Search

Wir studieren zwei Klassen singulärer stochastischer Systeme: Stochastische Spikes, die als Skalierungslimiten von Lösungen gewisser stochastischer Differenzialgleichungen auftreten und in der Quantenmechanik Anwendung finden sowie Fleming-Viot-artige Partikelsysteme, die als Approximationsalgorithmen in der mathematischen Statistik verwendet werden. Im Falle der stochastischen Spikes verallgemeinern wir Ergebnisse von [M. Bauer and D. Bernard, Stochastic spikes and strong noise limits of stochastic differential equations, Annales Henri Poincar\'e, 19, 2018, 653--693] bezüglich der Konvergenz gegen einen homogenen Poisson-Prozess unter Verwendung klassischer wahrscheinlichkeitstheoretischer Methoden und wenden die gefundenen abstrakten Kriterien auf zwei Beispielklassen an. Fleming-Viot-artige Partikelsysteme können in dem Sinne singuläres Verhalten aufweisen, dass es möglicherweise zu unendlich vielen Sprüngen in endlicher Zeit kommt. Während der Analyse des Problems stellen wir strukturelle Resultate auf und leiten eine hinreichende Bedingungen her, um zu entscheiden, ob dies passiert; dadurch sind wir in der Lage, neue Einsichten in den Fall von drei sich bewegender Partikel zu geben., We study two classes of singular stochastic systems: stochastic spikes appearing as scaling limits of the solutions of specific stochastic differential equations with applications in quantum mechanics and Fleming-Viot-type particle systems used as approximation algorithm in mathematical statistics. In the case of the stochastic spikes we generalize results of [M. Bauer and D. Bernard, Stochastic spikes and strong noise limits of stochastic differential equations, Annales Henri Poincar\'e, 19, 2018, 653--693] regarding the convergence to a homogeneous Poisson process using classical probabilistic tools and apply the obtained abstract criteria to two example classes. Fleming-Viot-type particle systems may exhibit singular behavior in the sense that there are possibly infinitely many particle jumps in finite time. Establishing structural results throughout the analysis of the problem we deduce a sufficient condition to decide whether this happens and are thereby able to give new insights in the case of three moving particles.

Additional file 4: Neurologic items in Gaucher type 3 patients (Table).

Purpose: There is some controversy whether or not saccades change with age. This cross-sectional study aims to clarify the characteristics of reflexive saccades at various ages to establish a normative cohort in a standardized set-up. Second objective is to investigate the feasibility of saccadometry in daily ophthalmological practice. Methods: One hundred healthy participants aged between 6 and 76 years underwent an ophthalmologic examination and saccadometry, using an infrared video-oculography device, sampling at 220 Hz. The reflexive saccades were evoked in four directions and three target displacements each (5°/15°/30° horizontally and of 5°/10°/20° vertically). Saccadic peak velocity, gain (amplitude/target displacement) and latency were measured. Results: Mean peak velocity of saccades was 213°/s (± 29°/s), 352°/s (± 50°/s) and 455°/s (± 67°/s) to a target position 5°, 15°and 30° horizontally, respectively, and 208°/s (± 36°/s), 303°/s (± 50°/s) and 391°/s (± 71°/s) to a target position 5°, 10° and 20° vertically. The association between peak velocity and eccentricity proved to be present at any age in all four directions. We found no relevant effect of age on peak velocity, gain and latency in a fitted linear mixed model. However, latency becomes shorter during childhood and adolescence, while in adulthood it is relatively stable with a slight trend to increase in the elderly. Saccades are more precise when the target displacement is small. Isometric saccades are most common, followed by hypometric ones. All children and elderly were able to perform good quality saccadometry in a recording time of approximately 10 minutes. Conclusion: The presented data may serve as normative control for further studies using such a video-oculography device for saccadometry. The means of peak velocity and the gain can be used independently from age respecting the target displacement. Latency is susceptible to age.