Biomedical subjects

J Kurths

Publications and source records attributed to J Kurths.

At least 37 records · Page 2Linked to original sources

PubMed2003

Constructive effects of noise in homoclinic chaotic systems.

Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point. We study influences of noise on homoclinic chaos. We demonstrate both numerically and experimentally on a CO2 laser various constructive effects of noise, including coherence resonance, noise-induced synchronization in uncoupled systems and noise-enhanced phase synchronization, deterministic resonance with respect to signal frequency, and stochastic resonance versus noise intensity in response to weak signals. The peculiar sensitivity of the system along the weak unstable manifold of the saddle point underlines the unified mechanism of these nontrivial and constructive noise-induced phenomena.

Journal Article↗

PubMed2003

Coherence resonance and polymodality in inhibitory coupled excitable oscillators.

We have analyzed the firing activity of two and three excitable FitzHugh-Nagumo oscillators, coupled via slow variable diffusion and under the action of an external noise. We find a different form of coherence resonance in this system, which is, in contrast to previous studies, intrinsically based on the antiphase behavior of coupled elements. Additionally, we show that an exchange, performed by this form of coupling, is remarkably rhythmogenic and results in polymodal interspike distributions without any external periodic stimuli. The dependence of these distributions on the noise amplitude and the coupling strength is studied.

Journal Article↗

PubMed2003

Observing and interpreting correlations in metabolomic networks.

MOTIVATION: Metabolite profiling aims at an unbiased identification and quantification of all the metabolites present in a biological sample. Based on their pair-wise correlations, the data obtained from metabolomic experiments are organized into metabolic correlation networks and the key challenge is to deduce unknown pathways based on the observed correlations. However, the data generated is fundamentally different from traditional biological measurements and thus the analysis is often restricted to rather pragmatic approaches, such as data mining tools, to discriminate between different metabolic phenotypes. METHODS AND RESULTS: We investigate to what extent the data generated networks reflect the structure of the underlying biochemical pathways. The purpose of this work is 2-fold: Based on the theory of stochastic systems, we first introduce a framework which shows that the emergent correlations can be interpreted as a 'fingerprint' of the underlying biophysical system. This result leads to a systematic relationship between observed correlation networks and the underlying biochemical pathways. In a second step, we investigate to what extent our result is applicable to the problem of reverse engineering, i.e. to recover the underlying enzymatic reaction network from data. The implications of our findings for other bioinformatics approaches are discussed.

Algorithms↗

PubMed2003

Noise-enhanced synchronization of homoclinic chaos in a CO2 laser.

Many chaotic oscillators have rather coherent phase dynamics but strong fluctuation in the amplitudes. Conversely, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals. We study the effects of noise on the synchronization of homoclinic chaos to a weak periodic signal and demonstrate numerically and experimentally in a CO2 laser system that noise enhances synchronization of homoclinic chaos. The system exhibits both conventional resonance versus driving frequency and stochastic resonance with respect to noise intensity.

Journal Article↗

PubMed2003

Doubly stochastic coherence via noise-induced symmetry in bistable neural models.

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.

Membrane Potentials↗

PubMed2003

Interpreting correlations in metabolomic networks.

Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. In this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways.

Biochemical Phenomena↗

PubMed2002

Comment on "Kullback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients".

In a recent paper Quian Quiroga et al. [R. Quian Quiroga et al., Phys. Rev. E 62, 8380 (2000)] found renormalized entropy, formerly introduced as a complexity measure for the different regimes of a dynamical system, to be closely related to the standard Kullback-Leibler entropy. They assure this finding by reanalyzing electroencephalographic data of epilepsy patients, previously examined by exclusive use of renormalized entropy [K. Kopitzki et al., Phys. Rev. E 58, 4859 (1998)]. We argue that the general considerations undertaken by the authors and the experimental results do not justify this conclusion.

Data Interpretation, Statistical↗

PubMed2002

Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Landau equation.

Turbulence control in the two-dimensional complex Ginzburg-Landau equation is investigated. An approach is proposed for the purpose of control. In the presence of a small spiral wave seed initiation, a fully developed turbulence can be completely annihilated by injecting a single periodic signal into a small fixed space area around the spiral wave tip. The control is achieved in a parameter region where the spiral wave of the uncontrolled system is absolutely unstable. The robustness, convenience, and high control efficiency of this method are emphasized, and the mechanism underlying these practical advantages is intuitively understood.

