Hyperuniformity and non-hyperuniformity of quasicrystals

We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic. Some of these examples are even anti-hyperuniform or have a positive asymptotic number variance. On the other hand we establish hyperuniformity for a large class of mathematical quasicrystals in Euclidean spaces of arbitrary dimension. For certain models of quasicrystals we moreover establish that hyperuniformity holds for a generic choice of the underlying parameters. For quasicrystals arising from the cut-and-project method we conclude that their hyperuniformity depends on subtle diophantine properties of the underlying lattice and window and is by no means automatic

Spectral theory of approximate lattices in nilpotent Lie groups

We consider approximate lattices in nilpotent Lie groups. With every such approximate lattice one can associate a hull dynamical system and, to every invariant measure of this system, a corresponding unitary representation. Our results concern both the spectral theory of the representation and the topological dynamics of the system. On the spectral side we construct explicit eigenfunctions for a large collection of central characters using weighted periodization against a twisted fiber density function. We construct this density function by establishing a parametric version of the Bombieri-Taylor conjecture and apply our results to locate high-intensity Bragg peaks in the central diffraction of an approximate lattice. On the topological side we show that under some mild regularity conditions the hull of an approximate lattice admits a sequence of continuous horizontal factors, where the final horizontal factor is abelian and each intermediate factor corresponds to a central extension. We apply this to extend theorems of Meyer and Dani-Navada concerning number-theoretic properties of Meyer sets to the nilpotent setting

Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula

We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical diffraction measure as the Mellin transform of the auto-correlation distribution. We show that uniform regular model sets in commutative spaces have a pure point spherical diffraction measure. The atoms of this measure are located at the spherical automorphic spectrum of the underlying lattice, and the diffraction coefficients can be characterized abstractly in terms of the so-called shadow transform of the characteristic functions of the window. In the case of the Heisenberg group we can give explicit formulas for these diffraction coefficients in terms of Bessel and Laguerre functions. (C) 2021 The Author(s). Published by Elsevier Inc

Development of virtual reality support to factory layout planning

Virtual reality (VR) technology has become ever mature today with affordable and yet powerful hardware. In the manufacturing industry, there is a growing interest of adopting VR to improve existing work procedures. Factory layout planning (FLP) is a long standing area in production engineering that sees great potentials of VR integration. Virtual reality supported layout planning (VLP) is gaining wider attention in research and practice as the virtual environment allows designers to test out “what if” scenarios in relative ease. However, previous research of VLP mostly focus on general layout planning but not the detailed level planning. Also, it is reported that the virtual modeling process is time-consuming and costly. In this study, we propose a point cloud based virtual factory modelling approach for the VLP tasks. It incorporates point cloud representation of physical environment with CAD data to model the virtual factory with the aims of simplifying the modelling process and improving decision-making for the VLP tasks. The proposed approach is exemplified and refined through three industrial cases. The implementations and results of the cases are highlighted and discussed in details. At the end, a general guidance for VLP is extracted and presented for future point cloud based VR support in FLP tasks

Treatment of congenital extrahepatic portosystemic shunts in dogs : a systematic review and meta‐analysis

Background Several options have been proposed for the treatment of congenital extrahepatic portosystemic shunts (cEHPSS) in dogs, but formal comparisons among different treatment options are currently unavailable. A previous evidence-based review (2012) found low quality of evidence for papers assessing the treatment of cEHPSS in dogs. Objectives To assess the quality of evidence available in the treatment of cEHPSS, summarize the current state of knowledge with respect to outcome after cEHPSS management, and compare different treatment techniques. Animals Not used. Methods A bibliographic search was performed without date or language restrictions. Studies were assessed for quality of evidence (study design, study group sizes, subject enrollment quality, and overall risk of bias) and outcome measures reported (perioperative outcome, clinical outcome, and surgical or interventional outcome), all reported with 95% confidence intervals. A network meta-analysis was performed. Results Forty-eight studies were included. Six retrospective studies (grade 4b) compared 2 techniques and 7 were abstracts (grade 5). The quality of evidence was low and risk of bias high. Regarding surgical outcome, statistically significant superiority of ameroid constrictor over thin film band was observed (P = .003). No other comparisons were statistically significant. Conclusions and Clinical Importance The evidence base of choice of treatment of cEHPSS in dogs remains weak despite recent publications on the subject. Ameroid is superior to thin film band in causing EHPSS closure. Blinded randomized studies comparing different treatment modalities, which routinely include postoperative imaging to assess cEHPSS closure and acquired portosystemic shunt development are essential

Genomics of Divergence along a Continuum of Parapatric Population Differentiation

MM received funding from the Max Planck innovation funds for this project. PGDF was supported by a Marie Curie European Reintegration Grant (proposal nr 270891). CE was supported by German Science Foundation grants (DFG, EI 841/4-1 and EI 841/6-1)

Cross-talk between phosphorylation and lysine acetylation in a genome-reduced bacterium

The effect of kinase, phosphatase and N-acetyltransferase deletions on proteome phosphorylation and acetylation was investigated in Mycoplasma pneumoniae. Bi-directional cross-talk between post-transcriptional modifications suggests an underlying regulatory molecular code in prokaryotes

Imaging Magnetic Focusing of Coherent Electron Waves

The magnetic focusing of electrons has proven its utility in fundamental studies of electron transport. Here we report the direct imaging of magnetic focusing of electron waves, specifically in a two-dimensional electron gas (2DEG). We see the semicircular trajectories of electrons as they bounce along a boundary in the 2DEG, as well as fringes showing the coherent nature of the electron waves. Imaging flow in open systems is made possible by a cooled scanning probe microscope. Remarkable agreement between experiment and theory demonstrates our ability to see these trajectories and to use this system as an interferometer. We image branched electron flow as well as the interference of electron waves. This technique can visualize the motion of electron waves between two points in an open system, providing a straightforward way to study systems that may be useful for quantum information processing and spintronics