2020

• Natural reweighted wake-sleep - Preprint
  Várady, Csongor; Volpi, Riccardo; Malagò, Luigi; Ay, Nihat
  2020
  Open Access
• Approaching a large deviation theory for complex systems - Preprint
  Tirnakli, Ugur; Tsallis, Constantino; Ay, Nihat
  2020
  Open Access
• Natural wake-sleep algorithm - Preprint
  Várady, Csongor; Volpi, Riccardo; Malagò, Luigi; Ay, Nihat
  2020
  Open Access
• Confounding ghost channels and causality: a new approach to causal information flows - Preprint
  Ay, Nihat
  2020
  Open Access
• The information-geometric perspective of compositional data analysis - Preprint
  Erb, Ionas; Ay, Nihat
  2020
  Open Access
• On the locality of the natural gradient for learning in deep Bayesian networks - Journal Article
  Ay, Nihat
  Information geometry, 2020, ISSN: 2511-2481.
  DOI
• Ingredients for robustnes - Journal Article
  Ay, Nihat
  Theory in biosciences, vol. 139, no. 4, pp. 309–318, 2020, ISSN: 1431-7613.
  DOI
• Information decomposition based on cooperative game theory - Journal Article
  Ay, Nihat; Polani, Daniel; Virgo, Nathaniel
  Kybernetika, vol. 56, no. 5, pp. 979–1014, 2020, ISSN: 0023-5954.
  DOI
• Special issue in memory of František Matúš,:,editorial - Journal Article
  Ay, Nihat; Studeny, Milan
  Kybernetika, vol. 56, no. 5, pp. 843–849, 2020, ISSN: 0023-5954.
  Open Access
• The information theory of individuality - Journal Article
  Krakauer, David C; Bertschinger, Nils; Olbrich, Eckehard; Flack, Jessica C; Ay, Nihat
  Theory in biosciences, vol. 139, no. 2, pp. 209–223, 2020, ISSN: 1431-7613.
  DOI
• Complexity as causal information integration - Journal Article
  Langer, Carlotta; Ay, Nihat
  Entropy, vol. 22, no. 10, pp. 1107, 2020, ISSN: 1099-4300.
  DOI
• A numerical effciency analysis of a common ancestor condition - Incollection
  Carlini, Luca; Ay, Nihat; Görgen, Christiane
  Slamanig, Daniel; Tsigaridas, Elias; Zafeirakopoulos, Zafeirakis (Ed.): Mathematical aspects of computer and information sciences,:,8th international conference, MACIS 2019, Gebze-Istanbul, Turkey, November 13-15, 2019,;,revised selected papers, vol. 11989, pp. 357–363, Springer, Cham, 2020, ISBN: 978-3-030-43119-8.
  Open Access | DOI
• Information and complexity, or: Where is the information? - Preprint
  Ay, Nihat; Bertschinger, Nils; Jost, Jürgen; Olbrich, Eckehard; Rauh, Johannes
  2020
  

2019

• Canonical Divergence for Flat α-Connections: Classical and Quantum - Journal Article
  Felice, Domenico; Ay, Nihat
  Entropy, vol. 21, no. 9, pp. 831, 2019, ISSN: 1099-4300.
  DOI
• Canonical divergence for measuring classical and quantum complexity - Journal Article
  Felice, Domenico; Mancini, Stefano; Ay, Nihat
  Entropy, vol. 21, no. 4, pp. 435, 2019, ISSN: 1099-4300.
  DOI
• A continuity result for optimal memoryless planning in POMDPs - Incollection
  Ay, Nihat; Rauh, Johannes; Montúfar, Guido
  RLDM 2019,:,4th multidisciplinary conference on reinforcement learning and decision making,;,July 7-10, 2019,;,Montréal, Canada, pp. 362–365, University, Montréal, Canada, 2019.
• Divergence functions in information geometry - Incollection
  Felice, Domenico; Ay, Nihat
  Nielsen, Frank; Barbaresco, Frédéric (Ed.): Geometric science of information,:,4th international conference, GSI 2019, Toulouse, France, August 27-29, 2019, proceedings, vol. 11712, pp. 433–442, Springer, Cham, 2019, ISBN: 978-3-030-26979-1.
  DOI
• Task-agnostic constraining in average reward POMDPs - Incollection
  Montúfar, Guido; Rauh, Johannes; Ay, Nihat
  Task-agnostic reinforcement learning,:,workshop at ICLR, 06 May 2019, New Orleans, ICLR, [S. L.], 2019.

