The results of a statistical study of hard x-ray solar flares are presented in this dissertation. Two methods of analysis were used, the Diffusion Entropy (DE) method coupled with an analysis of the data distributions and the Rescaled Range (R/S) Method, sometimes referred to as "Hurst's method". Chapter one provides an introduction to hard x-ray flares within the context of the solar environment and a summary of the statistical paradigms solar astronomers currently work under. Chapter two presents the theory behind the DE and R/S methods. Chapter three presents the results of the two analysis methodologies: most notably important evidence of the conflicting results of the R/S and DE methods, evidence of a Levy statistical signature for the underlying dynamics of the hard x-ray flaring process and a possible separate memory signature for the waiting times. In addition, the stationary and nonstationary characteristics of the waiting times and peak intensities, are revealed. Chapter four provides a concise summary and discussion of the results.

Einleitung & Problemstellung: Beschwerden nach Beschleunigungsverletzungen der Halswirbelsäule sind oft nur unzureichend einzuordnen und diagnostizierbar. Eine eindeutige Diagnostik ist jedoch für eine entsprechende Therapie wie auch möglicherweise entstehende versicherungsrechtliche Forderungen notwendig. Die Entwicklung eines geeigneten Diagnoseverfahrens liegt damit im Interesse von Betroffenen wie auch Kostenträgern. Neben Störungen der Weichteilgewebe ist fast immer die Funktion der Halsmuskulatur in Folge eines Traumas beeinträchtigt. Dabei wird vor allem die sensorische Funktion der HWS-Muskulatur, die an der Regulation des Gleichgewichts beteiligt ist, gestört. In Folge dessen kann angenommen werden, dass es zu einer Beeinträchtigung der Gleichgewichtsregulation kommt. Die Zielstellung der Arbeit lautete deshalb, die möglicherweise gestörte Gleichgewichtsregulation nach einem Trauma im HWS-Bereich apparativ zu erfassen, um so die Verletzung eindeutig diagnostizieren zu können. Methodik: Unter Verwendung eines posturographischen Messsystems mit Kraftmomentensensorik wurden bei 478 Probanden einer Vergleichsgruppe und bei 85 Probanden eines Patientenpools Kraftmomente unter der Fußsohle als Äußerung der posturalen Balanceregulation aufgezeichnet. Die gemessenen Balancezeitreihen wurden nichtlinear analysiert, um die hohe Variabilität der Gleichgewichtsregulation optimal zu beschreiben. Über die dabei gewonnenen Parameter kann überprüft werden, ob sich spezifische Unterschiede im Schwankungsverhalten anhand der plantaren Druckverteilung zwischen HWS-Traumatisierten und den Probanden der Kontrollgruppe klassifizieren lassen. Ergebnisse: Die beste Klassifizierung konnte dabei über Parameter erzielt werden, die das Schwankungsverhalten in Phasen beschreiben, in denen die Amplitudenschwankungen relativ gering ausgeprägt waren. Die Analysen ergaben signifikante Unterschiede im Balanceverhalten zwischen der Gruppe HWS-traumatisierter Probanden und der Vergleichsgruppe. Die höchsten Trennbarkeitsraten wurden dabei durch Messungen im ruhigen beidbeinigen Stand mit geschlossenen Augen erzielt. Diskussion: Das posturale Balanceverhalten wies jedoch in allen Messpositionen eine hohe individuelle Varianz auf, so dass kein allgemeingültiges Schwankungsmuster für eine Gruppengesamtheit klassifiziert werden konnte. Eine individuelle Vorhersage der Gruppenzugehörigkeit ist damit nicht möglich. Die verwendete Messtechnik und die angewandten Auswerteverfahren tragen somit zwar zu einem Erkenntnisgewinn und zur Beschreibung des Gleichgewichtsverhaltens nach HWS-Traumatisierung bei. Sie können jedoch zum derzeitigen Stand für den Einzelfall keinen Beitrag zu einer eindeutigen Bestimmung eines Schleudertraumas leisten. / Introduction & Problem definition: Disorders after acceleration injuries of the cervical spine can often be classified and diagnosed only inadequately. But an explicit diagnosis is necessary as a basis for an adequate therapy as well as for possibly arising demands pursuant to insurance law. The development of suitable diagnosis methods is in the interest of patients as well as the cost units. Apart from disorders of the soft tissues there are almost always impairments of the function of the neck musculature. Particularly the sensory function of the cervical spine musculature, which participates in the regulation of the equilibrium, is disturbed by that. As a result in can be assumed that the postural control is also disturbed. Therefore the aim of this study was to examine the possibly disturbed postural motor balance after a whiplash injury of the cervical spine with the help of apparatus-supported methods to be able to unambigiously diagnose. Methods: postural measuring system based on the force-moment sensortechnique was used to record the postural balance regulation of 478 test persons and 85 patients which had suffered a whiplash injury. Data analysis was accomplished by linear as well as by nonlinear time series methods in order to characterise the balance regulation in an optimal way. Thus it can be determined whether there can be classified specific differences in the plantar pressure distribution covering patients with a whiplash injury and the test persons of the control group. Results: The best classification