Laboratory for Mathematical Neuroscience

Amari Research Laboratory aims at elucidation of the principles of information processing in the brain mathematically, thus establishing foundations of mathematical neuroscience. Information is represented in the brain by spatio-temporal patterns of excitation in ensembles of neurons, and processed by dynamics of parallel interactions of neurons. It is a learning system which modifies its structures, equipped with memory and self-organizing ability. Through mathematical analysis of various parts and functions of the brain, we establish principles of the brain mathematically, and also we search for the performances of brain-style information processing systems. We further develop mathematical tools and methods such as information geometry. We are currently studying information geometry of learning machines, analysis of neuronal spike sequences, sparse signal analysis and statistical neurodynamics.

Research Subjects

• Information geometry of neuro manifolds
• Mathematical model of higher-order functions in cerebrum
• Mathematical analysis of spatio-temporal spiking pluse sequences
• Foundation of statistical neurodynamics
• Sparse signal analysis

Publications

1. Mitsudo, T., Gannon, C., and Takeichi, H.:
   " An electroencephalographic investigation of the filled-duration illusion"
   Frontiers in Integrative Neuroscience 5(84), 1-13 (2012).
2. Nakajima, Y., and Takeichi, H.:
   " Human processing of short temporal intervals as revealed by an ERP waveform analysis"
   Frontiers in Integrative Neuroscience 5(74), 1-10 (2011).
3. Ando, H., Sinha, S., Storni, R., and Aihara, K.:
   " Synthetic gene networks as potential flexible parallel logic gates"
   Europhysics Letters 93, 50001-p1-50001-p6 (2011).
4. Amari, S.:
   " On optimal data compression in multiterminal statistical inference"
   IEEE Transactions on Information Theory 57, 5577-5587 (2011).
5. Amari, S., and Ohara, A.:
   " Geometry of q-exponential family of probability distributions"
   Entropy 13, 1170-1185 (2011).
6. Amari, S., Ozeki, T., Cousseau, F., and Wei, H.:
   " Dynamics of learning in hierarchical models -Singularity and milnor attractor, Wang R, Gu F (eds.)"
   Advances in Cognitive Neurodynamics (II), 3-9, Springer (2011).
7. Lu, Y., Sato, Y., and Amari, S.:
   " Travelling Bumps and Their Collisions in a Two-Dimensional Neural Field"
   Neural Computation 23, 1248-1260 (2011).
8. Oizumi, M., Okada, M., and Amari, S.:
   " Information loss associated with imperfect observation and mismatched decoding"
   Frontiers in Computational Neuroscience 5(9), 1-13 (2011).
9. Magdoom, K. N., Subramanian, D., Chakravarthy, V. S., Ravindran, B., Amari, S., and Meenakshisundaram, N.:
   " Modeling Basal Ganglia for Understanding Parkinsonian Reaching Movements"
   Neural Computation 23, 477-516 (2011).
10. Cichocki, A., Cruces, S., and Amari, S.:
    " Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization"
    Entropy 13, 134-170 (2011).