2018

• Dynamical systems induced by canonical divergence in dually flat manifolds - Preprint
  Felice, Domenico; Ay, Nihat
  2018, ISSN: 2511-2481.
  Open Access
• Towards a canonical divergence within information geometry - Preprint
  Felice, Domenico; Ay, Nihat
  2018, ISSN: 2511-2481.
  Open Access
• Parametrized measure models - Journal Article
  Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J
  Bernoulli, vol. 24, no. 3, pp. 1692–1725, 2018, ISSN: 1350-7265.
  DOI
• Morphological computation,:,synergy of body and brain [Entropy, 19 (2017) 9, 456] - Incollection
  Ghazi-Zahedi, Keyan; Langer, Carlotta; Ay, Nihat
  Lizier, Joseph T; Bertschinger, Nils; Jost, Jürgen; Wibral, Michael (Ed.): Information decomposition of target effects from multi-source interactions,:,[collected articles from the special issue published in Entropy], pp. 267–281, MDPI, Basel, 2018, ISBN: 978-3-03897-015-6.
  DOI
• Comparison and connection between the joint and the conditional generalized iterative scaling algorithm - Incollection
  Langer, Carlotta; Ay, Nihat
  Kratochvíl, Václav (Ed.): Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018, pp. 105–116, MatfyzPress, Praha, 2018, ISBN: 978-80-7378-361-7.
  Open Access
• Uncertainty and stochasticity of optimal policies - Incollectionn
  Montúfar, Guido; Rauh, Johannes; Ay, Nihat
  Kratochvíl, Václav (Ed.): Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018, pp. 133–140, MatfyzPress, Praha, 2018, ISBN: 978-80-7378-361-7.
• Congruent families and invariant tensors - Incollection
  Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân
  Ay, Nihat; Gibilisco, Paolo; Matúš, František (Ed.): Information geometry and its applications,:,on the occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016, vol. 252, pp. 157–187, Springer, Cham, 2018, ISBN: 978-3-319-97797-3.
  DOI

2017

• Morphological computation,:,synergy of body and brain - Journal Article
  Ghazi-Zahedi, Keyan; Langer, Carlotta; Ay, Nihat
  Entropy, vol. 19, no. 9, pp. 456, 2017, ISSN: 1099-4300.
  DOI
• Comparing information-theoretic measures of complexity in Boltzmann machines - Journal Article
  Kanwal, Maxinder S; Grochow, Joshua A; Ay, Nihat
  Entropy, vol. 19, no. 7, pp. 310, 2017, ISSN: 1099-4300.
  DOI
• Parametrized measure models - Incollection
  Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J
  Information geometry, vol. 64, pp. 121–184, Springer, Cham, 2017, ISBN: 978-3-319-56477-7.
  DOI
• Stochasticity of optimal policies for POMDPs - Incollection
  Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat
  RLDM 2017,:,3rd multidisciplinary conference on reinforcement learning and decision making,;,June 11-14, 2017,;,Ann Arbor, Michigan, USA, pp. T97, University, Michigan, 2017.
  Open Access

