Surrogate time series

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at http://www.mpipks-dresden.mpg.de/~tisea

Detection of Spatial and Temporal Interactions in Renal Autoregulation Dynamics

Renal autoregulation stabilizes renal blood flow to protect the glomerular capillaries and maintain glomerular filtration rates through two mechanisms: tubuloglomerular feedback (TGF) and the myogenic response (MR). It is considered that the feedback mechanisms operate independently in each nephron (the functional unit of the kidney) within a kidney, but renal autoregulation dynamics can be coupled between vascular connected nephrons. It has also been shown that the mechanisms are time-varying and interact with each other. Understanding of the significance of such complex behavior has been limited by absence of techniques capable of monitoring renal flow signals among more than 2 or 3 nephrons simultaneously. The purpose of this thesis was to develop approaches to allow the identification and characterization of spatial and temporal properties of renal autoregulation dynamics. We present evidence that laser speckle perfusion imaging (LSPI) effectively captures renal autoregulation dynamics in perfusion signals across the renal cortex of anaesthetized rats and that spatial heterogeneity of the dynamics is present and can be investigated using LSPI. Next, we present a novel approach to segment LSPI of the renal surface into phase synchronized clusters representing areas with coupled renal autoregulation dynamics. Results are shown for the MR and demonstrate that when a signal is present phase synchronized regions can be identified. We then describe an approach to identify quadratic phase coupling between the TGF and MR mechanisms in time and space. Using this approach we can identify locations across the renal surface where both mechanisms are operating cooperatively. Finally, we show how synchronization between nephrons can be investigated in relation to renal autoregulation effectiveness by comparing phase synchronization estimates from LSPI with renal autoregulation system properties estimated from renal blood flow and blood pressure measurements. Overall, we have developed approaches to 1) capture renal autoregulation dynamics across the renal surface, 2) identify regions with phase synchronized renal autoregulation dynamics, 3) quantify the presence of the TGF-MR interaction across the renal surface, and 4) determine how the above vary over time. The described tools allow for investigations of the significance and mechanisms behind the complex spatial interactions and time-varying properties of renal autoregulation dynamics

The Application of Adaptive Linear and N on-Linear Filters to Fringe Order Identification in White-Light Interferometry Systems

Conventional optical interferometry systems driven by highly coherent light sources have a very short unambiguous operating range, a direct consequence of the flatness of the interference fringes visibility profile at the output of the system. The range can be extended by using a white-light interferometer (WU), which is driven by a low-coherence source and produces a Gaussian visibility profile with a unique maximum in correspondence of the central fringe. Due to system and/or measurement noise, however, the position of the maximum (from which an accurate measurement of the measurand - displacement, temperature, pressure, flow, etc. - can be derived) is not easily detectable, and can lead to large measurement errors. This is especially true in a multiplexing scheme, where the source power is distributed evenly among various sensors, with a corresponding drop in the overall signal-to-noise ratio. The inclusion of a signal processing scheme at the receiver end is thus a necessity. As the fringe pattern at the output of a WLI system is basically a noisy sine wave amplitude modulated by a Gaussian envelope, it can be classified as a non-stationary, narrow-band, linear but non-Gaussian signa\. So far, no attempt has been made to apply digital filtering techniques, as understood in the signal processing community, to the output signal of a WLI system. This thesis constitutes a first step in that direction. Since the only measurable information given by the system is contained in the output signal, the system is modelled as a "black box" driven by the system and measurement noise processes and containing an unknown set of parameters. Standard least squares techniques can then be applied to estimate the parameters of the model, as is usually done in the field of system identification when only noisy output measurements are available. It is shown that identification of the model parameters is equivalent to finding a set of coefficients for an inverse filter which takes the WU signal at its input and delivers the unknown noise process at the output. The non-stationarity of the signal is accounted for by allowing for time variations of the model parameters; this justifies the use of adaptive filters with time-varying coefficients. A new central fringe identification scheme is proposed, based on a modification of the standard least mean square (LMS) adaptive filtering algorithm in combination with amplitude thresholding of the fringe pattern. The new scheme is shown to offer considerable improvement in the identification rate when tested against current schemes over comparable operating ranges, while retaining the computational simplicity and operational speed of the standard LMS. Its performance is also shown to be largely independent of the step-size parameter controlling the rate of convergence and tracking in the standard LMS, which is known to be the main obstacle for a successful application of the algorithm in a practical setting. The non-Gaussianity of the signal is explored and an attempt is made to apply higher-order statistics (HOS) algorithms to central fringe identification. The effectiveness of Gaussianity tests on pilot Gaussian data is seen to depend not only on the number and length of records available but, perhaps more importantly, on the bandwidth of the process. Violation of the stationarity assumption is shown to lead to mis-classification of a seemingly non-Gaussian signal into a Gaussian one, as the visibility profile may alter the distribution of the underlying sinusoid making it appear Gaussian, even when beam diffraction and wavefront aberrations combine to produce a nonGaussian profile. HOS-based adaptive algorithms may still be of some benefit, however, if processing is confined to that region of the fringe pattern where sufficient non-Gaussianity is allowed to develop. Non-linear adaptive filters based on the Volterra theories are finally applied to compensate for possible non-linearities introduced by mismatches in optical components, chromatic aberrations, and analogue-to-digital converters. It is shown that although a Volterra filter is able to reproduce the low-amplitude distortions of the fringe pattern better than a linear filter does, the identification rate does not improve. Reasons are given for such behaviour

