Publications

Langer, C. and N. Ay:
*Apportionment of work among environment, body and brain of an agent*.
Bibtex MIS-Preprint: 2/2021

Ay, N.:
*On the locality of the natural gradient for learning in deep Bayesian networks*.
Information geometry,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 59/2020 [DOI] [ARXIV]

Ay, N.:
*Confounding ghost channels and causality : a new approach to causal information flows*.
Bibtex MIS-Preprint: 75/2020 [ARXIV]

Ay, N. ; Bertschinger, N. ; Jost, J. ; Olbrich, E. and J. Rauh:
*Information and complexity, or: Where is the information?*.
Bibtex MIS-Preprint: 102/2020

Ay, N. ; Polani, D. and N. Virgo:
*Information decomposition based on cooperative game theory*.
Kybernetika,
56 (2020) 5, p. 979-1014 Bibtex MIS-Preprint: 81/2020 [DOI] [ARXIV]

Ay, N. and M. Studeny:
*Special issue in memory of František Matúš : editorial*.
Kybernetika,
56 (2020) 5, p. 843-849 Bibtex [FREELINK]

Bennequin, D. and J. P. Vigneaux:
*A functional equation related to generalized entropies and the modular group*.
Aequationes mathematicae,
94 (2020) 6, p. 1201-1212 Bibtex [DOI] [ARXIV]

Carlini, L. ; Ay, N. and C. Görgen:
*A numerical effciency analysis of a common ancestor condition*.
Mathematical aspects of computer and information sciences : 8th international conference,
MACIS 2019, Gebze-Istanbul, Turkey, November 13-15, 2019 ; revised selected papers / D.
Slamanig... (eds.). Springer, 2020. - P. 357-363
(Lecture notes in computer science ; 11989)
Bibtex [DOI] [FREELINK]

Erb, I. and N. Ay:
*The information-geometric perspective of compositional data analysis*.
Bibtex [ARXIV]

Hlihor, P. ; Volpi, R. and L. Malagò:
*Evaluating the robustness of defense mechanisms based on autoencoder reconstructions
against Carlini-Wagner adversarial attacks*.
Proceedings of the northern lights deep learning workshop,
1 (2020), 5173 Bibtex [DOI]

Krakauer, D. C. ; Bertschinger, N. ; Olbrich, E. ; Flack, J. C. and N. Ay:
*The information theory of individuality*.
Theory in biosciences,
139 (2020) 2, p. 209-223 Bibtex [DOI] [ARXIV] [FREELINK]

Langer, C. and N. Ay:
*Complexity as causal information integration*.
Entropy,
22 (2020) 10, 1107 Bibtex MIS-Preprint: 85/2020 [DOI] [ARXIV]

Müller, J.:
*On the space-time expressivity of ResNets*.
ICLR 2020 workshop on integration of deep neural models and differential equations
: Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020 ICLR, 2020 Bibtex [ARXIV] [FREELINK]

Müller, J. and M. Zeinhofer:
*Deep Ritz revisited*.
ICLR 2020 workshop on integration of deep neural models and differential equations
: Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020 ICLR, 2020 Bibtex [ARXIV] [FREELINK]

Tirnakli, U. ; Tsallis, C. and N. Ay:
*Approaching a large deviation theory for complex systems*.
Bibtex [ARXIV]

Vigneaux, J. P.
:
*Generalized information structures and their cohomology*.
Theory and applications of categories,
35 (2020) 38, p. 1476-1529 Bibtex [ARXIV] [FREELINK]

Vigneaux, J. P.
:
*A homological characterization of generalized multinomial coefficients related to
the entropic chain rule*.
Bibtex [ARXIV]

Várady, C. ; Volpi, R. ; Malagò, L. and N. Ay:
*Natural wake-sleep algorithm*.
Bibtex MIS-Preprint: 84/2020 [ARXIV]

Várady, C. ; Volpi, R. ; Malagò, L. and N. Ay:
*Natural reweighted wake-sleep*.
Bibtex [FREELINK]

Winklmayr, C. ; Kao, A. B. ; Bak-Coleman, J. B. and P. Romanczuk:
*The wisdom of stalemates : consensus and clustering as filtering mechanisms for improving
collective accuracy*.
Proceedings of the Royal Society of London / B,
287 (2020) 1938, 20201802 Bibtex [DOI] [ARXIV] [CODELINK]

Witkowski, O. ; Ikegami, T. ; Virgo, N. ; Oka, M. and H. Iizuka:
*Artificial life : next generation perspectives - echoes from the 2018 conference in
Tokyo (editorial introduction to the ALIFE 2018 special issue)*.
Artificial life,
26 (2020) 1, p. 1-4 Bibtex [DOI]

Ay, N. ; Rauh, J. and G. Montúfar:
*A continuity result for optimal memoryless planning in POMDPs*.
RLDM 2019 : 4th multidisciplinary conference on reinforcement learning and decision
making ; July 7-10, 2019 ; Montréal, Canada University, 2019. - P. 362-365 Bibtex MIS-Preprint: 5/2021 [FREELINK]

Felice, D. and N. Ay:
*Divergence functions in information geometry*.
Geometric science of information : 4th international conference, GSI 2019, Toulouse,
France, August 27-29, 2019, proceedings / F.
Nielsen... (eds.). Springer, 2019. - P. 433-442
(Lecture notes in computer science ; 11712)
Bibtex [DOI] [ARXIV]

Felice, D. and N. Ay:
*Canonical divergence for flat \(\alpha\)-connections : classical and quantum*.
Entropy,
21 (2019) 9, 831 Bibtex [DOI] [ARXIV]

Felice, D. ; Mancini, S. and N. Ay:
*Canonical divergence for measuring classical and quantum complexity*.
Entropy,
21 (2019) 4, 435 Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K.:
*Morphological intelligence : measuring the body's contribution to intelligence*.
Springer, 2019. - XIII, 180 p. ISBN 978-3-030-20620-8 Bibtex [DOI]

Mariscal, C. ; Barahona, A. ; Aubert-Kato, N. ; Aydinoglu, A. U.
; Barlett, S. ; Cárdenas, M. L.
; Chandru, K. ; Cleland, C. ; Cocanougher, B. T. ; Comfort, N. ; Cornish-Bowden, A. ; Deacon, T. ; Froese, T. ; Giovannelli, D. ; Hernlund, J. ; Hut, P. ; Kimura, J. ; Maurel, M.-C. ; Merino, N. ; Moreno, A. ; Nakagawa, M. ; Peretó, J. ; Virgo, N. ; Witkowski, O. and H. J.
Cleaves:
*Hidden concepts in the history and philosophy of origins-of-life studies : a workshop
report*.
Origins of life and evolution of the biosphere,
49 (2019) 3, p. 111-145 Bibtex [DOI] [FREELINK]