2016

• Evaluating morphological computation in muscle and DC-motor driven models of hopping movements - Journal Article
  Ghazi-Zahedi, Keyan; Haeufle, Daniel F B; Montúfar, Guido; Schmitt, Syn; Ay, Nihat
  Frontiers in robotics and AI, vol. 3, pp. 42, 2016, ISSN: 2296-9144.
  DOI
• Hierarchical quantification of synergy in channels - Journal Article
  Perrone, Paolo; Ay, Nihat
  Frontiers in robotics and AI, vol. 2, pp. 35, 2016, ISSN: 2296-9144.
  DOI
• Information flow in learning a coin-tossing game - Journal Article
  Sato, Yuzuru; Ay, Nihat
  Nonlinear theory and its applications, vol. 7, no. 2, pp. 118–125, 2016, ISSN: 2185-4106.
  DOI
• Parametrized measure models and a generalization of Chentsov's theorem - Incollection
  Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân
  Ay, Nihat; Gibilisco, Paolo; Matúš, František (Ed.): International conference on information geometry and its applications IV,:,Liblice, June 12-17, 2016,;,in honor of Shun-ichi Amari, pp. 17–17, Matfyzpress, Praha, 2016, ISBN: 978-80-7378-316-7.
  Open Access
• Iterative scaling algorithm for channels - Preprint
  Perrone, Paolo; Ay, Nihat
  2016.
  Open Access
• Information theoretically aided reinforcement learning for embodied agents - Preprint
  Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat
  2016.
  Open Access

2015

• Information geometry on complexity and stochastic interaction - Journal Article
  Ay, Nihat
  Entropy, vol. 17, no. 4, pp. 2432–2458, 2015, ISSN: 1099-4300.
  DOI
• Geometric design principles for brains of embodied agents - Journal Article
  Ay, Nihat
  Künstliche Intelligenz,:,KI, vol. 29, no. 4, pp. 389–399, 2015, ISSN: 0933-1875.
  DOI
• A novel approach to canonical divergences within information geometry - Journal Article
  Ay, Nihat; Amari, Shun'ichi
  Entropy, vol. 17, no. 12, pp. 8111–8129, 2015, ISSN: 1099-4300.
  DOI
• Information geometry and sufficient statistics - Journal Article
  Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J
  Probability theory and related fields, vol. 162, no. 1-2, pp. 327–364, 2015, ISSN: 0178-8051.
  DOI
• The Umwelt of an embodied agent -- a measure-theoretic definition - Journal Article
  Ay, Nihat; Löhr, Wolfgang
  Theory in biosciences, vol. 134, no. 3-4, pp. 105–116, 2015, ISSN: 1431-7613.
  DOI
• Geometry and expressive power of conditional restricted Boltzmann machines - Journal Article
  Montúfar, Guido; Ay, Nihat; Ghazi-Zahedi, Keyan
  Journal of machine learning research, vol. 16, pp. 2405–2436, 2015, ISSN: 1533-7928.
• A theory of cheap control in embodied systems - Journal Article
  Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat
  PLoS computational biology, vol. 11, no. 9, pp. e1004427, 2015, ISSN: 1553-7358.
  DOI
• Operator-theoretic identification of closed sub-systems of dynamical systems - Journal Article
  Pfante, Oliver; Ay, Nihat
  An interdisciplinary journal of discontinuity, nonlinearity, and complexity, vol. 4, no. 1, pp. 91–109, 2015, ISSN: 2164-6376.
  DOI
• Zipf's law:balancing signal usage cost and communication efficiency - Journal Article
  Salge, Christoph; Ay, Nihat; Polani, Daniel; Prokopenko, Mikhail
  PLOS ONE, vol. 10, no. 10, pp. e0139475, 2015, ISSN: 1932-6203.
  Open Access | DOI
• Information-theoretic inference of common ancestors - Journal Article
  Steudel, Bastian; Ay, Nihat
  Entropy, vol. 17, no. 4, pp. 2304–2327, 2015, ISSN: 1099-4300.
  DOI
• Maximizing the divergence from a hierarchical model of quantum states - Journal Article
  Weis, Stephan; Knauf, Andreas; Ay, Nihat; Zhao, Ming-Jing
  Open systems and information dynamics, vol. 22, no. 1, pp. 1550006, 2015, ISSN: 1230-1612.
  DOI
• Standard divergence in manifold of dual affine connections - Incollection
  Amari, Shun'ichi; Ay, Nihat
  Nielsen, Frank; Barbaresco, Frédéric (Ed.): Geometric science of information,:,second international conference, GSI 2015, Palaiseau, France, October 28-30, 2015, proceedings, vol. 9389, pp. 320–325, Springer, Cham, 2015, ISBN: 978-3-319-25039-7.
  DOI
• Decomposition of Markov kernels - Incollection
  Perrone, Paolo; Ay, Nihat
  Kratochvíl, Václav (Ed.): Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech Republic, September 16-19, 2015, pp. 167–178, Oeconomica, Praha, 2015, ISBN: 978-80-245-2102-2.
  Open Access
• Invariant geometric structures on statistical models - Incollection
  Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân
  Nielsen, Frank; Barbaresco, Frédéric (Ed.): Geometric science of information,:,second international conference, GSI 2015, Palaiseau, France, October 28-30, 2015, proceedings, vol. 9389, pp. 150–158, Springer, Cham, 2015, ISBN: 978-3-319-25039-7.
  DOI
• Geometry and determinism of optimal stationary control in partially observable Markov decision processes - Preprint
  Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat
  2015.
  DOI

