Publications

2022

1.

van Oostrum, Jesse; Müller, Johannes; Ay, Nihat

Invariance properties of the natural gradient in overparametrised systems Journal Article

In: Information Geometry, 2022.

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2.

Eppe, Manfred; Gumbusch, Christian; Kerzel, Matthias; Nguyen, Phuong D. H.; Butz, Martin V.; Wermter, Stefan

Intelligent problem-solving as integrated hierarchical reinforcement learning Journal Article

In: Nature machine intelligence, vol. 4, pp. 10, 2022, ISSN: 2522-5839.

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2021

3.

Langer, Carlotta; Ay, Nihat

How Morphological Computation Shapes Integrated Information in Embodied Agents Journal Article

In: frontiers in Psychology | Cognition, 2021.

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4.

Tirnaklo, Ugur; Tsallis, Constantino; Ay, Nihat

Approaching a large deviation theory for complex systems Journal Article

In: Nonlinear Dyn, 2021.

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5.

van Oostrum, Jesse; Ay, Nihat

Parametrisation Independence of the Natural Gradient in Overparametrised Systems Inproceedings

In: 5th conference on Geometric Science of Information in PARIS, Sorbonne University, 21 July - 23 July 2021 , 2021.

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6.

Ay, Nihat

Confounding Ghost Channels and Causality: A New Approach to Causal Information Flows Journal Article

In: Vietnam Journal of Mathematics, pp. 30, 2021, ISSN: 2305-2228.

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7.

Felice, Domenico; Ay, Nihat

Towards a canonical divergence within information geometry Journal Article

In: Information Geometry, vol. 4, pp. 65–130 (2021), 2021.

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8.

Erb, Ionas; Ay, Nihat

The Information-Geometric Perspective of Compositional Data Analysis Book Chapter

In: Advances in Compositional Data Analysis, pp. Pages 21-43, Springer, Cham, 2021, ISBN: 978-3-030-71175-7.

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9.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Task-agnostic constraining in average reward POMDPs Miscellaneous

2021.

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10.

Rauh, Johannes; Ay, Nihat; Montúfar, Guido

A continuity result for optimal memoryless planning in POMDPs Miscellaneous

2021.

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11.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Uncertainty and Stochasticity of Optimal Policies Miscellaneous

2021.

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12.

Langer, Carlotta; Ay, Nihat

Apportionment of work among environment, body and brain of an agent Miscellaneous

2021.

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2020

13.

Várady, Csongor; Volpi, Riccardo; Malagò, Luigi; Ay, Nihat

Natural reweighted wake-sleep Miscellaneous

2020.

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14.

Tirnakli, Ugur; Tsallis, Constantino; Ay, Nihat

Approaching a large deviation theory for complex systems Miscellaneous

2020.

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15.

Várady, Csongor; Volpi, Riccardo; Malagò, Luigi; Ay, Nihat

Natural wake-sleep algorithm Miscellaneous

2020.

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16.

Ay, Nihat

Confounding ghost channels and causality: a new approach to causal information flows Miscellaneous

2020.

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17.

Erb, Ionas; Ay, Nihat

The information-geometric perspective of compositional data analysis Miscellaneous

2020.

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18.

Ay, Nihat

On the locality of the natural gradient for learning in deep Bayesian networks Journal Article

In: Information geometry, 2020, ISSN: 2511-2481.

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19.

Ay, Nihat

Ingredients for robustness Journal Article

In: Theory in biosciences, vol. 139, no. 4, pp. 309–318, 2020, ISSN: 1431-7613.

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20.

Ay, Nihat; Polani, Daniel; Virgo, Nathaniel

Information decomposition based on cooperative game theory Journal Article

In: Kybernetika, vol. 56, no. 5, pp. 979–1014, 2020, ISSN: 0023-5954.

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21.