Montúfar, G. ; Rauh, J. and N. Ay:
*Task-agnostic constraining in average reward POMDPs*.
Task-agnostic reinforcement learning : workshop at ICLR, 06 May 2019, New Orleans ICLR, 2019 Bibtex MIS-Preprint: 9/2021 [FREELINK]

Sokoloski, S.:
*Implementing Bayesian inference with neural networks*.
Dissertation, Univeristät Leipzig, 2019 Bibtex [FREELINK]

Vigneaux, J. P.
:
*Topology of statistical systems : a cohomological approach to information theory*.
Dissertation, Universität Paris, 2019 Bibtex [FREELINK]

Andreotti, E. ; Remondini, D. and A. Bazzani:
*Equivalence between spectral properties of graphs with and without loops*.
Bibtex [ARXIV]

Ay, N. ; Gibilisco, P. and F. Matúš (eds.):
*Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th
Birthday, IGAIA IV Liblice, Czech Republic, June 2016*.
Springer, 2018. - X, 456 p.
(Springer proceedings in mathematics and statistics ; 252)
ISBN 978-3-319-97797-3 Bibtex [DOI]

Ay, N. ; Jost, J. ; Lê, H. V.
and L. J. Schwachhöfer:
*Parametrized measure models*.
Bernoulli,
24 (2018) 3, p. 1692-1725 Bibtex MIS-Preprint: 69/2015 [DOI] [ARXIV]

Ay, N. ; Krakauer, D. C. and J. C. Flack:
*Robustness, causal networks, and experimental design*.
Princeton University Press, 2018 Bibtex

Banerjee, P. K.
; Rauh, J. and G. Montúfar:
*Computing the unique information*.
IEEE international symposium on information theory (ISIT) from June 17 to 22, 2018
at the Talisa Hotel in Vail, Colorado, USA IEEE, 2018. - P. 141-145 Bibtex MIS-Preprint: 73/2017 [DOI] [ARXIV] [CODELINK]

Felice, D. and N. Ay:
*Towards a canonical divergence within information geometry*.
Information geometry,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 43/2018 [ARXIV]

Felice, D. and N. Ay:
*Dynamical systems induced by canonical divergence in dually flat manifolds*.
Information geometry,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 103/2018 [ARXIV]

Felice, D. ; Cafaro, C. and S. Mancini:
*Information geometric methods for complexity*.
Chaos,
28 (2018) 3, 032101 Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K.:
*Morphological intelligence : information-theoretic quantifications of the morphological
contribution to intelligence*.
Habilitation, Univeristät Leipzig, 2018 Bibtex

Ghazi-Zahedi, K. ; Langer, C. and N. Ay:
*Morphological computation : synergy of body and brain [Entropy, 19 (2017) 9, 456]*.
Information decomposition of target effects from multi-source interactions : [collected
articles from the special issue published in Entropy] / J.
T. Lizier... (eds.). MDPI, 2018. - P. 267-281 Bibtex [DOI]

Langer, C. and N. Ay:
*Comparison and connection between the joint and the conditional generalized iterative
scaling algorithm*.
Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018 / V.
Kratochvíl (ed.). MatfyzPress, 2018. - P. 105-116 Bibtex [FREELINK]

Montúfar, G.:
*Illustration of maxout layer upper bound [Suppl. to: On the number of linear regions
of deep neural networks]*.
Bibtex [FREELINK]

Montúfar, G.:
*Restricted Boltzmann machines : introduction and review*.
Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th
Birthday, IGAIA IV Liblice, Czech Republic, June 2016 / N.
Ay... (eds.). Springer, 2018. - P. 75-115
(Springer proceedings in mathematics and statistics ; 252)
Bibtex MIS-Preprint: 87/2018 [DOI] [ARXIV]

Montúfar, G. ; Rauh, J. and N. Ay:
*Uncertainty and stochasticity of optimal policies*.
Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018 / V.
Kratochvíl (ed.). MatfyzPress, 2018. - P. 133-140 Bibtex MIS-Preprint: 8/2021 [FREELINK]

Muiños-Landin, S. ; Ghazi-Zahedi, K. and F. Cichos:
*Reinforcement learning of artificial microswimmers*.
Bibtex [ARXIV]

Rexiti, M. ; Felice, D. and S. Mancini:
*The volume of two-qubit states by information geometry*.
Entropy,
20 (2018) 2, 146 Bibtex [DOI] [ARXIV]

Sârbu, S. ; Volpi, R. ; Peşte, A. and L. Malagò:
*Learning in variational autoencoders with Kullback-Leibler and Renyi integral bounds*.
Bibtex [ARXIV]

Schwachhöfer, L. J. ; Ay, N. ; Jost, J. and H. V.
Lê:
*Congruent families and invariant tensors*.
Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th
Birthday, IGAIA IV Liblice, Czech Republic, June 2016 / N.
Ay... (eds.). Springer, 2018. - P. 157-187
(Springer proceedings in mathematics and statistics ; 252)
Bibtex [DOI] [ARXIV]

Ay, N. ; Jost, J. ; Lê, H. V.
and L. J. Schwachhöfer:
*Information geometry*.
Springer, 2017. - XI, 407 p.
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys
in mathematics ; 64)
ISBN 978-3-319-56477-7 Bibtex [DOI]

Ay, N. ; Jost, J. ; Lê, H. V.
and L. J. Schwachhöfer:
*Parametrized measure models*.
Information geometry / N.
Ay Springer, 2017. - P. 121-184
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys
in mathematics ; 64)
Bibtex MIS-Preprint: 69/2015 [DOI] [ARXIV]

Campbell-Borges, Y. C.
:
*Large deviation results for likelihood ratios and hypothesis testing on quantum spin
chains*.
Dissertation, Universität Leipzig, 2017 Bibtex

Der, R. and G. Martius:
*Self-organized behavior generation for musculoskeletal robots*.
Frontiers in neurorobotics,
11 (2017), 8 Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K. ; Deimel, R. ; Montúfar, G. ; Wall, V. and O. Brock:
*Morphological computation : the good, the bad, and the ugly*.
2017 IEEE/RSJ international conference on intelligent robots and systems (IROS) :
Vancouver, BC, Canada ; September 24-28, 2017 IEEE, 2017. - P. 464-469 Bibtex [DOI] [FREELINK]

Ghazi-Zahedi, K. ; Langer, C. and N. Ay:
*Morphological computation : synergy of body and brain*.
Entropy,
19 (2017) 9, 456 Bibtex [DOI]

