This thesis investigates the underlying causes of friction and ine ciency within an internal combustion engine, focusing on the ring-liner conjunction in the vicinity of the power-stroke top dead centre reversal. In such lubricated contacts, friction is the result of the interplay between numerous kinetics, with those at micro- and nano-scale interactions being signi cantly di erent than the ones at larger scales. A modi ed Elrod's cavitation algorithm is developed to determine the microscopic tribological characteristics of the piston ring-liner contact. Predicting lubricant tran- sient behaviour is critical when the inlet reversal leads to thin lms and inherent metal-to-metal interaction. The model clearly shows that cavitation at the trailing edge of the ring-liner contact generated pre-reversal, persists after reversal and pro- motes starvation and depletion of the oil lm. Hence, this will lead to boundary friction. A fractal based boundary friction model is developed for lightly loaded asperity con- tacts, separated by diminishing small lms, usually wetted by a layer of molecules adsorbed to the tips of the asperities. In nano-scale conjunctions, a lubricant layering e ect often takes place due to the smoothness of surfaces, which is governed by the surface and lubricant properties. A molecularly thin layer of lubricant molecules can adhere to the asperities, being the last barrier against direct surface contact. As a result, boundary friction (prevailing in such diminishing gaps) is actually determined by a combination of shearing of a thin adsorbed lm, adhesion of approaching as- perities and their plastic deformation. A model for physio-chemical hydrodynamic mechanism is successfully established, describing the formation of thin adsorbed lms between asperities. This model is e ectively integrated with separately devel- oped models that predict the adhesive and plastic contact of asperities.

The use of grading scales is common in clinical practice and research settings. A number of grading scales are available to the practitioner, however, despite their frequent use, they are only poorly understood and may be criticised for a number of things such as the variability of the assessments or the inequality of scale steps within or between scales. Hence, the global aim of this thesis was to study the McMonnies/Chapman-Davies (MC-D), Institute for Eye Research (IER), Efron, and validated bulbar redness (VBR) grading scales in order to (1) get a better understanding and (2) attempt a cross-calibration of the scales. After verifying the accuracy and precision of the objective and subjective techniques to be used (chapter 3), a series of experiments was conducted. The specific aims of this thesis were as follows: • Chapter 4: To use physical attributes of redness to determine the accuracy of the four bulbar redness grading scales. • Chapter 5: To use psychophysical scaling to estimate the perceived redness of the four bulbar redness grading scales. • Chapter 6: To investigate the effect of using reference anchors when scaling the grading scale images, and to convert grades between scales. • Chapter 7: To grade bulbar redness using cross-calibrated versions of the MC-D, IER, Efron, and VBR grading scales. Methods: • Chapter 4: Two image processing metrics, fractal dimension (D) and % pixel coverage (% PC), as well as photometric chromaticity (u’) were selected as physical measures to describe and compare redness in the four bulbar redness grading scales. Pearson correlation coefficients were calculated between each set of image metrics and the reference image grades to determine the accuracy of the scales. • Chapter 5: Ten naïve observers were asked to arrange printed copies of modified versions of the reference images (showing vascular detail only) across a distance of 1.5m for which only start and end point were indicated by 0 and 100, respectively (non-anchored scaling). After completion of scaling, the position of each image was hypothesised to reflect its perceived bulbar redness. The averaged perceived redness (across observers) for each image was used for comparison to the physical attributes of redness as determined in chapter 4. • Chapter 6: The experimental setup from chapter 