Stochastic Resonance (SR) is a counterintuitive phenomenon whereby noise under appropriate conditions can enhance the detection of weak signals rather than interfering with signal transmission. Originally described in nonlinear physical systems, SR is applicable as well for biological processes that are also frequently nonlinear. The first demonstration of SR in biology utilized the mechanoreceptive hairs of crayfish.

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.

In neuroscience, specifically electrophysiology, it is common to replace a measured sequence of action potentials or spike trains with delta functions prior to analysis. We apply a method called circular statistics to a time series of delta functions and show that the method is equivalent to the power spectrum. This technique allows us to easily visualize the idea of the power spectrum of spike trains and easily reveals oscillatory and stochastic behavior. We provide several illustrations of the method and an example suitable for students, and suggest that the method might be useful for courses in introductory biophysics and neuroscience.

We study the diffusion coefficient of Active Brownian particles in two dimensions. In addition to usual attributes of active motion we let the particles turn in preferred directions over random times. This angular motion is modeled by an effective Lorentz force with time dependent frequency switching between two values at exponentially distributed random times. The diffusion coefficient is calculated by the Taylor-Kubo formula where distributions found from a Fokker-Planck equation or from a continuous time random walk approach have been inserted for averaging. Eventually properties of the diffusion coefficient will be discussed.

We explore the variability that animals display in their movement choices as they forage in a finite-sized food patch with a uniform food distribution, and present a framework for how these choices may be adjusted to optimize foraging efficiency. Inspired by experimental studies of the zooplankton Daphnia, we model foraging animals as "agents" moving in two dimensions in repeated and successive sequences of hops, pauses, and turns. For Daphnia and other species, critical movement parameters such as hop lengths, pause times, and turning angles are typically reported as probability density functions. Similarly, the agents in our simulations choose their movement parameters at random from such distributions. Each distribution is defined by a characteristic width, which we interpret as a "noise width," available to be tuned for increased foraging efficiency. We investigate the sensitivity of the system by measuring the food gathered by the agents as the turning angle and hop length noise widths are varied. In all cases, we find a maximum in food gathered at some particular value of the noise width in question, suggesting that these results can be considered robust examples of natural stochastic resonance.

This special issue focuses on the most complex system we know: the brain.More precisely, it deals with the examination of the brain dynamics and disturbances which are clinically manifested in neurological and psychiatric disorders like epilepsy, Parkinson's disease or mental depression.These diseases are often associated with disturbances of autonomous functions like hormone secretion and sleep which also are under the control of the brain.Accordingly, the papers in this issue will refer to a diversity of physiological systems.Their common link is that they all are related to brain functions and dysfunctions and that these neurophysiological issues are addressed by physically based approaches of systems analysis with the use of computer models and tools for nonlinear data analysis.The high expectations in such interdisciplinary approaches towards a better understanding of brain dynamics is the major motivation for this issue.All the authors have expertise in interdisciplinary work and have already made essential contributions in their fields.Many of them are experimental physiologists or clinicians who have learnt to implement biophysical methods, mostly in cooperation with physicists and mathematicians.Vice versa, the physicists and mathematicians among the authors have successfully entered the life sciences in demonstrating that physical applications are not only of interest from a systems theoretical point of view; but can also have high physiological relevance.

Search strategies are currently of great interest, with reports on foraging ranging from albatrosses and spider monkeys to microzooplankton. Here, we investigate the role of noise in optimizing search strategies. We focus on the zooplankton Daphnia, which move in successive sequences consisting of a hop, a pause and a turn through an angle. Recent experiments have shown that their turning angle distributions (TADs) and underlying noise intensities are similar across species and age groups, suggesting an evolutionary origin of this internal noise. We explore this hypothesis further with a digital simulation (EVO) based solely on the three central Darwinian themes: inheritability, variability and survivability. Separate simulations utilizing stochastic resonance (SR) indicate that foraging success, and hence fitness, is maximized at an optimum TAD noise intensity, which is represented by the distribution's characteristic width, sigma. In both the EVO and SR simulations, foraging success is the criterion, and the results are the predicted characteristic widths of the TADs that maximize success. Our results are twofold: (1) the evolving characteristic widths achieve stasis after many generations; (2) as a hop length parameter is changed, variations in the evolved widths generated by EVO parallel those predicted by SR. These findings provide support for the hypotheses that (1) sigma is an evolved quantity and that (2) SR plays a role in evolution.

