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PubMed2002

Multiscale nonlinearity in a time series of weekly alcohol intake.

Several authors have discussed the possibility that nonlinear dynamics might clarify substance abuse and chemical dependence. Nonlinear dynamical structure implies the possibility of oscillatory dynamics and high sensitivity to external perturbation. In this single-subject case study we analyzed the alcohol intake of a substance-abusing participant over a period of about five years using nonlinear time series analysis. The intake is measured in ounces per week and ounces per four weeks--approximately one month--yielding time series at two different time scales. We present statistical evidence that the participant's alcohol intake is nonlinear on both weekly and monthly time scales. We then discuss the implications of this multiscale nonlinearity for our understanding of substance abuse.

Alcohol Drinking↗

PubMed1997

Mapping of retinal function in diabetic retinopathy using the multifocal electroretinogram.

PURPOSE: To investigate focal abnormalities in the electroretinogram (ERG) signal in diabetic patients, with and without retinopathy, using a multifocal ERG. METHODS: Sixteen patients with diabetes mellitus, 8 of whom had diabetic retinopathy (mean duration of diabetes: 18.5 years) and 19 approximately age-matched healthy volunteers underwent multifocal ERG testing. One hundred three retinal locations within the central 50 degrees were stimulated concurrently, according to a pseudorandom m-sequence. Response components were extracted for each stimulated retinal location. RESULTS: In diabetic patients with retinopathy, the overall amplitudes were reduced (P < 0.01), and peak implicit times were increased (P < 0.01) in the first-order component (mean flash response) and in the first slice of the second-order component (local two flash interaction). In addition, local reductions of amplitude could be seen in the first- and second-order components. In patients without retinopathy, only amplitudes of the second-order component were reduced (P < 0.01). Another salient difference was observed in a special feature of the second-order component that was reduced in diabetic patients, with and without retinopathy (P < 0.05). CONCLUSIONS: Second-order components depend on nonlinear dynamics. Thus our findings indicate changes in the nonlinear dynamics of a fast-gain control in diabetic patients, presumably located in the inner retina. This suggests that early functional changes of the inner retina are evident in diabetic patients before impairment of the outer retina is observed. Multifocal nonlinear analysis permits the detection of subclinical diabetic retinopathy and offers the advantage of topographic mapping of retinal dysfunction.

Adult↗

PubMed2005

Nonlinear lattice dynamics of Bose-Einstein condensates.

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop "experimental" techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems-including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECs, in particular, due to their widely ranging and easily manipulated dynamical apparatuses-with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials-provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.

Algorithms↗

PubMed2000

Variation of recruitment nonlinearity and dynamic response of ankle plantarflexors.

The ankle plantarflexor muscles of paraplegics may be trained to provide balance without support from the hands (in the laboratory environment) with the controller based on a two-block Hammerstein muscle model. This paper presents data on the variations of the recruitment curve block and linear dynamics block with electrode position, among various individuals and with fatigue. The tests were conducted in six groups: 'a' tests of a neurologically-intact subject were repeated on one day several times to record the effect of muscle fatigue; 'b' the same individual kept electrodes attached for a week and the muscle was identified every day; 'c' the same subject attached electrodes at marked positions every day for a week prior to identification; 'd' another normal attached electrodes at notionally the same positions over a period of one week; 'e' three normals and 'f' two paraplegics. Measurements were made with the Wobbler apparatus, in which the subject is supported upright in a standing posture. When comparing tests of fresh muscle every day, little difference was found between the nonlinear recruitment curves and linear dynamics of groups 'b' and 'c'. In fatigued muscle the dynamics were slower. When the electrode position was not carefully reproduced, and over a longer period, significant differences in nonlinearity appear in the curve shapes (group 'd') and a similar amount of variation occurs between normals, between paraplegics, and from normals to paraplegics. The paraplegic curves show wider deadbands. The effect of prolonged stimulation on normals is slight but on paraplegics it is significant.

Adult↗

PubMed1995

Monitoring changes in time of chaotic nonlinear systems.

