrosis. While inflammatory cytokines, including interleukin (IL)-6, are elevated in IPF, the molecular mechanisms that underlie this disease are incompletely understood, although the development of fibrosis is believed to depend on canonical transforming growth factor (TGF)-β signalling. We examined bleomycin-induced inflammation and fibrosis in mice carrying a mutation in the shared IL-6 family receptor gp130. Using genetic complementation, we directly correlate the extent of IL-6-mediated, excessive Stat3 activity with inflammatory infiltrates in the lung and the severity of fibrosis in corresponding gp130757F mice. The extent of fibrosis was attenuated in B lymphocyte-deficient gp130757F;µMT−/− compound mutant mice, but fibrosis still occurred in their Smad3−/− counterparts consistent with the capacity of excessive Stat3 activity to induce collagen 1α1 gene transcription independently of canonical TGF-β/Smad3 signalling. These findings are of therapeutic relevance, since we confirmed abundant STAT3 activation in fibrotic lungs from IPF patients and showed that genetic reduction of Stat3 protected mice from bleomycin-induced lung fibrosis

Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings

We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider rather large systems numerically. We show that the wave functions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wave packets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wave packet with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wave packet and propose a modified lower bound for the absolute continuous regime.Comment: 25 pages, 13 figure

On the Representation Theory of an Algebra of Braids and Ties

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic Combinatorics