Ay, Nihat; Studeny, Milan

Special issue in memory of František Matúš,:,editorial Journal Article

In: Kybernetika, vol. 56, no. 5, pp. 843–849, 2020, ISSN: 0023-5954.

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22.

Krakauer, David C; Bertschinger, Nils; Olbrich, Eckehard; Flack, Jessica C; Ay, Nihat

The information theory of individuality Journal Article

In: Theory in biosciences, vol. 139, no. 2, pp. 209–223, 2020, ISSN: 1431-7613.

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23.

Langer, Carlotta; Ay, Nihat

Complexity as causal information integration Journal Article

In: Entropy, vol. 22, no. 10, pp. 1107, 2020, ISSN: 1099-4300.

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24.

Carlini, Luca; Ay, Nihat; Görgen, Christiane

A numerical effciency analysis of a common ancestor condition Incollection

In: 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.

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25.

Ay, Nihat; Bertschinger, Nils; Jost, Jürgen; Olbrich, Eckehard; Rauh, Johannes

Information and complexity, or: Where is the information? Miscellaneous

2020.

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2019

26.

Sokoloski, S.

Implementing Bayesian inference with neural networks PhD Thesis

Univeristät Leipzig, 2019.

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27.

Vigneaux, J. P.

Topology of statistical systems : a cohomological approach to information theory PhD Thesis

Universität Paris, 2019.

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28.

Felice, Domenico; Ay, Nihat

Canonical divergence for flat $alpha$-connections,:,classical and quantum Journal Article

In: Entropy, vol. 21, no. 9, pp. 831, 2019, ISSN: 1099-4300.

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29.

Felice, Domenico; Mancini, Stefano; Ay, Nihat

Canonical divergence for measuring classical and quantum complexity Journal Article

In: Entropy, vol. 21, no. 4, pp. 435, 2019, ISSN: 1099-4300.

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30.

Ay, Nihat; Rauh, Johannes; Montúfar, Guido

A continuity result for optimal memoryless planning in POMDPs Incollection

In: RLDM 2019,:,4th multidisciplinary conference on reinforcement learning and decision making,;,July 7-10, 2019,;,Montréal, Canada, pp. 362–365, University, Montréal, Canada, 2019.

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31.

Felice, Domenico; Ay, Nihat

Divergence functions in information geometry Incollection

In: 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.

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32.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Task-agnostic constraining in average reward POMDPs Incollection

In: Task-agnostic reinforcement learning,:,workshop at ICLR, 06 May 2019, New Orleans, ICLR, [S. L.], 2019.

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2018

33.

Felice, Domenico; Ay, Nihat

Dynamical systems induced by canonical divergence in dually flat manifolds Miscellaneous

2018, ISSN: 2511-2481.

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34.

Felice, Domenico; Ay, Nihat

Towards a canonical divergence within information geometry Miscellaneous

2018, ISSN: 2511-2481.

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35.

Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J

Parametrized measure models Journal Article

In: Bernoulli, vol. 24, no. 3, pp. 1692–1725, 2018, ISSN: 1350-7265.

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36.

Ghazi-Zahedi, Keyan; Langer, Carlotta; Ay, Nihat

Morphological computation,:,synergy of body and brain [Entropy, 19 (2017) 9, 456] Incollection

In: 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.

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37.

Langer, Carlotta; Ay, Nihat

Comparison and connection between the joint and the conditional generalized iterative scaling algorithm Incollection

In: 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.

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38.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Uncertainty and stochasticity of optimal policies Incollection

In: 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.

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39.

Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân

Congruent families and invariant tensors Incollection

In: 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.

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40.

Ay, Nihat; Krakauer, David C.; Flack, Jessica C.

Robustness, causal networks, and experimental design Book

Princeton University Press, Princeton, 2018.

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41.

Ay, Nihat; Gibilisco, Paolo; Matúš, František (Ed.)

Information geometry and its applications Book

Springer, Cham, 2018, ISBN: 978-3-319-97797-3, (on the occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016).

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42.

