Resonances in Extreme Mass-Ratio Inspirals: Asymptotic and Hyperasymptotic Analysis

An expected source of gravitational waves for future detectors in space are the inspirals of small compact objects into much more massive black holes. These sources have the potential to provide a wealth of information about astronomy and fundamental physics. On short timescales the orbit of the small object is approximately geodesic. Generic geodesics for a Kerr black hole spacetime have a complete set of integrals and can be characterized by three frequencies of the motion. Over the course of an inspiral, a typical system will pass through resonances where two of these frequencies become commensurate. The effect of the resonance will be to alter significantly the rate of inspiral for the duration of the resonance. Understanding the impact of these resonances on gravitational wave phasing is important to detect and exploit these signals for astrophysics and fundamental physics. Two differential equations that might describe the passage of an inspiral through such a resonance are investigated. These differ depending on whether it is the phase or the frequency components of a Fourier expansion of the motion that are taken to be continuous through the resonance. Asymptotic and hyperasymptotic analysis are used to find the late-time analytic behavior of the solution for a system that has passed through a resonance. Linearly growing (weak resonances) or linearly decaying (strong resonances) solutions are found depending on the strength of the resonance. In the weak-resonance case, frequency resonances leave an imprint (a resonant memory) on the gravitational frequency evolution. The transition between weak and strong resonances is characterized by a square-root singularity, and as one approaches this transition from above, the solutions to the frequency resonance equation bunch up into families exponentially fast.Comment: 12 pages, 3 figures, submitted to JM

Advanced analysis of magnetic nanoflower measurements to leverage their use in biomedicine

Magnetic nanoparticles are an important asset in many biomedical applications ranging from the local heating of tumours to targeted drug delivery towards diseased sites. Recently, magnetic nanoflowers showed a remarkable heating performance in hyperthermia experiments thanks to their complex structure leading to a broad range of magnetic dynamics. To grasp their full potential and to better understand the origin of this unexpected heating performance, we propose the use of Kaczmarz' algorithm in interpreting magnetic characterisation measurements. It has the advantage that no a priori assumptions need to be made on the particle size distribution, contrasting current magnetic interpretation methods that often assume a lognormal size distribution. Both approaches are compared on DC magnetometry, magnetorelaxometry and AC susceptibility characterisation measurements of the nanoflowers. We report that the lognormal distribution parameters vary significantly between data sets, whereas Kaczmarz' approach achieves a consistent and accurate characterisation for all measurement sets. Additionally, we introduce a methodology to use Kaczmarz' approach on distinct measurement data sets simultaneously. It has the advantage that the strengths of the individual characterisation techniques are combined and their weaknesses reduced, further improving characterisation accuracy. Our findings are important for biomedical applications as Kaczmarz' algorithm allows to pinpoint multiple, smaller peaks in the nanostructure's size distribution compared to the monomodal lognormal distribution. The smaller peaks permit to fine-tune biomedical applications with respect to these peaks to e.g. boost heating or to reduce blurring effects in images. Furthermore, the Kaczmarz algorithm allows for a standardised data analysis for a broad range of magnetic nanoparticle samples. Thus, our approach can improve the safety and efficiency of biomedical applications of magnetic nanoparticles, paving the way towards their clinical use

The variance of the number of prime polynomials in short intervals and in residue classes

We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent equidistribution results of N. Katz.Comment: Revised according to referees' comment

Zero-Level-Set Encoder for Neural Distance Fields

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., to compute a signed distance or occupancy value at a specific spatial position. Previous methods tend to rely on the auto-decoder paradigm, which often requires densely-sampled and accurate signed distances to be known during training and testing, as well as an additional optimization loop during inference. This introduces a lot of computational overhead, in addition to having to compute signed distances analytically, even during testing. In this paper, we present a novel encoder-decoder neural network for embedding 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. Furthermore, the network is trained to solve the Eikonal equation and only requires knowledge of the zero-level set for training and inference. Additional volumetric samples can be generated on-the-fly, and incorporated in an unsupervised manner. This means that in contrast to most previous work, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. In other words, our network computes approximate solutions to the boundary-valued Eikonal equation. It also requires only a single forward pass during inference, instead of the common latent code optimization. We further propose a modification of the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surface-meshes and non-manifold geometry. We finally demonstrate the efficacy, generalizability and scalability of our method on datasets consisting of deforming 3D shapes, single class encoding and multiclass encoding, showcasing a wide range of possible applications

