| Course Unit Code | 460-4087/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| ZEL01 | prof. Ing. Ivan Zelinka, Ph.D. |
| Summary |
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| The aim of the lectures is to introduce to the students the problems of non-conventional algorithms, their biological - physical origin. In the lectures will be discussed the various areas of their origin, usually from natural complex systems with emphasis of their physical-mathematical and algorithmic description and implementation of the PC. The lectures will give the students an interdisciplinary perspective on the issue of non-conventional algorithms, complex systems and their dynamic behavior. Students get an overview of modern computational algorithms allowing to model and simulate the otherwise very complicated and complex systems (deterministic chaos, Thom's catastrophe theory, fractal geometry, swarm intelligence, algorithms, quantum mechanics, cellular automata, "physarium machines", "Self-Organized criticality", ...) and vice-versa will get insight on how are unconventional algorithms derived from above mentioned complex systems. After successfully completing the course will have an interdisciplinary graduate survey knowledge of unconventional algorithms and will be able to apply the methods discussed in the course to real problems. Students should be able to continue further in deeper self-study in this topic. |
| Learning Outcomes of the Course Unit |
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| The aim of the course is to acquaint its students with unconventional algorithms from physical, biological processes and complex systems. The graduate will gain an overview of modern computational procedures based on principles observed from complex processes and dynamics. Upon successful completion of the course, the graduate will be able to apply the methods discussed in the course to real problems. This course is not a free continuation of the BIA course. |
| Course Contents |
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Lectures:
1. Complexity. The current state of understanding of complex systems and their classification. Synergetics. Demonstration-motivational examples and videos demonstrating the occurrence of the behaviour of complex systems in everyday real life.
2. Artificial neural networks (ANN), basic concepts, principles and classifications. Training set, structure and topology ANN. Type of learning. Separability.
3. Artificial neural networks (ANN), Perceptron, multilayer perceptron and backpropagation learning.
4. Artificial neural networks (ANN), design of network topology, unconventional learning methods, training set and its construction from data.
5. Artificial neural networks (ANN), Examples of use.
6. Algorithms of deterministic chaos. Historical outline and classification of dynamical systems generating chaos. Simple models and examples. Determinism and the edge of chaos (according to Kaufmann). Typical chaotic systems: Lorenzo's model of weather and a strange attractor, electronic system and the problem of three bodies (binary and planet model). Divergence of close trajectories. Determinism and unpredictability. Invariants of chaotic behaviour. Feigenbaum constants, self-similarity, U-sequences, computers and chaos. Discrete dynamical systems. Basic simple models, Poincaré sections, bifurcations, bifurcation diagram as a holistic view of system behaviour, algorithms and examples. From order to chaos: paths leading to chaotic behaviour. Period doubling, quasi-periodicity, alternation and crisis. Bifurcations and Thom's disasters. Algorithmization of chaotic behaviour and methods of reconstruction. Use in cryptographic techniques, chaos control and its occurrence in economic systems
7. Thom's theory of disasters and connection with chaotic behaviour. Introduction to the issue, basic models and hierarchy of disasters. Their occurrence in system dynamics and identification algorithms according to symptoms in the measured data. Examples of occurrence: economic systems, physical systems, mechanical systems.
8. Algorithms of fractal geometry and visualization of complex structures. IFS algorithm. History, the definition of fractal, basic types of algorithms generating fractals. Fractal dimensions, interpolation and compression.
9. Fractal geometry algorithms - TEA algorithm and Mandelbrot set, Julius sets and their graphical preview. development systems and artificial life. L-systems, turtle graphics, parametric L-systems, algorithmization of L-systems from the point of view of fractal geometry.
10. Algorithms of fractal geometry - occurrence in nature, data, behaviour of systems and technology. Applications in graphic design, art, computer games and film - video demonstrations.
11. Algorithms and complex systems. Complex systems generating the effect of "self-organized criticality" (self-organized criticality - SOC), their modelling (models such as sand piles, ...) and occurrence in real complex systems (evolution, earthquakes, avalanches).
12. Cellular automata (BA) and complex systems. BA formalism, dynamics and classification of cellular automata according to Wolfram, Conway's game of life, modelling using BA. Cellular automata and space-time chaos. BA and music generation. BA and solving complex problems. Complex algorithmic behaviour of BA based on simple rules.