2014

• Quantifying unique information - Journal Article
  Bertschinger, Nils; Rauh, Johannes; Olbrich, Eckehard; Jost, Jürgen; Ay, Nihat
  Entropy, vol. 16, no. 4, pp. 2161–2183, 2014, ISSN: 1099-4300.
  DOI
• On the Fisher metric of conditional probability polytopes - Journal Article
  Montúfar, Guido; Rauh, Johannes; Ay, Nihat
  Entropy, vol. 16, no. 6, pp. 3207–3233, 2014, ISSN: 1099-4300.
  DOI
• Discriminating between causal structures in Bayesian networks given partial observations - Journal Article
  Moritz, Philipp; Reichardt, Jörg; Ay, Nihat
  Kybernetika, vol. 50, no. 2, pp. 284–295, 2014, ISSN: 0023-5954.
  DOI
• Comparison between different methods of level identification - Journal Article
  Pfante, Oliver; Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen
  Advances in complex systems, vol. 17, no. 2, pp. 1450007, 2014, ISSN: 0219-5259.
  DOI
• Closure measures for coarse-graining of the tent map - Journal Article
  Pfante, Oliver; Olbrich, Eckehard; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen
  Chaos, vol. 24, pp. 013136, 2014, ISSN: 1054-1500.
  DOI
• Robustness, canalyzing functions and systems design - Journal Article
  Rauh, Johannes; Ay, Nihat
  Theory in biosciences, vol. 133, no. 2, pp. 63–78, 2014, ISSN: 1431-7613.
  DOI
• On the causal structure of the sensorimotor loop - Incollection
  Ay, Nihat; Ghazi-Zahedi, Keyan
  Prokopenko, Mikhail (Ed.): Guided self-organization,:,inception, pp. 261–294, Springer, Berlin [u. a.], 2014, ISBN: 978-3-642-53733-2.
  DOI
• On the cross-disciplinary nature of guided self-organisation - Incollection
  Prokopenko, Mikhail; Polani, Daniel; Ay, Nihat
  Prokopenko, Mikhail (Ed.): Guided self-organization,:,inception, pp. 3–15, Springer, Berlin [u. a.], 2014, ISBN: 978-3-642-53733-2.
  DOI