Jeronymo, D. C.
; Campbell-Borges, Y. C.
and L. d.
Coelho:
*Image forgery detection by semi-automatic wavelet soft-thresholding with error level
analysis*.
Expert systems with applications,
85 (2017), p. 348-356 Bibtex [DOI]

Kanwal, M. S. ; Grochow, J. A. and N. Ay:
*Comparing information-theoretic measures of complexity in Boltzmann machines*.
Entropy,
19 (2017) 7, 310 Bibtex [DOI] [ARXIV]

Montúfar, G.:
*Notes on the number of linear regions of deep neural networks*.
2017 international conference on sampling theory and applications (SampTA) / G.
Anbarjafari... (eds.). IEEE, 2017. - P. 156-159 Bibtex [FREELINK]

Montúfar, G. ; Ghazi-Zahedi, K. and N. Ay:
*Stochasticity of optimal policies for POMDPs*.
RLDM 2017 : 3rd multidisciplinary conference on reinforcement learning and decision
making ; June 11-14, 2017 ; Ann Arbor, Michigan, USA University, 2017 Bibtex [FREELINK]

Montúfar, G. and J. Morton:
*Dimension of marginals of Kronecker product models*.
SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 126-151 Bibtex MIS-Preprint: 75/2015 [DOI] [ARXIV]

Montúfar, G. ; Morton, J. and J. Rauh:
*Restricted Boltzmann machines [In: Algebraic statistics ; 16 April - 22 April 2017
; report no. 20/2017]*.
Oberwolfach reports,
14 (2017) 2, p. 1241-1242 Bibtex [DOI] [FREELINK]

Montúfar, G. and J. Rauh:
*Geometry of policy improvement*.
Geometric science of information : Third International Conference, GSI 2017, Paris,
France, November 7-9, 2017, proceedings / F.
Nielsen... (eds.). Springer, 2017. - P. 282-290
(Lecture notes in computer science ; 10589)
Bibtex [DOI] [ARXIV]

Montúfar, G. and J. Rauh:
*Hierarchical models as marginals of hierarchical models*.
International journal of approximate reasoning,
88 (2017), p. 531-546 Bibtex MIS-Preprint: 27/2016 [DOI] [ARXIV]

Rauh, J.:
*The polytope of \(k\)-star densities*.
The electronic journal of combinatorics,
24 (2017) 1, P1.4 Bibtex [DOI]

Sokoloski, S.:
*Implementing a Bayes filter in a neural circuit : the case of unknown stimulus dynamics*.
Neural computation,
29 (2017) 9, p. 2450-2490 Bibtex MIS-Preprint: 30/2017 [DOI] [ARXIV]

Der, R.:
*In search for the neural mechanisms of individual development : behavior-driven differential
Hebbian learning*.
Frontiers in robotics and AI,
2 (2016), 37 Bibtex [DOI]

Ghazi-Zahedi, K. ; Haeufle, D. F. B. ; Montúfar, G. ; Schmitt, S. and N. Ay:
*Evaluating morphological computation in muscle and DC-motor driven models of hopping
movements*.
Frontiers in robotics and AI,
3 (2016), 42 Bibtex [DOI] [ARXIV]

Martius, G. ; Hostettler, R. ; Knoll, A. and R. Der:
*Compliant control for soft robots : emergent behavior of a tendon driven anthropomorphic
arm*.
2016 IEEE/RSJ international conference on intelligent robots and systems (IROS) :
October 9-14 2016 ; Daejeon, Korea IEEE, 2016. - P. 767-773 Bibtex [DOI]

Montúfar, G. ; Ghazi-Zahedi, K. and N. Ay:
*Information theoretically aided reinforcement learning for embodied agents*.
Bibtex [ARXIV]

Montúfar, G. and J. Rauh:
*Mode poset probability polytopes*.
Journal of algebraic statistics,
7 (2016) 1, p. 1-13 Bibtex MIS-Preprint: 22/2015 [DOI] [ARXIV]

Perrone, P. and N. Ay:
*Hierarchical quantification of synergy in channels*.
Frontiers in robotics and AI,
2 (2016), 35 Bibtex MIS-Preprint: 86/2015 [DOI] [ARXIV]

Pfante, O. ; Bertschinger, N. ; Olbrich, E. ; Ay, N. and J. Jost:
*Wie findet man eine geeignete Beschreibungsebene für ein komplexes System?*.
Jahrbuch der Max-Planck-Gesellschaft,
2016 (2016), Forschungsbericht - Max-Planck-Institut für Mathematik in den Naturwissenschaften Bibtex [FREELINK]

Rauh, J. and S. Sullivant:
*Lifting Markov bases and higher codimension toric fiber products*.
Journal of symbolic computation,
74 (2016), p. 276-307 Bibtex [DOI] [ARXIV]

Rodman, L. ; Spitkovsky, I. M. ; Szkoła, A. and S. Weis:
*Continuity of the maximum-entropy inference : convex geometry and numerical ranges
approach*.
Journal of mathematical physics,
57 (2016), 1 Bibtex MIS-Preprint: 18/2015 [DOI] [ARXIV]

Sato, Y. and N. Ay:
*Information flow in learning a coin-tossing game*.
Nonlinear theory and its applications,
7 (2016) 2, p. 118-125 Bibtex [DOI]

Schwachhöfer, L. J. ; Ay, N. ; Jost, J. and H. V.
Lê:
*Parametrized measure models and a generalization of Chentsov's theorem*.
International conference on information geometry and its applications IV : Liblice,
June 12-17, 2016 ; in honor of Shun-ichi Amari / N.
Ay... (eds.). Matfyzpress, 2016. - P. 17-17 Bibtex [FREELINK]

Amari, S. and N. Ay:
*Standard divergence in manifold of dual affine connections*.
Geometric science of information : second international conference, GSI 2015, Palaiseau,
France, October 28-30, 2015, proceedings / F.
Nielsen... (eds.). Springer, 2015. - P. 320-325
(Lecture notes in computer science ; 9389)
Bibtex [DOI]

Ay, N.:
*Information geometry on complexity and stochastic interaction*.
Entropy,
17 (2015) 4, p. 2432-2458 Bibtex MIS-Preprint: 95/2001 [DOI]

Ay, N.:
*Geometric design principles for brains of embodied agents*.
Künstliche Intelligenz : KI,
29 (2015) 4, p. 389-399 Bibtex [DOI]

Ay, N. and S. Amari:
*A novel approach to canonical divergences within information geometry*.
Entropy,
17 (2015) 12, p. 8111-8129 Bibtex MIS-Preprint: 73/2015 [DOI]