We study the response of a parallel ensemble of stochastic resonators to external signals. For small signals linear response theory is used. We show that for a large number of elements this ensemble can be used to process broadband signals without frequency distortions. Nonlinear eeects manifest themselves by the phenomenon of synchronization. Although synchronization is not observed at the output of single elements the mean frequency of the collective response is locked by the input signal. It takes place for a suuciently large number of elements in a wide range of internal noise intensities. We also show that the synchronization is accompanied by a nonmonotonous Shannon entropy of the collective output indicating noise-induced order. One of the major motivations in research on stochastic resonance (SR) 1] is the idea of improving the quality of small information signals passing through an optimally tuned bistable or threshold system 2,3]. Previous theoretical studies have shown that for extremely weak signals SR can be correctly described in terms of linear response theory (LRT) 4,5] using as measures the signal-to-noise ratio (SNR) or the spectral power ampliication (SPA). However , SR can also be understood as a synchronization phenomenon 6,7]. Using alternative measures employing residence-time distributions 8], Gammaitoni et al. have termed SR as a bona-de resonance in 6]. For a suuciently large magnitude of the input signal (but still subthreshold) the mean frequency of the output can be locked in a wide range of noise intensities 7]. Moreover, it has been shown that at the parameter plane \noise intensity{amplitude of the signal" regions of synchronizations can be obtained, similar to Arnold's tongues. Inside these tongues the mean frequency of the output is locked by the input signal. This phenomenon is accompanied by an increase of order at

Submitted for the MAR05 Meeting of The American Physical Society Modeling spatiotemporal patterns of neocortical activity in epileptic seizures DAISUKE TAKESHITA, FRANK MOSS, SONYA BAHAR, Center for Neurodynamics, Department of Physics and Astronomy, University of Missouri at St. Louis — Epileptic seizures are characterized by excess and synchronized neural activity. To investigate how seizures initiate and terminate, we develop a model of a neocortical network based on a model suggested by Wilson [1]. We simulate the effect of the potassium channel blocker 4-aminopyridine, which is often used in experiments to induce epileptic seizures, by decreasing the conductance of the potassium channels in a small fraction of neurons in our model. We show that the firing frequency of a single neuron is increased by decreasing the conductance in some cases. By coupling one normal neuron to another neuron which has decreased potassium conductance, changes in behavior such as an increase in firing rate, switching from spiking to bursting, and synchronized activity are observed depending on the coupling strength between the neurons. We will also discuss the effect of decreased conductance on the spread of activity through the network, and on the initiation and termination of seizure-like events. [1] Wilson HR, J. theor. Biol. (1999) 200, 375-388 Daisuke Takeshita Center for Neurodynamics, Department of Physics and Astronomy, University of Missouri at St. Louis Date submitted: 30 Nov 2004 Electronic form version 1.4

Objective: To review the stochastic resonance phenomena observed in sensory systems and to describe how a random process ('noise') added to a subthreshold stimulus can enhance sensory information processing and perception.Results: Nonlinear systems need a threshold, subthreshold information bearing stimulus and 'noise' for stochastic resonance phenomena to occur. These three ingredients are ubiquitous in nature and man-made systems, which accounts for the observation of stochastic resonance in fields and conditions ranging from physics and engineering to biology and medicine. The stochastic resonance paradigm is compatible with single-neuron models or synaptic and channels properties and applies to neuronal assemblies activated by sensory inputs and perceptual processes as well. Here we review a few of the landmark experiments (including psychophysics, electrophysiology, fMRI, human vision, hearing and tactile functions, animal behavior, single/multiunit activity recordings). Models and experiments show a peculiar consistency with known neuronal and brain physiology. A number of naturally occurring 'noise' sources in the brain (e.g. synaptic transmission, channel gating, ion concentrations, membrane conductance) possibly accounting for stochastic resonance phenomena are also reviewed. Evidence is given suggesting a possible role of stochastic resonance in brain function, including detection of weak signals, synchronization and coherence among neuronal assemblies, phase resetting, 'carrier' signals, animal avoidance and feeding behaviors.Conclusions: Stochastic resonance is a ubiquitous and conspicuous phenomenon compatible with neural models and theories of brain function. The available evidence suggests cautious interpretation, but justifies research and should encourage neuroscientists and clinical neurophysiologists to explore stochastic resonance in biology and medical science. (C) 2003 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Objective: To determine if a transcutaneous electrical stimulation (TENS) unit modified to deliver electrical impulses at random (R) or stochastic frequency, called TENS-R, provided better pain relief than conventional TENS.Design: A prospective, randomized, double-blinded, placebo-controlled study at an urban teaching hospital. A total of 13 adult subjects with radiculopathy on electromyogram and chronic radicular pain rated pain before and after walking 100 feet with proximal (axial) placement of TENS leads with randomized settings on conventional TENS, placebo, or TENS-R and, subsequently, with distal (limb) placement of TENS leads with randomized settings, all on the same day. The pain measures used were the McGill Pain Questionnaire, parts 1 and 2, and the Visual Analog Scale. The functional measure was speed of walking.Results: Four men and seven women completed the study pain scores, measured by McGill Pain Questionnaire part 2, significantly improved when the patient used TENS-R vs. conventional TENS (P = 0.006, analysis of variance). Placement of TENS electrodes on the back significantly decreased pain compared with lead placement on the legs for McGill Pain Questionnaire part 1 (P = 0.007), McGill Pain Questionnaire part 2 (P = 0.042), and the Visual Analog Scale (P = 0.026) measures.Conclusions: Qualitative pain scores significantly improved when the patient used TENS-R vs. conventional TENS. Lead placement of any TENS modality over the back vs. over the leg improved all pain scores.

