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At least 613 records · Page 34Linked to original sources

PubMed2025

Balanced state of networks of winner-take-all units.

Irregularly timed action potentials, or spikes, are pervasively observed in the brain activity of awake mammals. However, the role of this temporal irregularity in neural computation is still not well understood. In canonical network models irregular spiking emerges via balanced, fluctuating input currents, leading to collective responses that track inputs linearly. How networks characterized by irregular spiking could support flexible nonlinear dynamics needed for general-purpose computation remains under ongoing debate. Here we characterize the dynamics of networks whose elementary unit is not a single neuron but a small group of neurons, with distinct tunings, that compete at each timestep via a winner-take-all (WTA) interaction. While WTA has long been proposed as an elementary functional motif in the brain and represents a powerful computational primitive, how large networks of such units behave has received less investigation. We show that these networks, like classic excitatory-inhibitory balanced networks, exhibit a chaotic fluctuation-driven regime characterized by sustained irregular activity resembling realistic cortical spiking, which we interpret as a multidimensional balance spread over several competing neural populations with different tunings. We develop a mean-field theory for the network, which shows how irregular spiking sustained by time-varying input fluctuations can support flexible nonlinear collective dynamics. Using the theory we predict and verify network regimes in which input fluctuations alone yield multistability, stable sequence generation, or complex heterogeneous firing rate dynamics-three core dynamical primitives thought to underlie memory-dependent neural computation-via consistent Poisson-like spiking produced through chaos. Thus, networks of WTA units support a chaotic fluctuation-driven regime characterized by irregular spiking that can power complex nonlinear collective dynamics. This represents a new model of brain activity capable of simultaneously reproducing realistic spike trains and diverse nonlinear firing rate patterns well posed for flexible computation, and which can be trained or fit to data.

Models, Neurological↗

PubMed2001

Dynamics of localized and nonlocalized optical vortex solitons in cubic-quintic nonlinear media.

The nonlinear dynamics of laser beams carrying phase singularity in media with cubic-quintic nonlinearity changing from self-focusing to self-defocusing is examined. A novel kind of stable nonlocalized optical vortices appears in such media as well as localized vortex solitons. Linear stability analysis and numerical simulations show the stability of localized vortices only in the defocusing region.

Journal Article↗

PubMed2000

A system for the ambulatory recording and analysis of nonlinear heart rate dynamics.

The study of cardiac dynamics is a topic of great clinic and experimental concern. However, the ability to apply methods from the emerging field of nonlinear dynamics to cardiac time series has been limited by the demand for large amounts of relatively artifact-free data. Both the ability to collect such data and the capacity to analysis such large data sets represents limits. In the present paper we describe a system that allows for the collection of large amounts of high quality data and the analysis of large data sets. The recording system consists of a miniature, single-module electrocardiogram-recording device. This module consists of an integrated three-electrode device that is attached to the chest of the subject. A low power 8-bit micro-controller detects the R-spike and stores the time between R-spikes in milliseconds on a 512 KB EEPROM. This system can record continuously for over four days. The output of this system is down-loaded to a PC and the RR intervals fed to a suite of digital signal processing programs. Among other things, estimates of Approximate Entropy and Poincaire plots are generated. This system will expand the capability of researchers and clinicians to investigate nonlinear cardiac dynamics in ambulatory subjects.

Heart Rate↗

PubMed1989

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.

Action Potentials↗

PubMed1997

Transients, metastability, and neuronal dynamics.

This paper is about neuronal dynamics and how their special complexity can be understood in terms of nonlinear dynamics. There are many aspects of neuronal interactions and connectivity that engender the complexity of brain dynamics. In this paper we consider (i) the nature of this complexity and (ii) how it depends on connections between neuronal systems (e.g., neuronal populations or cortical areas). The main conclusion is that simulated neural systems show complex behaviors, reminiscent of neuronal dynamics, when these extrinsic connections are sparse. The patterns of activity that obtain, under these conditions, show a rich form of intermittency with the recurrent and self-limiting expression of stereotyped transient-like dynamics. Despite the fact that these dynamics conform to a single (complex) attractor this metastability gives the illusion of a dynamically changing attractor manifold (i.e., a changing surface upon which the dynamics unfold). This metastability is characterized using a measure that is based on the entropy of the time series' spectral density.

Animals↗

PubMed1999

Is breathing in infants chaotic? Dimension estimates for respiratory patterns during quiet sleep.