An Empirical Inquiry Into the Variation of Interest Rates, 1959-1983 (Time Series Analysis, Spectral, Money Supply, Inflation Rate).

The empirical relationships among nominal interest rates, the inflation rate, and the money supply are examined for the period, 1959-1983. Monthly data are analyzed. The analysis of these relations specifically focuses on (1) the determination of the causal order between the variables and (2) the estimation of empirical lag distributions. The Gibson test, the Granger test, the Box-Jenkins test, and the Haugh test are used for these purposes. In addition, vector autoregressive-moving average models are estimated to determine how the variables are correlated. Finally, spectral analysis is used to determine the periodic movements of interest rates and to test if there are significant correlations with the inflation rate and the money supply along these periodic movements. Empirical results suggest a positive response of nominal interest rates to changes in the money supply and the inflation rate. The estimated lags do not exceed one quarter in both cases. There is also a significant positive feedback from nominal interest rates to the money supply in both the short and long-run and a negative feedback from nominal interest rates to the money supply in the short-run. The statistical evidence suggests a very quick adjustment of bond markets to innovations in money and commodity markets. This evidence casts doubt on the Fisher approach which emphasizes the importance of past inflation rates in determination of current interest rates. The overall picture implies a response of interest rates to all kinds of information and not only to the information contained in the inflation rate series. This fact points out the highly efficient information processing character of the bond market. Multivariate analysis further confirms this point by showing that the variables are related to each other through the innovation series and unsystematic information is utilized in the assessment of nominal interest rates. In frequency domain, spectral analysis indicates a significant correlation between nominal interest rates and the inflation rate at the high frequency band. There is no significant correlation between the nominal interest rate and the inflation rate along the business cycles. There is, on the other hand, spectral evidence of a correlation between the money supply and interest rates along a nine-month cycle and minor business cycles. This last point suggests that the periodic movements of interest rates may be closely related to the stabilization policies pursued by the Federal Reserve

