Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory

We point out a caveat in the proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic O(a) improvement can fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic O(a) improvement. In order to illustrate explicitly automatic O(a) improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading O(a) effect, depending on the size of the quark mass.Comment: 27 pages, no figure

Depressive rumination and heart rate variability: A pilot study on the effect of biofeedback on rumination and its physiological concomitants

ObjectiveRecent studies suggest that lower resting heart rate variability (HRV) is associated with elevated vulnerability to depressive rumination. In this study, we tested whether increases in HRV after HRV-biofeedback training are accompanied by reductions in rumination levels. Materials and methodsSixteen patients suffering from depression completed a 6-week HRV-biofeedback training and fourteen patients completed a control condition in which there was no intervention (waitlist). The training included five sessions per week at home using a smartphone application and an ECG belt. Depressive symptoms and autonomic function at rest and during induced rumination were assessed before and after each of the two conditions. We used a well-established rumination induction task to provoke a state of pervasive rumination while recording various physiological signals simultaneously. Changes in HRV, respiration rate, skin conductance, and pupil diameter were compared between conditions and time points. ResultsA significant correlation was found between resting HRV and rumination levels, both assessed at the first laboratory session (r = -0.43, p < 0.05). Induction of rumination led to an acceleration of heart rate and skin conductance increases. After biofeedback training, resting vagal HRV was increased (p < 0.01) and self-ratings of state anxiety (p < 0.05), rumination (p < 0.05), perceived stress (p < 0.05), and depressive symptoms (QIDS, BDI; both p < 0.05) were decreased. In the control condition, there were no changes in autonomic indices or depressive symptomatology. A significant interaction effect group x time on HRV was observed. ConclusionOur results indicate that a smartphone-based HRV-biofeedback intervention can be applied to improve cardiovagal function and to reduce depressive symptoms including self-rated rumination tendencies

Benchmarking CPUs and GPUs on embedded platforms for software receiver usage

Smartphones containing multi-core central processing units (CPUs) and powerful many-core graphics processing units (GPUs) bring supercomputing technology into your pocket (or into our embedded devices). This can be exploited to produce power-efficient, customized receivers with flexible correlation schemes and more advanced positioning techniques. For example, promising techniques such as the Direct Position Estimation paradigm or usage of tracking solutions based on particle filtering, seem to be very appealing in challenging environments but are likewise computationally quite demanding. This article sheds some light onto recent embedded processor developments, benchmarks Fast Fourier Transform (FFT) and correlation algorithms on representative embedded platforms and relates the results to the use in GNSS software radios. The use of embedded CPUs for signal tracking seems to be straight forward, but more research is required to fully achieve the nominal peak performance of an embedded GPU for FFT computation. Also the electrical power consumption is measured in certain load levels.Peer ReviewedPostprint (published version

Rotating Chemical Waves in Small Circular Domains

The influence of the domain size on the properties of rotating waves in the NO+CO reaction on a microstructured Pt(100) surface is investigated for circular geometries. Below a critical domain size, determined by the spiral wavelength in an unbounded medium, the frequency of the rotating waves increases substantially due to interaction of the wave tip with the boundary. The phenomena are reproduced qualitatively with a reaction-diffusion model

Matching experimental and three dimensional numerical models for structural vibration problems with uncertainties

© 2017 The Author(s) The simulation model which examines the dynamic behavior of real structures needs to address the impact of uncertainty in both geometry and material parameters. This article investigates three-dimensional finite element models for structural dynamics problems with respect to both model and parameter uncertainties. The parameter uncertainties are determined via laboratory measurements on several beam-like samples. The parameters are then considered as random variables to the finite element model for exploring the uncertainty effects on the quality of the model outputs, i.e. natural frequencies. The accuracy of the output predictions from the model is compared with the experimental results. To this end, the non-contact experimental modal analysis is conducted to identify the natural frequency of the samples. The results show a good agreement compared with experimental data. Furthermore, it is demonstrated that geometrical uncertainties have more influence on the natural frequencies compared to material parameters and material uncertainties are about two times higher than geometrical uncertainties. This gives valuable insights for improving the finite element model due to various parameter ranges required in a modeling process involving uncertainty

Dynamical Model for Chemically Driven Running Droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets -- reaction-limited and saturated regime -- are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.Comment: 4 pages, 5 figure

Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page