High-Rate Capable Floating Strip Micromegas

We report on the optimization of discharge insensitive floating strip Micromegas (MICRO-MEsh GASeous) detectors, fit for use in high-energy muon spectrometers. The suitability of these detectors for particle tracking is shown in high-background environments and at very high particle fluxes up to 60MHz/cm$^2$. Measurement and simulation of the microscopic discharge behavior have demonstrated the excellent discharge tolerance. A floating strip Micromegas with an active area of 48cm$\times$50cm with 1920 copper anode strips exhibits in 120GeV pion beams a spatial resolution of 50$\mu$m at detection efficiencies above 95%. Pulse height, spatial resolution and detection efficiency are homogeneous over the detector. Reconstruction of particle track inclination in a single detector plane is discussed, optimum angular resolutions below $5^\circ$ are observed. Systematic deviations of this $\mu$TPC-method are fully understood. The reconstruction capabilities for minimum ionizing muons are investigated in a 6.4cm$\times$6.4cm floating strip Micromegas under intense background irradiation of the whole active area with 20MeV protons at a rate of 550kHz. The spatial resolution for muons is not distorted by space charge effects. A 6.4cm$\times$6.4cm floating strip Micromegas doublet with low material budget is investigated in highly ionizing proton and carbon ion beams at particle rates between 2MHz and 2GHz. Stable operation up to the highest rates is observed, spatial resolution, detection efficiencies, the multi-hit and high-rate capability are discussed.Comment: Presented at ICHEP 2014, accepted for publication in Nuclear Physics B Proceedings Supplement

A Large-scale Virtual Patient Cohort to Study ECG Features of Interatrial Conduction Block

Interatrial conduction block refers to a disturbance in the propagation of electrical impulses in the conduction pathways between the right and the left atrium. It is a risk factor for atrial fibrillation, stroke, and premature death. Clinical diagnostic criteria comprise an increased P wave duration and biphasic P waves in lead II, III and aVF due to retrograde activation of the left atrium. Machine learning algorithms could improve the diagnosis but require a large-scale, well-controlled and balanced dataset. In silico electrocardiogram (ECG) signals, optimally obtained from a statistical shape model to cover anatomical variability, carry the potential to produce an extensive database meeting the requirements for successful machine learning application. We generated the first in silico dataset including interatrial conduction block of 9,800 simulated ECG signals based on a bi-atrial statistical shape model. Automated feature analysis was performed to evaluate P wave morphology, duration and P wave terminal force in lead V1. Increased P wave duration and P wave terminal force in lead V1 were found for models with interatrial conduction block compared to healthy models. A wide variability of P wave morphology was detected for models with interatrial conduction block. Contrary to previous assumptions, our results suggest that a biphasic P wave morphology seems to be neither necessary nor sufficient for the diagnosis of interatrial conduction block. The presented dataset is ready for a classification with machine learning algorithms and can be easily extended

Are We There Yet?: The Development of a Corpus Annotated for Social Acts in Multilingual Online Discourse

We present the AAWD and AACD corpora, a collection of discussions drawn from Wikipedia talk pages and small group IRC discussions in English, Russian and Mandarin. Our datasets are annotated with labels capturing two kinds of social acts: alignment moves and authority claims. We describe these social acts, describe our annotation process, highlight challenges we encountered and strategies we employed during annotation, and present some analyses of resulting data set which illustrate the utility of our corpus and identify interactions among social acts and between participant status and social acts and in online discourse