5 was modified by providing the reference images of the VBR scale as additional, unlabelled anchors for psychophysical scaling (anchored scaling). Averaged perceived redness from anchored scaling was compared to non-anchored scaling, and perceived redness from anchored scaling was used to cross-calibrate grades between scales. • Chapter 7: The modified reference images of each grading scale were positioned within the 0 to 100 range according to their averaged perceived redness from anchored scaling, one scale at a time. The same 10 observers who had participated in the scaling experiments were asked to represent perceived bulbar redness of 16 sample images by placing them, one at a time, relative to the reference images of each scale. Perceived redness was taken as the measured position of the placed image from 0 and was averaged across observers. Results: • Chapter 4: Correlations were high between reference image grades and all sets of objective metrics (all Pearson’s r’s≥0.88, p≤0.05); each physical attribute pointed to a different scale as being most accurate. Independent of the physical attribute used, there were wide discrepancies between scale grades, with sometimes little overlap of equivalent levels when comparing the scales. • Chapter 5: The perceived redness of the reference images within each scale was ordered as expected, but not all consecutive within-scale levels were rated as having different redness. Perceived redness of the reference images varied between scales, with different ranges of severity being covered by the images. The perceived redness was strongly associated with the physical attributes of the reference images. • Chapter 6: There were differences in perceived redness range and when comparing reference levels between scales. Anchored scaling resulted in an apparent shift to lower perceived redness for all but one reference image compared to non-anchored scaling, with the rank order of the 20 images for both procedures remaining fairly constant (Spearman’s ρ=0.99). • Chapter 7: Overall, perceived redness depended on the sample image and the reference scale used (RM ANOVA; p=0.0008); 6 of the 16 images had a perceived redness that was significantly different between at least two of the scales. Between-scale correlation coefficients of concordance (CCC) ranged from 0.93 (IER vs. Efron) to 0.98 (VBR vs. Efron). Between-scale coefficients of repeatability (COR) ranged from 5 units (IER vs. VBR) to 8 units (IER vs. Efron) for the 0 to 100 range. Conclusions: • Chapter 4: Despite the generally strong linear associations between the physical characteristics of reference images in each scale, the scales themselves are not inherently accurate and are too different to allow for cross-calibration based on physical redness attributes. • Chapter 5: Subjective estimates of redness are based on a combination of chromaticity and vessel-based components. Psychophysical scaling of perceived redness lends itself to being used to cross calibrate the four clinical scales. • Chapter 6: The re-scaling of the reference images with anchored scaling suggests that redness was assessed based on within-scale characteristics and not using absolute redness scores, a mechanism that may be referred to as clinical scale constancy. The perceived redness data allow practitioners to modify the grades of the scale they commonly use so that comparisons of grading estimates between calibrated scales may be made. • Chapter 7: The use of the newly calibrated reference grades showed close agreement between grading estimates of all scales. The between-scale variability was similar to the variability typically observed when a single scale is repeatedly used. Perceived redness appears to be dependent upon the dynamic range of the reference images of the scale. In conclusion, this research showed that there are physical and perceptual differences between the reference images of all scales. A cross-calibration of the scales based on the perceived redness of the reference images provides practitioners with an opportunity to compare grades across scales, which is of particular value in research settings or if the same patient is seen by multiple practitioners who are familiar with using different scales.

