Evolving Structures in Mathematics - NMMB564

• Anglický název: Evolving Structures in Mathematics
• Zajišťuje: Katedra algebry (32-KA)
• Fakulta: Matematicko-fyzikální fakulta
• Platnost: od 2023
• Semestr: zimní
• E-Kredity: 2
• Rozsah, examinace: zimní s.:0/2, Z [HT]
• Počet míst: neomezen
• Minimální obsazenost: neomezen
• 4EU+: ne
• Virtuální mobilita / počet míst pro virtuální mobilitu: ne
• Stav předmětu: nevyučován
• Jazyk výuky: angličtina, čeština
• Způsob výuky: prezenční
• Způsob výuky: prezenční
• Poznámka: předmět lze zapsat opakovaně
• Garant: doc. RNDr. Jiří Tůma, DrSc.; Tomáš Mikolov
• Třída: M Mgr. MMIB; M Mgr. MMIB > Volitelné
• Kategorizace předmětu: Matematika > Algebra

Anotace

čeština

Poslední úprava: doc. Mgr. Petr Kaplický, Ph.D. (17.01.2020)

Seminář zabývající se vyvíjejícími se strukturami (evolving structures) v matematice.

angličtina

Poslední úprava: doc. Mgr. Petr Kaplický, Ph.D. (17.01.2020)

Seminar on evolving structures in mathematics.

Literatura

čeština

Poslední úprava: 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.

Sylabus

čeština

Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (15.05.2020)

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.

Neuroevolution

• 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.

angličtina

Poslední úprava: 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.

Neuroevolution

• 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.