could be achieved by parameters which describe the variation of the postural balance regulation in phases in which the differences of the amplitudes of the plantar pressure distribution were relatively small. The analyses showed significant differences in the postural motor balance between the group of patients with whiplash injuries and the control group. The most significant differences (highest discriminate rates) could be observed by measurements in both-legged position with closed eyes. Discussion: Although the results achieved support the hypothesis mentioned above, is must be conceded that the postural motor balance showed a high individual variation in all positions of measurement. Therefore no universal variation model could be classified for the entirety of either group. This way an individual forecast of the group membership is impossible. As a result the measurement technology being used and the nonlinear time series analyses can contribute to the gain of knowledge and to the description of the regulation of postural control after whiplash injury. But at present they cannot contribute to an explicit determination of a whiplash injury for a particular case.

The study of experimental recording of dynamical systems often consists in the analysis of signals produced by that system. Time series analysis consists of a wide range of methodologies ultimately aiming at characterizing the signals and, eventually, gaining insights on the underlying processes that govern the evolution of the system. A standard way to tackle this issue is spectrum analysis, which uses Fourier or Laplace transforms to convert time-domain data into a more useful frequency space. These analytical methods allow to highlight periodic patterns in the signal and to reveal essential characteristics of linear systems. Most experimental signals, however, exhibit strange and apparently unpredictable behavior which require more sophisticated analytical tools in order to gain insights into the nature of the underlying processes generating those signals. This is the case when nonlinearity enters into the dynamics of a system. Nonlinearity gives rise to unexpected and fascinating behavior, among which the emergence of deterministic chaos. In the last decades, chaos theory has become a thriving field of research for its potential to explain complex and seemingly inexplicable natural phenomena. The peculiarity of chaotic systems is that, despite being created by deterministic principles, their evolution shows unpredictable behavior and a lack of regularity. These characteristics make standard techniques, like spectrum analysis, ineffective when trying to study said systems. Furthermore, the irregular behavior gives the appearance of these signals being governed by stochastic processes, even more so when dealing with experimental signals that are inevitably affected by noise. Nonlinear time series analysis comprises a set of methods which aim at overcoming the strange and irregular evolution of these systems, by measuring some characteristic invariant quantities that describe the nature of the underlying dynamics. Among those quantities, the most notable are possibly the Lyapunov ex- ponents, that quantify the unpredictability of the system, and measure of dimension, like correlation dimension, that unravel the peculiar geometry of a chaotic system’s state space. These methods are ultimately analytical techniques, which can often be exactly estimated in the case of simulated systems, where the differential equations governing the system’s evolution are known, but can nonetheless prove difficult or even impossible to compute on experimental recordings. A different approach to signal analysis is provided by information theory. Despite being initially developed in the context of communication theory, by the seminal work of Claude Shannon in 1948, information theory has since become a multidisciplinary field, finding applications in biology and neuroscience, as well as in social sciences and economics. From the physical point of view, the most phenomenal contribution from Shannon’s work was to discover that entropy is a measure of information and that computing the entropy of a sequence, or a signal, can answer to the question of how much information is contained in the sequence. Or, alternatively, considering the source, i.e. the system, that generates the sequence, entropy gives an estimate of how much information the source is able to produce. Information theory comprehends a set of techniques which can be applied to study, among others, dynamical systems, offering a complementary framework to the standard signal analysis techniques. The concept of entropy, however, was not new in physics, since it had actually been defined first in the deeply physical context of heat exchange in thermodynamics in the 19th century. Half a century later, in the context of statistical mechanics, Boltzmann reveals the probabilistic nature of entropy, expressing it in terms of statistical properties of the particles’ motion in a thermodynamic system. A first link between entropy and the dynamical evolution of a system is made. In the coming years, following Shannon’s works, the concept of entropy has been further developed through the works of, to only cite a few, Von Neumann and Kolmogorov, being used as a tool