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PubMed2002

Precursor forms of cavity solitons in nonlinear semiconductor microresonators.

We study the transverse nonlinear dynamics of bulk and multi-quantum well AlGaAs microresonators, in the mixed dispersive and saturable absorptive regime, slightly below the band-gap edge energy. With a Gaussian beam excitation we observe strongly localized states of various shapes, bright or dark in reflection. Their dynamics appears to be ruled by strong thermally induced nonlinear mechanisms, acting as a dressing mechanism for electronic nonlinearities. Precursor forms of cavity solitons are also identified.

Journal Article↗

PubMedDate not supplied

Is local metabolism the basis of the fractal vascular structure in the heart?

The distribution of blood flow in the heart muscle is very heterogeneous and shows a self-similar fractal pattern, extending to small spatial scales. It is very likely that local oxygen consumption is more or less proportional to local blood flow and that local aerobic metabolism also is very heterogeneous. It is not yet clear whether local metabolism is heterogeneous in origin and the distribution of flow has secondarily adapted to metabolism, or, the other way around, whether flow is primarily heterogeneous because of the irregular structure of the coronary tree and flow has adapted to metabolism. Little is known yet about the developmental and adaptive mechanisms which bring about mutual adjustment between vascular growth and local metabolic demand, and genes and growth factors involved in shaping the structure of the coronary tree have only begun to be identified. Fractal and nonlinear dynamic mathematical models generate complex heterogeneous structures from simple nonlinear deterministic rules which are recursively applied. Such nonlinear models may thus help to explain the generation of large vascular trees regulated by synergy of a limited number of genes and signaling molecules. This may explain the relative regularity of space filling of the vascular tree and the asymmetry of branching and flow distribution in the tree.

Animals↗

PubMed2004

Nonlinearity from geometric interactions: a case example.

We propose a ladder model wherein dynamical nonlinearity arises from geometry. It includes two strings of particles which are set along rigid rails of a "railroad" and coupled by linear springs. Physical realizations of the model include dust-particle strings in plasma sheaths and chains of microparticles trapped in a strong optical lattice. The transverse couplings between the strings, along with the motion constraint imposed by the rails, generate nonlinearity. It gives rise to robust solitary waves, which are found analytically in the long-wavelength limit, and are obtained in simulations of the full system.

Journal Article↗

PubMed1994

A dynamic model of reaction time in a short-term memory task.

In this article we hypothesized that the trial to trial variability in speed of access to recently presented information is deterministic in nature and that it reflects important properties of immediate memory. Application of analytic techniques emerging from the science of nonlinear dynamical systems to data obtained from the Sternberg (1966, 1970) short-term memory task corroborates the view. A simple nonlinear difference equation, consistent with fuzzy-trace theory (Brainerd & Reyna, 1992), was then proposed to describe the dynamics underlying reaction time (RT) on the Sternberg task. The model posits that RT is a function of the interaction of two control parameters: susceptibility to interference (SI) and episodic activation (EA). Evaluation of the model indicated an exceptionally good fit with the raw empirical observations. Age comparisons of the model parameters revealed that adults exhibited higher levels of SI and EA. Although the finding that adults exhibited higher levels of SI than children runs counter to theory and other empirical results, further analysis revealed that adults exhibited lower levels of SI relative to EA than children. Thus, children may exhibit slower disintegration of verbatim memory traces than adults due to interference; however, adults may be more efficient at redintegrating verbatim memory traces than children.

Adult↗

PubMed1998

Neuronal complexity loss in interictal EEG recorded with foramen ovale electrodes predicts side of primary epileptogenic area in temporal lobe epilepsy: a replication study.

