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Course, academic year 2022/2023
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Evolving Structures in Mathematics - NMMB564
Title: Evolving Structures in Mathematics
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021 to 2022
Semester: winter
E-Credits: 2
Hours per week, examination: winter s.:0/2, C [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Note: you can enroll for the course repeatedly
Guarantor: doc. RNDr. Jiří Tůma, DrSc.
Tomáš Mikolov
Class: M Mgr. MMIB
M Mgr. MMIB > Volitelné
Classification: Mathematics > Algebra
Annotation -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (17.01.2020)
Seminar on evolving structures in mathematics.
Literature -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (20.01.2020)

A. W. Burks, Von Neumann's Self-Reproducing Automata, Ann Arbor, 1969.

C. G. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena Volume 22, Issues 1–3, October–November 1986, 120-149.

A. Lindenmayer, Mathematical Models for Cellular Interactions in Development, Journal of Theoretical Biology Volume 18, Issue 3, March 1968, 280-299.

M. Minsky The Society of Mind. (1986) New York: Simon & Schuster. ISBN 0-671-60740-5.

K. O. Stanley and R. Miikkulainen, Evolving neural networks through augmenting topologies, Evolutionary Computation 10(2): 99-127.

A. M. Turing, Computing Machinery and Intelligence. Mind 49 (1950): 433-460.

Syllabus -
Last update: doc. RNDr. Jiří Tůma, DrSc. (25.02.2020)

1) AI, Generalization, and Unsupervised Learning

  • history: Computing Machinery and Intelligence, A. Turing
  • present: deep learning, neural networks
  • possible future: more generalization from less training examples
  • evolution as an inspiration for AI research instead of neuroscience (the brain)

2) Wolfram's elementary cellular automata (ECA): simple evolving models where structures emerge

Barbora Hudcova: more formal classification of ECAs using their transition lengths

3) Towards metrics of complexity: Occam's razor, Minimum description length, Kolmogorov complexity, Algorithmic probability

The Quark and The Jaguar, Murray Gell-Mann: measures of complexity proposed by Gell-Mann

4) Hugo Cisneros: Evolving Structures in Complex Systems

  • metric of structured complexity based on compression algorithms

5) Von Neumann's Self-Reproducing Automata, A. W. Burks

  • maybe the first attempt to design non-trivial self-reproducing systems capable of evolution

6) Studying Artificial Life with Cellular Automata, C. G. Langton

  • mathematical structures that can have similar properties to how we define life: self-reproduction, evolution

7) Other related topics:

Genetic Algorithms, J. Holland

  • We will discuss the basic ideas behind evolutionary and genetic algorithms and genetic programming, and compare these algorithms with the previously discussed

attempts to design objects that can evolve.


  • Evolving neural networks through augmenting topologies, K. O. Stanley and R. Miikkulainen
  • Another attempt to simulate evolution that uses neural networks. In this talk, we will briefly discuss the basics of artificial neural networks, and extend these to

models that can grow in complexity.

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