for computer science and complexity theory. It is in particular in Kolmogorov’s work, that information theory and entropy are revisited from an algorithmic perspective: given an input sequence and a universal Turing machine, Kolmogorov found that the length of the shortest set of instructions, i.e. the program, that enables the machine to compute the input sequence was related to the sequence’s entropy. This definition of the complexity of a sequence already gives hint of the differences between random and deterministic signals, in the fact that a truly random sequence would require as many instructions for the machine as the size of the input sequence to compute, as there is no other option than programming the machine to copy the sequence point by point. On the other hand, a sequence generated by a deterministic system would simply require knowing the rules governing its evolution, for example the equations of motion in the case of a dynamical system. It is therefore through the work of Kolmogorov, and also independently by Sinai, that entropy is directly applied to the study of dynamical systems and, in particular, deterministic chaos. The so-called Kolmogorov-Sinai entropy, in fact, is a well-established measure of how complex and unpredictable a dynamical system can be, based on the analysis of trajectories in its state space. In the last decades, the use of information theory on signal analysis has contributed to the elaboration of many entropy-based measures, such as sample entropy, transfer entropy, mutual information and permutation entropy, among others. These quantities allow to characterize not only single dynamical systems, but also highlight the correlations between systems and even more complex interactions like synchronization and chaos transfer. The wide spectrum of applications of these methods, as well as the need for theoretical studies to provide them a sound mathematical background, make information theory still a thriving topic of research. In this thesis, I will approach the use of information theory on dynamical systems starting from fundamental issues, such as estimating the uncertainty of Shannon’s entropy measures on a sequence of data, in the case of an underlying memoryless stochastic process. This result, beside giving insights on sensitive and still-unsolved aspects when using entropy-based measures, provides a relation between the maximum uncertainty on Shannon’s entropy estimations and the size of the available sequences, thus serving as a practical rule for experiment design. Furthermore, I will investigate the relation between entropy and some characteristic quantities in nonlinear time series analysis, namely Lyapunov exponents. Some examples of this analysis on recordings of a nonlinear chaotic system are also provided. Finally, I will discuss other entropy-based measures, among them mutual information, and how they compare to analytical techniques aimed at characterizing nonlinear correlations between experimental recordings. In particular, the complementarity between information-theoretical tools and analytical ones is shown on experimental data from the field of neuroscience, namely magnetoencefalography and electroencephalography recordings, as well as mete- orological data.

This dissertation describes the electrochemical behavior of nickel and iron that was studied in different acid solutions via linear sweep voltammetry, cyclic voltammetry, and potentiostatic measurements over a range of temperatures at specific potential ranges. The presented work displays novel experiments where a nickel electrode was heated locally with an inductive heating system, and a platinum (Pt) electrode was used to change the proton concentration at iron and nickel electrode surfaces to control the periodic oscillations (frequency and amplitude) produced and to gain a greater understanding of the systems (kinetics), oscillatory processes, and corrosion processes. Temperature pulse voltammetry, linear sweep voltammetry, and cyclic voltammetry were used for temperature calibration at different heating conditions. Several other metal systems (bismuth, lead, zinc, and silver) also produce periodic oscillations as corrosion occurs; however, creating these with pure metal electrodes is very expensive. In this work, metal systems were created via electrodeposition by using inexpensive, efficient, coupled microelectrode array sensors (CMASs) as a substrate. CMASs are integrated devices with multiple electrodes that are connected externally in a circuit in which all of the electrodes have the same amount of potential applied or current passing through them. CMASs have been used for many years to study different forms of corrosion (crevice corrosion, pitting corrosion, intergranular corrosion, and galvanic corrosion), and they are beneficial because they can simulate single electrodes of the same size. The presented work also demonstrates how to construct CMASs and shows that the unique phenomena of periodic oscillations that can be created and studied by using coated and bare copper CMASs. Furthermore, these systems can be controlled by implementing external forcing with a Pt electrode at the CMAS surface. The data from the single Ni electrode experiments and CMAS experiments were analyzed by using the Nonlinear Time-Series Analysis approach.