We extend our method for classifying signals from chaotic nonlinear dynamical systems to the problem of monitoring chaotic nonlinear dynamical systems with the goal of detecting that the state of a system has changed. One potential application would be to systems where the changes are not easily detectable by spectral analysis or other linear techniques. The method is expected to be most useful in comparison to other techniques when there are other signals or noise present, some of which have a broad band frequency spectrum, and the signal of interest is associated with either a low dimensional dynamical system or a low dimensional chaotic attractor. The method is applied to data from a laboratory model of a fluidized bed reactor and to data from a gyroscope as well as to numerically generated signals from mathematical models. For the dynamical systems considered in the paper, the proposed method provides significantly better discrimination than spectral analysis. (c) 1995 American Institute of Physics.

Journal Article↗

PubMed1998

The topography of non-linear cortical dynamics at rest, in mental calculation and moving shape perception.

Differential cortical activation by cognitive processing was studied using dimensional complexity, a measure derived from nonlinear dynamics that indicates the degrees of freedom (complexity) of a dynamic system. We examined the EEG of 32 healthy subjects at rest, during a visually presented calculation task, and during a moving shape perception task. As a nonlinear measure of connectivity, the mutual dimension of selected electrode pairs was used. The first Lyapunov coefficient was also calculated. Data were tested for non-linearity using a surrogate data method and compared to spectral EEG measures (power, coherence). Surrogate data testing confirmed the presence of nonlinear structure in the data. Cognitive activation led to a highly significant rise in dimensional complexity. While both tasks activated central, parietal and temporal areas, mental arithmetic showed frontal activation and an activity maximum at T3, while the moving shape task led to occipital activation and a right parietal activity maximum. Analysis of mutual dimension showed activation of a bilateral temporal-right frontal network in calculation. The Lyapunov coefficient showed clear topographic variation, but was not significantly changed by mental tasks (p<.09). While dimensional complexity was almost unrelated to power values, nonlinear (mutual dimension) and linear (coherence) measures of connectivity shared up to 37% of variance. Data are interpreted in terms of increased cortical complexity as a result of recruitment of asynchronously active, distributed neuronal assemblies in cognition. The topography of nonlinear dynamics are related to neuropsychological and neuroimaging findings on mental calculation and moving shape perception.

Adult↗

PubMed2005

Passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems.

The potential clinical applications of adaptive neural network control for pharmacology in general, and anesthesia and critical care unit medicine in particular, are clearly apparent. Specifically, monitoring and controlling the depth of anesthesia in surgery is of particular importance. Nonnegative and compartmental models provide a broad framework for biological and physiological systems, including clinical pharmacology, and are well suited for developing models for closed-loop control of drug administration. In this paper, we develop a neural adaptive output feedback control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. The approach is applicable to nonlinear nonnegative systems with unmodeled dynamics of unknown dimension and guarantees that the physical system states remain in the nonnegatiye orthant of the state-space for nonnegative initial conditions. Finally, a numerical example involving the infusion of the anesthetic drug midazolam for maintaining a desired constant level of depth of anesthesia for noncardiac surgery is provided to demonstrate the efficacy of the proposed approach.

Adaptation, Physiological↗

PubMed1999

The analysis of animal bioelectric brain activity influenced by microwaves or by the introduction of strychnine.

The widespread impact made by technology has raised concerns about the safety of human exposure to electromagnetic radiation in the environment. The brain is especially sensitive to the influence of microwaves. The most effective method for estimation of the organism's functional states is an analysis of electroencephalograms. The statistical and spectral methods are usually used for analysis of animal electrocorticograms. The information obtained in such way is the integrated character and it is sometimes insufficient for identification of the brain state charging caused by various factors, especially microwaves altering the ecological situation. The nonlinear dynamics method is used in our work concurrent with the spectral correlation method for animal electrocorticogram processing. The correlation dimensionality represents a numerical criterion allowing for comparative investigation of various dynamic states of the system. In the process of investigation, it has been found that the nonlinear dynamics method may be used to analyze the electrocorticograms of experimental animal in different functional states being confirmed by increasing parameter of the correlation dimensionality in electrocorticograms of animal irradiated by microwaves or subjected to the introduction of strychnine.