Ay, N. ; Jost, J. ; Lê, H. V.
and L. J. Schwachhöfer:
*Information geometry and sufficient statistics*.
Probability theory and related fields,
162 (2015) 1-2, p. 327-364 Bibtex MIS-Preprint: 65/2012 [DOI] [ARXIV]

Ay, N. and W. Löhr:
*The Umwelt of an embodied agent : a measure-theoretic definition*.
Theory in biosciences,
134 (2015) 3-4, p. 105-116 Bibtex MIS-Preprint: 74/2015 [DOI] [ARXIV]

Bernigau, H.:
*Causal models over infinite graphs and their application to the sensorimotor loop
: general stochastic aspects and gradient methods for optimal control*.
Dissertation, Universität Leipzig, 2015 Bibtex [FREELINK]

Bernigau, H. ; Kastoryano, M. J. and J. Eisert:
*Mutual information area laws for thermal free fermions*.
Journal of statistical mechanics,
2015 (2015) 2, P02008 Bibtex [DOI] [ARXIV]

Der, R. and G. Martius:
*Novel plasticity rule can explain the development of sensorimotor intelligence*.
Proceedings of the National Academy of Sciences of the United States of America,
112 (2015) 45, p. E6224-E6232 Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K. and J. Rauh:
*Quantifying morphological computation based on an information decomposition of the
sensorimotor loop*.
Proceedings of the european conference on artificial life 2015, ECAL 2015 / P.
Andrews... (eds.). MIT Press, 2015. - P. 70-77 Bibtex MIS-Preprint: 21/2015 [DOI] [ARXIV] [FREELINK]

Montúfar, G.:
*Deep narrow Boltzmann machines are universal approximators*.
Third international conference on learning representations - ICLR 2015 : May 7-9 2015,
San Diego, CA. USA ICLR, 2015 Bibtex MIS-Preprint: 113/2014 [ARXIV] [FREELINK]

Montúfar, G.:
*Universal approximation of Markov kernels by shallow stochastic feedforward networks*.
Bibtex MIS-Preprint: 23/2015 [ARXIV]

Montúfar, G.:
*A comparison of neural network architectures*.
Deep learning Workshop, ICML '15, Vauban Hall at Lille Grande Palais, France, July
10 and 11, 2015 Bibtex [FREELINK]

Montúfar, G. ; Ay, N. and K. Ghazi-Zahedi:
*Geometry and expressive power of conditional restricted Boltzmann machines*.
Journal of machine learning research,
16 (2015), p. 2405-2436 Bibtex MIS-Preprint: 16/2014 [ARXIV] [FREELINK]

Montúfar, G. ; Ghazi-Zahedi, K. and N. Ay:
*A theory of cheap control in embodied systems*.
PLoS computational biology,
11 (2015) 9, e1004427 Bibtex MIS-Preprint: 70/2014 [DOI] [ARXIV]

Montúfar, G. ; Ghazi-Zahedi, K. and N. Ay:
*Geometry and determinism of optimal stationary control in partially observable Markov
decision processes*.
Bibtex MIS-Preprint: 22/2016 [ARXIV]

Montúfar, G. and J. Morton:
*Discrete restricted Boltzmann machines*.
Journal of machine learning research,
16 (2015), p. 653-672 Bibtex MIS-Preprint: 106/2014 [ARXIV] [FREELINK]

Montúfar, G. and J. Morton:
*When does a mixture of products contain a product of mixtures?*.
SIAM journal on discrete mathematics,
29 (2015) 1, p. 321-347 Bibtex MIS-Preprint: 98/2014 [DOI] [ARXIV]

Montúfar, G. and J. Rauh:
*Mode poset probability polytopes*.
Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech
Republic, September 16-19, 2015 / V.
Kratochvíl (ed.). Oeconomica, 2015. - P. 147-154 Bibtex MIS-Preprint: 22/2015 [ARXIV] [FREELINK]

Montúfar, G. and J. Rauh:
*Hierarchical models as marginals of hierarchical models*.
Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech
Republic, September 16-19, 2015 / V.
Kratochvíl (ed.). Oeconomica, 2015. - P. 131-145 Bibtex MIS-Preprint: 27/2016 [ARXIV] [FREELINK]

Perrone, P. and N. Ay:
*Decomposition of Markov kernels*.
Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech
Republic, September 16-19, 2015 / V.
Kratochvíl (ed.). Oeconomica, 2015. - P. 167-178 Bibtex [FREELINK]

Pfante, O. and N. Ay:
*Operator-theoretic identification of closed sub-systems of dynamical systems*.
An interdisciplinary journal of discontinuity, nonlinearity, and complexity,
4 (2015) 1, p. 91-109 Bibtex MIS-Preprint: 4/2015 [DOI]

Salge, C. ; Ay, N. ; Polani, D. and M. Prokopenko:
*Zipf's law : balancing signal usage cost and communication efficiency*.
PLOS ONE,
10 (2015) 10, e0139475 Bibtex [DOI] [FREELINK]

Schwachhöfer, L. J. ; Ay, N. ; Jost, J. and H. V.
Lê:
*Invariant geometric structures on statistical models*.
Geometric science of information : second international conference, GSI 2015, Palaiseau,
France, October 28-30, 2015, proceedings / F.
Nielsen... (eds.). Springer, 2015. - P. 150-158
(Lecture notes in computer science ; 9389)
Bibtex [DOI]

Steudel, B. and N. Ay:
*Information-theoretic inference of common ancestors*.
Entropy,
17 (2015) 4, p. 2304-2327 Bibtex [DOI] [ARXIV]

Weis, S.:
*The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics*.
Bayesian inference and maximum entropy methods in science and engineering : (MaxEnt
2014) : Clos Lucé, Amboise, France, September 21-26 2014 / A.
Mohammad-Djafari (ed.). AIP Publising, 2015. - P. 173-180
(AIP conference proceedings ; 1641)
Bibtex [DOI] [ARXIV]

Weis, S. ; Knauf, A. ; Ay, N. and M.-J. Zhao:
*Maximizing the divergence from a hierarchical model of quantum states*.
Open systems and information dynamics,
22 (2015) 1, 1550006 Bibtex MIS-Preprint: 58/2014 [DOI] [ARXIV]

Ay, N. and K. Ghazi-Zahedi:
*On the causal structure of the sensorimotor loop*.
Guided self-organization : inception / M.
Prokopenko (ed.). Springer, 2014. - P. 261-294
(Emergence, complexity, and computation)
Bibtex [DOI]

Bertschinger, N. and J. Rauh:
*The Blackwell relation defines no lattice*.
IEEE international symposium on information theory proceedings (ISIT) 2014 : June
29-July 4, 2014 in Honolulu, USA IEEE, 2014. - P. 2479-2483 Bibtex [DOI] [ARXIV]

