Purpose: We investigated motor-respiratory coordination (MRC) in visually guided forearm tracking movements focusing on two main questions: (1) Does attentional demand, training or complexity of the tracking task have an effect on the degree of MRC? (2) Does MRC impair the precision of those movements? We hypothesized that (1) enhanced attention to the tracking task and training increase the degree of MRC while higher task complexity would reduce it, and (2) MRC impairs tracking precision. Methods: Thirty-five volunteers performed eight tracking trials with several conditions: positive (direct) signal–response relation (SRR), negative (inverse) SRR to increase task complexity, specific instruction for enhanced attention to maximize tracking precision (“strict” instruction), and specific instruction that tracking precision would not be evaluated (“relaxed” instruction). The trials with positive and negative SRR were performed three times each to study training effects. Results: While the degree of MRC remained in the same range throughout all experimental conditions, a switch in phase-coupling pattern was observed. In conditions with positive SRR or with relaxed instruction, we found one preferred phase-relationship per period. With higher task complexity (negative SRR) or increased attentional demand (strict instruction), a tighter coupling pattern with two preferred phase-relationships per period was adopted. Our main result was that MRC improved tracking precision in all conditions except for that with relaxed instruction. Reduction of amplitude errors mainly contributed to this precision improvement. Conclusion: These results suggest that attention devoted to a precision movement intensifies its phase-coupling with breathing and enhances MRC-related improvement of tracking precision.

In der vorliegenden Dissertation wird eine Beschreibung der Phasendynamik irregulärer Oszillationen und deren Wechselwirkungen vorgestellt. Hierbei werden chaotische und stochastische Oszillationen autonomer dissipativer Systeme betrachtet. Für eine Phasenbeschreibung stochastischer Oszillationen müssen zum einen unterschiedliche Werte der Phase zueinander in Beziehung gesetzt werden, um ihre Dynamik unabhängig von der gewählten Parametrisierung der Oszillation beschreiben zu können. Zum anderen müssen für stochastische und chaotische Oszillationen diejenigen Systemzustände identifiziert werden, die sich in der gleichen Phase befinden. Im Rahmen dieser Dissertation werden die Werte der Phase über eine gemittelte Phasengeschwindigkeitsfunktion miteinander in Beziehung gesetzt. Für stochastische Oszillationen sind jedoch verschiedene Definitionen der mittleren Geschwindigkeit möglich. Um die Unterschiede der Geschwindigkeitsdefinitionen besser zu verstehen, werden auf ihrer Basis effektive deterministische Modelle der Oszillationen konstruiert. Hierbei zeigt sich, dass die Modelle unterschiedliche Oszillationseigenschaften, wie z. B. die mittlere Frequenz oder die invariante Wahrscheinlichkeitsverteilung, nachahmen. Je nach Anwendung stellt die effektive Phasengeschwindigkeitsfunktion eines speziellen Modells eine zweckmäßige Phasenbeziehung her. Wie anhand einfacher Beispiele erklärt wird, kann so die Theorie der effektiven Phasendynamik auch kontinuierlich und pulsartig wechselwirkende stochastische Oszillationen beschreiben. Weiterhin wird ein Kriterium für die invariante Identifikation von Zuständen gleicher Phase irregulärer Oszillationen zu sogenannten generalisierten Isophasen beschrieben: Die Zustände einer solchen Isophase sollen in ihrer dynamischen Entwicklung ununterscheidbar werden. Für stochastische Oszillationen wird dieses Kriterium in einem mittleren Sinne interpretiert. Wie anhand von Beispielen demonstriert wird, lassen sich so verschiedene Typen stochastischer Oszillationen in einheitlicher Weise auf eine stochastische Phasendynamik reduzieren. Mit Hilfe eines numerischen Algorithmus zur Schätzung der Isophasen aus Daten wird die Anwendbarkeit der Theorie anhand eines Signals regelmäßiger Atmung gezeigt. Weiterhin zeigt sich, dass das Kriterium der Phasenidentifikation für chaotische Oszillationen nur approximativ erfüllt werden kann. Anhand des Rössleroszillators wird der tiefgreifende Zusammenhang zwischen approximativen Isophasen, chaotischer Phasendiffusion und instabilen periodischen Orbits dargelegt. Gemeinsam ermöglichen die Theorien der effektiven Phasendynamik und der generalisierten Isophasen eine umfassende und einheitliche Phasenbeschreibung irregulärer Oszillationen. / Many natural systems embedded in a complex surrounding show irregular oscillatory dynamics. The oscillations can be parameterized by a phase variable in order to obtain a simplified theoretical description of the dynamics. Importantly, a phase description can be easily extended to describe the interactions of the system with its surrounding. It is desirable to define an invariant phase that is independent of the observable or the arbitrary parameterization, in order to make, for example, the phase characteristics obtained from different experiments comparable. In this thesis, we present an invariant phase description of irregular oscillations and their interactions with the surrounding. The description is