In den vergangenen Jahrzehnten wurden extreme Ereignisse, die nicht durch Gauß-Verteilungen beschrieben werden können, in einer Vielzahl an physikalischen Systemen beobachtet. Während statistische Methoden eine zuverlässige Identifikation von extremen Ereignissen ermöglichen, ist deren Entstehungsmechanismus nicht vollständig geklärt. Das Auftreten von extremen Ereignissen ist nicht vollkommen verstanden, da sie nur selten beobachtet werden können und häufig unter schwer reproduzierbaren Bedingungen auftreten. Deshalb ist es erstrebenswert Experimente zu entwickeln, die eine einfache Beobachtung von extremen Ereignissen erlauben. In dieser Dissertation werden extreme Ereignisse untersucht, die bei Multi-Filamentation von Femtosekundenlaserimpulsen entstehen. In den Experimenten, die in dieser Dissertation vorgestellt werden, werden Multi-Filamente durch Hochgeschwindigkeitskameras analysiert. Die Untersuchung der raum-zeitlichen Dynamik der Multi-Filamente zeigt eine L-förmige Wahrscheinlichkeitsverteilung, Diese Beobachtung impliziert das Auftreten von extremen Ereignissen. Lineare Analyse liefert Hinweise auf die physikalischen Prozesse, die zur Entstehung der extremen Ereignisse führen und nicht-lineare Zeitreihen-Analyse charakterisiert die Dynamik des Systems. Die Analyse der Multi-Filamente wird außerdem auf extreme Ereignisse in Wellen-Messungen und optische Superkontinua angewandt. Die durchgeführten Analysen zeigen Unterschiede in den physikalischen Prozessen, die zur Entstehung von extremen Ereignissen führen. Extreme Ereignisse in optischen Fasern werden durch stochastische Fluktuationen von verstärktem Quantenrauschen dominiert. In Multi-Filamenten und Ozeanwellen resultieren extreme Ereignisse dagegen aus klassischer mechanischer Turbulenz, was deren Vorhersagbarkeit impliziert. In dieser Arbeit wird anhand der von Multi-Filament-Zeitreihen die Vorhersagbarkeit in einem kurzen Zeitfenster vor Auftreten des extremen Ereignisses bewiesen. / In the last decades, extreme events, i.e., high-magnitude phenomena that cannot be described within the realm of Gaussian probability distributions have been observed in a multitude of physical systems. While statistical methods allow for a reliable identification of extreme event systems, the underlying mechanism behind extreme events is not understood. Extreme events are not well understood due to their rare occurrence and their onset under conditions that are difficult to reproduce. Thus, it is desirable to identify extreme event scenarios that can serve as a test bed. Optical systems exhibiting extreme events have been discovered to be ideal for such tests, and it is now desired to find more different examples to improve the understanding of extreme events. In this thesis, multifilamentation formed by femtosecond laser pulses is analyzed. Observation of the spatio-temporal dynamics of multifilamentation shows a heavy-tailed fluence probability distribution. This finding implies the onset of extreme events during multifilamentation. Linear analysis gives hints on the processes that drive the formation of extreme events. The multifilaments are also analyzed by nonlinear time series analysis, which provides information on determinism and chaos in the system. The analysis of the multifilament s is compared to an analysis of extreme event time series from ocean wave measurements and the supercontinuum output of an optical fiber. The analysis performed in this work shows fundamental differences in the extreme event mechnaism. While the extreme events in the optical fiber system are ruled by the stochastic changes of amplified quantum noise, in the multifilament and the ocean system extreme events appear as a result of the classical mechanical process of turbulence. This implies the predictability of extreme events. In this work, the predictability of extreme events is proven to be possible in a brief time window before the onset of the extreme event.

