Probabilistic Exponential Integrators

Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability. This issue is greatly alleviated in semi-linear problems by the probabilistic exponential integrators developed in this paper. By including the fast, linear dynamics in the prior, we arrive at a class of probabilistic integrators with favorable properties. Namely, they are proven to be L-stable, and in a certain case reduce to a classic exponential integrator -- with the added benefit of providing a probabilistic account of the numerical error. The method is also generalized to arbitrary non-linear systems by imposing piece-wise semi-linearity on the prior via Jacobians of the vector field at the previous estimates, resulting in probabilistic exponential Rosenbrock methods. We evaluate the proposed methods on multiple stiff differential equations and demonstrate their improved stability and efficiency over established probabilistic solvers. The present contribution thus expands the range of problems that can be effectively tackled within probabilistic numerics

Calibrated Adaptive Probabilistic ODE Solvers

Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.Comment: 17 pages, 10 figures

Propagation of a realistic magnetar jet through binary neutron star merger medium and implications for short gamma-ray bursts

The origin of short gamma-ray bursts (sGRBs) is associated with outflows powered by the remnant of a binary neutron star merger. This remnant can be either a black hole or a highly magnetized, fastly spinning neutron star, also known as a magnetar. Here, we present the results of two relativistic magnetohydrodynamical (RMHD) simulations aimed at investigating the large-scale dynamics and propagation of magnetar collimated outflows through the medium surrounding the remnant. The first simulation evolves a realistic jet by injecting external simulation data, while the second evolves an analytical model jet with similar properties for comparison. We find that both outflows remain collimated and successfully emerge through the static medium surrounding the remnant. However, they fail to attain relativistic velocities and only reach a mean maximum speed of ~0.7c for the realistic jet, and ~0.6c for the analytical jet. We also find that the realistic jet has a much more complex structure. The lack of highly relativistic speeds, that makes these jets unsuitable as short GRB sources, is due to numerical limitations and not general to all possible magnetar outflows. A jet like the one we study, however, could give rise to or augment a blue kilonova component. In addition, it would make the propagation of a relativistic jet easier, should one be launched after the neutron star collapses into a black hole.Comment: 11 pages, 7 figures, accepted to Ap

Towards an MI-proper Predictive Mean Matching

Abstract Statistical analysis with missing data is commonly conducted using the concept of Multiple Imputation (MI

Brauchen wir die Ausbildungsplatzabgabe?

Die Bundesregierung wird voraussichtlich noch im Laufe der nächsten Wochen den Gesetzesentwurf für eine Ausbildungsabgabe in den Bundestag einbringen. Vor einer solchen Abgabe warnen Dieter Philipp, Zentralverband des Deutschen Handwerks, und Michael Knipper, Hauptverband der Deutschen Bauindustrie. Prof. Dr. Dorothea Alewell, Universität Jena, sowie Prof. Dr. Bernhard Nagel und Roman Jaich, Universität Kassel, entwickeln alternative Lösungen. Prof. Dr. Gerhard Bosch, Institut Arbeit und Technik im Wissenschaftszentrum Nordrhein-Westfalen, schlägt eine Orientierung an den europäischen Nachbarstaaten vor.Lehrstellenmarkt, Berufsausbildung, Unternehmen, Ausbildungsfinanzierung, Ausbildungssystem, Selbstverpflichtung, Berufsausbildung, Globalisierung, Industrie, Duale Berufsausbildung, Deutschland, Ausbildungsplatzabgabe

Coherent Feedback Cooling of a Nanomechanical Membrane with Atomic Spins

Coherent feedback stabilizes a system toward a target state without the need of a measurement, thus avoiding the quantum backaction inherent to measurements. Here, we employ optical coherent feedback to remotely cool a nanomechanical membrane using atomic spins as a controller. Direct manipulation of the atoms allows us to tune from strong coupling to an overdamped regime. Making use of the full coherent control offered by our system, we perform spin-membrane state swaps combined with stroboscopic spin pumping to cool the membrane in a room-temperature environment to T=216  mK (¯nm=2.3×103  phonons) in 200  μs. We furthermore observe and study the effects of delayed feedback on the cooling performance. Starting from a cryogenically precooled membrane, this method would enable cooling of the mechanical oscillator close to its quantum mechanical ground state and the preparation of nonclassical states

Adaptive integration of research and policy for sustainable development (AIRP-SD) - prospect for the European research agenda : milestone one

The main objective of AIRP-SD was to address the urgent need to stimulate innovation in Research, Technological development and Demonstration (RTD) processes in order to enhance the prospects of RTD contributing positively to processes and strategies leading to radical improvements in the sustainability of production-consumption systems. This Milestone One Report was the first of three status reports, summarising the interim findings of the first three work packages since the start of the project in January 2002