The use of grading scales is common in clinical practice and research settings. A number of grading scales are available to the practitioner, however, despite their frequent use, they are only poorly understood and may be criticised for a number of things such as the variability of the assessments or the inequality of scale steps within or between scales. Hence, the global aim of this thesis was to study the McMonnies/Chapman-Davies (MC-D), Institute for Eye Research (IER), Efron, and validated bulbar redness (VBR) grading scales in order to (1) get a better understanding and (2) attempt a cross-calibration of the scales. After verifying the accuracy and precision of the objective and subjective techniques to be used (chapter 3), a series of experiments was conducted. The specific aims of this thesis were as follows: • Chapter 4: To use physical attributes of redness to determine the accuracy of the four bulbar redness grading scales. • Chapter 5: To use psychophysical scaling to estimate the perceived redness of the four bulbar redness grading scales. • Chapter 6: To investigate the effect of using reference anchors when scaling the grading scale images, and to convert grades between scales. • Chapter 7: To grade bulbar redness using cross-calibrated versions of the MC-D, IER, Efron, and VBR grading scales. Methods: • Chapter 4: Two image processing metrics, fractal dimension (D) and % pixel coverage (% PC), as well as photometric chromaticity (u’) were selected as physical measures to describe and compare redness in the four bulbar redness grading scales. Pearson correlation coefficients were calculated between each set of image metrics and the reference image grades to determine the accuracy of the scales. • Chapter 5: Ten naïve observers were asked to arrange printed copies of modified versions of the reference images (showing vascular detail only) across a distance of 1.5m for which only start and end point were indicated by 0 and 100, respectively (non-anchored scaling). After completion of scaling, the position of each image was hypothesised to reflect its perceived bulbar redness. The averaged perceived redness (across observers) for each image was used for comparison to the physical attributes of redness as determined in chapter 4. • Chapter 6: The experimental setup from chapter 5 was modified by providing the reference images of the VBR scale as additional, unlabelled anchors for psychophysical scaling (anchored scaling). Averaged perceived redness from anchored scaling was compared to non-anchored scaling, and perceived redness from anchored scaling was used to cross-calibrate grades between scales. • Chapter 7: The modified reference images of each grading scale were positioned within the 0 to 100 range according to their averaged perceived redness from anchored scaling, one scale at a time. The same 10 observers who had participated in the scaling experiments were asked to represent perceived bulbar redness of 16 sample images by placing them, one at a time, relative to the reference images of each scale. Perceived redness was taken as the measured position of the placed image from 0 and was averaged across observers. Results: • Chapter 4: Correlations were high between reference image grades and all sets of objective metrics (all Pearson’s r’s≥0.88, p≤0.05); each physical attribute pointed to a different scale as being most accurate. Independent of the physical attribute used, there were wide discrepancies between scale grades, with sometimes little overlap of equivalent levels when comparing the scales. • Chapter 5: The perceived redness of the reference images within each scale was ordered as expected, but not all consecutive within-scale levels were rated as having different redness. Perceived redness of the reference images varied between scales, with different ranges of severity being covered by the images. The perceived redness was strongly associated with the physical attributes of the reference images. • Chapter 6: There were differences in perceived redness range and when comparing reference levels between scales. Anchored scaling resulted in an apparent shift to lower perceived redness for all but one reference image compared to non-anchored scaling, with the rank order of the 20 images for both procedures remaining fairly constant (Spearman’s ρ=0.99). • Chapter 7: Overall, perceived redness depended on the sample image and the reference scale used (RM ANOVA; p=0.0008); 6 of the 16 images had a perceived redness that was significantly different between at least two of the scales. Between-scale correlation coefficients of concordance (CCC) ranged from 0.93 (IER vs. Efron) to 0.98 (VBR vs. Efron). Between-scale coefficients of repeatability (COR) ranged from 5 units (IER vs. VBR) to 8 units (IER vs. Efron) for the 0 to 100 range. Conclusions: • Chapter 4: Despite the generally strong linear associations between the physical characteristics of reference images in each scale, the scales themselves are not inherently accurate and are too different to allow for cross-calibration based on physical redness attributes. • Chapter 5: Subjective estimates of redness are based on a combination of chromaticity and vessel-based components. Psychophysical scaling of perceived redness lends itself to being used to cross calibrate the four clinical scales. • Chapter 6: The re-scaling of the reference images with anchored scaling suggests that redness was assessed based on within-scale characteristics and not using absolute redness scores, a mechanism that may be referred to as clinical scale constancy. The perceived redness data allow practitioners to modify the grades of the scale they commonly use so that comparisons of grading estimates between calibrated scales may be made. • Chapter 7: The use of the newly calibrated reference grades showed close agreement between grading estimates of all scales. The between-scale variability was similar to the variability typically observed when a single scale is repeatedly used. Perceived redness appears to be dependent upon the dynamic range of the reference images of the scale. In conclusion, this research showed that there are physical and perceptual differences between the reference images of all scales. A cross-calibration of the scales based on the perceived redness of the reference images provides practitioners with an opportunity to compare grades across scales, which is of particular value in research settings or if the same patient is seen by multiple practitioners who are familiar with using different scales.

