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13593Fakultät 1 – MINT – Mathematik, Informatik, Physik, Elektro- und Informationstechnik
Angewandte algebraische Quantentheorie
Titel auf Englisch: Applied Algebraic Quantum Theory
Lernergebnisse
After successfully completing the module, students will have a in-depth knowledge of algebraic quantum theory. They know its application in different areas. They can assess the importance of algebraic quantum theory in the context of artificial intelligence.
Inhalte
- The ideas of pioneer quantum theory as motivation: Systems, state preparation, measurement, dynamics. Operator algebras on Hilbert space.
- Coordinate-free (Dirac) and representation-free (von Neumann) descriptions: C*-algebras, W*-algebras, GNS-construction and representation theory.
- Classical dynamical systems: symbolic dynamics, neural automata and vector symbolic architectures.
- Contextual emergence: context states, weak topologies, singular perturbations, emergent descriptions.
- Projector lattices: ontology inference for cognitive dynamical systems.
Voraussetzungen
Verpflichtende Voraussetzungen
Keine
Empfohlene Voraussetzungen
Keine
Prüfungsmodalitäten
- Written examination, 120 min. OR
- Oral examination, 30-40 min. (with small number of participants)
Angeboten in
- Applied MathematicsM.Sc.
Wahlpflichtkomplex: Analysis / Algebra / Combinatorics
- Artificial IntelligenceM.Sc.
Wahlpflichtkomplex: Knowledge Acquisition, Representation, and Processing
- Artificial Intelligence EngineeringM.Sc.
Wahlpflichtkomplex: Cognitive Science and Neuroscience
| Studiengang | Abschluss | Wahlpflichtkomplex |
|---|---|---|
| Applied Mathematics | M.Sc. | Analysis / Algebra / Combinatorics |
| Artificial Intelligence | M.Sc. | Knowledge Acquisition, Representation, and Processing |
| Artificial Intelligence Engineering | M.Sc. | Cognitive Science and Neuroscience |
Literatur und Materialien
- Primas, H. (1981). Chemistry, Quantum Mechanics and Reductionism. Lecture Notes in Chemistry. Springer, Berlin.
- Haag, R. (1992). Local Quantum Physics: Fields, Particles, Algebras. Texts and Monographs in Physics. Springer, Berlin.
- Sakai, S. (1971). C*-Algebras and W*-Algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer, Berlin.
- beim Graben, P. & Atmanspacher, H. (2006). Complementarity in classical dynamical systems. Foundations of Physics, 36, 291 – 306.
- beim Graben, P.; Barrett, A. & Atmanspacher, H. (2009). Stability criteria for the contextual emergence of macrostates in neural networks. Network: Computation in Neural Systems, 20, 178 – 196.
- Carmantini, G. S.; beim Graben, P.; Desroches, M. & Rodrigues, S. (2017). A modular architecture for transparent computation in recurrent neural networks. Neural Networks, 85, 85 – 105.
- beim Graben, P.; Huber, M.; Meyer, W.; Römer, R. & Wolff, M. (2021). Vector symbolic architectures for context-free grammars. Cognitive Computation, 10.1007/s12559-021-09974-y.
- Huber-Liebl, M.; Römer, R.; Wirsching, G.; Schmitt, I.; beim Graben, P. & Wolff, M. (subm.). Quantum-inspired cognitive agents. Frontiers in Applied Mathematics and Statistics.
Bewertungen von Studierenden
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