applicable to stochastic and chaotic irregular oscillations of autonomous dissipative systems. For this it is necessary to interrelate different phase values in order to allow for a parameterization-independent phase definition. On the other hand, a criterion is needed, that invariantly identifies the system states that are in the same phase. To allow for a parameterization-independent definition of phase, we interrelate different phase values by the phase velocity. However, the treatment of stochastic oscillations is complicated by the fact that different definitions of average velocity are possible. For a better understanding of their differences, we analyse effective deterministic phase models of the oscillations based upon the different velocity definitions. Dependent on the application, a certain effective velocity is suitable for a parameterization-independent phase description. In this way, continuous as well pulse-like interactions of stochastic oscillations can be described, as it is demonstrated with simple examples. On the other hand, an invariant criterion of identification is proposed that generalizes the concept of standard (Winfree) isophases. System states of the same phase are identified to belong to the same generalized isophase using the following invariant criterion: All states of an isophase shall become indistinguishable in the course of time. The criterion is interpreted in an average sense for stochastic oscillations. It allows for a unified treatment of different types of stochastic oscillations. Using a numerical estimation algorithm of isophases, the applicability of the theory is demonstrated by a signal of regular human respiration. For chaotic oscillations, generalized isophases can only be obtained up to a certain approximation. The intimate relationship between these approximate isophase, chaotic phase diffusion, and unstable periodic orbits is explained with the example of the chaotic roes oscillator. Together, the concept of generalized isophases and the effective phase theory allow for a unified, and invariant phase description of stochastic and chaotic irregular oscillations.

Au-delà de son utilisation en géophysique ou en métrologie à grande échelle, la télémétrie laser des longues distances devrait trouver de nombreuses applications pour les missions spatiales. Les instruments d'observation par synthèse ouverture en vols en formation demandent que la géométrie de la constellation soit connue et contrôlée à bien mieux que la longueur d’onde de la fenêtre d’observation. Pour répondre à ces besoins, nous avons étudié un nouveau schéma de mesure qui combine une mesure interférométrique, réalisée sur un faisceau à deux modes et une mesure de temps de vols. Mon travail de thèse a porté sur la conception, mise en œuvre et la caractérisation de la mesure interférométrique. Pour qu'elles ne soient pas affectées par les dérives lentes de l'instrumentation microonde, les deux mesures de phase de longueur d’onde optique (1.55 µm) et de longueur d’onde synthétique (15 mm) sont extraites d'un même signal d’interférence à deux modes en utilisant une procédure de mesure dédiée : on réalise des mesures du signal d’interférence à trois valeurs de la fréquence optique de la source, calculées d'après le résultat de la mesure de temps de vol. Le télémètre met à profit les propriétés du signal d'interférence à deux modes et exploite la phase et l'amplitude du signal à 20 GHz de façon à éliminer les dérives de phase à long terme du signal microonde dans les chaînes de mesure. On peut en attendre, en moins de 0.1 s, une mesure de résolution et d'exactitude inférieures au nanomètre. Le montage expérimental a permis de montrer que le principe de mesure est correct. Sur la mesure d’un chemin optique dans l'air, nous avons obtenu une résolution de 100 pm à 100 µs, qui nous permet d'observer le bruit acoustique. Le bruit sur la mesure des signaux permet d'espérer une résolution de à 10 pm à 43 ms. Les imperfections optiques du montage ont été mises en évidence: elles ont été décrites par une expression analytique, puis à l’aide d’optiques dédiées réduites au niveau nécessaire pour le fonctionnement de l'instrument. La phase des signaux de battement à 20 GHz est affectée d'erreurs de plusieurs 10-3 cycles qui, si elles ne sont pas corrigées, provoquent des erreurs de la mesure de longueur par une ou plusieurs fois la longueur d'onde optique. Nous avons réalisé une étude spécifique du couplage amplitude-phase à l'origine de cette déformation, et montré qu'il est en partie d'origine thermique, lié à la puissance de plusieurs kW/cm² dissipée dans les photodiodes à 20 GHz. Cet effet, voisin de ce qui est connu depuis quelques années en instrumentation microonde sous le nom d' "effet mémoire", est difficile à prendre en compte et la correction qui est faite sur les données ne parvient pas totalement à éviter que le télémètre délivre des valeurs erronées de la distance. En conclusion de ce mémoire deux options sont présentées afin de remédier à cette déformation du signal et d'aboutir à un instrument de haute exactitude. / Beyond its use in geophysics or in large scale metrology, laser-based measurement of long distances is expected to find numerous applications in space missions. Synthetic