Minimal surface singularities are Lipschitz normally embedded

Any germ of a complex analytic space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the ambient space and the {\it inner metric}, which is the associated riemannian metric on the germ. We show that minimal surface singularities are Lipschitz normally embedded (LNE), i.e., the identity map is a bilipschitz homeomorphism between outer and inner metrics, and that they are the only rational surface singularities with this property.Comment: This paper is a major revision of the 2015 version. It now builds on the paper arXiv:1806.11240 by the same authors which gives a general characterization of Lipschitz normally embedded surface singularitie

Deep transfer learning for improving single-EEG arousal detection

Datasets in sleep science present challenges for machine learning algorithms due to differences in recording setups across clinics. We investigate two deep transfer learning strategies for overcoming the channel mismatch problem for cases where two datasets do not contain exactly the same setup leading to degraded performance in single-EEG models. Specifically, we train a baseline model on multivariate polysomnography data and subsequently replace the first two layers to prepare the architecture for single-channel electroencephalography data. Using a fine-tuning strategy, our model yields similar performance to the baseline model (F1=0.682 and F1=0.694, respectively), and was significantly better than a comparable single-channel model. Our results are promising for researchers working with small databases who wish to use deep learning models pre-trained on larger databases.Comment: Accepted for presentation at EMBC202

Model for reflection and transmission matrices of nanowire end facets

Nanowires show a large potential for various electrooptical devices, such as light emitting diodes, solar cells and nanowire lasers. We present a direct method developed to calculate the modal reflection and transmission matrix at the end facets of a waveguide of arbitrary cross section, resulting in a generalized version of the Fresnel equations. The reflection can be conveniently computed using Fast Fourier Transforms. We demonstrate that the reflection is qualitatively described by two main parameters, the modal field confinement and the average Fresnel reflection of the plane waves constituting the waveguide mode.Comment: 11 pages,14 figure

Towards a Flexible Deep Learning Method for Automatic Detection of Clinically Relevant Multi-Modal Events in the Polysomnogram

Much attention has been given to automatic sleep staging algorithms in past years, but the detection of discrete events in sleep studies is also crucial for precise characterization of sleep patterns and possible diagnosis of sleep disorders. We propose here a deep learning model for automatic detection and annotation of arousals and leg movements. Both of these are commonly seen during normal sleep, while an excessive amount of either is linked to disrupted sleep patterns, excessive daytime sleepiness impacting quality of life, and various sleep disorders. Our model was trained on 1,485 subjects and tested on 1,000 separate recordings of sleep. We tested two different experimental setups and found optimal arousal detection was attained by including a recurrent neural network module in our default model with a dynamic default event window (F1 = 0.75), while optimal leg movement detection was attained using a static event window (F1 = 0.65). Our work show promise while still allowing for improvements. Specifically, future research will explore the proposed model as a general-purpose sleep analysis model.Comment: Accepted for publication in 41st International Engineering in Medicine and Biology Conference (EMBC), July 23-27, 201

beta-Cu2V2O7: a spin-1/2 honeycomb lattice system

We report on band structure calculations and a microscopic model of the low-dimensional magnet beta-Cu2V2O7. Magnetic properties of this compound can be described by a spin-1/2 anisotropic honeycomb lattice model with the averaged coupling \bar J1=60-66 K. The low symmetry of the crystal structure leads to two inequivalent couplings J1 and J1', but this weak spatial anisotropy does not affect the essential physics of the honeycomb spin lattice. The structural realization of the honeycomb lattice is highly non-trivial: the leading interactions J1 and J1' run via double bridges of VO4 tetrahedra between spatially separated Cu atoms, while the interactions between structural nearest neighbors are negligible. The non-negligible inter-plane coupling Jperp~15 K gives rise to the long-range magnetic ordering at TN~26 K. Our model simulations improve the fit of the magnetic susceptibility data, compared to the previously assumed spin-chain models. Additionally, the simulated ordering temperature of 27 K is in remarkable agreement with the experiment. Our study evaluates beta-Cu2V2O7 as the best available experimental realization of the spin-1/2 Heisenberg model on the honeycomb lattice. We also provide an instructive comparison of different band structure codes and computational approaches to the evaluation of exchange couplings in magnetic insulators.Comment: 11 pages, 10 figures, 2 tables: revised version, extended description of simulation result

Coupling of growth rate and developmental tempo reduces body size heterogeneity in C. elegans.

Animals increase by orders of magnitude in volume during development. Therefore, small variations in growth rates among individuals could amplify to a large heterogeneity in size. By live imaging of C. elegans, we show that amplification of size heterogeneity is prevented by an inverse coupling of the volume growth rate to the duration of larval stages and does not involve strict size thresholds for larval moulting. We perturb this coupling by changing the developmental tempo through manipulation of a transcriptional oscillator that controls the duration of larval development. As predicted by a mathematical model, this perturbation alters the body volume. Model analysis shows that an inverse relation between the period length and the growth rate is an intrinsic property of genetic oscillators and can occur independently of additional complex regulation. This property of genetic oscillators suggests a parsimonious mechanism that counteracts the amplification of size differences among individuals during development

A bilateral shear layer between two parallel Couette flows

We consider a shear layer of a kind not previously studied to our knowledge. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on some simplifying assumptions, an analytic solution has been derived for the new shear layer. These assumptions have been justified by a comparison with numerical solutions of the full Navier-Stokes equations, which accord with the analytical solution to better than 1% in the entire domain. An explicit formula is found for the width of the shear zone as a function of wall-normal coordinate. This width is independent of wall velocities in the laminar regime. Preliminary results for a co-current laminar-turbulent shear layer in the same geometry are also presented. Shear-layer instabilities were then developed and resulted in an unsteady mixing zone at the interface between the two co-current streams.Comment: 6 pages, 7 figures. Accepted for publication in Phys. Rev.

A characterization of Lipschitz normally embedded surface singularities

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeomorphism. We give a necessary and sufficient condition for a normal surface singularity to be Lipschitz normally embedded (LNE), i.e., to have bilipschitz equivalent outer and inner metrics. In a partner paper [15] we apply it to prove that rational surface singularities are LNE if and only if they are minimal.Comment: 30 page

Metal-Organic Frameworks in Germany: from Synthesis to Function

Metal-organic frameworks (MOFs) are constructed from a combination of inorganic and organic units to produce materials which display high porosity, among other unique and exciting properties. MOFs have shown promise in many wide-ranging applications, such as catalysis and gas separations. In this review, we highlight MOF research conducted by Germany-based research groups. Specifically, we feature approaches for the synthesis of new MOFs, high-throughput MOF production, advanced characterization methods and examples of advanced functions and properties