W. Löhr, A. Szkoła, N. Ay, Process dimension of classical and non-commutative processes. Open systems and information dynamics (2012) 19:1, pp: 1250007 Arxiv 1108.3984 [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]

N. Ay, E. Olbrich, N. Bertschinger, J. Jost, A geometric approach to complexity. Chaos (2011) 21:3, pp: 037103 [pdf] MIS-Preprint 53/2011 [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] MIS-Preprint 28/2009 [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] MIS-Preprint 23/2010 [pdf]

J. Rauh, N. Ay, Robustness and Conditional Independence Ideals. arXiv (2011), Arxiv 1110.1338 [pdf] MIS-Preprint 63/2011 [pdf]

N. Ay, R. Der, M. Prokopenko, Information Driven Self-Organization: The Dynamical System Approach to Autonomous Robot Behavior. Theory in Biosciences (2011), [pdf] Santa Fe Working Paper 10-09-018 [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 Arxiv 0912.4450 [pdf] MIS-Preprint 81/2009 [pdf] [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]

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]

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

W. Löhr, N. Ay, On the Generative Nature of Prediction. Advances in Complex Systems (2009) 12, pp: 169-194 [pdf] Santa Fe Working Paper 08-02-004 [pdf] MIS-Preprint 8/2008 [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]

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] MIS-Preprint 30/2008 [pdf]

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

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

N. Ay, D. Polani, Information Flows in Causal Networks. Advances in Complex Systems (2008) 11:1, pp: 17-41 [pdf] MIS-Preprint 47/2006 [pdf]

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

N. Ay, N. Bertschinger, R. Der, F. Güttler, E. Olbrich, Predictive information and explorative behavior of autonomous robots. The European physical journal / B (2008) 63:3, pp: 329-339 [pdf] [pdf]

N. Ay, D. C. Krakauer, Geometric robustness theory and biological networks. Theory in Biosciences (2007), pp: 93-121 [pdf] MIS-Preprint 14/2006 [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]

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]

N. Ay, A. Knauf, Maximizing Multi-Information. Kybernetika (2007) 42:5, pp: 517-538 Arxiv 0702002 [pdf] MIS-Preprint 42/2003 [pdf]

N. Ay, J. C. Flack, D. C. Krakauer, Robustness and Complexity Co-constructed in Multi-modal Signaling Networks. Philosophical transactions of the Royal Society of London / B (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]

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

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

N. Ay, I. Erb, On a notion of linear replicator equations. Journal of dynamics and differential equations (2005) 17:2, pp: 427-451 [pdf]

I. Erb, N. Ay, Multi-Information in the Thermodynamic Limit. Journal of Statistical Physics (2004) 115, pp: 949-976 [pdf] MIS-Preprint 58/2003 [pdf]

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

N. Ay, T. Wennekers, Dynamical properties of strongly interacting Markov chains. Neural Networks (2003) 16:10, pp: 1483-1497 [pdf] MIS-Preprint 107/2001 [pdf]

T. Wennekers, N. Ay, Temporal Infomax on Markov chains with input leads to finite state automata. Neurocomputing (2003) 52:4, pp: 431-436

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

N. Ay, W. Tuschmann, Duality versus Dual Flatness in Quantum Information Geometry. Journal of Mathematical Physics (2003) 44:4, pp: 1512-1518 [pdf] MIS-Preprint 69/2002 [pdf]

N. Ay, An Information-Geometric Approach to a Theory of Pragmatic Structuring. The Annals of Probability (2002) 30:1, pp: 416-436 [pdf]

N. Ay, Locality of Global Stochastic Interaction in Directed Acyclic Networks. Neural Computation (2002) 14:12, pp: 2959-2980 [pdf] MIS-Preprint 54/2001 [pdf]

N. Ay, W. Tuschmann, Dually Flat Manifolds and Global Information Geometry. Open Systems & Information Dynamics (2002) 9, pp: 195-200 [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] MIS-Preprint 35/1999 [pdf]

N. Ay, G. Montufar, J. Rauh, Selection criteria for neuromanifolds of stochastic dynamics. Advances in cognitive neurodynamics III, (2012). MIS-Preprint 15/2011 [pdf]

N. Ay, K. Zahedi, An Information Theoretic Approach to Intention and Deliberative Decision-Making of Embodied Systems. Advances in cognitive neurodynamics III, (2012). MIS Preprint 2011/22 [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).

D. C. Krakauer, J. C. Flack, N. Ay, Probabilistic design principles for robust multimodal communication networks. Modelling perception with artificial neural networks, pp: 255-268 (2011). [pdf]

G. Montúfar, J. Rauh, N. Ay, Expressive Power and Approximation Errors of Restricted Boltzmann Machines. Advances in neural information processing systems 24 : 25th Annual Conference on Neural Information Processing Systems 2011, Granada, Spain December 12th - 15th, (2011). [pdf] MIS Preprint 27/2011 [pdf]

W. Löhr, N. Ay, Non-Sufficient Memories that are Sufficient for Prediction. Complex sciences : first international conference, Complex 2009, Shanghai, China, February 23 - 25, 2009, revised papers. Pt. 1, (2009). [pdf]

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

T. Kahle, N. Ay, Support Sets of Distributions with given Interaction Order. Proceedings of WUPES'06, pp: 52-61 (2006). [pdf] Santa Fe Working Paper 06-08-027 [pdf] MIS Preprint 2006/94 [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]

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]

N. Ay, W. Wenzel, On solution sets of information inequalities. (2011) MIS-Preprint 16/2011 [pdf]

B. Steudel, N. Ay, Information-theoretic inference of common ancestors. (2010) Arxiv 1010.5720 [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.