G. Montúfar, J. Rauh, N. Ay, Expressive Power and Approximation Errors of Restricted Boltzmann Machines. (submitted), MIS Preprint 27/2011 [pdf]

N. Ay, R. Der, M. Prokopenko, Information Driven Self-Organization: The Dynamical System Approach to Autonomous Robot Behavior. Theory in Biosciences (to appear), Santa Fe Working Paper 10-09-018 [pdf]

J. Rauh, T. Kahle, N. Ay, Support sets in exponential families and oriented matroid theory. International Journal of Approximate Reasoning (2011) 52:5, pp: 613-626 Arxiv 0906.5462 [pdf] Article [pdf]

G. Montúfar, N. Ay, Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines. Neural Computation (2011) 23:5, pp: 1306-1319 [pdf]

J. Rauh, N. Ay, Robustness and Conditional Independence Ideals. arXiv (2011), [pdf]

N. Ay, M. Müller, A. Szkoła, Effective Complexity of Stationary Process Realizations. Entropy (2011) 13, pp: 1200-1211 [pdf] Santa Fe Working Paper 11-04-014 [pdf]

M. Prokopenko, N. Ay, O. Obst, D. Polani, Phase transitions in least-effort communications. Journal of Statistical Mechanics (2010) P11025, [pdf]

N. Ay, M. Müller, A. Szkoła, Effective Complexity and Its Relation to Logical Depth. Information Theory, IEEE Transactions on (2010) 56:9, pp: 4593-4607 Arxiv 0810.5663 [pdf] Santa Fe Working Paper 08-12-046 [pdf]

E. Olbrich, T. Kahle, N. Bertschinger, N. Ay, J. Jost, Quantifying structure in networks. The European Physical Journal B - Condensed Matter and Complex Systems (2010) 77, pp: 239-247 [pdf]

K. Zahedi, N. Ay, R. Der, Higher coordination with less control -- A result of information maximization in the sensori-motor loop. Adaptive Behavior (2010) 18:3--4, pp: 338-355 [pdf]

T. Kahle, W. Wenzel, N. Ay, Hierarchical models, marginal polytopes, and linear codes. Kybernetika (2009) 45:2, pp: 189-207 Santa Fe Working Paper 09-01-001 [pdf]

T. Kahle, E. Olbrich, J. Jost, N. Ay, Complexity measures from interaction structures. Phys. Rev. E (2009) 79:2, pp: 026201 Arxiv 0806.2552 [pdf]

W. Löhr, N. Ay, On the Generative Nature of Prediction. Advances in Complex Systems (2009) 12, pp: 169-194 Santa Fe Working Paper 08-02-004 [pdf]

N. Ay, A refinement of the common cause principle. Discrete Appl. Math. (2009) 157, pp: 2439-2457 [pdf] Santa Fe Working Paper 08-01-001 [pdf]

E. Olbrich, N. Bertschinger, N. Ay, J. Jost, How should complexity scale with system size?. Eur. Phys. J. B (2008) 63:3, pp: 407-415 [pdf]

N. Ay, D. Polani, Information Flows in Causal Networks. Advances in Complex Systems (2008) 11:1, pp: 17-41 [pdf]

N. Bertschinger, E. Olbrich, N. Ay, J. Jost, Autonomy: An information theoretic perspective. Biosystems (2008) 91:2, pp: 331-345 [pdf]

N. Ay, N. Bertschinger, R. Der, F. Güttler, E. Olbrich, Predictive information and explorative behavior of autonomous robots. The European Physical Journal B - Condensed Matter and Complex Systems (2008) 63:3, pp: 329-339 [pdf]

N. Ay, D. C. Krakauer, Geometric robustness theory and biological networks. Theory in Biosciences (2007), pp: 93-121 [pdf]

N. Ay, A. Knauf, Maximizing Multi-Information. Kybernetika (2007) 42:5, pp: 517-538 Arxiv 0702002 [pdf]

T. Wennekers, N. Ay, P. Andras, High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal stochastic interactions.. Biosystems (2007) 89:1-3, pp: 190-197 [pdf]