Ghazi-Zahedi, K.

Morphological intelligence : information-theoretic quantifications of the morphological contribution to intelligence PhD Thesis

Univeristät Leipzig, 2018.

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2017

43.

Ghazi-Zahedi, Keyan; Langer, Carlotta; Ay, Nihat

Morphological computation,:,synergy of body and brain Journal Article

In: Entropy, vol. 19, no. 9, pp. 456, 2017, ISSN: 1099-4300.

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44.

Kanwal, Maxinder S; Grochow, Joshua A; Ay, Nihat

Comparing information-theoretic measures of complexity in Boltzmann machines Journal Article

In: Entropy, vol. 19, no. 7, pp. 310, 2017, ISSN: 1099-4300.

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45.

Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J

Parametrized measure models Incollection

In: Information geometry, vol. 64, pp. 121–184, Springer, Cham, 2017, ISBN: 978-3-319-56477-7.

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46.

Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat

Stochasticity of optimal policies for POMDPs Incollection

In: RLDM 2017,:,3rd multidisciplinary conference on reinforcement learning and decision making,;,June 11-14, 2017,;,Ann Arbor, Michigan, USA, pp. T97, University, Michigan, 2017.

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47.

Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J.

Information geometry Book

Springer, Cham, 2017, ISBN: 978-3-319-56477-7.

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48.

Campbell-Borges, Y. C.

Large deviation results for likelihood ratios and hypothesis testing on quantum spin chains PhD Thesis

Universität Leipzig, 2017.

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2016

49.

Ghazi-Zahedi, Keyan; Haeufle, Daniel F B; Montúfar, Guido; Schmitt, Syn; Ay, Nihat

Evaluating morphological computation in muscle and DC-motor driven models of hopping movements Journal Article

In: Frontiers in robotics and AI, vol. 3, pp. 42, 2016, ISSN: 2296-9144.

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50.

Perrone, Paolo; Ay, Nihat

Hierarchical quantification of synergy in channels Journal Article

In: Frontiers in robotics and AI, vol. 2, pp. 35, 2016, ISSN: 2296-9144.

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51.

Sato, Yuzuru; Ay, Nihat

Information flow in learning a coin-tossing game Journal Article

In: Nonlinear theory and its applications, vol. 7, no. 2, pp. 118–125, 2016, ISSN: 2185-4106.

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52.

Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân

Parametrized measure models and a generalization of Chentsov's theorem Incollection

In: 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.

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53.

Perrone, Paolo; Ay, Nihat

Iterative scaling algorithm for channels Miscellaneous

2016.

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54.

Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat

Information theoretically aided reinforcement learning for embodied agents Miscellaneous

2016.

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2015

55.

Bernigau, H.

Causal models over infinite graphs and their application to the sensorimotor loop : general stochastic aspects and gradient methods for optimal control PhD Thesis

Universität Leipzig, 2015.

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56.

Ay, Nihat

Information geometry on complexity and stochastic interaction Journal Article

In: Entropy, vol. 17, no. 4, pp. 2432–2458, 2015, ISSN: 1099-4300.

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57.

Ay, Nihat

Geometric design principles for brains of embodied agents Journal Article

In: Künstliche Intelligenz,:,KI, vol. 29, no. 4, pp. 389–399, 2015, ISSN: 0933-1875.

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58.

Ay, Nihat; Amari, Shun'ichi

A novel approach to canonical divergences within information geometry Journal Article

In: Entropy, vol. 17, no. 12, pp. 8111–8129, 2015, ISSN: 1099-4300.

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59.

Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J

Information geometry and sufficient statistics Journal Article

In: Probability theory and related fields, vol. 162, no. 1-2, pp. 327–364, 2015, ISSN: 0178-8051.

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60.

Ay, Nihat; Löhr, Wolfgang

The Umwelt of an embodied agent,:,a measure-theoretic definition Journal Article

In: Theory in biosciences, vol. 134, no. 3-4, pp. 105–116, 2015, ISSN: 1431-7613.