Algorithms↗

PubMed2001

Nonlinear magnetization dynamics under circularly polarized field.

Exact analytical results are presented for the nonlinear large motion of the magnetization vector in a body with uniaxial symmetry subject to a circularly polarized field. The absence of chaos, the existence of pure time-harmonic magnetization modes with no generation of higher-order harmonics, and the existence of quasiperiodic magnetization modes with spontaneous breaking of the rotational symmetry are proven. Application to ferromagnetic resonance and connection with the Stoner-Wohlfarth model are discussed.

Journal Article↗

PubMed2006

Nonlinear analysis and prediction of coarse particulate matter concentration in ambient air.

This study attempts to characterize and predict coarse particulate matter (PM10) concentration in ambient air using the concepts of nonlinear dynamical theory. PM10 data observed daily from 1999 to 2002 at a site in Mumbai, India, was used to study the applicability of the chaos theory. First, the autocorrelation function and Fourier power spectrum were used to analyze the behavior of the time-series. The dynamics of the time-series was additionally studied through correlation integral analysis and phase space reconstruction. The nonlinear predictions were then obtained using local polynomial approximation based on the reconstructed phase space. The results were then compared with the autoregressive model. The results of nonlinear analysis indicated the presence of chaotic character in the PM10 time-series. It was also observed that the nonlinear local approximation outperforms the autoregressive model, because the observed relative error of prediction for the autoregressive model was greater than the local approximation model. The invariant measures of nonlinear dynamics computed for the predicted time-series using the two models also supported the same findings.

Air Pollutants↗

PubMed1997

Dynamical analysis of schizophrenia courses.

In order to assess the working hypothesis that schizophrenia may be viewed as a nonlinear dynamical disease, we examined the long-term psychoticity dynamics of 14 patients. The data consist of daily ratings of psychopathology observed for 200 or more consecutive days in each patient. We implemented nonlinear dynamical analysis methods with a potential of being applicable even to relatively short and noisy time series: two different forecasting approaches combined with surrogate methods that allow statistical testing in each single case. The resulting classification of dynamics gives evidence that eight patients show nonlinear evolutions of symptom courses. Four cases can be modeled linearly, two as random processes. Thus, a larger proportion of the schizophrenic psychoses we studied shows nonlinear time courses. In this way the validity of the concept of dynamical diseases could be supported on statistical grounds in this important area of psychopathology. The nonlinear view-a low-dimensional nonlinear system generating psychotic symptoms--may provide the foundation for a more parsimonious theory of schizophrenia compared to traditional multicausal models. In several of the nonlinear cases we also observed the qualitative "fingerprint" of deterministic chaos: a decay of deterministic features of the course of disorder with time.

Adolescent↗

PubMed1999

Human fetuses have nonlinear cardiac dynamics.

Approximate entropy (ApEn) is a statistic that quantifies regularity in time series data, and this parameter has several features that make it attractive for analyzing physiological systems. In this study, ApEn was used to detect nonlinearities in the heart rate (HR) patterns of 12 low-risk human fetuses between 38 and 40 wk of gestation. The fetal cardiac electrical signal was sampled at a rate of 1,024 Hz by using Ag-AgCl electrodes positioned across the mother's abdomen, and fetal R waves were extracted by using adaptive signal processing techniques. To test for nonlinearity, ApEn for the original HR time series was compared with ApEn for three dynamic models: temporally uncorrelated noise, linearly correlated noise, and linearly correlated noise with nonlinear distortion. Each model had the same mean and SD in HR as the original time series, and one model also preserved the Fourier power spectrum. We estimated that noise accounted for 17.2-44.5% of the total between-fetus variance in ApEn. Nevertheless, ApEn for the original time series data still differed significantly from ApEn for the three dynamic models for both group comparisons and individual fetuses. We concluded that the HR time series, in low-risk human fetuses, could not be modeled as temporally uncorrelated noise, linearly correlated noise, or static filtering of linearly correlated noise.