Bertschinger, N. ; Rauh, J. ; Olbrich, E. ; Jost, J. and N. Ay:
*Quantifying unique information*.
Entropy,
16 (2014) 4, p. 2161-2183 Bibtex MIS-Preprint: 102/2013 [DOI] [ARXIV] [CODELINK]

Der, R.:
*On the role of embodiment for self-organizing robots : behavior as broken symmetry*.
Guided self-organization : inception / M.
Prokopenko (ed.). Springer, 2014. - P. 193-221
(Emergence, complexity, and computation)
Bibtex [DOI]

Kahle, T. and J. Rauh:
*Toric fiber products versus Segre products*.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg,
84 (2014) 2, p. 187-201 Bibtex [DOI] [ARXIV]

Kahle, T. ; Rauh, J. and S. Sullivant:
*Positive margins and primary decomposition*.
Journal of commutative algebra,
6 (2014) 2, p. 173-208 Bibtex [DOI] [ARXIV]

Krüger, T. ; Montúfar, G. ; Seiler, R. and R. Siegmund-Schultze:
*Sequential recurrence-based multidimensional universal source coding of Lempel-Ziv
type*.
Bibtex MIS-Preprint: 86/2014 [ARXIV]

Martius, G. ; Der, R. and J. M.
Herrmann:
*Robot learning by guided self-organization*.
Guided self-organization : inception / M.
Prokopenko (ed.). Springer, 2014. - P. 223-260
(Emergence, complexity, and computation)
Bibtex [DOI]

Martius, G. ; Jahn, L. ; Hauser, H. and V. V. Hafner:
*Self-exploration of the Stumpy robot with predictive information maximization*.
From Animals to Animats 13 : 13th International Conference on Simulation of Adaptive
Behavior, SAB 2014, Castellón, Spain, July 22-25, 2014 ; proceedings / A.
P. Del Pobil... (eds.). Springer, 2014. - P. 32-42
(Lecture notes in computer science ; 8575)
Bibtex [DOI] [FREELINK]

Montúfar, G.:
*Universal approximation depth and errors of narrow belief networks with discrete units*.
Neural computation,
26 (2014) 7, p. 1386-1407 Bibtex MIS-Preprint: 74/2014 [DOI] [ARXIV]

Montúfar, G. and J. Morton:
*Geometry of hidden-visible products of statistical models*.
Algebraic Statistics 2014 : May 19-22 Illinois Institute of Technology, 2014 Bibtex [FREELINK]

Montúfar, G. ; Pascanu, R. ; Cho, K. and Y. Bengio:
*On the number of linear regions of deep neural networks*.
NIPS'14 Proceedings of the 27th international conference on neural information processing
systems - volume 2 ; Montreal, Quebec, Canada, December 8th-13th MIT Press, 2014. - P. 2924-2932 Bibtex MIS-Preprint: 73/2014 [ARXIV] [FREELINK]

Montúfar, G. and J. Rauh:
*Scaling of model approximation errors and expected entropy distances*.
Kybernetika,
50 (2014) 2, p. 234-245 Bibtex [DOI] [ARXIV]

Montúfar, G. ; Rauh, J. and N. Ay:
*On the Fisher metric of conditional probability polytopes*.
Entropy,
16 (2014) 6, p. 3207-3233 Bibtex MIS-Preprint: 87/2014 [DOI] [ARXIV]

Moritz, P. ; Reichardt, J. and N. Ay:
*Discriminating between causal structures in Bayesian networks given partial observations*.
Kybernetika,
50 (2014) 2, p. 284-295 Bibtex [DOI]

Pascanu, R. ; Montúfar, G. and Y. Bengio:
*On the number of inference regions of deep feed forward networks with piece-wise linear
activations*.
Second international conference on learning representations - ICLR 2014 : 14-16 April
2014, Banff, Canada ICLR, 2014 Bibtex MIS-Preprint: 72/2014 [ARXIV] [FREELINK]

Pfante, O. ; Bertschinger, N. ; Olbrich, E. ; Ay, N. and J. Jost:
*Comparison between different methods of level identification*.
Advances in complex systems,
17 (2014) 2, 1450007 Bibtex [DOI]

Pfante, O. ; Olbrich, E. ; Bertschinger, N. ; Ay, N. and J. Jost:
*Closure measures for coarse-graining of the tent map*.
Chaos,
24 (2014), 013136 Bibtex MIS-Preprint: 108/2013 [DOI]

Prokopenko, M. ; Polani, D. and N. Ay:
*On the cross-disciplinary nature of guided self-organisation*.
Guided self-organization : inception / M.
Prokopenko (ed.). Springer, 2014. - P. 3-15
(Emergence, complexity, and computation)
Bibtex [DOI]

Rauh, J. and N. Ay:
*Robustness, canalyzing functions and systems design*.
Theory in biosciences,
133 (2014) 2, p. 63-78 Bibtex MIS-Preprint: 66/2012 [DOI] [ARXIV]

Rauh, J. ; Bertschinger, N. ; Olbrich, E. and J. Jost:
*Reconsidering unique information : towards a multivariate information decomposition*.
IEEE international symposium on information theory proceedings (ISIT) 2014 : June
29-July 4, 2014 in Honolulu, USA IEEE, 2014. - P. 2232-2236 Bibtex [DOI] [ARXIV]

Weis, S.:
*Information topologies on non-commutative state spaces*.
Journal of convex analysis,
21 (2014) 2, p. 339-399 Bibtex MIS-Preprint: 75/2011 [ARXIV] [FREELINK]

Weis, S.:
*Continuity of the maximum-entropy inference*.
Communications in mathematical physics,
330 (2014) 3, p. 1263-1292 Bibtex MIS-Preprint: 6/2012 [DOI] [ARXIV]

Weis, S.:
*Erratum to: Continuity of the maximum-entropy inference*.
Communications in mathematical physics,
331 (2014) 3, p. 1301-1301 Bibtex MIS-Preprint: 6/2012 [DOI]

Ay, N. and K. Ghazi-Zahedi:
*Causal effects for prediction and deliberative decision making of embodied systems*.
Advances in cognitive neurodynamics III : proceedings of the 3rd International Conference
on Cognitive Neurodynamics 2011 ; [June 9-13, 2011, Hilton Niseko Village, Hokkaido,
Japan] / Y.
Yamaguchi (ed.). Springer, 2013. - P. 499-506
(Advances in cognitive neurodynamics)
Bibtex MIS-Preprint: 22/2011 [DOI]

Ay, N. and W. Löhr:
*A measure-theoretic description of the intrinsic view of embodied agents*.
Bibtex [FREELINK]