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61.

Montúfar, Guido; Ay, Nihat; Ghazi-Zahedi, Keyan

Geometry and expressive power of conditional restricted Boltzmann machines Journal Article

In: Journal of machine learning research, vol. 16, pp. 2405–2436, 2015, ISSN: 1533-7928.

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62.

Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat

A theory of cheap control in embodied systems Journal Article

In: PLoS computational biology, vol. 11, no. 9, pp. e1004427, 2015, ISSN: 1553-7358.

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63.

Pfante, Oliver; Ay, Nihat

Operator-theoretic identification of closed sub-systems of dynamical systems Journal Article

In: An interdisciplinary journal of discontinuity, nonlinearity, and complexity, vol. 4, no. 1, pp. 91–109, 2015, ISSN: 2164-6376.

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64.

Salge, Christoph; Ay, Nihat; Polani, Daniel; Prokopenko, Mikhail

Zipf's law,:,balancing signal usage cost and communication efficiency Journal Article

In: PLOS ONE, vol. 10, no. 10, pp. e0139475, 2015, ISSN: 1932-6203.

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65.

Steudel, Bastian; Ay, Nihat

Information-theoretic inference of common ancestors Journal Article

In: Entropy, vol. 17, no. 4, pp. 2304–2327, 2015, ISSN: 1099-4300.

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66.

Weis, Stephan; Knauf, Andreas; Ay, Nihat; Zhao, Ming-Jing

Maximizing the divergence from a hierarchical model of quantum states Journal Article

In: Open systems and information dynamics, vol. 22, no. 1, pp. 1550006, 2015, ISSN: 1230-1612.

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67.

Amari, Shun'ichi; Ay, Nihat

Standard divergence in manifold of dual affine connections Incollection

In: 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.

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68.

Perrone, Paolo; Ay, Nihat

Decomposition of Markov kernels Incollection

In: 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.

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69.

Schwachhöfer, Lorenz J; Ay, Nihat; Jost, Jürgen; Lê, Hông Vân

Invariant geometric structures on statistical models Incollection

In: 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.

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70.

Montúfar, Guido; Ghazi-Zahedi, Keyan; Ay, Nihat

Geometry and determinism of optimal stationary control in partially observable Markov decision processes Miscellaneous

2015.

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2014

71.

Bertschinger, Nils; Rauh, Johannes; Olbrich, Eckehard; Jost, Jürgen; Ay, Nihat

Quantifying unique information Journal Article

In: Entropy, vol. 16, no. 4, pp. 2161–2183, 2014, ISSN: 1099-4300.

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72.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

On the Fisher metric of conditional probability polytopes Journal Article

In: Entropy, vol. 16, no. 6, pp. 3207–3233, 2014, ISSN: 1099-4300.

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73.

Moritz, Philipp; Reichardt, Jörg; Ay, Nihat

Discriminating between causal structures in Bayesian networks given partial observations Journal Article

In: Kybernetika, vol. 50, no. 2, pp. 284–295, 2014, ISSN: 0023-5954.

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74.

Pfante, Oliver; Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen

Comparison between different methods of level identification Journal Article

In: Advances in complex systems, vol. 17, no. 2, pp. 1450007, 2014, ISSN: 0219-5259.

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75.

Pfante, Oliver; Olbrich, Eckehard; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen

Closure measures for coarse-graining of the tent map Journal Article

In: Chaos, vol. 24, pp. 013136, 2014, ISSN: 1054-1500.

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76.

Rauh, Johannes; Ay, Nihat

Robustness, canalyzing functions and systems design Journal Article

In: Theory in biosciences, vol. 133, no. 2, pp. 63–78, 2014, ISSN: 1431-7613.

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77.

Ay, Nihat; Ghazi-Zahedi, Keyan

On the causal structure of the sensorimotor loop Incollection

In: Prokopenko, Mikhail (Ed.): Guided self-organization,:,inception, pp. 261–294, Springer, Berlin [u. a.], 2014, ISBN: 978-3-642-53733-2.

