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Mathematical Sciences (Namiki) Lab
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Research that reads the complexity arising from simple rules through the lens of dynamical systems.
AboutAbout the lab
Complexity arising from simple rules
Prof. Namiki studies the field collectively known as complex systems.
A cellular automaton is a dynamical system that simply updates the 0s and 1s in a row of cells according to a simple rule, yet shows a wide variety of behavior.
The lab treats this using ideas from thermodynamics and statistical mechanics, aiming to grasp the properties of the system from how its entropy decreases.
The lab also works on quantum walks, which are related to quantum computation, chaotic time-series analysis of EEG (brainwave) data, and the construction of a digital library of mathematics.
Key terms
- Cellular automaton
- A mathematical model in which the states of cells arranged in a row are all updated at once according to fixed rules
- Entropy
- A quantity expressing how spread out the states are, that is, the degree of disorder
- Quantum walk
- The motion of a randomly moving particle (a random walk) recast according to the rules of quantum mechanics
ResearchResearch themes
The lab studies the field known as complex systems from the viewpoint of dynamical systems and entropy. It is also pursuing informatics research: building a digital library that brings together mathematics journals.
*Illustrative imageMathematics of Cellular Automata
The lab investigates cellular automata, in which simple rules give rise to diverse behavior, from the standpoint of thermodynamics and statistical mechanics. Repeated time evolution from a random initial state reduces spatial entropy, and the goal is to capture the properties of the system through this rate of decrease.
*Illustrative imageQuantum Walks
The lab studies quantum walks, a topic related to quantum computation, which has advanced remarkably in recent years. They are an intriguing subject; for example, their limit distribution looks entirely different from that of an ordinary random walk.
*Illustrative imageChaos Analysis of EEG Data
As an application of chaotic time-series analysis, the lab analyzes EEG data from patients with brain disorders. The aim is to characterize EEG during seizures and between seizures separately, and to develop this work to the point where it can contribute to treatment.
*Illustrative imageDigital Library of Mathematics
The lab is building DML-JP, the Japanese part of the Digital Mathematics Library. This informatics research integrates mathematics journals scattered across digital repositories and adds the information needed for mathematics.
MembersFaculty
- ProfessorTakao Namiki
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “CA3061-81k7” Maxter315 / CC BY-SA 4.0 (cropped)
- Mathematics of Cellular Automata: “Cellular automata ( )” Sergio Martínez from Austin, US / CC BY-SA 2.0 (cropped)
- Quantum Walks: “Rec8 3kc2p” WingkLEE / CC BY-SA 3.0 (cropped)
- Chaos Analysis of EEG Data: “Attractor Poisson Saturne” Nicolas Desprez / CC BY-SA 3.0 (cropped)
- Digital Library of Mathematics: “Depositos” BibliotecaUCLM / CC BY-SA 4.0 (cropped)
- Related lab (数理科学系): “Belousov Zhabotinsky reaction ( )” Stephen Morris / CC BY 2.0 (cropped)
- Related lab (解析系
（宮尾忠宏） ): “Hofstadter's butterfly” Mytomi / Public domain (cropped) - Related lab (数理科学系
（佐藤讓） ): “Japanese attractor on black background” Yapparina / CC0 (cropped) - Related lab (解析系
（浜向直） ): “Real snowflake macro photo” Alexey Kljatov / CC BY-SA 4.0 (cropped)
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