13. Algorithms and complex networks. Introduction to complex networks, methods of visualization and algorithmization of their dynamics. Examples of the occurrence of complex networks (social networks, dynamics of evolutionary processes, ...). Visualization of complex network dynamics using models of chaotic systems. Visualization of the dynamics of evolutionary techniques using complex networks.
14. Course summary. Mutual connections between individual types of algorithms, their dynamics and behaviour of complex systems.
Laboratories (for PC classrooms):
The seminar will focus on the practical application of the discussed techniques and solutions of selected problem examples.
• Implementation of a perceptron and its application to a simple linearly separable problem.
• Implementation of a multilayer perceptron (including backpropagation of an error) and its implementation on a linearly inseparable problem.
• Implementation of Hopfield networks and their application to simple patterns
• Implementation of Q-learning (Reinforcement learning) within the creation of a simple game.
• Application of neural networks and Q-learning to the so-called pole-balancing problem
• Fractal geometry. Implementation of L-systems.
• Fractal geometry. IFS. Implementation of selected IFS.
• Fractal geometry. The use of fractal geometry to create a simple landscape, or. surface (2D or 3D)
• Chaos theory. Logistics function. Neural network applications for the prediction of numbers generated by a logistic function.
• Chaos theory. Chaotic movement. Visualization of double pendulum movement
• Cellular automata: Implementation (and visualization) of the fire algorithm (Forest-fire) |
| Recommended or Required Reading |
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| Required Reading: |
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1. Back T., Fogel D. B. & Michalewicz Z., Handbook of Evolutionary Computation, (Institute of Physics, London), 1997
2. Hilborn R.C.1994, Chaos and Nonlinear Dynamics, Oxford University Press, ISBN 0-19-508816-8, 1994
3. Ilachinsky A., Cellular Automata: A Discrete Universe, World Scientific Publishing, ISBN 978-9812381835, 2001
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1. Zelinka I., Oplatková Z., Šeda M., Ošmera P., Včelař F., Evoluční výpočetní techniky, principy a aplikace, BEN, 2008, Praha
2. Zelinka I., Včelař F., Čandík M., Fraktální geometrie – principy a aplikace, BEN, 2006, 160 p., ISBN 80-7300-191-8
3. Horák J., Krlín L.1996, Deterministický chaos, Academia, ISBN 80-200-0416-5, 1996
4. Kolář I.1988, Úvod do Thomovy teorie katastrof, Academia, ISBN 21-056-88, 1988
5. Arnold V.I.1986, Teória katastróf, Alfa, ISBN 63-204-86, 1986
6. Back T., Fogel D. B. & Michalewicz Z., Handbook of Evolutionary Computation, (Institute of Physics, London), 1997
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| Recommended Reading: |
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Bekenstein J. D., Information in the Holographic Universe, Scientific American, August, 2003
R. Gilmore 1993, Catastrophe Theory for Scientists and Engineers, John Wiley and Sons, ISBN 0-486-67-539-4, 1993
Gheorghe Paun (Author), Grzegorz Rozenberg (Author), Arto Salomaa, DNA Computing: New Computing Paradigms, Springer, ISBN 978-3540641964
Zelinka I, Celikovsky S, Richter H and Chen G., (2010) Evolutionary Algorithms and Chaotic Systems, (Eds), Springer, Germany, 550s, 2010.
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Zelinka I., Oplatková Z., Šeda M., Ošmera P., Včelař F., Evoluční výpočetní techniky, principy a aplikace, BEN, 2008, Praha
Bekenstein J. D., Informace v holografickém vesmíru, Scientific American, česká edice, 03/2006
Mařík V. Štěpánková O., Lažanský J., Umělá inteligence IV, Academia, Praha, ISBN 80-200-1044-0, 2004
Mařík V. Štěpánková O., Lažanský J., Umělá inteligence III, Academia, Praha, ISBN 80-200-0472-6, 2001
Krempaský J. 1994, Synergetika, Vydavatelství STU Bratislava, ISBN 80-227-0707-4, 1994
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 45 | 20 |
| Examination | Examination | 55 | 6 |