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78.

Prokopenko, Mikhail; Polani, Daniel; Ay, Nihat

On the cross-disciplinary nature of guided self-organisation Incollection

In: Prokopenko, Mikhail (Ed.): Guided self-organization,:,inception, pp. 3–15, Springer, Berlin [u. a.], 2014, ISBN: 978-3-642-53733-2.

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2013

79.

Ghazi-Zahedi, Keyan; Ay, Nihat

Quantifying morphological computation Journal Article

In: Entropy, vol. 15, no. 5, pp. 1887–1915, 2013, ISSN: 1099-4300.

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80.

Ghazi-Zahedi, Keyan; Martius, Georg; Ay, Nihat

Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting,:,a critical analysis Journal Article

In: Frontiers in psychology / Frontiers in cognitive science, vol. 4, pp. 801, 2013, ISSN: 1664-1078.

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81.

Lohmann, Gabriele; Stelzer, Johannes; Neumann, Jane; Ay, Nihat; Turner, Robert

'More is different' in functional magnetic resonance imaging,:,a review of recent data analysis techniques Journal Article

In: Brain Connectivity, vol. 3, no. 3, pp. 223–239, 2013, ISSN: 2158-0014.

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82.

Martius, Georg; Der, Ralf; Ay, Nihat

Information driven self-organization of complex robotic behaviors Journal Article

In: PLOS ONE, vol. 8, no. 5, pp. e63400, 2013, ISSN: 1932-6203.

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83.

Ay, Nihat; Ghazi-Zahedi, Keyan

Causal effects for prediction and deliberative decision making of embodied systems Inproceedings

In: 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.

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84.

Ay, Nihat; Montúfar, Guido; Rauh, Johannes

Selection criteria for neuromanifolds of stochastic dynamics Inproceedings

In: 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.

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85.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Maximal information divergence from statistical models defined by neural networks Incollection

In: 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.

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86.

Ay, Nihat; Löhr, Wolfgang

A measure-theoretic description of the intrinsic view of embodied agents Miscellaneous

2013.

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2012

87.

Montúfar, G.

On the expressive power of discrete mixture models, restricted Boltzmann machines, and deep belief networks - a unified mathematical treatment PhD Thesis

Univeristät Leipzig, 2012.

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88.

Ay, Nihat; Bernigau, Holger; Der, Ralf; Prokopenko, Mikhail

Information-driven self-organization,:,the dynamical system approach to autonomous robot behavior Journal Article

In: Theory in biosciences, vol. 131, no. 3, pp. 161–179, 2012, ISSN: 1431-7613.

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89.

Ay, Nihat; Der, Ralf; Prokopenko, Mikhail

Guided self-organization,:,perception-action loops of embodied systems Journal Article

In: Theory in biosciences, vol. 131, no. 3, pp. 125–127, 2012, ISSN: 1431-7613.

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90.

Ay, Nihat; Wenzel, Walter

On solution sets of information inequalities Journal Article

In: Kybernetika, vol. 48, no. 5, pp. 845–864, 2012, ISSN: 0023-5954.

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91.

Löhr, Wolfgang; ł, Arleta Szko; Ay, Nihat

Process dimension of classical and non-commutative processes Journal Article

In: Open systems and information dynamics, vol. 19, no. 1, pp. 1250007, 2012, ISSN: 1230-1612.

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92.

Moritz, Philipp; Reichardt, Jörg; Ay, Nihat

A new common cause principle for bayesian networks Incollection

In: 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.

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93.

Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz J.

A characterization of the Fisher metric and the Amari-Chentsov tensor in information geometry Miscellaneous

2012.

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2011

94.

Rauh, J.

Finding the maximizers of the information divergence from an exponential family PhD Thesis

Univeristät Leipzig, 2011.

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95.