Algorithms↗

PubMed2006

Dynamic pacing strategies during the cycle phase of an Ironman triathlon.

INTRODUCTION: A nonlinear dynamic systems model has previously been proposed to explain pacing strategies employed during exercise. PURPOSE: This study was conducted to examine the pacing strategies used under varying conditions during the cycle phase of an Ironman triathlon. METHODS: The bicycles of six well-trained male triathletes were equipped with SRM power meters set to record power output, cadence, speed, and heart rate. The flat, three-lap, out-and-back cycle course, coupled with relatively consistent wind conditions (17-30 km x h(-1)), enabled comparisons to be made between three consecutive 60-km laps and relative wind direction (headwind vs tailwind). RESULTS: Participants finished the cycle phase (180 km) with consistently fast performance times (5 h, 11 +/- 2 min; top 10% of all finishers). Average power output (239 +/- 25 to 203 +/- 20 W), cadence (89 +/- 6 to 82 +/- 8 rpm), and speed (36.5 +/- 0.8 to 33.1 +/- 0.8 km x h(-1)) all significantly decreased with increasing number of laps (P < 0.05). These variables, however, were not significantly different between headwind and tailwind sections. The deviation (SD) in power output and cadence did not change with increasing number of laps; however, the deviations in torque (6.8 +/- 1.6 and 5.8 +/- 1.3 N x m) and speed (2.1 +/- 0.5 and 1.6 +/- 0.3 km x h(-1)) were significantly greater under headwind compared with tailwind conditions, respectively. The median power frequency tended to be lower in headwind (0.0480 +/- 0.0083) compared with tailwind (0.0531 +/- 0.0101) sections. CONCLUSION: These data show evidence that a nonlinear dynamic pacing strategy is used by well-trained triathletes throughout various segments and conditions of the Ironman cycle phase. Moreover, an increased variation in torque and speed was found in the headwind versus the tailwind condition.

Adult↗

PubMed2006

Nonlinear pedagogy: a constraints-led framework for understanding emergence of game play and movement skills.

Team sport competition can be characterized as a complex adaptive system in which concepts from nonlinear dynamics can provide a sound theoretical framework to understand emergent behavior such as movement coordination and decision making in game play. Nonlinear Pedagogy is presented as a methodology for games teaching, capturing how phenomena such as movement variability, self-organization, emergent decision making, and symmetry-breaking occur as a consequence of interactions between agent-agent and agent-environment constraints. Empirical data from studies of basketball free-throw shooting and dribbling are used as task vehicles to exemplify how nonlinear phenomena characterize game play in sport. In this paper we survey the implications of these data for Nonlinear Pedagogy, focusing particularly on the manipulation of constraints in team game settings. The data and theoretical modeling presented in this paper provide a rationale in nonlinear dynamics for the efficacy of a prominent model of game play teaching, Teaching Games for Understanding approach.

Basketball↗

PubMed2006

Nonlinear time series analysis of food intake in the dab and the rainbow trout.

Evidence suggests that dab and rainbow trout are able to quickly adjust their food intake to an appropriate level when offered novel diets. In addition day-to-day and meal-to-meal food intake varies greatly and meal timing is plastic. Why this is the case is not clear: Food intake in fish is influenced by many factors, however the hierarchy and mechanisms by which these interact is not yet fully understood. A model of food intake may be helpful to understand these phenomena; to determine model type it is necessary to understand the qualitative nature of food intake. Food intake can be regarded as an autoregressive (AR) time series, as the amount of food eaten at time t will be influenced by previous meals, and this allows food intake to be considered using time series analyses. Here, time series data were analysed using nonlinear techniques to obtain qualitative information from which evidence for the hierarchy of mechanisms controlling food intake may be drawn. Time series were obtained for a group of dab and individuals and a group of rainbow trout for analysis. Surrogate data sets were generated to test several null hypotheses describing linear processes and all proved significantly different to the real data, suggesting nonlinear dynamics. Examination of topography and recurrence diagrams suggested that all series were deterministic and non-stationary. The point correlation dimension (PD2i) suggested low-dimensional dynamics. Our findings suggest therefore that any model of appetite should create output that is deterministic, non-stationary, low-dimensional and having nonlinear dynamics.

