Helmut Schwegler

Coarse coding: calculation of the resolution achieved by a population of large receptive field neurons

Abstract. Electrophysiological studies in various sensory systems of different species show that many neurons involved in object localization have large receptive fields. This seems to contradict the high sensory resolution and the behavioral precision observed in localization experiments. Assuming a coarse coding mechanism, the resolution obtained by an ensemble of neurons is analytically calculated as a function of receptive field size. It is shown that particularly large receptive fields yield a high resolution.

Path integration -- a network model

Path integration is a primary means of navigation for a number of animals. We present a model which performs path integration with a neural network. This model is based on a neural structure called a sinusoidal array, which allows an efficient representation of vector information with neurons. We show that exact path integration can easily be achieved by a neural network. Thus deviations from the direct home trajectory, found previously in experiments with ants, can not be explained by computational limitations of the nervous system. Instead we suggest that the observed deviations are caused by a strategy to simplify landmark navigation.

Complex dynamics is abolished in delayed recurrent systems with distributed feedback times

Feedback systems with a single delay time—as described by delay-differential equations—are known to exhibit various dynamical behaviors including complex oscillations and chaos. Here we show that the consideration of a broad distribution of delay times instead of a single delay results in a shift of the dynamical bifurcations toward higher parameter values, yielding a larger set of parameters with fixed point behavior or simple oscillatory behavior. We demonstrate similar phenomena in three different systems: neuronal feedback in the hippocampus, white blood cell production, i.e., the Mackey-Glass equation, and population dynamics in theoretical ecology. Our results suggest that the observed simplification of the dynamics is independent of the shape of the delay distribution and the precise nature of the feedback. The existence of distributed delay times may yield a mechanism to avoid irregular fluctuations in biological feedback systems.

Physico-chemical model of a protocell

A physico-chemical model of a self-maintaining unity or protocell is constructed on the basis of reaction and diffusion processes. The surface motion of the protocell is taken into account explicitly by a so-called Stefan condition, which leads to a nonlinear feedback to the reaction and diffusion processes. The spatio-temporal dynamics in the neighbourhood of the steady states is investigated in the framework of linear stability analysis with the use of an expansion in terms of spherical harmonicsYlm. It is shown that modes with l⩾2 become successively unstable with increasing nutrient supply. The leading instability with l=2 initiates a process of the nonlinear dynamics which is interpreted as the onset of division. A stabilizing effect of surface tension is also discussed.

Modeling stochastic spike train responses of neurons: an extended Wiener series analysis of pigeon auditory nerve fibers.

Abstract.A general method for developing data-based, stochastic nonlinear models of neurons by means of extended functional series expansions was applied to neural activities of pigeon auditory nerve fibers responding to Gaussian white noise stimuli. To determine Wiener series representations of the investigated neurons the fast orthogonal search algorithm was used. The results suggest that nonlinearities are only instantaneous and that the signal transduction of the investigated sensory system can be described by cascades of dynamic linear and static nonlinear devices. However, only slight improvements result from the nonlinear terms. Considerable improvements are, nevertheless, possible by generalizing the ordinary Wiener series, so that prior neural activity can be taken into account. These extended series were used to develop stochastic models of spiking neurons. The models are able to generate realistic interspike interval distributions and rate-intensity functions. Finally, it will be shown that the irregularity in real and modeled action potential trains has advantages concerning the decoding of neural responses.

Coarse coding: applications to the visual system of salamanders

Abstract. In a previous study, we calculated the resolution obtained by a population of overlapping receptive fields, assuming a coarse coding mechanism. The results, which favor large receptive fields, are applied to the visual system of tongue-projecting salamanders. An analytical calculation gives the number of neurons necessary to determine the direction of their prey. Direction localization and distance determination are studied in neural network simulations of the orienting movement an d the tongue projection, respectively. In all cases, large receptive fields are found to be essential to yield a high sensory resolution. The results are in good agreement with anatomical, electrophysiological and behavioral data.

Simulander: A neural network model for the orientation movement of salamanders

Simulander is a feedforward neural network simulating the orientation movement of salamanders. The orientation movement is part of the prey capture behavior; it is performed with the head alone. Simulander is a network which consists of 300 neurons incorporating several cytoarchitectonic and electrophysiological features of the salamander brain. The network is trained by means of an evolution strategy. Although only 100 tectum neurons with fairly large receptive fields are used (“coarse coding”), Simulander is able to localize an irregularly moving prey precisely. It is demonstrated that large receptive field neurons are important for successful prey localization. The removal of a model tectum hemisphere leads to a network which accounts for investigations made in living monocular salamanders. The model also yields an understanding of electrical stimulation experiments in toads.

Parallel versus sequential processing of relational stimulus structures

Organisms are often faced with sets of stimuli bearing specifiable relationships to each other. Experimental data suggest that even animals not suspected of being particularly rational can solve problems involving consistent linear relationships. We examine the information processing required to cope with these and related stimulus structures from a theoretical point of view. We show that both a parallel processing neural network model and a serially processing Turing machine model require minimal complexities to process linear hierarchical structures. When dealing with other relational stimulus structures, the models need differing, greater minimal complexities. Siemann and Delius (1994) report experimental results indicating that both pigeons and humans appear to operate according to the parallel, neural network model we propose here. Further experiments likely to be diagnostic are proposed.

A nonlinear treatment of the protocell model by a boundary layer approximation

The “protocell” is a mathematical model of a self-maintaining unity based on the dynamics of simple reaction-diffusion processes and a self-controlled dynamics of the surface. In this paper its spatio-temporal behaviour far from the stationary structure is investigated by means of a boundary layer approximation. It is shown in detail how a simplified and mathematically feasible equation can be derived from the original parabolic problem. It turns out that the known instability which is initiated in the linear region around the stationary structure is continued further in the direction to a division by nonlinear dynamics.

Principles of Self-Generation and Self-Maintenance

Living systems are characterized as self-generating and self-maintaining systems. This type of characterization allows integration of a wide variety of detailed knowledge in biology. The paper clarifies general notions such as processes, systems, and interactions. Basic properties of self-generating systems, i.e. systems which produce their own parts and hence themselves, are discussed and exemplified. This makes possible a clear distinction between living beings and ordinary machines. Stronger conditions are summarized under the concept of self-maintenance as an almost unique character of living systems. Finally, we discuss the far-reaching consequences that the principles of self-generation and self-maintenance have for the organization, structure, function, and evolution of single- and multi-cellular organisms.