2013

• Quantifying morphological computation - Journal Article
  Ghazi-Zahedi, Keyan; Ay, Nihat
  Entropy, vol. 15, no. 5, pp. 1887–1915, 2013, ISSN: 1099-4300.
  DOI
• Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting: a critical analysis - Journal Article
  Ghazi-Zahedi, Keyan; Martius, Georg; Ay, Nihat
  Frontiers in psychology / Frontiers in cognitive science, vol. 4, pp. 801, 2013, ISSN: 1664-1078.
  DOI
• 'More is different' in functional magnetic resonance imaging,:,a review of recent data analysis techniques - Journal Article
  Lohmann, Gabriele; Stelzer, Johannes; Neumann, Jane; Ay, Nihat; Turner, Robert
  Brain Connectivity, vol. 3, no. 3, pp. 223–239, 2013, ISSN: 2158-0014.
  DOI
• Information driven self-organization of complex robotic behaviors - Journal Article
  Martius, Georg; Der, Ralf; Ay, Nihat
  PLOS ONE, vol. 8, no. 5, pp. e63400, 2013, ISSN: 1932-6203.
  DOI
• Causal effects for prediction and deliberative decision making of embodied systems - Inproceedings
  Ay, Nihat; Ghazi-Zahedi, Keyan
  Yamaguchi, Yoko (Ed.): Advances in cognitive neurodynamics III,:,proceedings of the 3rd International Conference on Cognitive Neurodynamics 2011,;,[June 9-13, 2011, Hilton Niseko Village, Hokkaido, Japan], pp. 499–506, Springer, Dordrecht, 2013, ISBN: 978-94-007-4791-3.
  DOI
• Selection criteria for neuromanifolds of stochastic dynamics - Inproceedings
  Ay, Nihat; Montúfar, Guido; Rauh, Johannes
  Yamaguchi, Yoko (Ed.): Advances in cognitive neurodynamics III,:,proceedings of the 3rd International Conference on Cognitive Neurodynamics 2011,;,[June 9-13, 2011, Hilton Niseko Village, Hokkaido, Japan], pp. 147–154, Springer, Dordrecht, 2013, ISBN: 978-94-007-4791-3.
  DOI
• Maximal information divergence from statistical models defined by neural networks - Incollection
  Montúfar, Guido; Rauh, Johannes; Ay, Nihat
  Nielsen, Frank; Barbaresco, Frédéric (Ed.): Geometric science of information,:,first international conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings, vol. 8085, pp. 759–766, Springer, Berlin [u. a.], 2013, ISBN: 978-3-642-40019-3.
  DOI
• A measure-theoretic description of the intrinsic view of embodied agents - Preprint
  Ay, Nihat; Löhr, Wolfgang
  2013.
  Open Access

2012

• Information-driven self-organization,:,the dynamical system approach to autonomous robot behavior - Journal Article
  Ay, Nihat; Bernigau, Holger; Der, Ralf; Prokopenko, Mikhail
  Theory in biosciences, vol. 131, no. 3, pp. 161–179, 2012, ISSN: 1431-7613.
  DOI
• Guided self-organization: perception-action loops of embodied systems - Journal Article
  Ay, Nihat; Der, Ralf; Prokopenko, Mikhail
  Theory in biosciences, vol. 131, no. 3, pp. 125–127, 2012, ISSN: 1431-7613.
  DOI
• On solution sets of information inequalities - Journal Article
  Ay, Nihat; Wenzel, Walter
  Kybernetika, vol. 48, no. 5, pp. 845–864, 2012, ISSN: 0023-5954.
• Process dimension of classical and non-commutative processes - Journal Article
  Löhr, Wolfgang; ł, Arleta Szko; Ay, Nihat
  Open systems and information dynamics, vol. 19, no. 1, pp. 1250007, 2012, ISSN: 1230-1612.
  DOI
• A new common cause principle for bayesian networks - Incollection
  Moritz, Philipp; Reichardt, Jörg; Ay, Nihat
  Proceedings of the 9th workshop on uncertainty processing WUPES '12,:,Marianske Lazne, Czech Republik,;,12-15th September 2012, pp. 149–162, Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, Praha, 2012, ISBN: 978-80-245-1885-5.
  Open Access
• A characterization of the Fisher metric and the Amari-Chentsov tensor in information geometry - Preprint
  Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J.
  2012.