PURPOSE: To investigate whether a correct lateralization of the primary epileptogenic area by means of neuronal complexity loss analysis can be obtained from interictal EEG recordings using semi-invasive foramen ovale electrodes. In a previous study with recordings from intrahippocampal depth and subdural strip electrodes it was shown that the dynamics of the primary epileptogenic area can be characterized by an increased loss of neuronal complexity in patients with unilateral temporal lobe epilepsy (TLE). METHODS: Neuronal complexity loss analysis was applied. This analysis method is derived from the theory of nonlinear dynamics and provides a topological diagnosis even in cases where no actual seizure activity can be recorded. We examined interictal EEG recorded intracranially from multipolar foramen ovale electrodes in 19 patients with unilateral TLE undergoing presurgical evaluation. RESULTS: The primary epileptogenic area was correctly lateralized in 16 of the 19 investigated patients. The misclassification of the side of seizure onset in three patients might be attributed to the larger distance between the foramen ovale electrodes and the mesial temporal structures as compared to intrahippocampal depth electrodes. CONCLUSIONS: Our results confirm the previous findings and provide further evidence for the usefulness of nonlinear time-series analysis for the characterization of the spatiotemporal dynamics of the primary epileptogenic area in mesial temporal lobe epilepsy.

Adult↗

PubMed2003

Nonlinear analysis of the development of sitting postural control.

The development of sitting postural control in five normal infants was examined longitudinally at three stages of sitting: Stage 1, when infants could hold up their head and upper trunk, but could not sit independently; Stage 2, when infants began to sit independently briefly; and Stage 3, when infants could sit independently. Methods from nonlinear dynamics were used to analyze center of pressure (COP) data during sitting in terms of stability of the neuromuscular system (Lyapunov Exponent), movement dimensionality (Correlation Dimension), and complexity/regularity (Approximate Entropy). Results indicated significant changes in the nonlinear measures over time, with increased stability and increased regularity revealing a more stable and periodic strategy of maintaining postural control. Dimensionality decreased from Stage 1 to 2, indicating a constraint of the degrees of freedom. Subsequently, dimensionality increased from Stage 2 to 3, indicating a release of the degrees of freedom as sitting independence emerged. Nonlinear analysis of the COP time series supports the perspective that the development of postural control is a dynamic process whereby the infant learns to control the body's degrees of freedom to achieve the sitting posture.

Child Development↗

PubMed2002

Dynamics of two overlapping spin ensembles interacting by spin exchange.

We describe linear and nonlinear dynamics of spin-polarized K and 3He ensembles interacting by spin exchange. The interactions are dominated by the imaginary part of the spin-exchange cross section and each spin species is primarily affected by the average magnetization of the other. Operating in a very low magnetic field we demonstrate novel dynamics when the electron and nuclear spin precession frequencies are nearly matched. We observe transverse damping as well as a dynamic instability of the 3He spins interacting with polarized K vapor. We also demonstrate operation as a self-compensating comagnetometer, useful for tests of CPT violation and other precision measurements.

Journal Article↗

PubMed2002

Microbial population dynamics in laboratory-scale activated sludge reactors.

As a first step in understanding nonlinear dynamics in activated sludge systems, two laboratory-scale sequencing batch reactors were operated under identical conditions and changes in their microbial communities were followed through microscopic examination, macroscopic observation, and denaturing gradient gel electrophoresis (DGGE) of PCR-amplified 16S rRNA gene segments from the prokaryotic community. Two experiments were performed. The first used activated sludge from a local wastewater treatment plant to start the replicate reactors. The second used the biomass from the first experiment as a source by intermixing the two and equally redistributing the biomass into the two replicate reactors. For both experiments, the two reactors behaved fairly similarly and had similar microbial communities for a period of 60 days following start-up. Beyond that, the microbial communities in the two reactors in the first experiment diverged in composition, while those in the second experiment remained fairly similar. This suggests that the degree of change occurring in replicate reactors depends upon the severity of perturbation to which they are exposed. The DGGE data showed that the bacterial communities in both experiments were highly dynamic, even though the system performance of the replicate reactors were very similar, suggesting that dynamics within the prokaryotic community is not necessarily reflected in system performance. Moreover, a significant finding from this study is that replicate activated sludge systems are not identical, although they can be very similar if started appropriately.

Bacteria↗

PubMed2006

Moderate exercise and chronic stress produce counteractive effects on different areas of the brain by acting through various neurotransmitter receptor subtypes: a hypothesis.