J. Jost, N. Bertschinger, E. Olbrich, N. Ay, S. Frankel, An information theoretic approach to system differentiation on the basis of statistical dependencies between subsystems. Physica A: Statistical Mechanics and its Applications (2007) 378:1, pp: 1-10 [pdf]

N. Ay, J. C. Flack, D. C. Krakauer, Robustness and Complexity Co-constructed in Multi-modal Signaling Networks. Philos Trans R Soc Lond B Biol Sci (2007), pp: 441-447 [pdf]

T. Wennekers, N. Ay, A temporal learning rule in recurrent systems supports high spatio-temporal stochastic interactions. Neurocomputing (2006) 69, pp: 1199-1202 [pdf]

N. Ay, J. Crutchfield, Reductions of Hidden Information Sources. Journal of Statistical Physics (2005) 120, pp: 659-684 [pdf]

T. Wennekers, N. Ay, Stochastic interaction in associative nets. Neurocomput. (2005) 65-66, pp: 387-392 [pdf]

T. Wennekers, N. Ay, Finite State Automata Resulting from Temporal Information Maximization and a Temporal Learning Rule. Neural Computation (2005) 17:10, pp: 2258-2290 [pdf]

I. Erb, N. Ay, Multi-Information in the Thermodynamic Limit. Journal of Statistical Physics (2004) 115, pp: 949-976 [pdf]

T. Wennekers, N. Ay, Spatial and Temporal Stochastic Interaction in Neuronal Assemblies. Theory in Biosciences (2003) 122:1, pp: 5-18 [pdf]

N. Ay, T. Wennekers, Dynamical properties of strongly interacting Markov chains. Neural Networks (2003) 16:10, pp: 1483-1497 [pdf]

N. Ay, T. Wennekers, Temporal Infomax Leads to Almost Deterministic Dynamical Systems. Neurocomputing (2003) 52-54, pp: 461-466 [pdf]

N. Ay, W. Tuschmann, Duality versus Dual Flatness in Quantum Information Geometry. Journal of Mathematical Physics (2003) 44:4, pp: 1512-1518 [pdf]

N. Ay, An Information-Geometric Approach to a Theory of Pragmatic Structuring. The Annals of Probability (2002) 30, pp: 416-436 [pdf]

N. Ay, W. Tuschmann, Dually Flat Manifolds and Global Information Geometry. Open Systems & Information Dynamics (2002) 9, pp: 195-200 [pdf]

N. Ay, Locality of Global Stochastic Interaction in Directed Acyclic Networks. Neural Computation (2002) 14:12, pp: 2959-2980 [pdf]

W. Wenzel, N. Ay, F. Pasemann, Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes. Advances in Applied Mathematics (2000) 25:3, pp: 284-306 [pdf]

N. Ay, K. Zahedi, An Information Theoretic Approach to Intention and Deliberative Decision-Making of Embodied Systems. ICCN 2011, (accepted). MIS Preprint 2011/22 [pdf]

N. Ay, G. Montúfar, J. Rauh, Selection Criteria for Neuromanifolds of Stochastic Dynamics. ICCN 2011, (accepted). MIS Preprint 15/2011 [pdf]

D. C. Krakauer, J. C. Flack, N. Ay, Probabilistic design principles for robust multimodal communication networks. Modeling Perception with Artificial Neural Networks, pp: 255-268 (2011).

