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We show that a network of spiking neurons exhibits robust self-organized criticality if the synaptic efficacies follow realistic dynamics. Deriving analytical expressions for the average coupling strengths and inter-spike intervals, we demonstrate that networks with dynamical synapses exhibit critical avalanche dynamics for a wide range of interaction… (More)

- Thomas Villmann, Ralf Der, J. Michael Herrmann, Thomas Martinetz
- IEEE Trans. Neural Networks
- 1997

The neighborhood preservation of self-organizing feature maps like the Kohonen map is an important property which is exploited in many applications. However, if a dimensional conflict arises this property is lost. Various qualitative and quantitative approaches are known for measuring the degree of topology preservation. They are based on using the… (More)

- Dmitri Bibitchkov, J Michael Herrmann, Theo Geisel
- Network
- 2002

Neurophysiological experiments show that the strength of synaptic connections can undergo substantial changes on a short time scale. These changes depend on the history of the presynaptic input. Using mean-field techniques, we study how short-time dynamics of synaptic connections influence the performance of attractor neural networks in terms of their… (More)

- Hans-Ulrich Bauer, J. Michael Herrmann, Thomas Villmann
- Neural Networks
- 1999

|Neural maps combine the representation of data by codebook vectors, like a vector quantizer, with the property of topography, like a continuous function. While the distortions due to the vector quantization are simple to compute and to compare between diierent maps, topography of a map is diicult to deene and to quantify. Yet, topography of a neural map is… (More)

- Anna Levina, J Michael Herrmann, Theo Geisel
- Physical review letters
- 2009

We analytically describe a transition scenario to self-organized criticality (SOC) that is new for physics as well as neuroscience; it combines the criticality of first and second-order phase transitions with a SOC phase. We consider a network of pulse-coupled neurons interacting via dynamical synapses, which exhibit depression and facilitation as found in… (More)

- Ralf Der, J. Michael Herrmann
- ESANN
- 1994

- Silke Dodel, J. Michael Herrmann, Theo Geisel
- Neurocomputing
- 2002

- Joachim Haß, J. Michael Herrmann
- Neural Computation
- 2012

A prominent finding in psychophysical experiments on time perception is Weber's law, the linear scaling of timing errors with duration. The ability to reproduce this scaling has been taken as a criterion for the validity of neurocomputational models of time perception. However, the origin of Weber's law remains unknown, and currently only a few models… (More)

- Thomas Villmann, Ralf Der, J. Michael Herrmann, Thomas Martinetz
- Fuzzy Days
- 1994

- Silke Dodel, J. Michael Herrmann, Theo Geisel
- Neurocomputing
- 2000