2011

• Effective complexity of stationary process realizations - Journal Article
  Ay, Nihat; Müller, Markus; ł, Arleta Szko
  Entropy, vol. 13, no. 6, pp. 1200–1211, 2011, ISSN: 1099-4300.
  DOI
• A geometric approach to complexity - Journal Article
  Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen
  Chaos, vol. 21, no. 3, pp. 037103, 2011, ISSN: 1054-1500.
  DOI
• Refinements of universal approximation results for deep belief networks and restricted Boltzmann machines - Journal Article
  Montúfar, Guido; Ay, Nihat
  Neural computation, vol. 23, no. 5, pp. 1306–1319, 2011, ISSN: 0899-7667.
  DOI
• Support sets in exponential families and oriented matroid theory - Journal Article
  Rauh, Johannes; Kahle, Thomas; Ay, Nihat
  International journal of approximate reasoning, vol. 52, no. 5, pp. 613–626, 2011, ISSN: 0888-613x.
  DOI
• Expressive power and approximation errors of restricted Boltzmann machines - Incollection
  Montúfar, Guido; Rauh, Johannes; Ay, Nihat
  Shawe-Taylor, J (Ed.): Advances in neural information processing systems 24,:,25th annual conference on neural information processing systems 2011, Granada, Spain December 12th - 15th,;,NIPS 2011, pp. 415–423, Neural Information Processing Systems, La Jolla, CA, 2011.
• Robustness and conditional independence ideals - Preprint
  Rauh, Johannes; Ay, Nihat
  2011.
  Open Access

2010

• Effective complexity and its relation to logical depth - Journal Article
  Ay, Nihat; Müller, Markus; ł, Arleta Szko
  IEEE transactions on information theory, vol. 56, no. 9, pp. 4593–4607, 2010, ISSN: 0018-9448.
  DOI
• Higher coordination with less control,:,a result of information maximization in the sensorimotor loop - Journal Article
  Ghazi-Zahedi, Keyan; Ay, Nihat; Der, Ralf
  Adaptive behavior, vol. 18, no. 3/4, pp. 338–355, 2010, ISSN: 1059-7123.
  DOI
• Quantifying structure in networks - Journal Article
  Olbrich, Eckehard; Kahle, Thomas; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen
  The European physical journal / B, vol. 77, no. 2, pp. 239–247, 2010, ISSN: 1434-6028.
  DOI
• Phase transitions in least-effort communications - Journal Article
  Prokopenko, Mikhail; Ay, Nihat; Obst, Oliver; Polani, Daniel
  Journal of statistical mechanics, vol. 2010, no. 11, pp. P11025, 2010, ISSN: 1742-5468.
  DOI
• Probabilistic design principles for robust multimodal communication networks - Incollection
  Krakauer, David C; Flack, Jessica C; Ay, Nihat
  Tosh, Colin R; Ruxton, Graeme D (Ed.): Modelling perception with artificial neural networks, pp. 255–268, Cambridge University Press, Cambridge, 2010, ISBN: 978-0-511-77914-5.
  DOI

2009

• A refinement of the common cause principle - Journal Article
  Ay, Nihat
  Discrete applied mathematics, vol. 157, no. 10, pp. 2439–2457, 2009, ISSN: 0166-218x.
  DOI
• Complexity measures from interaction structures - Journal Article
  Kahle, Thomas; Olbrich, Eckehard; Jost, Jürgen; Ay, Nihat
  Physical review / E, vol. 79, no. 2, pt. 2, pp. 026201, 2009, ISSN: 1063-651x.
  DOI
• Hierarchical models, marginal polytopes, and linear codes - Journal Article
  Kahle, Thomas; Wenzel, Walter; Ay, Nihat
  Kybernetika, vol. 45, no. 2, pp. 189–207, 2009, ISSN: 0023-5954.
• On the generative nature of prediction - Journal Article
  Löhr, Wolfgang; Ay, Nihat
  Advances in complex systems, vol. 12, no. 2, pp. 169–194, 2009, ISSN: 0219-5259.
  DOI
• Non-sufficient memories that are sufficient for prediction - Incollection
  Löhr, Wolfgang; Ay, Nihat
  Zhou, Jie (Ed.): Complex sciences,:,first international conference, Complex 2009, Shanghai, China, February 23 - 25, 2009, revised papers. Pt. 1, vol. 4, pp. 265–276, Springer, Berlin [u. a.], 2009, ISBN: 978-3-642-02465-8.
  DOI