aperture instruments in formation flight require that the constellation geometry be known and controlled to much better than the wavelength of the observation window. To meet these needs, we have been studying a novel laser ranging scheme that combine an interferometric measurement, performed on a two-mode laser beam, and a time of flight measurement. My thesis focused on the design, implementation, and characterization of the interferometric measurement. To prevent systematic errors due to slow drifts in the microwave components, the two phase measurements of optical wavelength (1.55 microns) and the synthetic wavelength (15 mm) are extracted from the same two-mode interference signal by using a dedicated measurement procedure: we perform interference signal measurements at three optical frequency values of the laser source, calculated based on the time of flight measurement result. The rangefinder utilizes the two-mode interference signal properties and exploits phase and amplitude of the 20 GHz signal in a manner to eliminate long-term phase drifts of the microwave signal in the measurement chain. We can expect in less than 0.1 s, a measurement with sub-nanometer accuracy and resolution. The experimental setup showed that the principle is correct. On an optical path measurement in air, we obtained a 100 pm resolution in 100 us, which allows us to observe the acoustic noise. The measurement signal noise allows expecting a 10 pm resolution in 43 ms. Optical imperfections in the setup have been observed. They were described by an analytical expression, then, using dedicated optics, they were reduced to the level required for the instrument operation. The phase of two-mode signal is affected to several 10-3 cycle errors which, if not corrected, result in errors in the measurement length by multiples of the optical wavelength. We performed a specific study of amplitude-to-phase coupling causing this deformation, and showed that it is part of thermal origin, related to the power of several kW/cm² dissipated in the 20 GHz photodiodes. This effect, close to what has been known for some years in microwave instrumentation under the name of "memory effects", is difficult to take into account and the correction made on the data can not completely prevent the rangefinder from delivering incorrect values of the distance. In concluding this thesis two options are presented to remedy this signal distortion and result in a high accuracy instrument.

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper methods and statistics, and estimate the variance of the estimates by the weighted jackknife method. I will discuss its applicability and usefulness in nonlinear quadratic phase coupling detection and analysis for multivariate random processes. Furthermore, I will develop the time-varying canonical bicoherence for the nonlinear analysis of non-stationary random processes. In this thesis, the canonical bicoherence is mainly applied in two types of data: a) three-component geomagnetic field data, and b) high-dimensional brain electroencephalogram data. Both results obtained will be linked with physical or physiological interpretations. In particular, this thesis is the first work where the novel method of ``canonical bicoherence'' is introduced and applied to the nonlinear quadratic phase coupling detection and analysis for multivariate random processes. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596

Purpose: We investigated motor-respiratory coordination (MRC) in visually guided forearm tracking movements focusing on two main questions: (1) Does attentional demand, training or complexity of the tracking task have an effect on the degree of MRC? (2) Does MRC impair the precision of those movements? We hypothesized that (1) enhanced attention to the tracking task and training increase the degree of MRC while higher task complexity would reduce it, and (2) MRC impairs tracking precision. Methods: Thirty-five volunteers performed eight tracking trials with several conditions: positive (direct) signal–response relation (SRR), negative (inverse) SRR to increase task complexity, specific instruction for enhanced attention to maximize tracking precision (“strict” instruction), and specific instruction that tracking precision would not be evaluated (“relaxed” instruction). The trials with positive and negative SRR were performed three times each to study training effects. Results: While the degree of MRC remained in the same range throughout all experimental conditions, a switch in phase-coupling pattern was observed. In conditions with positive SRR or with relaxed instruction, we found one preferred phase-relationship per period. With higher task complexity (negative SRR) or increased attentional demand (strict instruction), a tighter coupling pattern with two preferred phase-relationships per period was adopted. Our main result was that MRC improved tracking precision in all conditions except for that with relaxed instruction. Reduction of amplitude errors mainly contributed to this precision improvement. Conclusion: These results suggest that attention devoted to a precision movement intensifies its phase-coupling with breathing and enhances MRC-related improvement of tracking precision.