Hans-Otto Carmesin

A Taxonomy of Spatial Knowledge for Navigation and its Application to the Bremen Autonomous Wheelchair

A new taxonomy is proposed that relates different navigational behaviors in a hierarchical and compositional way. Elementary navigation tactics are combined to tactical navigation in routes; landmarks in space are contrasted to routemarks in networks of passages. Survey knowledge comes in at the level of strategic navigation. The Bremen Autonomous Wheelchair is then presented as a vehicle for experimentation in robotics, both to model biologically plausible navigational behaviors and to develop efficient navigational mechanisms for a technical application. The implementation on the autonomous system is based on the use of basic behaviors and the identification of routemarks. The actual recognition of artificial routemarks is described and early results of the current work on the identification of natural 3-D marks are presented.

Continuous phase transitions in the perception of multistable visual patterns

Abstract.The phenomenon of stroboscopic alternative motion exhibits five different percepts that are seen with an increase in the frequency of presentation: (a) succession, (b) fluttering motion, (c) reversible clockwise and counter-clockwise turning motion, (d) oppositional motion and (e) simultaneity. From a synergetic point of view the increase in frequency is a control parameter and the different percepts are order parameters with phase transitions in between. The neural network model of Carmesin and Arndt is applied to receive predictions about hysteresis and phase transitions between these order parameters. Empirical data show the different motion percepts (b), (c) and (e) have lognormal distributions. Following the theoretical model, it is argued that there are three different phases, (a), (c) and (e), with two continuous phase transitions, (b) and (d), between them. The experimental data substantially match the theoretical ssumptions.

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 neural network model for stroboscopic alternative motion

Abstract.A neural network which models multistable perception is presented. The network consists of sensor and inner neurons. The dynamics is established by a stochastic neuronal dynamics, a formal Hebb-type coupling dynamics and a resource mechanism that corresponds to saturation effects in perception. From this a system of coupled differential equations is derived and analyzed. Single stimuli are bound to exactly one percept, even in ambiguous situations where multistability occurs. The network exhibits discontinuous as well as continuous phase transitions and models various empirical findings, including the percepts of succession, alternative motion and simultaneity; the percept of oscillation is explained by oscillating percepts at a continuous phase transition.

Multilinear back-propagation convergence theorem

Abstract For neutral networks, back-propagation is a traditional, efficient and popular learning algorithm that relies on a transparent gradient method. However, there is no general convergence theorem. This shortcoming is completely resolved by a generalization to multilinear neural networks.

Models of continuous neural networks

A neural network is investigated, in which the state of a neuron is described by any real number, while its mean quadratic activation is one. The Hopfield learning rule is assumed and generalized. The net is equivalent to one spin in a 22l-polar external field, and its capacity is at most lN, where N is the number of neurons. The infinite-polar net exhibits infinite capacity and both continuous and discontinuous phase transitions.

Slow dynamics at the liquid-glass transition

A fluid with isotropic particles is analyzed from first principles. Below the visco-elastic transition temperature, the relaxation time for the specific heat diverges according to a Vogel-Fulcher law. The reason for the discovered singularity is the volume excluded by a particle. So, the singularity is of quite general nature. Formally, the classical fluid undergoes a phase transition of first order at the singularity. For o-terphenyl, the theory is in agreement with experiments. Comparisons with other properties below the melting temperature are presented and further experiments are suggested.