Journal Article↗

PubMed2002

Stable heteroclinic cycles for ensembles of chaotic oscillators.

We study the formation of synchronous clusters in ensembles of globally coupled chaotic oscillators. We reveal that at least three clusters of identical synchronization are formed in such a system for large enough values of coupling strength. Our main result is an unexpected intermittent process of clusterization. This process gives strong indication to the existence of a stable heteroclinic cycle.

Journal Article↗

PubMed2002

Vibrational resonance in a noise-induced structure.

We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise-induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.

Journal Article↗

PubMed2002

Estimation of parameters and unobserved components for nonlinear systems from noisy time series.

We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.

Journal Article↗

PubMed2002

Collective phase locked states in a chain of coupled chaotic oscillators.

We discuss the emergence of a collective phase locked state in an open chain of N unidirectionally weakly coupled nonidentical chaotic oscillators. Such a regime is characterized by a Lyapunov spectrum where N-1 exponents that were zero in the uncoupled regime assume negative values as the coupling strength increases. The dynamics of such collective state is studied, and a comparison is drawn with the case of phase synchronization of a pair of coupled chaotic oscillators. In particular, it is shown that a full phase synchronized state cannot be constructed without at least partial correlation in the chaotic amplitudes.

Journal Article↗

PubMed2002

The mutual information: detecting and evaluating dependencies between variables.

MOTIVATION: Clustering co-expressed genes usually requires the definition of 'distance' or 'similarity' between measured datasets, the most common choices being Pearson correlation or Euclidean distance. With the size of available datasets steadily increasing, it has become feasible to consider other, more general, definitions as well. One alternative, based on information theory, is the mutual information, providing a general measure of dependencies between variables. While the use of mutual information in cluster analysis and visualization of large-scale gene expression data has been suggested previously, the earlier studies did not focus on comparing different algorithms to estimate the mutual information from finite data. RESULTS: Here we describe and review several approaches to estimate the mutual information from finite datasets. Our findings show that the algorithms used so far may be quite substantially improved upon. In particular when dealing with small datasets, finite sample effects and other sources of potentially misleading results have to be taken into account.

Algorithms↗

PubMed2002

Model based analysis of the heart rate and blood pressure relationship.

The main intention of this contribution is to measure the coupling between bivariate time series using the dual sequence method to estimate the baroreflex as well as a nonlinear regression approach, namely the maximal correlation method, to get a better understanding of the underlying processes. The data we analyse are heart rate and blood pressure variability time series from 27 patients with dilated cardiomyopathy as well as from a control group of 27 age- and sex-matched healthy subjects. The results strongly indicate and confirm the mechanisms of respiratory sinus arrhythmia in heart rate. Revealing the coupling direction and the strength of coupling between heart rate and blood pressure via optimal transformations in addition to the baroreflex estimation seems to be a very promising approach.

Adult↗

PubMed2002

Bone modeling and structural measures of complexity.

We test sensitivity and powerfulness of recently suggested Structure Measures of Complexity (SMC) with simulated test objects, represented by simple structures or modelled on the basis of a real bone image. We check how these SMC reflect the local and global disordering processes, as well as a deterioration of the bone structure. We show that applications of SMC provide additional information about any changes of the bone structure in comparison to bone mineral density (BMD), and that they can be potentially helpful in the diagnosis of osteoporosis.

Journal Article↗

PubMed2001

Noise induced propagation in monostable media.

We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium is observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.

Journal Article↗

PubMed2001

Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise.

We demonstrate the effect of coherence resonance in a heterogeneous array of coupled Fitz Hugh-Nagumo neurons. It is shown that coupling of such elements leads to a significantly stronger coherence compared to that of a single element. We report nontrivial effects of parameter heterogeneity and spatial independence of noise on array-enhanced coherence resonance; especially, we find that (i) the coherence increases as spatial correlation of the noise decreases, and (ii) inhomogeneity in the parameters of the array enhances the coherence. Our results have the implication that generic heterogeneity and background noise can play a constructive role to enhance the time precision of firing in neural systems.

Journal Article↗

PubMed2001

Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors.

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

Data Interpretation, Statistical↗