We describe an analysis of dynamic behavior apparent in times-series recordings of infant breathing during sleep. Three principal techniques were used: estimation of correlation dimension, surrogate data analysis, and reduced linear (autoregressive) modeling (RARM). Correlation dimension can be used to quantify the complexity of time series and has been applied to a variety of physiological and biological measurements. However, the methods most commonly used to estimate correlation dimension suffer from some technical problems that can produce misleading results if not correctly applied. We used a new technique of estimating correlation dimension that has fewer problems. We tested the significance of dimension estimates by comparing estimates with artificial data sets (surrogate data). On the basis of the analysis, we conclude that the dynamics of infant breathing during quiet sleep can best be described as a nonlinear dynamic system with large-scale, low-dimensional and small-scale, high-dimensional behavior; more specifically, a noise-driven nonlinear system with a two-dimensional periodic orbit. Using our RARM technique, we identified the second period as cyclic amplitude modulation of the same period as periodic breathing. We conclude that our data are consistent with respiration being chaotic.

Algorithms↗

PubMed2006

Testing the assumptions of linear prediction analysis in normal vowels.

In this paper we develop an improved surrogate data test to show experimental evidence, for all the simple vowels of U.S. English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modeling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modeling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance.

Female↗

PubMed2005

Modelling the thermal evolution of enzyme-created bubbles in DNA.

The formation of bubbles in nucleic acids (NAs) is fundamental in many biological processes such as DNA replication, recombination, telomere formation and nucleotide excision repair, as well as RNA transcription and splicing. These processes are carried out by assembled complexes with enzymes that separate selected regions of NAs. Within the frame of a nonlinear dynamics approach, we model the structure of the DNA duplex by a nonlinear network of coupled oscillators. We show that, in fact, from certain local structural distortions, there originate oscillating localized patterns, that is, radial and torsional breathers, which are associated with localized H-bond deformations, reminiscent of the replication bubble. We further study the temperature dependence of these oscillating bubbles. To this aim, the underlying nonlinear oscillator network of the DNA duplex is brought into contact with a heat bath using the Nosé-Hoover method. Special attention is paid to the stability of the oscillating bubbles under the imposed thermal perturbations. It is demonstrated that the radial and torsional breathers sustain the impact of thermal perturbations even at temperatures as high as room temperature. Generally, for non-zero temperature, the H-bond breathers move coherently along the double chain, whereas at T=0 standing radial and torsional breathers result.

DNA↗

PubMed1987

Application of non-linear dynamics to the characterization of cardiac electrical instability.

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

Animals↗

PubMed2004

Nonlinear phenomena in contemporary vocal music.

Complex and multiphonic voice signals of vocal improvisors are analyzed within the framework of nonlinear dynamics. Evidence is given that nonlinear phenomena are extensively used by performers associated with contemporary music. Narrow-band spectrograms of complex vocalizations are used to visualize the appearance of nonlinear phenomena (spectral bifurcation diagrams). Possible production mechanisms are discussed in connection with previous research, personal performance and pedagogical experience. Examples for period doubling, biphonation and irregular aperiodic phonation in vocal sonorities of contemporary vocal improvisors are given, and glottal whistle production encompassed with biphonation and triphonation is shown. Furthermore, coincidences of harmonics-formant matching associated with abrupt transitions to subharmonics and biphonation in the vocal output are provided. This also shows the recurrent use of nonlinear phenomena by performers. It is argued that mechanisms such as source-tract coupling or vocal fold desynchronization due to asymmetry are used in a reproducible way for musical tasks.

Acoustics↗

PubMed2001

Chaos-nonchaos phase transitions induced by external noise in ensembles of nonlinearly coupled oscillators.

Nonlinear dynamical behaviors of ensembles of nonlinearly coupled oscillators subjected to external noise are studied on the basis of nonlinear Fokker-Planck equations. The effects of two kinds of noise, the Langevin noise and the noise introduced in the coupling strength, are investigated, and phase transitions involving chaos-nonchaos bifurcations are found to occur as the noise level is changed. An H theorem is proposed for the nonlinear Fokker-Planck equation to ensure stability of the Gaussian type solution that is approached for large times.

Journal Article↗

PubMed2005

Dynamics of granular avalanches caused by local perturbations.

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by the nonlinear coupling between a mobile layer and an erodible bed of static grains. Following previous studies, we use mass and momentum conservation to derive St. Venant-like equations for the evolution of the thickness R of the mobile layer and the profile Z of the bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in detail the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for nonstationary avalanches triggered by a localized amount of mobile grains on a bed of initially constant slope. We solve analytically the nonlinear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude, and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.

Journal Article↗

PubMed2000

[Segments of the recovery story of a patient with anorexia nervosa from the viewpoint of self-organization theory].

In order to examine the dynamics of anorectic processes we interviewed a 16-year-old girl which had recently recovered from her illness. She portrayed her experiences for a time span of 22 months from the beginning of her self-starvation until the date of the interview. After clustering all informations into variables she rated the degree of these variables for 11 important events during the time of her recovery. Synergies between cognition, emotion and behaviour during recovery are displayed. Activated feedback dynamics (positive, negative, and mixed feedback-loops) give rise of the interpretation of recovery from anorexia nervosa as a dynamic, self-organizing system. Nonlinear dynamics are salient in psychological change even if we are adopting a qualitative view on the phenomena.