Humans are experts at understanding what they see. Similarity and analogy play a significant role in making sense of the visual world by forming analogies to similar images encountered previously. Yet, while these acts of visual reasoning may be commonplace, the processes of visual analogy are not yet well understood. In this dissertation, I investigate the utility of representing visual information in a fractal manner for computing visual similarity and analogy. In particular, I develop a computational technique of fractal reasoning for addressing problems of visual similarity and novelty. I illustrate the effectiveness of fractal reasoning on problems of visual similarity and analogy on the Raven’s Progressive Matrices and Miller’s Analogies tests of intelligence, problems of visual novelty and oddity on the Odd One Out test of intelligence, and problems of visual similarity and oddity on the Dehaene test of core geometric reasoning. I show that the performance of my computational model on these various tests is comparable to human performance. Fractal reasoning provides a new method for computing answers to such problems. Specifically, I show that the choice of the level of abstraction of problem representation determines the degree to which an answer may be regarded as confident, and that that choice of abstraction may be controlled automatically by the algorithm as a means of seeking that confident answer. This emergence of ambiguity and its remedy via problem re-representation is afforded by the fractal representation. I also show how reasoning over sparse data (at coarse levels of abstraction) or homogeneous data (at finest levels of abstraction) could both drive the automatic exclusion of certain levels of abstraction, as well as provide a signal to shift the analogical reasoning from consideration of simple analogies (such as analogies between pairs of objects) to more complex analogies (such as analogies among triplets, or larger groups of objects). My dissertation also explores fractal reasoning in perception, including both biologically-inspired imprinting and bistable perception. In particular, it provides a computational explanation of bistable perception in the famous Necker cube problem that is directly tied to the process of determining a confident interpretation via re-representation. Thus, my research makes two primary contributions to AI theories of visual similarity and analogy. The first contribution is the Extended Analogy By Recall (ABR*) algorithm, the computational technique for visual reasoning that automatically adjusts fractal representations to an appropriate level of abstraction. The second contribution is the fractal representation itself, a knowledge representation that add the notion of self-similarity and re-representation to analogy making.

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京都大学 / 新制・課程博士 / 博士(医学) / 甲第23077号 / 医博第4704号 / 新制||医||1049(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 中本 裕士, 教授 溝脇 尚志, 教授 羽賀 博典 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

Assessment of diffuse brain disorders, where the brain may appear normal, has proven difficult to translate into personalized treatments. Previous methods based on brain magnetic resonance imaging (MRI) resting state blood oxygen level dependent (rs-BOLD) signal routinely rely on group analysis where large data sets are assessed using region-of interest (ROI) or probabilistic independent component analysis (PICA) to identify temporal synchrony or desynchrony among regions of the brain. Brain connectivity occurs in a complex, multilevel and multi-temporal manner, driving the fluctuations observed in local oxygen demand. These fluctuations have previously been characterized as fractal, as they auto-correlate at different time scales. In this study we propose a model-free complexity analysis based on the fractal dimension of the rs-BOLD signal, acquired with MRI. The fractal dimension can be interpreted as a measure of signal complexity and connectivity. Previous studies have suggested that reduction in signal complexity can be associated with disease. Therefore, we hypothesized that a detectable differences in rs-BOLD signal complexity could be observed between patients with diffuse or heterogeneous brain disorders and healthy controls. In this study, we obtained anatomical and functional data from patients with brain disorders where traditional methods have been insufficient to fully assess the condition. More specifically, we tested our method on mild traumatic brain injury, autism spectrum disorder, chemotherapy-induced cognitive impairment and chronic fatigue syndrome patients. Three major databases from the Neuroimaging Informatics Tools and Resources Clearinghouse (NITRC) project were used to acquire large numbers of age matched healthy controls. Healthy control data was downloaded from the the Autism Brain Imaging Data Exchange (ABIDE), the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Human