Active Brownian Particles are self-propelled particles that move in a dissipative medium subject to random forces, or noise . Additionally, they can be confined by an external field and/or they can interact with one another. The external field may actually be an attractive marker, for example a light field (as in the experiment) or an energy potential or a chemical gradient (as in the theory). The potential energy can also be the result of interparticle attractive and/or repulsive forces summed over all particles (a mean field potential). Four, qualitatively different motions of the particles are possible: at small particle density their motions are approximately independent of one another subject only to the external field and the noise, which results in moving randomly through or performing rotational motions about a central point in space. At increasing densities interactions play an important role and individuals form a swarm performing several types of self-organized collective motion. We apply this model for the description of zooplankton Daphnia swarms. In the case of the zooplankton Daphnia (and probably many other aquatic animals that form similar motions as well) this vortex is hydrodynamical but motivated by the self-propelled motion of the individuals. Similar vortex-type motions have been observed for other creatures ranging in size from bacteria to flocks of birds and schools of fish. However, our experiment with Daphnia is unique in that all four motions can be observed in controlled laboratory conditions with the same animal. Moreover, the theory, presented in both continuous differential equation and random walk forms, offers a quantitative, physically based explanation of the four motions.

Stochastic synchronization analysis is applied to intracellular calcium oscillations in astrocyte cultures prepared from epileptic human temporal lobe. The same methods are applied to astrocyte cultures prepared from normal rat hippocampus. Our results indicate that phase-repulsive coupling in epileptic human astrocyte cultures is stronger, leading to an increased synchronization in epileptic human compared to normal rat astrocyte cultures.

We review here the nonlinear dynamical properties of the crayfish mechanoreceptor system from the hydrodynamically sensitive hairs on the tailfan through the caudal photoreceptor neurons embedded in the 6th ganglion. Emphasis is on the extraction of low dimensional behavior from the random processes (noise) that dominate this neural system. We begin with stochastic resonance in the sensory root afferents and continue with a discussion of the photoreceptor oscillator and its instabilities. Stochastic synchronization, rectification and the generation of second harmonic responses in the photoreceptors are finally discussed.

Techniques for detecting encounters with unstable periodic orbits (UPOs) have been very successful in the analysis of noisy, experimental time series. We present here a technique for applying the topological recurrence method of UPO detection to spatially extended systems. This approach is tested on a network of diffusively coupled chaotic Rossler systems, with both symmetric and asymmetric coupling schemes. We demonstrate how to extract encounters with UPOs from such data, and present a preliminary method for analyzing the results and extracting dynamical information from the data, based on a linear correlation analysis of the spatiotemporal occurrence of encounters with these low period UPOs. This analysis can provide an insight into the coupling structure of such a spatially extended system.

Elderly but healthy people are often seriously injured in falls. Exploiting the phenomenon of stochastic resonance, biological physicists have designed a shoe with a vibrating insole that helps maintain balance.