Ongoing temporal dynamics of broadband EEG during movement intention for BCI

Brain Computer Interface (BCI) empowers individuals with severe movement impairing conditions to interact with the computers directly by their thoughts, without the involvement of any motor pathways. Motor-based BCIs can offer intuitive control by merely intending to move. Hence, to develop effective motor-based non-invasive BCIs, it is essential to understand the mechanisms of neural processes involved in motor command generation in electroencephalography (EEG). The EEG consists of complex narrowband oscillatory and broadband arrhythmic processes. However, there is more focus on the oscillations in different frequency bands for studying motor command generation in the literature. The narrowband processes such as event-related (de)synchronisation (ERD/S) and movement-related cortical potential (MRCP) are commonly used for movement detection. Analysis of these narrowband EEG components disregards the information existing in the rest of the frequencies and their dynamics. Hence, this thesis investigates various facets of previously unexplored temporal dynamics of neuronal processes in the broadband arrhythmic EEG to fill the gap in the knowledge of motor command generation on a single trial basis in the BCI framework. The temporal dynamics of the broadband EEG were characterised by the decay of its autocorrelation. The autocorrelation decayed according to the power-law resulting in the longrange temporal correlations (LRTC). The instantaneous ongoing changes in the broadband LRTC were uniquely quantified by the Hurst exponent on very short EEG sliding windows. There was an increase in the temporal dependencies in the EEG leading to slower decay of autocorrelation during the movement and significant increase in the LRTC (p<0.05). Different types of temporal dependencies in the broadband EEG were comprehensively examined further by modelling the long and short-range correlations together using autoregressive fractionally integrated moving average model (ARFIMA). The short-range correlations also changed significantly (p<0.05) during the movement. These ongoing changes in the dynamics of the broadband EEG were able to predict the movement 1 s before its onset with accuracy higher than ERD and MRCP. The LRTCs were robust across participants and did not require determination of participant specific parameters such as most responsive spectral or spatial components

On the identification and parametric modelling of offshore dynamic systems

This thesis describes an investigation into the analysis methods arising from identification aspects of the theory of dynamic systems with application to full-scale offshore monitoring and marine environmental data including target spectra. Based on the input and output of the dynamic system, the System Identification (SI) techniques are used first to identify the model type and then to estimate the model parameters. This work also gives an understanding of how to obtain a meaningful matching between the target (power spectra or time series data sets) and SI models with minimal loss of information. The SI techniques, namely. Autoregressive (AR), Moving Average (MA) and Autoregressive Moving Average (ARMA) algorithms are formulated in the frequency domain and also in the time domain. The above models can only be economically applicable provided the model order is low in the sense that it is computationally efficient and the lower order model can most appropriately represent the offshore time series records or the target spectra. For this purpose, the orders of the above SI models are optimally selected by Least Squares Error, Akaike Information Criterion and Minimum Description Length methods. A novel model order reduction technique is established to obtain the reduced order ARMA model. At first estimations of higher order AR coefficients are determined using modified Yule-Walker equations and then the first and second order real modes and their energies are determined. Considering only the higher energy modes, the AR part of the reduced order ARMA model is obtained. The MA part of the reduced order ARMA model is determined based on partial fraction and recursive methods. This model order reduction technique can remove the spurious noise modes which are present in the time series data. Therefore, firstly using an initial optimal AR model and then a model order reduction technique, the time series data or target spectrum can be reduced to a few parameters which are the coefficients of the reduced order ARMA model. The above univariate SI models and model order reduction techniques are successfully applied for marine environmental and structural monitoring data, including ocean waves, semi-submersible heave motions, monohull crane vessel motions and theoretical (Pierson- Moskowitz and JONSWAP) spectra. Univariate SI models are developed based on the assumption that the offshore dynamic systems are stationary random processes. For nonstationary processes, such as, measurements of combined sea waves and swells, or coupled responses of offshore structures with short period and long period motions, the time series are modelled by the Autoregressive Integrated Moving Average algorithms. The multivariate autoregressive (MAR) algorithm is developed to reduce the time series wave data sets into MAR model parameters. The MAR algorithms are described by feedback weighting coefficients matrices and the driving noise vector. These are obtained based on the estimation of the partial correlation of the time series data sets. Here the appropriate model order is selected based on auto and cross correlations and multivariate Akaike information criterion methods. These algorithms are applied to estimate MAR power spectral density spectra and then phase and coherence spectra of two time series wave data sets collected at a North Sea location. The estimation of MAR power spectral densities are compared with spectral estimates computed from a two variable fast Fourier transform, which show good agreement