Connectome Project specifically matching our experimental design. In all of our studies, the voxel-wise rs-BOLD signal fractal dimension was calculated following a procedure described by Eke and Herman et al. 2000. This method was previously used to assess brain rs-BOLD signal in small mammals and humans. The method consists of estimating the Hurst exponent in the frequency domain using a power spectral density approach and refining the estimation in the time domain with de-trended fluctuation analysis and signal summation conversion methods. Voxel-wise fractal dimension (FD) was then calculated for every subject in the control and patient groups to create ROI-based Z-scores for each individual patient. Voxel-wise validation of FD normality across controls was studied and non-Gaussian voxels, determined using kurtosis and skewness calculations, were eliminated from subsequent analysis. To maintain a 95 % confidence level, only regions where Z-score values were at least 2 standard deviations away from the mean were included in the analysis. In the case of chronic fatigue patients and chemotherapy induced cognitive impairment, DTI analysis was added to also determine whether white matter abnormalities were also relevent. Similar Z-score analysis on DTI metrics was also performed. Brain microscopic networks, modeled as complex systems, become affected in diffuse brain disorders. Z-scoring of the fractal rs-BOLD frequency domain delineated patient-specific regional brain anomalies which correlated with patient-specific symptoms. This technique can be used alone, or in combination with DTI Z-scoring, to characterize a single patient without any need for group analysis, making it ideal for personalized diagnostics. / Thesis / Doctor of Philosophy (PhD)

Physiological signals, electroencephalogram (EEG) and heart rate variability (HRV), are generated by complex self-regulating systems. These signals are extremely inhomogeneous and nonstationary, and fluctuate in an irregular and highly complex manner. These fluctuations are due to underlying dynamics of the system. The synchronous neural activity measured as scalp EEG indicates underlying neural dynamics of the brain. Hence, quantitative EEG analysis has become a very useful tool in interpreting results from physiological experiments. The analysis of HRV provides valuable information to assess the autonomous nervous system (ANS). The HRV can be significantly affected by physiological state changes and many disease states. Hence, HRV analysis is becoming a major experimental and diagnostic tool. In this thesis, we focus on the study of EEG and HRV time series using tools from nonlinear time series analysis with special emphasis on its implications in detecting physiological state changes such as, in diseases like epileptic seizure and schizophrenia, and in altered states of consciousness as in sleep and meditation. The proposed nonlinear techniques are used in discriminating different physiological states from control states. Artifact processing of EEG signal Interferences (artifacts) from various sources unavoidably contaminate EEG recordings. In quantitative analysis, results can differ significantly by these artifacts, which may lead to wrong interpretation of the results. In this part of the thesis, we have devised methods to minimize ocular and muscle artifacts in EEG. The artifact correction methods are based on blind source separation (BSS) techniques such as singular value decomposition (SVD), algorithm for multiple signal extraction (AMUSE), canonical correlation analysis (CCA), information maximization (INFOMAX) independent component analysis (ICA) and joint approximate diagonalization of eigen-matrices (JADE) ICA. We have proposed a method to simulate clean and artifact corrupted EEG data based on the BSS methods. In order to enhance the performance of BSS methods, a technique called wavelet-filtered component inclusion method has been introduced. In addition, second-order statistics (SOS) and higher-order statistics (HOS) based BSS methods have been studied considering less number of EEG channels; and performance comparison of these methods has also been made. We have also addressed the problem of simultaneous correction of ocular and muscle artifacts in EEG recordings using the BSS methods. Irrespective of the BSS methods, the component elimination method has introduced high spectral error in all the bands after reconstruction of clean EEG. However, the wavelet filtered component inclusion method has retained almost all spectral powers of EEG channels in theta, alpha, and beta bands after ocular artifact minimization. When the number of EEG channels is very less, the enhanced CCA (SOS BSS) has given superior artifact minimization results than HOS BSS methods, especially in delta band. The component elimination method is used in muscle artifact minimization, and hence the SVD method cannot be used for this purpose since it leads to large spectral