BACKGROUND: Regular, "moderate", physical exercise is an established non-pharmacological form of treatment for depressive disorders. Brain lateralization has a significant role in the progress of depression. External stimuli such as various stressors or exercise influence the higher functions of the brain (cognition and affect). These effects often do not follow a linear course. Therefore, nonlinear dynamics seem best suited for modeling many of the phenomena, and putative global pathways in the brain, attributable to such external influences. HYPOTHESIS: The general hypothesis presented here considers only the nonlinear aspects of the effects produced by "moderate" exercise and "chronic" stressors, but does not preclude the possibility of linear responses. In reality, both linear and nonlinear mechanisms may be involved in the final outcomes. The well-known neurotransmitters serotonin (5-HT), dopamine (D) and norepinephrine (NE) all have various receptor subtypes. The article hypothesizes that 'Stress' increases the activity/concentration of some particular subtypes of receptors (designated nts) for each of the known (and unknown) neurotransmitters in the right anterior (RA) and left posterior (LP) regions (cortical and subcortical) of the brain, and has the converse effects on a different set of receptor subtypes (designated nth). In contrast, 'Exercise' increases nth activity/concentration and/or reduces nts activity/concentration in the LA and RP areas of the brain. These effects may be initiated by the activation of Brain Derived Neurotrophic Factor (BDNF) (among others) in exercise and its suppression in stress. CONCLUSION: On the basis of this hypothesis, a better understanding of brain neurodynamics might be achieved by considering the oscillations caused by single neurotransmitters acting on their different receptor subtypes, and the temporal pattern of recruitment of these subtypes. Further, appropriately designed and planned experiments will not only corroborate such theoretical models, but also shed more light on the underlying brain dynamics.

Brain↗

PubMed1993

Entropy and convergence in dynamics and demography.

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.

Demography↗

PubMed1999

Noise improves transfer of near-threshold, phase-locked activity of the cochlear nerve: evidence for stochastic resonance?

Stochastic resonance can be described as improved detection of weak periodic stimuli by a dynamic nonlinear system, resulting from the simultaneous presentation of a restricted dynamic range of low-intensity noise. This property has been reported in simple physical and biological activities. The present study describes data consistent with the interpretation that stochastic resonance can be observed in the response of cochlear neurons. These experiments utilized low levels (-5 to 25 dB SPL) of stimuli and noise (5 to 30 dB SPL). Stimuli consisted of simultaneously presented 8 kHz (F1) and 8.8 kHz (F2) tone bursts, which generated an 800 Hz F2-F1 cochlear nerve envelope ensemble response in the gerbil. The mean response threshold was approximately -3 dB SPL. Simultaneous presentation of a low-intensity wideband noise increased the amplitude of this response. This was observed with tonal stimuli having intensities of 0-5 dB SPL; responses to stimulus levels > 10 dB were attenuated by noise. Response amplitude was increased by noise levels of 10-15 dB; the amplitude was unaffected by lower levels of noise, and decreased in the presence of higher noise levels. These properties are compatible with those of stochastic resonance.

Acoustic Stimulation↗

PubMed1993

Temporal processing in the visual brain.

In conclusion these three results taken together--the single-unit data, the Gerstein and Mandelbrot model, and the modeled collection of neurons--suggest that the analysis of the temporal dynamics of neural systems can be furthered by the application of nonlinear dynamical theory. Furthermore, it appears that the range of temporal dynamics possible in visual cortex is quite broad, encompassing simple oscillations and more complex, perhaps chaotic, dynamics. Lastly, it appears that there are powerful principles at work that are leading to the organized behavior of a population of neurons. We suggest that these principles are constrained not only by the biological properties of the nervous system, but by profound mathematical principles that have already been described in many physical nonlinear systems under the aegis of chaos theory. If such constraints exist, we may have available to us mathematical and physical constructs that will allow us to study, model, and predict the behaviors of large collections of neurons that ultimately underlie the neural functioning of the brain.

Action Potentials↗

PubMed1991

A dynamical system for biological development: the case of Caenorhabditis elegans.