Ay, N. ; Montúfar, G. and J. Rauh:
*Selection criteria for neuromanifolds of stochastic dynamics*.
Advances in cognitive neurodynamics III : proceedings of the 3rd International Conference
on Cognitive Neurodynamics 2011 ; [June 9-13, 2011, Hilton Niseko Village, Hokkaido,
Japan] / Y.
Yamaguchi (ed.). Springer, 2013. - P. 147-154
(Advances in cognitive neurodynamics)
Bibtex MIS-Preprint: 15/2011 [DOI]

Bengtsson, I. ; Weis, S. and K. Zyczkowski:
*Geometry of the set of mixed quantum states : an apophatic approach*.
Geometric methods in physics : XXX Workshop, Bialowieza, Poland, June 26 to July 2,
2011 / P.
Kielanowski (ed.). Springer, 2013. - P. 175-197
(Trends in mathematics)
Bibtex MIS-Preprint: 83/2011 [DOI] [ARXIV]

Bertschinger, N. ; Rauh, J. ; Olbrich, E. and J. Jost:
*Shared information : new insights and problems in decomposing information in complex
systems*.
Proceedings of the European Conference on Complex Systems 2012 / T.
Gilbert... (eds.). Springer, 2013. - P. 251-269
(Springer proceedings in complexity)
Bibtex [DOI] [ARXIV]

Der, R. and G. Martius:
*Behavior as broken symmetry in embodied self-organizing robots*.
Advances in Artificial Life, ECAL 2013 : Proceedings of the Twelfth European Conference
on the Synthesis and Simulation of Living Systems / P.
Lió... (eds.). MIT Press, 2013. - P. 601-608 Bibtex [DOI]

Ghazi-Zahedi, K. and N. Ay:
*Quantifying morphological computation*.
Entropy,
15 (2013) 5, p. 1887-1915 Bibtex MIS-Preprint: 11/2013 [DOI] [ARXIV]

Ghazi-Zahedi, K. ; Martius, G. and N. Ay:
*Linear combination of one-step predictive information with an external reward in an
episodic policy gradient setting : a critical analysis*.
Frontiers in psychology,
4 (2013), 801 Bibtex MIS-Preprint: 60/2013 [DOI] [ARXIV]

Krüger, T. ; Montúfar, G. ; Seiler, R. and R. Siegmund-Schultze:
*Universally typical sets for ergodic sources of multidimensional data*.
Kybernetika,
49 (2013) 6, p. 868-882 Bibtex MIS-Preprint: 20/2011 [ARXIV] [FREELINK]

Lohmann, G. ; Stelzer, J. ; Neumann, J. ; Ay, N. and R. Turner:
*'More is different' in functional magnetic resonance imaging : a review of recent
data analysis techniques*.
Brain Connectivity,
3 (2013) 3, p. 223-239 Bibtex [DOI]

Martius, G. ; Der, R. and N. Ay:
*Information driven self-organization of complex robotic behaviors*.
PLOS ONE,
8 (2013) 5, e63400 Bibtex MIS-Preprint: 15/2013 [DOI] [ARXIV]

Montúfar, G.:
*Mixture decompositions of exponential families using a decomposition of their sample
spaces*.
Kybernetika,
49 (2013) 1, p. 23-39 Bibtex MIS-Preprint: 39/2010 [ARXIV] [FREELINK]

Montúfar, G. ; Rauh, J. and N. Ay:
*Maximal information divergence from statistical models defined by neural networks*.
Geometric science of information : first international conference, GSI 2013, Paris,
France, August 28-30, 2013. Proceedings / F.
Nielsen... (eds.). Springer, 2013. - P. 759-766
(Lecture notes in computer science ; 8085)
Bibtex MIS-Preprint: 31/2013 [DOI] [ARXIV]

Rauh, J.:
*Optimally approximating exponential families*.
Kybernetika,
49 (2013) 2, p. 199-215 Bibtex MIS-Preprint: 73/2011 [ARXIV] [FREELINK]

Rauh, J.:
*Generalized binomial edge ideals*.
Advances in applied mathematics,
50 (2013) 3, p. 409-414 Bibtex [DOI] [ARXIV]

Weis, S.:
*Discontinuities in the maximum-entropy inference*.
Bayesian inference and maximum entropy methods in science and engineering / U.
v.
Toussaint (ed.). AIP Publising, 2013. - P. 192-199
(AIP conference proceedings ; 1553)
Bibtex [DOI]

Ay, N. ; Bernigau, H. ; Der, R. and M. Prokopenko:
*Information-driven self-organization : the dynamical system approach to autonomous
robot behavior*.
Theory in biosciences,
131 (2012) 3, p. 161-179 Bibtex [DOI]

Ay, N. ; Der, R. and M. Prokopenko:
*Guided self-organization : perception-action loops of embodied systems*.
Theory in biosciences,
131 (2012) 3, p. 125-127 Bibtex [DOI]

Ay, N. ; Jost, J. ; Lê, H. V.
and L. J. Schwachhöfer:
*A characterization of the Fisher metric and the Amari-Chentsov tensor in information
geometry*.
Bibtex

Ay, N. and W. Wenzel:
*On solution sets of information inequalities*.
Kybernetika,
48 (2012) 5, p. 845-864 Bibtex MIS-Preprint: 16/2011 [FREELINK]

Janzing, D. ; Mooij, J. ; Zhang, K. ; Lemeire, J. ; Zscheischler, J. ; Daniusis, P. ; Steudel, B. and B. Schölkopf:
*Information-geometric approach to inferring causal directions*.
Artificial intelligence,
182/183 (2012), p. 1-31 Bibtex [DOI]

Löhr, W.:
*Predictive models and generative complexity*.
Journal of systems science and complexity,
25 (2012) 1, p. 30-45 Bibtex [DOI]

Löhr, W. ; Szkoła, A. and N. Ay:
*Process dimension of classical and non-commutative processes*.
Open systems and information dynamics,
19 (2012) 1, 1250007 Bibtex MIS-Preprint: 52/2011 [DOI] [ARXIV]

Montúfar, G.:
*On the expressive power of discrete mixture models, restricted Boltzmann machines,
and deep belief networks - a unified mathematical treatment*.
Dissertation, Universität Leipzig, 2012 Bibtex [FREELINK]

Montúfar, G. and J. Morton:
*When does a mixture of products contain a product of mixtures?*.
NIPS 2012 - deep learning and unsupervised feature learning workshop : [be held in
conjunction with neural information processing systems on December 8, 2012 (TBD) at
Lake Tahoe, USA] Neural Information Processing Systems, 2012 Bibtex MIS-Preprint: 98/2014 [ARXIV]