Ay, Nihat; Müller, Markus; ł, Arleta Szko

Effective complexity of stationary process realizations Journal Article

In: Entropy, vol. 13, no. 6, pp. 1200–1211, 2011, ISSN: 1099-4300.

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96.

Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen

A geometric approach to complexity Journal Article

In: Chaos, vol. 21, no. 3, pp. 037103, 2011, ISSN: 1054-1500.

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97.

Montúfar, Guido; Ay, Nihat

Refinements of universal approximation results for deep belief networks and restricted Boltzmann machines Journal Article

In: Neural computation, vol. 23, no. 5, pp. 1306–1319, 2011, ISSN: 0899-7667.

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98.

Rauh, Johannes; Kahle, Thomas; Ay, Nihat

Support sets in exponential families and oriented matroid theory Journal Article

In: International journal of approximate reasoning, vol. 52, no. 5, pp. 613–626, 2011, ISSN: 0888-613x.

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99.

Montúfar, Guido; Rauh, Johannes; Ay, Nihat

Expressive power and approximation errors of restricted Boltzmann machines Incollection

In: 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.

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100.

Rauh, Johannes; Ay, Nihat

Robustness and conditional independence ideals Miscellaneous

2011.

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2010

101.

Kahle, T.

On boundaries of statistical models PhD Thesis

Univeristät Leipzig, 2010.

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102.

Löhr, W.

Models of discrete-time stochastic processes and associated complexity measures PhD Thesis

Univeristät Leipzig, 2010.

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103.

Ay, Nihat; Müller, Markus; ł, Arleta Szko

Effective complexity and its relation to logical depth Journal Article

In: IEEE transactions on information theory, vol. 56, no. 9, pp. 4593–4607, 2010, ISSN: 0018-9448.

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104.

Ghazi-Zahedi, Keyan; Ay, Nihat; Der, Ralf

Higher coordination with less control,:,a result of information maximization in the sensorimotor loop Journal Article

In: Adaptive behavior, vol. 18, no. 3/4, pp. 338–355, 2010, ISSN: 1059-7123.

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105.

Olbrich, Eckehard; Kahle, Thomas; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen

Quantifying structure in networks Journal Article

In: The European physical journal / B, vol. 77, no. 2, pp. 239–247, 2010, ISSN: 1434-6028.

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106.

Prokopenko, Mikhail; Ay, Nihat; Obst, Oliver; Polani, Daniel

Phase transitions in least-effort communications Journal Article

In: Journal of statistical mechanics, vol. 2010, no. 11, pp. P11025, 2010, ISSN: 1742-5468.

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107.

Krakauer, David C; Flack, Jessica C; Ay, Nihat

Probabilistic design principles for robust multimodal communication networks Incollection

In: 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.

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2009

108.

Ghazi-Zahedi, K.

Self-regulating neurons : a model for synaptic plasticity in artificial recurrent neural networks PhD Thesis

Universität Osnabrück, 2009.

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109.

Ay, Nihat

A refinement of the common cause principle Journal Article

In: Discrete applied mathematics, vol. 157, no. 10, pp. 2439–2457, 2009, ISSN: 0166-218x.

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110.

Kahle, Thomas; Olbrich, Eckehard; Jost, Jürgen; Ay, Nihat

Complexity measures from interaction structures Journal Article

In: Physical review / E, vol. 79, no. 2, pt. 2, pp. 026201, 2009, ISSN: 1063-651x.

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111.

Kahle, Thomas; Wenzel, Walter; Ay, Nihat

Hierarchical models, marginal polytopes, and linear codes Journal Article

In: Kybernetika, vol. 45, no. 2, pp. 189–207, 2009, ISSN: 0023-5954.

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112.

Löhr, Wolfgang; Ay, Nihat

On the generative nature of prediction Journal Article

In: Advances in complex systems, vol. 12, no. 2, pp. 169–194, 2009, ISSN: 0219-5259.