Animals↗

PubMed1995

Measuring "chaos" in the brain: a tutorial review of EEG dimension estimation.

The technique of dimension estimation is currently a leading application of nonlinear dynamics (popularly termed "chaos theory") to EEG analysis. A tutorial review of this technique is presented along with some elementary background concepts from nonlinear dynamics. Practical aspects of applying dimension estimation to EEG data are also reviewed, and the possible role of deterministic chaos in brain function is discussed.

Brain↗

PubMed1989

Dissection of the neuron network in the catfish inner retina. III. Interpretation of spike kernels.

1. Three independent sets of evidence have been obtained to show that similar first- and second-order light-evoked kernels are computed for the ganglion cell when the system output is taken to be either the spike train (discrete signal) or the postsynaptic potential (analog signal). In this paper we show that the similarity of postsynaptic potential (PSP) kernels and spike kernels is readily explained by assuming an underlying cascade structure for the neural information processing. The cascade structure enables spike kernels to be mathematically related very simply to the process of generating the postsynaptic potentials of ganglion cells. 2. Mathematical analysis of the cascade structure also suggests why spike kernels appear to differ slightly from PSP kernels. The relation between the two sets of kernels predicted from our analysis is substantiated here by experiment and reveals an interconnection between several of the signals measured. 3. Our experimental results, in particular, suggest that the neuronal circuitry leading from the light stimulus to the generation of ganglion cell spike discharges can be represented as follows: either a Wiener (LN) or a dynamic linear-static nonlinear-dynamic linear (LNL) structure is followed by a highly nonlinear process [static or brief-memory Hammerstein static-nonlinear dynamic-linear (NL) structure] of spike generation. Cross-correlation between the analog input and spike output enables identification of these structures.

Action Potentials↗

PubMed1999

Dynamic behavior of heart rate in ischemic stroke.

BACKGROUND AND PURPOSE: Traditional spectral and nonspectral methods have shown that heart rate (HR) variability is reduced after stroke. Some patients with poor outcome, however, show randomlike, complex patterns of HR behavior that traditional analysis techniques are unable to quantify. Therefore, we designed the present study to evaluate the complexity and correlation properties of HR dynamics after stroke by using new analysis methods based on nonlinear dynamics and fractals ("chaos theory"). METHODS: In addition to the traditional spectral components of HR variability, we measured instantaneous beat-to-beat variability and long-term continuous variability analyzed from Poincaré plots, fractal correlation properties, and approximate entropy of R-R interval dynamics from 24-hour ambulatory ECG recordings in 30 healthy control subjects, 31 hemispheric stroke patients, and 15 brain stem stroke patients (8 medullary, 7 pontine) in the acute phase of stroke and 6 months after stroke. RESULTS: In the acute phase, the traditional spectral components of HR variability and the long-term continuous variability from Poincaré plots were impaired (P<0.01) in patients with hemispheric and medullary brain stem stroke, but not in patients with pontine brain stem stroke, in comparison with control subjects. At 6 months after stroke, measures of HR variability in hemispheric stroke patients were still lower (P<0.05) than those of the control subjects. Various complexity and fractal measures of HR variability were similar in patients and control subjects. The conventional frequency domain measures of HR variability as well as the Poincaré measures showed strong correlations (Pearson correlation coefficient, r=0.68 to r=0.90) with each other but only weak correlations (r=0.09 to r=0.56) with the complexity and fractal measures of HR variability. CONCLUSIONS: Hemispheric and medullary brain stem infarctions seem to damage the cardiovascular autonomic regulatory system and appear as abnormalities in the magnitude of HR variability. These abnormalities can be more easily detected with the use of analysis methods of HR variability, which are based on moment statistics, than by methods based on nonlinear dynamics. Abnormal HR variability may be involved in prognostically unfavorable cardiac complications and other known manifestations of autonomic failure associated with stroke.

Acute Disease↗