Montúfar, G. and J. Rauh:
*Scaling of model approximation errors and expected entropy distances*.
Proceedings of the 9th workshop on uncertainty processing WUPES '12 : Marianske Lazne,
Czech Republik ; 12-15th September 2012 Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, 2012. - P. 137-148 Bibtex [ARXIV] [FREELINK]

Moritz, P. ; Reichardt, J. and N. Ay:
*A new common cause principle for bayesian networks*.
Proceedings of the 9th workshop on uncertainty processing WUPES '12 : Marianske Lazne,
Czech Republik ; 12-15th September 2012 Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, 2012. - P. 149-162 Bibtex [FREELINK]

Weis, S.:
*Duality of non-exposed faces*.
Journal of convex analysis,
19 (2012) 3, p. 815-835 Bibtex MIS-Preprint: 76/2011 [ARXIV] [FREELINK]

Weis, S. and A. Knauf:
*Entropy distance : new quantum phenomena*.
Journal of mathematical physics,
53 (2012) 10, 102206 Bibtex MIS-Preprint: 72/2011 [DOI]

Ay, N. ; Müller, M. and A. Szkoła:
*Effective complexity of stationary process realizations*.
Entropy,
13 (2011) 6, p. 1200-1211 Bibtex MIS-Preprint: 2/2010 [DOI] [ARXIV]

Ay, N. ; Olbrich, E. ; Bertschinger, N. and J. Jost:
*A geometric approach to complexity*.
Chaos,
21 (2011) 3, 037103 Bibtex MIS-Preprint: 53/2011 [DOI]

Campbell-Borges, Y. C.
and J. Roberto C. Piqueira:
*Classical hierarchical correlation quantification on tripartite qubit mixed state
families*.
Bibtex [ARXIV]

Der, R. and G. Martius:
*The playful machine : theoretical foundation and practical realization of self-organizing
robots*.
Springer, 2011. - XIII, 333 p.
(Cognitive systems monographs ; 15)
ISBN 978-3-642-20253-7 Bibtex [DOI]

Matúš, F. and J. Rauh:
*Maximization of the information divergence from an exponential family and criticality*.
IEEE international symposium on information theory proceedings (ISIT) 2011 : July
31-August 5, 2011 in St. Petersburg, Russia IEEE, 2011. - P. 903-907 Bibtex [DOI]

Montúfar, G. and N. Ay:
*Refinements of universal approximation results for deep belief networks and restricted
Boltzmann machines*.
Neural computation,
23 (2011) 5, p. 1306-1319 Bibtex MIS-Preprint: 23/2010 [DOI] [ARXIV]

Montúfar, G. ; Rauh, J. and 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 ; NIPS 2011 / J. Shawe-Taylor (ed.). Neural Information Processing Systems, 2011. - P. 415-423 Bibtex MIS-Preprint: 27/2011 [ARXIV] [FREELINK]

Nussbaum, M. and A. Szkoła:
*Asymptotically optimal discrimination between pure quantum states*.
Theory of quantum computation, communication, and cryptography : 5th conference, TQC
2010, Leeds, UK, April 13 - 15, 2010, revised selected papers / W.
v.
Dam... (eds.). Springer, 2011. - P. 1-8
(Lecture notes in computer science ; 6519)
Bibtex MIS-Preprint: 1/2010 [DOI] [FREELINK]

Nussbaum, M. and A. Szkoła:
*An asymptotic error bound for testing multiple quantum hypotheses*.
The annals of statistics,
39 (2011) 6, p. 3211-3233 Bibtex MIS-Preprint: 54/2011 [DOI] [ARXIV]

Rauh, J.:
*Finding the maximizers of the information divergence from an exponential family*.
IEEE transactions on information theory,
57 (2011) 6, p. 3236-3247 Bibtex MIS-Preprint: 82/2009 [DOI] [ARXIV]

Rauh, J.:
*Finding the maximizers of the information divergence from an exponential family*.
Dissertation, Universität Leipzig, 2011 Bibtex [FREELINK]

Rauh, J. and N. Ay:
*Robustness and conditional independence ideals*.
Bibtex MIS-Preprint: 63/2011 [ARXIV]

Rauh, J. ; Kahle, T. and N. Ay:
*Support sets in exponential families and oriented matroid theory*.
International journal of approximate reasoning,
52 (2011) 5, p. 613-626 Bibtex MIS-Preprint: 28/2009 [DOI] [ARXIV]

Ay, N. ; Müller, M. and A. Szkoła:
*Effective complexity and its relation to logical depth*.
IEEE transactions on information theory,
56 (2010) 9, p. 4593-4607 Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K. ; Ay, N. and R. Der:
*Higher coordination with less control : a result of information maximization in the
sensorimotor loop*.
Adaptive behavior,
18 (2010) 3/4, p. 338-355 Bibtex [DOI] [ARXIV]

Güttler, F. ; Rabe, W. ; Hoffmann, J. ; Bogdan, M. and R. Der:
*Transposing simulated self-organizing robots into reality using the plug and learn
architecture*.
Proceedings of the International Conference on Fuzzy Computation and International
Conference on Neural Computation : Valencia, Spain, October 24 - 26, 2010 SciTePress - Science and Techn. Publ., 2010. - P. 350-357 Bibtex [DOI]

Herzog, J. ; Hibi, T. ; Hreinsdottir, F. ; Kahle, T. and J. Rauh:
*Binomial edge ideals and conditional independence statements*.
Advances in applied mathematics,
45 (2010) 3, p. 317-333 Bibtex [DOI] [ARXIV]

Janzing, D. and B. Steudel:
*Justifying additive noise model-based causal discovery via algorithmic information
theory*.
Open systems and information dynamics,
17 (2010) 2, p. 189-212 Bibtex [DOI] [ARXIV]

Kahle, T.:
*Neighborliness of marginal polytopes*.
Beiträge zur Algebra und Geometrie,
51 (2010) 1, p. 45-56 Bibtex MIS-Preprint: 57/2008 [ARXIV] [FREELINK]

Kahle, T.:
*On boundaries of statistical models*.
Dissertation, Universität Leipzig, 2010 Bibtex [FREELINK]

Krakauer, D. C. ; Flack, J. C. and N. Ay:
*Probabilistic design principles for robust multimodal communication networks*.
Modelling perception with artificial neural networks / C.
R. Tosh... (eds.). Cambridge University Press, 2010. - P. 255-268 Bibtex [DOI]

Löhr, W.:
*Models of discrete-time stochastic processes and associated complexity measures*.
Dissertation, Universität Leipzig, 2010 Bibtex [FREELINK]