To identify extreme changes in the dynamics of the Indian Summer Monsoon (ISM) in the past, I propose a new approach based on the quantification of fluctuations of a nonlinear similarity measure, to identify regimes of distinct dynamical complexity in short time series. I provide an analytical derivation for the relationship of the new measure with the dynamical invariants such as dimension and Lyapunov exponents of the underlying system. A statistical test is also developed to estimate the significance of the identified transitions. Our method is justified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real world situation, we apply the method to identify millennial-scale dynamical transitions in Pleistocene proxy records of the south Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the tropical Walker circulation. Although this new method has general applicability, it is particularly useful in analysing short palaeo-climate records. Rainfall during the ISM over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. I present a detailed analysis of summer monsoon rainfall over the Indian peninsular using Event Synchronization (ES), a measure of nonlinear correlation for point processes such as rainfall. First, using hierarchical clustering I identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. I also provide a method to reconstruct the time delay patterns of rain events. Moreover, further analysis is carried out employing the tools of complex network theory. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the ISM (June to September). I furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps in visualising the structure of the extremeevent rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last six decades. Some supplementary results on the evolution of monsoonal rainfall extremes over the last sixty years are also presented. / Um Extremereignisse in der Dynamik des indischen Sommermonsuns (ISM) in der geologischen Vergangenheit zu identifizieren, schlage ich einen neuartigen Ansatz basierend auf der Quantifikation von Fluktuationen in einem nichtlinearen Ähnlichkeitsmaß vor. Dieser reagiert empfindlich auf Zeitabschnitte mit deutlichen Veränderungen in der dynamischen Komplexität kurzer Zeitreihen. Ein mathematischer Zusammenhang zwischen dem neuen Maß und dynamischen Invarianten des zugrundeliegenden Systems wie fraktalen Dimensionen und Lyapunovexponenten wird analytisch hergeleitet. Weiterhin entwickle ich einen statistischen Test zur Schätzung der Signifikanz der so identifizierten dynamischen Übergänge. Die Stärken der Methode werden durch die Aufdeckung von Bifurkationsstrukturen in paradigmatischen Modellsystemen nachgewiesen, wobei im Vergleich zu den traditionellen Lyapunovexponenten eine Identifikation komplexerer dynamischer Übergänge möglich ist. Wir wenden die neu entwickelte Methode zur Analyse realer Messdaten an, um ausgeprägte dynamische Veränderungen auf Zeitskalen von Jahrtausenden in Klimaproxydaten des südasiatischen Sommermonsunsystems während des Pleistozäns aufzuspüren. Dabei zeigt sich, dass viele dieser Übergänge durch den externen Einfluss der veränderlichen Sonneneinstrahlung, sowie durch dem Klimasystem interne Einflussfaktoren auf das Monsunsystem (Eiszeitzyklen der nördlichen Hemisphäre und Einsatz der tropischenWalkerzirkulation) induziert werden. Trotz seiner Anwendbarkeit auf allgemeine Zeitreihen ist der diskutierte Ansatz besonders zur Untersuchung von kurzen Paläoklimazeitreihen geeignet. Die während des ISM über dem indischen Subkontinent fallenden Niederschläge treten, bedingt durch die zugrundeliegende Dynamik der atmosphärischen Zirkulation und topographische Einflüsse, in äußerst komplexen, raumzeitlichen Mustern auf. Ich stelle eine detaillierte Analyse der Sommermonsunniederschläge über der indischen Halbinsel vor, die auf Ereignissynchronisation (ES) beruht, einem Maß für die nichtlineare Korrelation von Punktprozessen wie Niederschlagsereignissen. Mit hierarchischen Clusteringalgorithmen identifiziere ich zunächst Regionen mit besonders kohärenten oder homogenen Monsunniederschlägen. Dabei können auch die Zeitverzögerungsmuster von Regenereignissen rekonstruiert werden. Darüber hinaus führe ich weitere Analysen auf Basis der Theorie komplexer Netzwerke durch. Diese Studien ermöglichen wertvolle Einsichten in räumliche Organisation, Skalen und Strukturen von starken Niederschlagsereignissen oberhalb der 90% und 94% Perzentilen während des ISM (Juni bis September). Weiterhin untersuche ich den Einfluss von verschiedenen, kritischen synoptischen Systemen der Atmosphäre sowie der steilen Topographie des Himalayas auf diese Niederschlagsmuster. Die vorgestellte Methode ist nicht nur geeignet, die Struktur extremer Niederschlagsereignisse zu visualisieren, sondern kann darüber hinaus über der Region atmosphärische Transportwege von Wasserdampf und Feuchtigkeitssenken auf dekadischen Skalen identifizieren.Weiterhin wird ein einfaches, auf komplexen Netzwerken basierendes Verfahren zur Entschlüsselung der räumlichen Feinstruktur und Zeitentwicklung von Monsunniederschlagsextremen während der vergangenen 60 Jahre vorgestellt.

