Nonlinear phenomena are ubiquitous in our world. We develop new theories, methods and algorithms for analyzing and predicting nonlinear phenomena.
- Bootstrap nonlinear prediction
- Nonlinear DPCM for image signals
- Nonlinear analysis on complex movements of dishwasher
- Nonlinear models for headway of bus and nonlinear prediction for traffic flows
- Prediction systems of lightning
- Nonlinear analysis on mechanisms and prediction systems for seismic events
- Local weather prediction
- Nonlinear analysis on the Internet traffic
- Nonlinear analysis and prediction for the Nikkei Stock Average and exchange markets
- Statistical analysis on neuronal spikes
- Prediction and control for harvest of crops
- Nonlinear analysis on brain waves and pulse waves and for human status diagnostics
- Nonlinear analysis and synthesis of the audio signals
In our brain, many neurons connect each other and construct huge neural networks. What is the basic principle of information processing in our brain? In this project, we will clarify new information processing principles used in our brain and apply it to resolve engineering issues.
- Analysis on synchronous firing phenomena using spike-timing-dependent plasticity (STDP) learning rules
- Firing mechanism
- Phase consistency (Consistency of firing timing)
- Temporal coding (Depending on the timing when neuron fires)?
- Rate coding (Depending on the firing rate)?
- Dual information coding (Both temporal coding and rate coding)?
- What happens when we use chaotic dynamics?
- What happens when we use chaos as noise?
- Estimation of Lyapunov exponents by diagonalization of large-scale matrix using techniques of numerical calculations
In our world, we are often asked to solve combinatorial optimization problems. In this project, we develop a new framework for solving very large scale combinatorial optimization problems by chaotic dynamics.
- Traveling salesman problems
- Quadratic assignment problems
- Lin-Kernighan algorithms controlled by chaotic dynamics
- Dynamic shortest path search problems
- Packets routing problems
- Controlling traffics and signals
Many complex networks exist in our world. Using the novel complex network theory, we analyse how complex networks are constructed in our real world.
- Analysis on spike-timing-dependent plasticity (STDP) learning rules using the complex network theory
- Developing quantification techniques as weighted digraph
- Estimation of network structures from multi-variable time series
- Estimation of network structures from multi neuronal spike data