Montúfar, G.:
*Mixture models and representational power of RBM's, DBN's, and DBM's*.
NIPS 2010 : Deep learning and unsupervised feature learning workshop ; December 19,
2010, Hilton, Vancouver, Canada NIPS, 2010. - P. 1-9 Bibtex [FREELINK]

Nussbaum, M. and A. Szkoła:
*Exponential error rates in multiple state discrimination on a quantum spin chain*.
Journal of mathematical physics,
51 (2010) 7, 072203 Bibtex MIS-Preprint: 3/2010 [DOI] [ARXIV]

Olbrich, E. ; Kahle, T. ; Bertschinger, N. ; Ay, N. and J. Jost:
*Quantifying structure in networks*.
The European physical journal / B,
77 (2010) 2, p. 239-247 Bibtex MIS-Preprint: 81/2009 [DOI] [ARXIV]

Prokopenko, M. ; Ay, N. ; Obst, O. and D. Polani:
*Phase transitions in least-effort communications*.
Journal of statistical mechanics,
2010 (2010) 11, P11025 Bibtex [DOI]

Ay, N.:
*A refinement of the common cause principle*.
Discrete applied mathematics,
157 (2009) 10, p. 2439-2457 Bibtex [DOI]

Kahle, T. ; Olbrich, E. ; Jost, J. and N. Ay:
*Complexity measures from interaction structures*.
Physical review / E,
79 (2009) 2, pt. 2, 026201 Bibtex MIS-Preprint: 44/2008 [DOI] [ARXIV]

Kahle, T. ; Wenzel, W. and N. Ay:
*Hierarchical models, marginal polytopes, and linear codes*.
Kybernetika,
45 (2009) 2, p. 189-207 Bibtex MIS-Preprint: 30/2008 [ARXIV] [FREELINK]

Löhr, W.:
*Properties of the statistical complexity functional and partially deterministic HMMs*.
Entropy,
11 (2009) 3, p. 385-401 Bibtex MIS-Preprint: 24/2009 [DOI]

Löhr, W. and N. Ay:
*On the generative nature of prediction*.
Advances in complex systems,
12 (2009) 2, p. 169-194 Bibtex MIS-Preprint: 8/2008 [DOI]

Löhr, W. and 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 / J.
Zhou (ed.). Springer, 2009. - P. 265-276
(Lecture notes of the Institute for Computer Science, Social Informatics and Telecommunications
Engineering ; 4)
Bibtex [DOI]

Nussbaum, M. and A. Szkoła:
*The Chernoff lower bound for symmetric quantum hypothesis testing*.
The annals of statistics,
37 (2009) 2, p. 1040-1057 Bibtex MIS-Preprint: 69/2006 [DOI] [ARXIV]

Audenaert, K. M. R. ; Nussbaum, M. ; Szkoła, A. and F. Verstraete:
*Asymptotic error rates in quantum hypothesis testing*.
Communications in mathematical physics,
279 (2008) 1, p. 251-283 Bibtex MIS-Preprint: 84/2007 [DOI] [ARXIV]

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

Ay, N. and D. Polani:
*Information flows in causal networks*.
Advances in complex systems,
11 (2008) 1, p. 17-41 Bibtex MIS-Preprint: 47/2006 [DOI]

Bertschinger, N. ; Olbrich, E. ; Ay, N. and J. Jost:
*Autonomy : an information-theoretic perspective*.
Biosystems,
91 (2008) 2, p. 331-345 Bibtex [DOI]

Der, R. ; Güttler, F. and 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 MIT Press, 2008. - P. 166-172 Bibtex

Ghazi-Zahedi, K. ; Twickel, A. v.
and F. Pasemann:
*YARS : A physical 3D simulator for evolving controllers for real robots*.
Simulation, modeling, and programming for autonomous robots : first international
conference, SIMPSR 2008 Venice, Italy, November 3-7, 2008 proceedings / S.
Carpin... (eds.). Springer, 2008. - P. 75-86
(Lecture notes in artificial intelligence ; 5325)
Bibtex [DOI]

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

Ay, N. ; Flack, J. C. and D. C. Krakauer:
*Robustness and complexity co-constructed in multimodal signalling networks*.
Philosophical transactions of the Royal Society of London / B,
362 (2007) 1479, p. 441-447 Bibtex [DOI]

Ay, N. and D. C. Krakauer:
*Geometric robustness theory and biological networks*.
Theory in biosciences,
125 (2007) 2, p. 93-121 Bibtex MIS-Preprint: 14/2006 [DOI]

Ghazi-Zahedi, K. and F. Pasemann:
*Adaptive behavior control by self-regulating neurons*.
50 years of artificial intelligence : essays dedicated to the 50th aniversary of artificial
intelligence / M.
Lungarella... (eds.). Springer, 2007. - P. 196-205
(Lecture notes in computer science ; 4850 : Lecture notes in artificial intelligence)
Bibtex [DOI]

Jost, J. ; Bertschinger, N. ; Olbrich, E. ; Ay, N. and S. Frankel:
*An information theoretic approach to system differentiation on the basis of statistical
dependencies between subsystems*.
Physica / A,
378 (2007) 1, p. 1-10 Bibtex [DOI]

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

Ay, N. and A. Knauf:
*Maximizing multi-information*.
Kybernetika,
42 (2006) 5, p. 517-538 Bibtex MIS-Preprint: 42/2003 [ARXIV]

Ay, N. ; Olbrich, E. ; Bertschinger, N. and J. Jost:
*A unifying framework for complexity measures of finite systems*.
ECCS'06 : proceedings of the European Conference on Complex Systems 2006 ; towards
a science of complex systems / J.
Jost... (eds.). European Complex Systems Society, 2006. - P. 80-80 Bibtex [FREELINK]

Ay, N. and G. Struck:
*Stochastic independence of crosstalk variables in the hopfield model*.
Bibtex MIS-Preprint: 65/2006

Bertschinger, N. ; Olbrich, E. ; Ay, N. and J. Jost:
*Information and closure in systems theory*.
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 / S. Artmann... (eds.). IOS Press, 2006. - P. 9-19 Bibtex

Bertschinger, N. ; Olbrich, E. ; Ay, N. and J. Jost:
*Autonomy : an information theoretic perspective*.
Artificial life X : proceedings of the tenth international conference on the synthesis
and simulation of living systems / L.
M.
Rocha... (eds.). MIT Press, 2006. - P. 7-12 Bibtex

Kahle, T. and N. Ay:
*Support sets of distributions with given interaction structure*.
7th Workshop on Uncertainty Processing : WUPES'06 ; Mikulov, Czech Republik ; 16-20th
September 2006 Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, 2006. - P. 52-61 Bibtex MIS-Preprint: 94/2006 [FREELINK]