Einleitung & Problemstellung: Beschwerden nach Beschleunigungsverletzungen der Halswirbel-säule sind oft nur unzureichend einzuordnen und diagnostizierbar. Eine eindeutige Diagnostik ist jedoch für eine entsprechende Therapie wie auch möglicherweise entstehende versicherungsrechtliche Forderungen notwendig. Die Entwicklung eines geeigneten Diagnoseverfahrens liegt damit im Interesse von Betroffenen wie auch Kostenträgern. Neben Störungen der Weichteilgewebe ist fast immer die Funktion der Halsmuskulatur in Folge eines Traumas beeinträchtigt. Dabei wird vor allem die sensorische Funktion der HWS-Muskulatur, die an der Regulation des Gleichgewichts beteiligt ist, gestört. In Folge dessen kann angenommen werden, dass es zu einer Beeinträchtigung der Gleichgewichtsregulation kommt. Die Zielstellung der Arbeit lautete deshalb, die möglicherweise gestörte Gleichgewichtsregulation nach einem Trauma im HWS-Bereich apparativ zu erfassen, um so die Verletzung eindeutig diagnostizieren zu können. Methodik: Unter Verwendung eines posturographischen Messsystems mit Kraftmomentensensorik wurden bei 478 Probanden einer Vergleichsgruppe und bei 85 Probanden eines Patientenpools Kraftmomente unter der Fußsohle als Äußerung der posturalen Balanceregulation aufgezeichnet. Die gemessenen Balancezeitreihen wurden nichtlinear analysiert, um die hohe Variabilität der Gleichgewichtsregulation optimal zu beschreiben. Über die dabei gewonnenen Parameter kann überprüft werden, ob sich spezifische Unterschiede im Schwankungsverhalten anhand der plantaren Druckverteilung zwischen HWS-Traumatisierten und den Probanden der Kontrollgruppe klassifizieren lassen. Ergebnisse: Die beste Klassifizierung konnte dabei über Parameter erzielt werden, die das Schwankungsverhalten in Phasen beschreiben, in denen die Amplitudenschwankungen relativ gering ausgeprägt waren. Die Analysen ergaben signifikante Unterschiede im Balanceverhalten zwischen der Gruppe HWS-traumatisierter Probanden und der Vergleichsgruppe. Die höchsten Trennbarkeitsraten wurden dabei durch Messungen im ruhigen beidbeinigen Stand mit geschlossenen Augen erzielt. Diskussion: Das posturale Balanceverhalten wies jedoch in allen Messpositionen eine hohe individuelle Varianz auf, so dass kein allgemeingültiges Schwankungsmuster für eine Gruppen-gesamtheit klassifiziert werden konnte. Eine individuelle Vorhersage der Gruppenzugehörigkeit ist damit nicht möglich. Die verwendete Messtechnik und die angewandten Auswerteverfahren tragen somit zwar zu einem Erkenntnisgewinn und zur Beschreibung des Gleichgewichtsverhaltens nach HWS-Traumatisierung bei. Sie können jedoch zum derzeitigen Stand für den Einzelfall keinen Beitrag zu einer eindeutigen Bestimmung eines Schleudertraumas leisten. / Introduction & Problem definition: Disorders after acceleration injuries of the cervical spine can often be classified and diagnosed only inadequately. But an explicit diagnosis is necessary as a basis for an adequate therapy as well as for possibly arising demands pursuant to insurance law. The development of suitable diagnosis methods is in the interest of patients as well as the cost units. Apart from disorders of the soft tissues there are almost always impairments of the function of the neck musculature. Particularly the sensory function of the cervical spine musculature, which participates in the regulation of the equilibrium, is disturbed by that. As a result in can be assumed that the postural control is also disturbed. Therefore the aim of this study was to examine the possibly disturbed postural motor balance after a whiplash injury of the cervical spine with the help of apparatus-supported methods to be able to unambigiously diagnose. Methods: postural measuring system based on the force-moment sensortechnique was used to record the postural balance regulation of 478 test persons and 85 patients which had suffered a whiplash injury. Data analysis was accomplished by linear as well as by nonlinear time series methods in order to characterise the balance regulation in an optimal way. Thus it can be determined whether there can be classified specific differences in the plantar pressure distribution covering patients with a whiplash injury and the test persons of the control group. Results: The best classification could be achieved by parameters which describe the variation of the postural balance regulation in phases in which the differences of the amplitudes of the plantar pressure distribution were relatively small. The analyses showed significant differences in the postural motor balance between the group of patients with whiplash injuries and the control group. The most significant differences (highest discriminate rates) could be observed by measurements in both-legged position with closed eyes. Discussion: Although the results achieved support the hypothesis mentioned above, is must be conceded that the postural motor balance showed a high individual variation in all positions of measurement. Therefore no universal variation model could be classified for the entirety of either group. This way an individual forecast of the group membership is impossible. As a result the measurement technology being used and the nonlinear time series analyses can contribute to the gain of knowledge and to the description of the regulation of postural control after whiplash injury. But at present they cannot contribute to an explicit determination of a whiplash injury for a particular case.