distortion of reconstructed EEG. The AMUSE and CCA methods have given comparable performance in muscle artifact minimization. In addition, the JADE method has introduced less mean spectral error compared to other methods. The CCA method has shown superior performance in simultaneous minimization of ocular and muscle artifacts, and AMUSE and JADE methods have given comparable results. Furthermore, the less computation time of wavelet enhanced SOS BSS methods make them very useful in real clinical environments. Fractal characterization of time series In biomedical signal analysis, fractal dimension (FD) is used as a quantitative measure to estimate complexity of physiological signals. Such analysis helps to study physiological processes of underlying systems. The FD can also be used to study dynamics of transitions between different states of systems like brain and ANS, in various physiological and pathological states. In this part, we have proposed a method to estimate FD of time series, called multiresolution box-counting (MRBC) method. A modification of this method resulted in multiresolution length (MRL) method. The estimation performance of the proposed methods is compared with that of Katz, Sevcik, and Higuchi methods, by simulating mathematically defined fractal signals, and also the computation time is compared between the methods. The MRBC and MRL methods have given comparable performance to that of Higuchi method, in estimating FD of waveforms, with the advantage of less computational time. In addition, various properties of the FD are studied and discussed in connection with classical signal processing concepts such as amplitude, frequency, sampling frequency, effect of noise, band width, correlation, etc. The FD value of signals has increased with number of harmonics, noise variance, band-width, and mid-band frequency, and decreased with degree of correlation in AR signal. An analogy between Katz FD and smoothed Teager energy operator has also been made. Application of fractal analysis to EEG and HRV time series The fluctuation of EEG potentials normally depends upon degree of alertness, and varies in amplitude and frequency. Hence, the EEG is an important clinical tool for studying sleep and sleep related disorders, epileptic seizures, schizophrenia, and meditation. In this part of the thesis, we have used FD which gives signal complexity, and detrended fluctuation analysis (DFA) which gives multiscale exponent of time series to quantify EEG. We have extended the concept of FD to multiscale FD to compute complexity of time series at multiple scales. The main applications of the proposed method are epileptic seizure detection, sleep stage detection, schizophrenia EEG analysis, and analysis of heart rate variability during meditation. For seizure detection, we have used intracranial EEG recordings with seizure-free and seizure intervals. In sleep EEG analysis, whole-night sleep EEG is used and results are compared with the manually scored hypnogram. The schizophrenia symptom is further categorized into positive and negative symptoms and complexity is estimated using FD and DFA. We have also analyzed HRV data of Chi and Kundalini meditation using FD and DFA techniques. In all the applications considered, we have tested for statistical significance of the computed parameters, between the case of interest and corresponding control cases, to discriminate between the physiological states. The ocular artifact has reduced FD while muscle artifact increased FD of EEG. The FD of seizure EEG has shown high value compared to that of seizure-free EEG. In addition, the seizure-free EEG has more DFA exponent-1 than seizure EEG. The value of FD of EEG is decreased with deepening of sleep, wake state having high FD value. The FD of REM state sleep EEG showed value between that of wake and state-1. The DFA exponent-1 has increased with deepening of sleep state, having small value for wake state. The REM state has given exponent-1 value between wake and state-1. The schizophrenia subjects have shown lower FD value than healthy controls in all the EEG channels except the bilateral temporal and occipital regions. The positive symptom sub-group has shown comparatively high FD values than healthy controls as well as overall schizophrenia sample in the bilateral tempero-parietal-occipital region. In addition, the positive symptom sub-group has shown significantly higher regional FD values than negative symptom sub-group especially in right temporal region. The overall schizophrenia samples as well as the positive and negative subgroup have shown least FD values in the bilateral frontal region. The values of DFA exponent-2 have shown significant high value in schizophrenia samples. In addition, the schizophrenia group has shown less DFA exponent-1 in bilateral temporal region than healthy control. The FD, multiscale FD, DFA exponents have shown significant performance in discriminating different physiological states from