Reflex syncope : an integrative physiological approach

Síncope, a forma mais comum de perda temporária de consciência é responsável por até 5% das idas aos serviços de emergência e até 3% dos internamentos hospitalares. É um problema médico frequente, com múltiplos gatilhos, incapacitante, potencialmente perigoso e desafiante em termos diagnósticos e terapêuticos. Assim, é necessária uma anamnese detalhada para primeiro estabelecer a natureza da perda de consciência, mas, após o diagnóstico, as medidas terapêuticas existentes são pouco eficazes. Embora a fisiopatologia da síncope vasovagal ainda não tenha sido completamente esclarecida, alguns mecanismos subjacentes foram já desvendados. Em última análise, a síncope depende de uma falha transitória na perfusão cerebral pelo que qualquer factor que afecte a circulação sanguínea cerebral pode determinar a ocorrência de síncope. Assim, o objectivo do presente estudo é caracterizar o impacto hemodinâmico e autonómico nos mecanismos subjacentes à síncope reflexa, para melhorar o diagnóstico, o prognóstico e a qualidade de vida dos doentes e dos seus cuidadores. Para isso, desenhámos e implementámos novas ferramentas matemáticas e computacionais que permitem uma avaliação autonómica e hemodinâmica integrada, de forma a aprofundar a compreensão do seu envolvimento nos mecanismos de síncope reflexa. Além disso, refinando a precisão do diagnóstico, a sensibilidade e a especificidade do teste de mesa de inclinação (“tilt test”), estabelecemos uma ferramenta preditiva do episódio iminente de síncope. Isso permitiu-nos estabelecer alternativas de tratamento eficazes e personalizadas para os doentes refractários às opções convencionais, sob a forma de um programa de treino de ortostatismo (“tilt training”), contribuindo para o aumento da sua qualidade de vida e para a redução dos custos directos e indirectos da sua assistência médica. Assim, num estudo verdadeiramente multidisciplinar envolvendo doentes com síncope reflexa refractária à terapêutica, conseguimos demonstrar uma assincronia funcional das respostas reflexas autonómicas e hemodinâmicas, expressas por um desajuste temporal entre o débito cardíaco e as adaptações de resistência total periférica, uma resposta baroreflexa atrasada e um desequilíbrio incremental do tónus autonómico que, em conjunto, poderão resultar de uma disfunção do sistema nervoso autónomo que se traduz por uma reserva simpática diminuída. Igualmente, desenhámos, testámos e implementámos uma plataforma computacional e respectivo software associado - a plataforma FisioSinal –incluindo novas formas, mais dinâmicas, de avaliação integrada autonómica e hemodinâmica, que levaram ao desenvolvimento de algoritmos preditivos para a estratificação de doentes com síncope. Além disso, na aplicação dessas ferramentas, comprovámos a eficácia de um tratamento não invasivo, não disruptivo e integrado, focado na neuromodulação das variáveis autonómicas e cardiovasculares envolvidas nos mecanismos de síncope. Esta terapêutica complementar levou a um aumento substancial da qualidade de vida dos doentes e à abolição dos eventos sincopais na grande maioria dos doentes envolvidos. Em conclusão, o nosso trabalho contribuiu para preencher a lacuna entre a melhor informação científica disponível e sua aplicação na prática clínica, sustentando-se nos três pilares da medicina translacional: investigação básica, clínica e comunidade.Syncope, the most common form of transient loss of consciousness, accounts for up to 5% of emergency room visits and up to 3% of hospital admissions. It is a frequent medical problem with multiple triggers, potentially dangerous, incapacitating, and challenging to diagnose. Therefore, a detailed clinical history is needed first to establish the nature of the loss of consciousness. However, after diagnosis, the therapeutic measures available are still very poor. Although the exact pathophysiology of vasovagal syncope remains to be clarified, some underlying mechanisms have been unveiled, dependent not only on the cause of syncope but also on age and various other factors that affect clinical presentation. Ultimately, syncope depends on a failure of the circulation to perfuse the brain, so any factor affecting blood circulation may determine syncope occurrence. Thus, the purpose of the present study is to understand the impact of the hemodynamic and autonomic functions on reflex syncope mechanisms to improve patients diagnose, prognosis and general quality of life. Bearing that in mind, we designed and implemented new mathematical and computational tools for autonomic and hemodynamic evaluation, in order to deepen the understanding of their involvement in reflex syncope mechanisms. Furthermore, by refining the diagnostic accuracy, sensitivity and specificity of the head-up tilt-table test, we established a predictive tool for the impending syncopal episode. This allowed us to establish effective and personalised treatment alternatives to patient’s refractory to conventional options, contributing to their increase in the quality of life and a reduction of health care and associated costs. In accordance, in a truly multidisciplinary study involving reflex syncope patients, we were able to show an elemental functional asynchrony of hemodynamic and autonomic reflex responses, expressed through a temporal mismatch between cardiac output and total peripheral resistance adaptations, a deferred baroreflex response and an unbalanced, but incremental, autonomic tone, all contributing to autonomic dysfunction, translated into a decreased sympathetic reserve. Through the design, testing and implementation of a computational platform and the associated software - FisioSinal platform -, we developed novel and dynamic ways of autonomic and hemodynamic evaluation, whose data lead to the development of predictive algorithms for syncope patients’risk stratification. Furthermore, through the application of these tools, we showed the effectiveness of a non-invasive, non-disruptive and integrated treatment, focusing on neuromodulation of the autonomic and cardiovascular variables involved in the syncope mechanisms, leading to a substantial increase of quality of life and the abolishment of syncopal events in a vast majority of the enrolled patients. In conclusion, our work contributed to fill the gap between the best available scientific information and its application in the clinical practice by tackling the three pillars of translational medicine: bench-side, bedside and community

