Algorithmic analysis of irrational rotations in a single neuron model |
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| Affiliation: | 1. Department of Statistical Science, The Graduate University for Advanced Studies, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan;2. Department of Mathematical Engineering and Information Physics, Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;3. CREST, Japan Science and Technology Corporation (JST), 4-1-8 Hon-Cho, Kawaguchi, Saitama 332-0012, Japan |
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| Abstract: | We study computability of real-valued functions and the information needed for simulation of dynamical systems. In particular, we describe application of Kolmogorov complexity theory to computer simulation of irrational rotations in a single neuron model. We deduce the information needed for a parameter in simulating the dynamics by showing a difference in Kolmogorov complexity between a computable parameter and a non-computable parameter. Finally, we show that all trajectories generated by irrational rotations are non-computable iff its parameter is non-computable. |
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