Adolescent↗

PubMed1996

Fractals and the birth of Gothic: reflections on the biologic basis of creativity.

The birth of Gothic, one of the great triumphs of human spiritual and artistic expression, would appear to be a topic remote from the enterprise of contemporary neurobiology. The intent of this brief essay is to explore the possibility that this singular architectural movement may have important implications for understanding the nonlinear dynamics of the brain. We explore the hypothesis that the Gothic cathedral, with its porous, scale-free structures, may represent an externalization of the fractal properties of our physiology in general, and of our neural architectures and neuro-dynamics, in particular.

Creativity↗

PubMed2004

Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars.

A closed-form description is proposed to explain nonlinear and slow dynamics effects exhibited by sandstone bars in longitudinal resonance experiments. Along with the fast subsystem of longitudinal nonlinear displacements we examine the strain-dependent slow subsystem of broken intergrain and interlamina cohesive bonds. We show that even the simplest but phenomenologically correct modeling of their mutual feedback elucidates the main experimental findings typical for forced longitudinal oscillations of sandstone bars, namely, (i) hysteretic behavior of a resonance curve on both its upward and downward slopes, (ii) linear softening of resonant frequency with an increase of driving level, and (iii) gradual recovery (increase) of resonant frequency at low dynamical strain after the sample was conditioned by high strain. In order to reproduce the highly nonlinear elastic features of sandstone grained structure a realistic nonperturbative form of stress-strain relation was adopted. In our theory slow dynamics associated with the experimentally observed memory of peak strain history are attributed to strain-induced kinetic changes in concentration of ruptured intergrain and interlamina cohesive bonds, causing a net hysteretic effect on the elastic Young's modulus. Finally, we explain how enhancement of hysteretic phenomena originates from an increase in equilibrium concentration of ruptured cohesive bonds that are due to water saturation.

Journal Article↗

PubMed1996

Controlling the dynamical behavior of a circle map model of the human heart.

One-dimensional circle maps are good models for describing the nonlinear dynamical behavior of two interacting oscillators. They have been employed to characterize the interaction between a periodic external forcing stimulus and an in vitro preparation of chick embryonic cardiac cells. They have also been used to model some human cardiac arrythmias such as modulated ventricular parasystole. In this paper, we describe several techniques involving engineering feedback control theory applied to a circle map model of human heart parasystole. Through simulations of the mathematical model, we demonstrate that a desired target phase relationship between the normal sinus rhythm and an abnormal ectopic pacemaker can be achieved rapidly with low-level external stimulation applied to the system. Specifically, we elucidate the linear, self-tuning, and nonlinear feedback approaches to control. The nonlinear methods are the fastest and most accurate, yet the most complex and computationally expensive to implement of the three types. The linear approach is the easiest to implement but may not be accurate enough in real applications, and the self-tuning methods are a compromise between the other two. The latter was successful in tracking a variety of period-1, period-2, and period-3 target phase trajectories of the heart model.

Biological Clocks↗

PubMed1997

Nonlinear acoustic waves in porous media in the context of Biot's theory.

The nonlinear dynamic equations introduced by Biot to model porous media have not been implemented to describe nonlinear acoustic waves in such media. In this work the equations are revised and a mathematical model depicting the physical nonlinearity is established. A perturbation technique is then applied to find solutions to the nonlinear Biot equations. An important feature of the developed model is the introduction of the dependence of the structural parameters of the medium on its porosity. The model establishes a correlation between the measurable effective nonlinear parameter and structural parameters of the porous medium. This suggests employing nonlinear measurements as a diagnostic tool for porous media.

Acoustics↗

PubMed2000

Nonstationary time-series analysis applied to investigation of brainstem system dynamics.

Previous investigations of the dynamic organization of the lower brainstem and its relation to peripheral and other central nervous systems were predominantly performed by linear methods. These are based on time-averaging algorithms, which merely can be applied to stationary signal intervals. Thus, the current concept of the common brainstem system (CBS) in the reticular formation (RF) of the lower brainstem and basic types of its functional organization have been developed. Here, we present experiments where neuronal activities of the RF and the nucleus tractus solitarii (NTS, first relay station of baroreceptor afferents) were recorded together with related parameters of electroencephalogram (EEG), respiration, and cardiovascular system. The RF neurons are part of the CBS, which participates in regulation and coordination of cardiovascular, respiratory, and motor systems, and vigilance. The physiological time series, thus acquired, yield information about the internal dynamic coordination of the participating regulation processes. The major problem in evaluating these data is the nonlinearity and nonstationarity of the signals. We used a set of especially designed time resolving methods to evaluate nonlinear dynamic couplings in the interaction between CBS neurons and cardiovascular signals, respiration and the EEG, and between NTS neurons (influenced by baroreceptor afferents) and CBS neurons.

Algorithms↗