[pt] O objetivo desta dissertação é propor um mecanismo de testes para a avaliação dos resultados obtidos em uma modelagem TS-TARX.A principal motivação é encontrar uma solução para um problema comum na modelagem TS-TARX : os modelos espúrios que são gerados durante o processo de divisão do espaço das variáveis independentes.O modelo é uma heurística baseada em análise de árvore de regressão, como discutido por Brieman -3, 1984-. O modelo proposto para a análise de séries temporais é chamado TARX - Threshold Autoregressive with eXternal variables-. A idéia central é encontrar limiares que separem regimes que podem ser explicados através de modelos lineares. Este processo é um algoritmo que preserva o método de regressão por mínimos quadrados recursivo -MQR-. Combinando a árvore de decisão com a técnica de regressão -MQR-, o modelo se tornou o TS-TARX -Tree Structured - Threshold AutoRegression with external variables-.Será estendido aqui o trabalho iniciado por Aranha em -1, 2001-. Onde a partir de uma base de dados conhecida, um algoritmo eficiente gera uma árvore de decisão por meio de regras, e as equações de regressão estimadas para cada um dos regimes encontrados. Este procedimento pode gerar alguns modelos espúrios ou por construção,devido a divisão binária da árvore, ou pelo fato de não existir neste momento uma metodologia de comparação dos modelos resultantes.Será proposta uma metodologia através de sucessivos testes de Chow -5, 1960- que identificará modelos espúrios e reduzirá a quantidade de regimes encontrados, e consequentemente de parâmetros a estimar. A complexidade do modelo final gerado é reduzida a partir da identificação de redundâncias, sem perder o poder preditivo dos modelos TS-TARX .O trabalho conclui com exemplos ilustrativos e algumas aplicações em bases de dados sintéticas, e casos reais que auxiliarão o entendimento. / [en] The goal of this dissertation is to propose a test mechanism to evaluate the results obtained from the TS-TARX modeling procedure.The main motivation is to find a solution to a usual problem related to TS-TARX modeling: spurious models are generated in the process of dividing the space state of the independent variables.The model is a heuristics based on regression tree analysis, as discussed by Brieman -3, 1984-. The model used to estimate the parameters of the time series is a TARX -Threshold Autoregressive with eXternal variables-.The main idea is to find thresholds that split the independent variable space into regimes which can be described by a local linear model. In this process, the recursive least square regression model is preserved. From the combination of regression tree analysis and recursive least square regression techniques, the model becomes TS-TARX -Tree Structured - Threshold Autoregression with eXternal variables-.The works initiated by Aranha in -1, 2001- will be extended. In his works, from a given data base, one efficient algorithm generates a decision tree based on splitting rules, and the corresponding regression equations for each one of the regimes found.Spurious models may be generated either from its building procedure, or from the fact that a procedure to compare the resulting models had not been proposed.To fill this gap, a methodology will be proposed. In accordance with the statistical tests proposed by Chow in -5, 196-, a series of consecutive tests will be performed.The Chow tests will provide the tools to identify spurious models and to reduce the number of regimes found. The complexity of the final model, and the number of parameters to estimate are therefore reduced by the identification and elimination of redundancies, without bringing risks to the TS-TARX model predictive power.This work is concluded with illustrative examples and some applications to real data that will help the readers understanding.