control states. The FD value of HRV time series during meditation is less compared to pre-meditation state in both Chi and Kundalini meditation. Irrespective of the type of meditation, meditation state has shown significantly high DFA exponent-1 than pre-meditation state, and significantly high DFA exponent-2 in pre-meditation state compared to meditation state. Functional connectivity analysis of brain during meditation In functionally related regions of the brain, even in those regions separated by substantial distances, the EEG fluctuations are synchronous, which is termed as functional connectivity. In this part, a novel application of functional connectivity analysis of brain using graph theoretic approach has been made on the EEG recorded from meditation practitioners. We have used 16 channel EEG data from subjects while performing Raja Yoga meditation. The pre-meditation condition is used as control state, against which meditation state is compared. For finding connectivity between EEG of various channels, we have computed pair-wise linear correlation and mutual information between the EEG channels, to form a connection matrix of size 16x16. Then, various graph parameters, such as average connection density, degree of nodes, characteristic path length, and cluster index, are computed from the connection matrix. The computed parameters are projected on to the scalp to get topographic head maps that give spatial variation of the parameter, and results are compared between meditation and pre-meditation states. The meditation state has shown low average connection density, less characteristic path length, and high average degree in fronto-central and central regions. Furthermore, high cluster index is shown in frontal and central regions than pre-meditation state. The parameters such as complexity, characteristic path length and average connection density are used as features in quadratic discriminant classifier to classify meditation and pre-meditation state, and have given good accuracy performance. Connectivity analysis using mutual information has given high average connection density in meditation state in theta, alpha and beta bands compared to pre-meditation state. The characteristic path length is high in delta, alpha and beta bands in meditation state. In addition, the meditation state has shown high degree and cluster index in theta and beta bands compared to pre-meditation state. Nonlinear dynamical characterization of HRV during meditation The cardiovascular system is influenced by internal dynamics as well as from various external factors, which makes the system more dynamic and nonlinear. In this part of the thesis, a novel application of using HRV data for studying Chi and Kundalini meditation has been made. The HRV time series are embedded into higher dimensional phase-space using Takens’ embedding theorem to reconstruct the attractor. After estimating the minimum embedding dimension to unfold the attractor dynamics, the complexity of the attractor is computed using correlation dimension, Lyapunov exponent, and nonlinearity scores. In all the analyses, the pre-meditation state is used as control state against which meditation state is compared. The statistical significance of the parameters estimated is tested to discriminate meditation state from control state. The HRV time series of both pre-meditation and meditation have shown similar minimum embedding dimensions in both Chi and Kundalini meditation. Irrespective of the type of meditation, the meditation state has shown high correlation dimension, largest Lyapunov exponent, and low nonlinearity score compared to pre-meditation state. Recurrent quantification analysis of HRV during meditation In this part, a novel application of recurrent quantification analysis (RQA) to HRV during meditation is studied. Here, the time series is embedded into a higher dimensional phase-space and Euclidean distance between the embedded vectors is calculated to form a distance matrix. The matrix is converted into binary matrix by applying a suitable threshold, and plotted as image to get recurrence plot. Various parameters are extracted from the recurrence plot such as percent recurrence rate, diagonal parameters (determinism, divergence, entropy, ratio), and vertical or horizontal parameters (laminarity, trapping time, maximal vertical line length). The procedure is applied to HRV data during meditation and pre-meditation (control) to discriminate between the states. The HRV of meditation state has shown more diagonal line structure whereas more black patches are observed in pre-meditation state. In addition, at low embedding dimensions, the meditation state has shown low recurrence rate, high determinism, low divergence, low entropy, high ratio, high laminarity, high trapping time, and less maximal vertical line length compared to pre-meditation state. These RQA parameters have shown superior performance in discriminating meditation state from control state.