Optical coherent feedback control of a mechanical oscillator

Feedback is a powerful and ubiquitous technique both in classical and quantum system control. Its standard implementation relies on measuring the state of a system, processing the classical signal, and feeding it back to the system. In quantum physics, however, measurements not only read out the state of the system but also modify it irreversibly. Coherent feedback is a different kind of feedback that coherently processes and feeds back quantum signals without actually measuring the system. Here, we report on the experimental realization and the theoretical analysis of an optical coherent feedback platform to control the motional state of a nanomechanical membrane in an optical cavity. The coherent feedback loop consists of a light field interacting twice with the same mechanical mode through different cavity modes, without {performing any} measurement. Tuning the optical phase and delay of the feedback loop allows us to control the motional state of the mechanical oscillator, its resonance frequency and also its damping rate, which we use to cool the membrane close to the quantum ground state. Our theoretical analysis provides the optimal cooling conditions, showing that this new technique enables ground-state cooling. Experimentally, we show that we can cool the membrane to a state with $\bar{n}_m = 4.89 \pm 0.14$ phonons (${480}\,{\mu \mathrm{K}}$) in a ${20}\,\mathrm{K}$ environment. This lies below the theoretical limit of cavity dynamical backaction cooling in the unresolved sideband regime and is achieved with only 1$\%$ of the optical power required for cavity cooling. Our feedback scheme is very versatile, offering new opportunities for quantum control in a variety of optomechanical systems.Comment: 17 pages, 7 figure

Intra‐scan RF power amplifier drift correction

Purpose The drift in radiofrequency (RF) power amplifiers (RFPAs) is assessed and several contributing factors are investigated. Two approaches for prospective correction of drift are proposed and their effectiveness is evaluated. Methods RFPA drift assessment encompasses both intra-pulse and inter-pulse drift analyses. Scan protocols with varying flip angle (FA), RF length, and pulse repetition time (TR) are used to gauge the influence of these parameters on drift. Directional couplers (DICOs) monitor the forward waveforms of the RFPA outputs. DICOs data is stored for evaluation, allowing calculation of correction factors to adjust RFPAs' transmit voltage. Two correction methods, predictive and run-time, are employed: predictive correction necessitates a calibration scan, while run-time correction calculates factors during the ongoing scan. Results RFPA drift is indeed influenced by the RF duty-cycle, and in the cases examined with a maximum duty-cycle of 66%, the potential drift is approximately 41% or 15%, depending on the specific RFPA revision. Notably, in low transmit voltage scenarios, FA has minimal impact on RFPA drift. The application of predictive and run-time drift correction techniques effectively reduces the average drift from 10.0% to less than 1%, resulting in enhanced MR signal stability. Conclusion Utilizing DICO recordings and implementing a feedback mechanism enable the prospective correction of RFPA drift. Having a calibration scan, predictive correction can be utilized with fewer complexity; for enhanced performance, a run-time approach can be employed

Embolic strokes of undetermined source: prevalence and patient features in the ESUS Global Registry

Background: Recent evidence supports that most non-lacunar cryptogenic strokes are embolic. Accordingly, these strokes have been designated as embolic strokes of undetermined source (ESUS). Aims: We undertook an international survey to characterize the frequency and clinical features of ESUS patients across global regions. Methods: Consecutive patients hospitalized for ischemic stroke were retrospectively surveyed from 19 stroke research centers in 19 different countries to collect patients meeting criteria for ESUS. Results: Of 2144 patients with recent ischemic stroke, 351 (16%, 95% CI 15% to 18%) met ESUS criteria, similar across global regions (range 16% to 21%), and an additional 308 (14%) patients had incomplete evaluation required for ESUS diagnosis. The mean age of ESUS patients (62 years; SD = 15) was significantly lower than the 1793 non-ESUS ischemic stroke patients (68 years, p ≤ 0.001). Excluding patients with atrial fibrillation (n = 590, mean age = 75 years), the mean age of the remaining 1203 non-ESUS ischemic stroke patients was 64 years (p = 0.02 vs. ESUS patients). Among ESUS patients, hypertension, diabetes, and prior stroke were present in 64%, 25%, and 17%, respectively. Median NIHSS score was 4 (interquartile range 2–8). At discharge, 90% of ESUS patients received antiplatelet therapy and 7% received anticoagulation. Conclusions: This cross-sectional global sample of patients with recent ischemic stroke shows that one-sixth met criteria for ESUS, with additional ESUS patients likely among those with incomplete diagnostic investigation. ESUS patients were relatively young with mild strokes. Antiplatelet therapy was the standard antithrombotic therapy for secondary stroke prevention in all global regions