2008

• Predictive information and explorative behavior of autonomous robots - Journal Article
  Ay, Nihat; Bertschinger, Nils; Der, Ralf; Güttler, Frank; Olbrich, Eckehard
  The European physical journal / B, vol. 63, no. 3, pp. 329–339, 2008, ISSN: 1434-6028.
  DOI
• Information flows in causal networks - Journal Article
  Ay, Nihat; Polani, Daniel
  Advances in complex systems, vol. 11, no. 1, pp. 17–41, 2008, ISSN: 0219-5259.
  DOI
• Autonomy: an information-theoretic perspective - Journal Article
  Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen
  Biosystems, vol. 91, no. 2, pp. 331–345, 2008, ISSN: 0303-2647.
  DOI
• How should complexity scale with system size? - Journal Article
  Olbrich, Eckehard; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen
  The European physical journal / B, vol. 63, no. 3, pp. 407–415, 2008, ISSN: 1434-6028.
  DOI
• Predictive information and emergent cooperativity in a chain of mobile robots - Inproceedings
  Der, Ralf; Güttler, Frank; Ay, Nihat
  Artificial Life XI,:,Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pp. 166–172, MIT Press, Cambridge, MA, 2008, ISBN: 978-0-262-75017-2.

2007

• Robustness and complexity co-constructed in multimodal signalling networks - Journal Article
  Ay, Nihat; Flack, Jessica C; Krakauer, David C
  Philosophical transactions of the Royal Society of London / B, vol. 362, no. 1479, pp. 441–447, 2007, ISSN: 0962-8436.
  DOI
• Geometric robustness theory and biological networks - Journal Article
  Ay, Nihat; Krakauer, David C
  Theory in biosciences, vol. 125, no. 2, pp. 93–121, 2007, ISSN: 1431-7613.
  DOI
• An information theoretic approach to system differentiation on the basis of statistical dependencies between subsystems - Journal Article
  Jost, Jürgen; Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Frankel, Sidney
  Physica / A, vol. 378, no. 1, pp. 1–10, 2007, ISSN: 0378-4371.
  DOI
• High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal stochastic interactions - Journal Article
  Wennekers, Thomas; Ay, Nihat; Andras, Peter
  Biosystems, vol. 89, no. 1/3, pp. 190–197, 2007, ISSN: 0303-2647.
  DOI

2006

• Maximizing multi-information - Journal Article
  Ay, Nihat; Knauf, Andreas
  Kybernetika, vol. 42, no. 5, pp. 517–538, 2006, ISSN: 0023-5954.
• A temporal learning rule in recurrent systems supports high spatio-temporal stochastic interactions - Journal Article
  Wennekers, Thomas; Ay, Nihat
  Neurocomputing, vol. 69, no. 10/12, pp. 1199–1202, 2006, ISSN: 0925-2312.
  DOI
• A unifying framework for complexity measures of finite systems - Inproceedings
  Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen
  Jost, Jürgen; Reed-Tsochas, Felix; Schuster, Peter (Ed.): ECCS'06,:,proceedings of the European Conference on Complex Systems 2006,;,towards a science of complex systems, pp. 80–80, European Complex Systems Society, Paris, 2006, ISBN: 0-9554123-0-7.
  Open Access
• Information and closure in systems theory - Incollection
  Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen
  Artmann, S; Dittrich, P (Ed.): Explorations in the complexity of possible life,:,abstracting and synthesizing the principles of living systems,;,proceedings of the 7th German Workshop on Artificial Life, July 26 - 28, 2006, Jena, Germany, pp. 9–19, IOS Press, Amsterdam, 2006, ISBN: 978-3-89838-076-8.
• Autonomy,:,an information theoretic perspective - Incollection
  Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen
  Rocha, Luis Mateus; Yaeger, Larry S; Bedau, Mark A; Floreano, Dario; Goldstone, Robert L; Vespignani, Alessando (Ed.): Artificial life X,:,proceedings of the tenth international conference on the synthesis and simulation of living systems, pp. 7–12, MIT Press, Cambridge, Mass., 2006, ISBN: 978-0-262-68162-9.
• Support sets of distributions with given interaction structure - Incollection
  Kahle, Thomas; Ay, Nihat
  7th Workshop on Uncertainty Processing,:,WUPES'06,;,Mikulov, Czech Republik,;,16-20th September 2006, pp. 52–61, Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, Praha, 2006.
• Adaptive dynamics for interacting Markovian processes - Preprint
  Sato, Yuzuru; Ay, Nihat
  2006.
  Open Access
• Stochastic independence of crosstalk variables in the hopfield model - Preprint
  Ay, Nihat; Struck, Gerald
  2006.