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes: (i) on one hand the cell proliferation under successive divisions; (ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenrhabditis elegans by looking at the early stages of embryogenesis, up to several hundreds of cells ("lima bean" larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of teh control parameters with time.

Animals↗

PubMed1997

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

Journal Article↗

PubMedDate not supplied

Approximate entropy and point correlation dimension of heart rate variability in healthy subjects.

The contribution of nonlinear dynamics to heart rate variability in healthy humans was examined using surrogate data analysis. Several measures of heart rate variability were used and compared. Heart rates were recorded for three hours and original data sets of 8192 R-R intervals created. For each original data set (n = 34), three surrogate data sets were made by shuffling the order of the R-R intervals while retaining their linear correlations. The difference in heart rate variability between the original and surrogate data sets reflects the amount of nonlinear structure in the original data set. Heart rate variability was analyzed by two different nonlinear methods, point correlation dimension and approximate entropy. Nonlinearity, though under 10 percent, could be detected with both types of heart rate variability measures. More importantly, not only were the correlations between these measures and the standard deviation of the R-R intervals weak, the correlation among the nonlinear measures themselves was also weak (generally less than 0.6). This suggests that in addition to standard linear measures of heart rate variability, the use of multiple nonlinear measures of heart rate variability might be useful in monitoring heart rate dynamics.

Adult↗

PubMed2002

Relationship of nonlinear analysis, MRI and SPECT in the lateralization of temporal lobe epilepsy.

OBJECTIVES: The purpose of this study was to investigate the correlation of lateralization by nonlinear analysis, magnetic resonance imaging (MRI) and interictal single-photon emission computed tomography (SPECT) in patients with temporal lobe epilepsy. METHODS: Twenty-three patients (7 males, 16 females) were examined by MRI, interictal SPECT and EEG. Nonlinear dynamic properties of neuronal networks were estimated by calculating correlation dimensions on interictal EEG signals and corresponding surrogate data. Lateralization was detected based on the criteria introduced in this study. Concordance rates of the results among the three methods were compared. RESULTS: Epileptogenic foci were shown in the temporal areas in 21 patients using the nonlinear method (8 left, 2 right, 11 both), while 20 patients showed abnormalities in temporal lobes on MR images (13 left, 5 right, 2 both). Low cerebral blood flows of the temporal lobes were detected in all patients (11 left, 8 right, 4 both). Completely concordant lateralization was observed in 8 patients (35%) for the nonlinear method and MRI, in 9 patients (39%) for the nonlinear method and SPECT, and in 10 patients (43%) for MRI and SPECT. There were no significant differences among the concordance rates for these different methods. CONCLUSIONS: Our results revealed that correlation dimension is useful for differentiating dynamic properties of neuronal networks in the interictal state, and can provide informative data for localizing epileptogenic foci in epileptic patients. Therefore, the present nonlinear method is recommended for use with patients during presurgical evaluation.

Adolescent↗

PubMed2006

On-line adaptive and nonlinear process monitoring of a pilot-scale sequencing batch reactor.

This article describes the application of on-line nonlinear monitoring of a sequencing batch reactor (SBR). Three-way batch data of SBR are unfolded batch-wisely, and then a adaptive and nonlinear multivariate monitoring method is used to capture the nonlinear characteristics of normal batches. The approach is successfully applied to an 80 L SBR for biological wastewater treatment, where the SBR poses an interesting challenge in view of process monitoring since it is characterized by nonstationary, batchwise, multistage, and nonlinear dynamics. In on-line batch monitoring, the developed adaptive and nonlinear process monitoring method can effectively capture the nonlinear relationship among process variables of a biological process in a SBR. The results of this pilot-scale SBR monitoring system using simple on-line measurements clearly demonstrated that the adaptive and nonlinear monitoring technique showed lower false alarm rate and physically meaningful, that is, robust monitoring results.

Bioreactors↗

PubMed2006

Temporal extensivity of Tsallis' entropy and the bound on entropy production rate.

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by q is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be 1/ absolute value (1-q). The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

Journal Article↗