We study the avalanche dynamics of a system of globally coupled threshold elements receiving random input. The model belongs to the same universality class as the random-neighbor version of the Olami-Feder-Christensen stick-slip model. A closed expression for avalanche size distributions is derived for arbitrary system sizes N using geometrical arguments in the system's configuration space. For finite systems, approximate power-law behavior is obtained in the nonconservative regime, whereas for N--> infinity, critical behavior with an exponent of -3/2 is found in the conservative case only. We compare these results to the avalanche properties found in networks of integrate-and-fire neurons, and relate the different dynamical regimes to the emergence of synchronization with and without oscillatory components.

Correlation functions with multiple scaling regions occur in the description of the fluctuations in the center of pressure during quiet standing. Postural sway is modeled as an inverted pendulum with a delayed feedback constructed such that for deviations beyond a spatial threshold a constant restoring force is engaged. In the absence of noise, two stable limit cycles coexist. The correlation function depends on the added noise intensity: at intermediate noise levels three scaling regions appear whereas only two occur for high noise levels. Our observations suggest that correlation functions with multiple scaling regions reflect noise-induced transitions in bistable dynamical systems.

The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, tau(n), be greater than a critical delay tau(c) that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when theta exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.

Fisher information is used to analyze the accuracy with which a neural population encodes D stimulus features. It turns out that the form of response variability has a major impact on the encoding capacity and therefore plays an important role in the selection of an appropriate neural model. In particular, in the presence of baseline firing, the reconstruction error rapidly increases with D in the case of Poissonian noise but not for additive noise. The existence of limited-range correlations of the type found in cortical tissue yields a saturation of the Fisher information content as a function of the population size only for an additive noise model. We also show that random variability in the correlation coefficient within a neural population, as found empirically, considerably improves the average encoding quality. Finally, the representational accuracy of populations with inhomogeneous tuning properties, either with variability in the tuning widths or fragmented into specialized subpopulations, is superior to the case of identical and radially symmetric tuning curves usually considered in the literature.

One of the fundamental and puzzling questions in vision research is how objects are segmented from their backgrounds and how object formation evolves in time. The recently discovered shine-through effect allows one to study object segmentation and object formation of a masked target depending on the spatiotemporal Gestalt of the masking stimulus (Herzog & Koch, 2001). In the shine-through effect, a vernier (two abutting lines) precedes a grating for a very short time. For small gratings, the vernier remains invisible while it regains visibility as a shine-through element for extended and homogeneous gratings. However, even subtle deviations from the homogeneity of the grating diminish or even abolish shine-through. At first glance, these results suggest that explanations of these effects have to rely on high-level Gestalt terminology such as homogeneity rather than on low-level properties such as luminance (Herzog, Fahle, & Koch, 2001). Here, we show that a simple neural network model of the Wilson-Cowan type qualitatively and quantitatively explains the basic effects in the shine-through paradigm, although the model does not contain any explicit, global Gestalt processing. Visibility of the target vernier corresponds to transient activation of neural populations resulting from the dynamics of local lateral interactions of excitatory and inhibitory layers of neural populations.

The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.

We consider the effect of distributed delays in predator-prey models and ecological food webs. Whereas the occurrence of delays in population dynamics is usually regarded a destabilizing factor leading to the extinction of species, we here demonstrate complementarily that delay distributions yield larger stability regimes than single delays. Food webs with distributed delays closely resemble nondelayed systems in terms of ecological stability measures. Thus, we state that dependence of dynamics on multiple instances in the past is an important, but so far underestimated, factor for stability in dynamical systems.

Adaptation of interaction delays is essential for the functioning of many natural and technical systems. We introduce a novel framework for studying the dynamics of delay adaptation in systems which optimize coincidence of inputs. For the important case of periodically modulated input we derive conditions for the existence and stability of solutions which constrain the set of mechanisms for reliable delay adaptation. Using numerical examples we show that our approach is applicable to more general than periodic input patterns such as Poissonian point processes with coordinated rate fluctuations.[S0031-9007(99)