Do abnormalities in dynamic cerebral auto-regulation underlie the pathophysiological processes behind syncope in older people?

Do abnormalities in dynamic cerebral auto-regulation underlie the pathophysiological processes behind syncope in older people? Introduction: The aim of this thesis was to investigate whether abnormalities in dynamic cerebral auto-regulation (dCA) explain the symptoms associated with orthostatic (OH) and post-prandial hypotension (PPH). Methods: Based on clinical symptoms and signs for the OH study: 4 Groups: Asymptomatic No OH (control), Symptomatic No OH, Asymptomatic OH, and Symptomatic OH. PPH study: double-blind placebo controlled cross-over study of glucose (50g) drink. 2 Groups: No PPH (control) and PPH. Baseline and head-up-tilt (HUT, for OH maximum 30 minutes study or to symptoms; PPH study maximum 60 minutes per visit). All had Transcranial Doppler ultrasound, beat-to-beat BP, ECG and CO2 monitoring. Baseline autonomic function, arterial stiffness, cardiac baroreceptor sensitivity (BRS) were calculated and dynamic cerebral auto-regulation (as the autoregulatory index ARI) assessed before and during tilt. Results: OH: n=85, mean age 73.9±7.1 years; PPH: n= 40, mean age 73.4±7.3 years Baseline: No significant differences were found between groups for cardiac BRS, arterial stiffness, cerebral blood flow velocity (CBFV) or dCA in either study. HUT both studies: falls in BP, CO2 and CBFV, increases in HR, and fall in ARI amongst symptomatic subjects prior to the end of HUT (maximum duration or symptom onset) compared to pre-HUT values. PPH study: fall in ARI with HUT irrespective of whether glucose or placebo phase. Conclusions: The development of symptoms during tilt in both studies was related to a fall in CBFV and impaired cerebral auto-regulation. Abnormalities in cerebral autoregulation may explain the symptoms of OH and PPH although these changes can only be detected during head-up-tilt