J. Rauh, T. Kahle, N. Ay, Support Sets in Exponential Families and Oriented Matroid Theory. Proceedings of WUPES'09, (2009). Arxiv 0906.5462 [pdf]

W. Löhr, N. Ay, Non-Sufficient Memories that are Sufficient for Prediction. 1st International Conference on Complex Sciences: Theory and Application, (2009). [pdf]

R. Der, F. Güttler, N. Ay, Predictive information and emergent cooperativity in a chain of mobile robots. Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pp: 166-172 (2008). [pdf]

N. Ay, E. Olbrich, N. Bertschinger, J. Jost, A Unifying Framework for Complexity Measures of Finite Systems. Proceedings ECCS'06, (2006). Santa Fe Working Paper 06-08-028 [pdf]

N. Bertschinger, E. Olbrich, N. Ay, J. Jost, Information and closure in systems theory. The Proceedings of the 7th German Workshop of Artificial Life, pp: 26-28 (2006). [pdf]

T. Kahle, N. Ay, Support Sets of Distributions with given Interaction Order. Proceedings of WUPES'06, pp: 52-61 (2006). [pdf] MIS Preprint 2006/94 [pdf]

F. Matúŝ, N. Ay, On maximization of the information divergence from an exponential family. Proceedings of WUPES'03, pp: 199-204 (2003). MIS Preprint 46/2003 [pdf]

Y. Sato, N. Ay, Adaptive Dynamics for Interacting Markovian Processes. (2006) Arxiv 0611032 [pdf]

T. Wennekers, N. Ay, Information-theoretic grounding of finite automata in neural systems. Max Planck Insitute for Mathematics in the Sciences, (2002) MIS Preprint 52/2002 [pdf]

N. Ay, Information Geometry on Complexity and Stochastic Interaction. (2001) MIS Preprint 95/2001 [pdf]

N. Ay, Multi-Information as Guiding Scheme for Complexity Theory. Friedreich-Alexander University Erlangen-Nuremberg. Habilitation Thesis. (2009)

N. Ay, Aspects of a Theory of Pragmatic Information Structuring. University of Leipzig. PhD Thesis. (2001)

N. Ay, A Combinatorial Geometric Approach to the Hopfield Model.. Ruhr University Bochum. Master/Diploma Thesis. (1996)

B. Steudel, N. Ay. Inferring common roots from high mutual information.
In preparation.

S. Weis, A. Knauf, N. Ay. Entropy distance: New Quantum Phenomena.

J. Rauh, T. Kahle, N. Ay. Support Sets in Exponential Families and Oriented Matroid Theory.
Extended version of above-listed conference contribution.

E. Olbrich, T. Kahle, N. Bertschinger, J. Jost, N. Ay. Quantifying structure in networks.
Extended version of above-listed conference contribution.

B. Steudel, N. Ay. An Information Bound in Generalized Bayesian Nets and its Causal Interpretation.

N. Ay. Information Geometry of Markov Kernels.

K. Zahedi, N. Ay. Transfer entropy and the sensori-motor loop.

N. Ay, D.C. Krakauer, A. Samal. The Genetic Code Exploits Codon Usage Bias for Robustness of Translation into Amino Acids.

N. Ay. Principles of Robustness
(in German). Annual Report of the Max Planck Society (2006).

N. Ay, T. Wennekers. Complexity of Cognitive Systems
(in German). Annual Report of the Max Planck Society (2003).

Virtual creatures and robots take on `a life of their own'.
Telegraph (London) August 11, 2008 by Roger Highfield.

Robots learn to move themselves.
BBC News August 6, 2008 by Jason Palmer.

Künstliches Leben: Roboter ringen im Rechner.
Tagesanzeiger (Zürich).

Roboter werden aus Erfahrung klug.
Die Welt (Hamburg).

Roboter entfalten mit einem Mathemodell Eigenleben.
Computer Zeitung Online.

Roboter entfalten ein Eigenleben.
Pressemitteilung der Max-Planck-Gesellschaft (MPG, München).

TV: Eigensinnige Roboter.
3sat (Newton, 2008).

Die Klugheit der Dinge.
Max-Planck-Forschung, Wissenschaftsmagazin der MPG, Heft 1, 2009.

Die Klugheit der Dinge.
Wissenschaftsvideo der MPG 2009, to appear.

Selbstbestimmte künstliche Wesen.
Spektrum der Wissenschaft, to appear in February 2010.

Eine Maschine wird Mensch.
FOCUS Nr. 27, 2009.

Spielplatz der Roboter.
Berliner Zeitung, September 5, 2009.