J. Michael Herrmann

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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)
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)
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)
|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)
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)
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)