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113.

Löhr, Wolfgang; Ay, Nihat

Non-sufficient memories that are sufficient for prediction Incollection

In: 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.

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114.

Ay, Nihat

Multi-information as guiding scheme for complexity theory PhD Thesis

Friedrich-Alexander-Universität Erlangen-Nürnberg, 2009.

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2008

115.

Ay, Nihat; Bertschinger, Nils; Der, Ralf; Güttler, Frank; Olbrich, Eckehard

Predictive information and explorative behavior of autonomous robots Journal Article

In: The European physical journal / B, vol. 63, no. 3, pp. 329–339, 2008, ISSN: 1434-6028.

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116.

Ay, Nihat; Polani, Daniel

Information flows in causal networks Journal Article

In: Advances in complex systems, vol. 11, no. 1, pp. 17–41, 2008, ISSN: 0219-5259.

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117.

Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen

Autonomy,:,an information-theoretic perspective Journal Article

In: Biosystems, vol. 91, no. 2, pp. 331–345, 2008, ISSN: 0303-2647.

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118.

Olbrich, Eckehard; Bertschinger, Nils; Ay, Nihat; Jost, Jürgen

How should complexity scale with system size? Journal Article

In: The European physical journal / B, vol. 63, no. 3, pp. 407–415, 2008, ISSN: 1434-6028.

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119.

Der, Ralf; Güttler, Frank; Ay, Nihat

Predictive information and emergent cooperativity in a chain of mobile robots Inproceedings

In: 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.

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2007

120.

Ay, Nihat; Flack, Jessica C; Krakauer, David C

Robustness and complexity co-constructed in multimodal signalling networks Journal Article

In: Philosophical transactions of the Royal Society of London / B, vol. 362, no. 1479, pp. 441–447, 2007, ISSN: 0962-8436.

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121.

Ay, Nihat; Krakauer, David C

Geometric robustness theory and biological networks Journal Article

In: Theory in biosciences, vol. 125, no. 2, pp. 93–121, 2007, ISSN: 1431-7613.

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122.

Jost, Jürgen; Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Frankel, Sidney

An information theoretic approach to system differentiation on the basis of statistical dependencies between subsystems Journal Article

In: Physica / A, vol. 378, no. 1, pp. 1–10, 2007, ISSN: 0378-4371.

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123.

Wennekers, Thomas; Ay, Nihat; Andras, Peter

High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal stochastic interactions Journal Article

In: Biosystems, vol. 89, no. 1/3, pp. 190–197, 2007, ISSN: 0303-2647.

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2006

124.

Ay, Nihat; Knauf, Andreas

Maximizing multi-information Journal Article

In: Kybernetika, vol. 42, no. 5, pp. 517–538, 2006, ISSN: 0023-5954.

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125.

Wennekers, Thomas; Ay, Nihat

A temporal learning rule in recurrent systems supports high spatio-temporal stochastic interactions Journal Article

In: Neurocomputing, vol. 69, no. 10/12, pp. 1199–1202, 2006, ISSN: 0925-2312.

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126.

Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen

A unifying framework for complexity measures of finite systems Inproceedings

In: 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.

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127.

Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen

Information and closure in systems theory Incollection

In: 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.

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128.

Bertschinger, Nils; Olbrich, Eckehard; Ay, Nihat; Jost, Jürgen

Autonomy,:,an information theoretic perspective Incollection

In: 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.

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129.

Kahle, Thomas; Ay, Nihat

Support sets of distributions with given interaction structure Incollection

In: 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.

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130.

Sato, Yuzuru; Ay, Nihat

Adaptive dynamics for interacting Markovian processes Miscellaneous

2006.

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131.

Ay, Nihat; Struck, Gerald

Stochastic independence of crosstalk variables in the hopfield model Miscellaneous

2006.

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2005

132.

Ay, Nihat; Crutchfield, James P

Reductions of hidden information sources Journal Article

In: Journal of statistical physics, vol. 120, no. 3-4, pp. 659–684, 2005, ISSN: 0022-4715.