2005

• Reductions of hidden information sources - Journal Article
  Ay, Nihat; Crutchfield, James P
  Journal of statistical physics, vol. 120, no. 3-4, pp. 659–684, 2005, ISSN: 0022-4715.
  DOI
• On a notion of linear replicator equations - Journal Article
  Ay, Nihat; Erb, Ionas
  Journal of dynamics and differential equations, vol. 17, no. 2, pp. 427–451, 2005, ISSN: 1040-7294.
  DOI
• Finite state automata resulting from temporal information maximization and a temporal learning rule - Journal Article
  Wennekers, Thomas; Ay, Nihat
  Neural computation, vol. 17, no. 10, pp. 2258–2290, 2005, ISSN: 0899-7667.
  DOI
• Stochastic interaction in associative nets - Journal Article
  Wennekers, Thomas; Ay, Nihat
  Neurocomputing, vol. 65, pp. 387–392, 2005, ISSN: 0925-2312.
  DOI

2004

• Multi-information in the thermodynamic limit - Journal Article
  Erb, Ionas; Ay, Nihat
  Journal of statistical physics, vol. 115, no. 3-4, pp. 949–976, 2004, ISSN: 0022-4715.
  DOI

2003

• Duality versus dual flatness in quantum information geometry - Journal Article
  Ay, Nihat; Tuschmann, Wilderich
  Journal of mathematical physics, vol. 44, no. 4, pp. 1512–1518, 2003, ISSN: 0022-2488.
  DOI
• Dynamical properties of strongly interacting Markov chains - Journal Article
  Ay, Nihat; Wennekers, Thomas
  Neural networks, vol. 16, no. 10, pp. 1483–1497, 2003, ISSN: 0893-6080.
  DOI
• Temporal infomax leads to almost deterministic dynamical systems - Journal Article
  Ay, Nihat; Wennekers, Thomas
  Neurocomputing, vol. 52, no. 4, pp. 461–466, 2003, ISSN: 0925-2312.
  DOI
• Temporal Infomax on Markov chains with input leads to finite state automata - Journal Article
  Wennekers, Thomas; Ay, Nihat
  Neurocomputing, vol. 52, no. 4, pp. 431–436, 2003, ISSN: 0925-2312.
  DOI
• Spatial and temporal stochastic interaction in neuronal assemblies - Journal Article
  Wennekers, Thomas; Ay, Nihat
  Theory in biosciences, vol. 122, no. 1, pp. 5–18, 2003, ISSN: 1431-7613.
  DOI
• On maximization of the information divergence from an exponential family - Incollection
  Matúš, František; Ay, Nihat
  Proceedings of 6th workshop on uncertainty processing,:,Hejnice, September 24-27, 2003, pp. 199–204, Oeconomica, [Praha], 2003, ISBN: 978-80-245-0546-6.

2002

• An information-geometric approach to a theory of pragmatic structurin - Journal Article
  Ay, Nihat
  The annals of probability, vol. 30, no. 1, pp. 416–436, 2002, ISSN: 0091-1798.
• Locality of global stochastic interaction in directed acyclic networks - Journal Article
  Ay, Nihat
  Neural computation, vol. 14, no. 12, pp. 2959–2980, 2002, ISSN: 0899-7667.
  DOI
• Dually flat manifolds and global information geometry - Journal Article
  Ay, Nihat; Tuschmann, Wilderich
  Open systems and information dynamics, vol. 9, no. 2, pp. 195–200, 2002, ISSN: 1230-1612.
  DOI
• Information-theoretic grounding of finite automata in neural systems - Preprint
  Wennekers, Thomas; Ay, Nihat
  2002.

2000

• Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes - Journal Article
  Wenzel, Walter; Ay, Nihat; Pasemann, Frank
  Advances in applied mathematics, vol. 25, no. 3, pp. 284–306, 2000, ISSN: 0196-8858.
  DOI