Der technologische Fortschritt hat in jüngster Zeit zu einer großen Zahl von Zeitreihenmessdaten über komplexe dynamische Systeme wie das Klimasystem, das Gehirn oder das globale ökonomische System geführt. Beispielsweise treten im Klimasystem Prozesse wie El Nino-Southern Oscillation (ENSO) mit dem indischen Monsun auf komplexe Art und Weise durch Telekonnektionen und Rückkopplungen in Wechselwirkung miteinander. Die Analyse der Messdaten zur Rekonstruktion der diesen Wechselwirkungen zugrunde liegenden kausalen Mechanismen ist eine Möglichkeit komplexe Systeme zu verstehen, insbesondere angesichts der unendlich-dimensionalen Komplexität der physikalischen Prozesse. Diese Dissertation verfolgt zwei Hauptfragen: (i) Wie können, ausgehend von multivariaten Zeitreihen, kausale Wechselwirkungen praktisch detektiert werden? (ii) Wie kann die Stärke kausaler Wechselwirkungen zwischen mehreren Prozessen in klar interpretierbarer Weise quantifiziert werden? Im ersten Teil der Arbeit werden die Theorie zur Detektion und Quantifikation nichtlinearer kausaler Wechselwirkungen (weiter-)entwickelt und wichtige Aspekte der Schätztheorie untersucht. Zur Quantifikation kausaler Wechselwirkungen wird ein physikalisch motivierter, informationstheoretischer Ansatz vorgeschlagen, umfangreich numerisch untersucht und durch analytische Resultate untermauert. Im zweiten Teil der Arbeit werden die entwickelten Methoden angewandt, um Hypothesen über kausale Wechselwirkungen in Klimadaten der vergangenen hundert Jahre zu testen und zu generieren. In einem zweiten, eher explorativen Schritt wird ein globaler Luftdruck-Datensatz analysiert, um wichtige treibende Prozesse in der Atmosphäre zu identifizieren. Abschließend wird aufgezeigt, wie die Quantifizierung von Wechselwirkungen Aufschluss über mögliche qualitative Veränderungen in der Klimadynamik (Kipppunkte) geben kann und wie kausal treibende Prozesse zur optimalen Vorhersage von Zeitreihen genutzt werden können. / Today''s scientific world produces a vastly growing and technology-driven abundance of time series data of such complex dynamical systems as the Earth''s climate, the brain, or the global economy. In the climate system multiple processes (e.g., El Nino-Southern Oscillation (ENSO) or the Indian Monsoon) interact in a complex, intertwined way involving teleconnections and feedback loops. Using the data to reconstruct the causal mechanisms underlying these interactions is one way to better understand such complex systems, especially given the infinite-dimensional complexity of the underlying physical equations. In this thesis, two main research questions are addressed: (i) How can general causal interactions be practically detected from multivariate time series? (ii) How can the strength of causal interactions between multiple processes be quantified in a well-interpretable way? In the first part of this thesis, the theory of detecting and quantifying general (linear and nonlinear) causal interactions is developed alongside with the important practical issues of estimation. To quantify causal interactions, a physically motivated, information-theoretic formalism is introduced. The formalism is extensively tested numerically and substantiated by rigorous mathematical results. In the second part of this thesis, the novel methods are applied to test and generate hypotheses on causal interactions in climate time series covering the 20th century up to the present. The results yield insights on an understanding of the Walker circulation and teleconnections of the ENSO system, for example with the Indian Monsoon. Further, in an exploratory way, a global surface pressure dataset is analyzed to identify key processes that drive and govern interactions in the global atmosphere. Finally, it is shown how quantifying interactions can be used to determine possible structural changes, termed tipping points, and as optimal predictors, here applied to the prediction of ENSO.

近幾年來，非線性時間數列分析有快速的發展。其中的門檻自迴歸模式(SETAR)，以具有許多線性ARIMA模式所不能配適的特性而受到重視。但是，自1978年Tong建立SETAR模式以來，門檻參數估計的問題一直是SETAR模式在發展應用上的一個瓶頸。本文將探討以實數編碼遺傳演算法，結合統計學上的模式選取準則，建構SETAR模式門檻與延遲參數估計程序的可行性。並從這個基礎上，進一步地研究較精確的門檻參數估計法。 / Non-linear time series analysis has rapidly developed in recent years. Self-exciting threshold autoregression(SETAR) model of non-linear time series models is attentive, because it has some characters which linear ARIMA model fail to fit. But, It has not yet been applied widely because the question of estimation of threshold parameter limits its development and application since Tong proposed SETAR model in 1978. In this paper, we will study the feasibility which constructs a procedure of estimation of SETAR's threshod and delay parameters with real-coded genetic algorithm and statistical criterion of model selection, and develop a more precise estimation of threshold parameter in the basis.