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133.

Ay, Nihat; Erb, Ionas

On a notion of linear replicator equations Journal Article

In: Journal of dynamics and differential equations, vol. 17, no. 2, pp. 427–451, 2005, ISSN: 1040-7294.

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134.

Wennekers, Thomas; Ay, Nihat

Finite state automata resulting from temporal information maximization and a temporal learning rule Journal Article

In: Neural computation, vol. 17, no. 10, pp. 2258–2290, 2005, ISSN: 0899-7667.

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135.

Wennekers, Thomas; Ay, Nihat

Stochastic interaction in associative nets Journal Article

In: Neurocomputing, vol. 65, pp. 387–392, 2005, ISSN: 0925-2312.

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2004

136.

Erb, Ionas; Ay, Nihat

Multi-information in the thermodynamic limit Journal Article

In: Journal of statistical physics, vol. 115, no. 3-4, pp. 949–976, 2004, ISSN: 0022-4715.

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2003

137.

Ay, Nihat; Tuschmann, Wilderich

Duality versus dual flatness in quantum information geometry Journal Article

In: Journal of mathematical physics, vol. 44, no. 4, pp. 1512–1518, 2003, ISSN: 0022-2488.

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138.

Ay, Nihat; Wennekers, Thomas

Dynamical properties of strongly interacting Markov chains Journal Article

In: Neural networks, vol. 16, no. 10, pp. 1483–1497, 2003, ISSN: 0893-6080.

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139.

Ay, Nihat; Wennekers, Thomas

Temporal infomax leads to almost deterministic dynamical systems Journal Article

In: Neurocomputing, vol. 52, no. 4, pp. 461–466, 2003, ISSN: 0925-2312.

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140.

Wennekers, Thomas; Ay, Nihat

Temporal Infomax on Markov chains with input leads to finite state automata Journal Article

In: Neurocomputing, vol. 52, no. 4, pp. 431–436, 2003, ISSN: 0925-2312.

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141.

Wennekers, Thomas; Ay, Nihat

Spatial and temporal stochastic interaction in neuronal assemblies Journal Article

In: Theory in biosciences, vol. 122, no. 1, pp. 5–18, 2003, ISSN: 1431-7613.

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142.

Matúš, František; Ay, Nihat

On maximization of the information divergence from an exponential family Incollection

In: Proceedings of 6th workshop on uncertainty processing,:,Hejnice, September 24-27, 2003, pp. 199–204, Oeconomica, [Praha], 2003, ISBN: 978-80-245-0546-6.

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2002

143.

Ay, Nihat

An information-geometric approach to a theory of pragmatic structuring Journal Article

In: The annals of probability, vol. 30, no. 1, pp. 416–436, 2002, ISSN: 0091-1798.

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144.

Ay, Nihat

Locality of global stochastic interaction in directed acyclic networks Journal Article

In: Neural computation, vol. 14, no. 12, pp. 2959–2980, 2002, ISSN: 0899-7667.

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145.

Ay, Nihat; Tuschmann, Wilderich

Dually flat manifolds and global information geometry Journal Article

In: Open systems and information dynamics, vol. 9, no. 2, pp. 195–200, 2002, ISSN: 1230-1612.

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146.

Wennekers, Thomas; Ay, Nihat

Information-theoretic grounding of finite automata in neural systems Miscellaneous

2002.

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2001

147.

Ay, Nihat

Aspekte einer Theorie pragmatischer Informationsstrukturierung PhD Thesis

Universität Leipzig, 2001.

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2000

148.

Wenzel, Walter; Ay, Nihat; Pasemann, Frank

Hyperplane arrangements separating arbitrary vertex classes in $mathscr n$-cubes Journal Article

In: Advances in applied mathematics, vol. 25, no. 3, pp. 284–306, 2000, ISSN: 0196-8858.

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