Publications

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]

Banerjee, P.
K.
; Rauh, J.
and G. Montúfar:
*Computing the unique information*.
Bibtex MIS-Preprint: 73/2017 [ARXIV]

Boege, T.
; D'Ali, A.
; Kahle, T.
and B.
Sturmfels:
*The geometry of Gaussoids*.
Bibtex MIS-Preprint: 70/2017 [ARXIV]

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

Czabarka, E.
; Rauh, J.
; Sadeghi, K.
; Short, T.
and L.
Székely:
*On the number of non-zero elements of joint degree vectors*.
The electronic journal of combinatorics,
24 (2017) 1, P1.55Bibtex[ARXIV] [FREELINK]

Ghazi-Zahedi, K.
; Langer, C.
and N. Ay:
*Morphological computation : synergy of body and brain*.
Entropy,
19 (2017) 9, 456Bibtex [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. 348-356Bibtex [DOI]

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

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

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. 531-546Bibtex MIS-Preprint: 27/2016 [DOI] [ARXIV]

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

Rauh, J.
:
*Secret sharing and shared information*.
Entropy,
19 (2017) 11, 601Bibtex MIS-Preprint: 72/2017 [DOI] [ARXIV]

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

Der, R.
and G. Martius:
*The world as its own best controller : a case study with anthropomimetic robots*.
Bibtex[ARXIV]

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), 42Bibtex [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. 767-773Bibtex [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. 1-13Bibtex MIS-Preprint: 22/2015 [DOI] [ARXIV]

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

Rauh, J.
and S.
Sullivant:
*Lifting Markov bases and higher codimension toric fiber products*.
Journal of symbolic computation,
74 (2016), p. 276-307Bibtex [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), 1Bibtex MIS-Preprint: 18/2015 [DOI] [ARXIV]

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. 2432-2458Bibtex MIS-Preprint: 95/2001 [DOI]

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

Ay, N.
and S.
Amari:
*A novel approach to canonical divergences within information geometry*.
Entropy,
17 (2015) 12, p. 8111-8129Bibtex 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. 327-364Bibtex MIS-Preprint: 65/2012 [DOI] [ARXIV]

Ay, N.
; Jost, J.
; Lê, H.
V.
and L.
J. Schwachhöfer:
*Parametrized measure models*.
Bibtex MIS-Preprint: 69/2015 [ARXIV]

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

Bernigau, H.
; Kastoryano, M. J. and J. Eisert:
*Mutual information area laws for thermal free fermions*.
Journal of statistical mechanics,
2015 (2015), P02008Bibtex [DOI] [ARXIV]

Der, R.
:
*In search for the neural mechanisms of individual development : behavior-driven differential
Hebbian learning*.
Frontiers in robotics and AI,
2 (2015), 37Bibtex [DOI]

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-E6232Bibtex [DOI] [ARXIV]

Ghazi-Zahedi, K.
and J. Rauh:
*Quantifying morphological computation based on an information decomposition of the
sensorimotor loop*.
Bibtex MIS-Preprint: 21/2015 [ARXIV] [FREELINK]

Krakauer, D.
C. ; Bertschinger, N.
; Olbrich, E.
; Ay, N.
and J.
C. Flack:
*The information theory of individuality*.
The philosophy of individuality / L.
Nyhart... (eds.). University of Chicago Press, 2015Bibtex[ARXIV]

Martius, G.
and E.
Olbrich:
*Quantifying emergent behavior of autonomous robots*.
Entropy,
17 (2015) 10, p. 7266-7297Bibtex [DOI] [ARXIV]

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

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, 2015Bibtex

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. 2405-2436Bibtex 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, e1004427Bibtex 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. 653-672Bibtex 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. 321-347Bibtex MIS-Preprint: 98/2014 [DOI] [ARXIV]

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 16-19th, 2015 / V.
Kratochvíl (ed.). Oeconomica, 2015. - P. 131-145Bibtex MIS-Preprint: 27/2016 [ARXIV] [FREELINK]

Olbrich, E.
; Bertschinger, N.
and J. Rauh:
*Information decomposition and synergy*.
Entropy,
17 (2015) 5, p. 3501-3517Bibtex [DOI]

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. 91-109Bibtex 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, e0139475Bibtex [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. 2304-2327Bibtex [DOI] [ARXIV] [FREELINK]

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, 21-26 September 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.
Zhao:
*Maximizing the divergence from a hierarchical model of quantum states*.
Open systems and information dynamics,
22 (2015) 1, 1550006Bibtex 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. 2479-2483Bibtex [DOI] [ARXIV]

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

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. 187-201Bibtex [DOI] [ARXIV]

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

Krakauer, D.
C. ; Bertschinger, N.
; Olbrich, E.
; Ay, N.
and J.
C. Flack:
*The information theory of individuality*.
The philosophy of individuality / L.
Nyhart... (eds.). University of Chicago Press, 2015Bibtex[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. 1386-1407Bibtex 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, 2014Bibtex[FREELINK]

Montúfar, G.
; Pascanu, R.
; Cho, K.
and Y.
Bengio:
*On the number of linear regions of deep neural networks*.
Annual Conference on Neural Information Processing Systems : NIPS 2014, Montreal,
Quebec, Canada, December 8th - 13th Neural Information Processing Systems, 2014Bibtex MIS-Preprint: 73/2014 [ARXIV]

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

Montúfar, G.
; Rauh, J.
and N. Ay:
*On the Fisher metric of conditional probability polytopes*.
Entropy,
16 (2014) 6, p. 3207-3233Bibtex 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. 284-295Bibtex [DOI]

Pascanu, R.
; Montúfar, G.
and Y.
Bengio:
*On the number of response regions of deep feedforward networks with piecewise linear
activations*.
International conference on learning representations - ICLR 2014 : 14-16 April 2014,
Banff, Canada ICLR, 2014Bibtex MIS-Preprint: 72/2014 [ARXIV]

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, 1450007Bibtex [DOI] [FREELINK]

Pfante, O.
; Olbrich, E.
; Bertschinger, N.
; Ay, N.
and J.
Jost:
*Closure measures for coarse-graining of the tent map*.
Chaos,
24 (2014), 013136Bibtex 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. 63-78Bibtex 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. 2232-2236Bibtex [DOI] [ARXIV]

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

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

Weis, S.
:
*Erratum to: Continuity of the maximum-entropy inference*.
Communications in mathematical physics,
331 (2014) 3, p. 1301-1301Bibtex 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.
Lio... (eds.). MIT Press, 2013. - P. 601-608Bibtex [DOI]

Ghazi-Zahedi, K.
and N. Ay:
*Quantifying morphological computation*.
Entropy,
15 (2013) 5, p. 1887-1915Bibtex 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 / Frontiers in cognitive science,
4 (2013), 801Bibtex 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. 868-882Bibtex MIS-Preprint: 20/2011 [ARXIV]

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. 223-239Bibtex [DOI]

Martius, G.
:
*Robustness of guided self-organization against sensorimotor disruptions*.
Advances in complex systems,
16 (2013) 2/3, 1350001Bibtex [DOI]

Martius, G.
; Der, R.
and N. Ay:
*Information driven self-organization of complex robotic behaviors*.
PLoS one,
8 (2013) 5, e63400Bibtex 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. 23-39Bibtex 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]

Piqueira, J.
Roberto C. and Y. C. Campbell-Borges:
*Extending SDL and LMC complexity measures to quantum states*.
Physica / A,
392 (2013) 20, p. 5255-5259Bibtex [DOI]

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

Rauh, J.
:
*Generalized binomial edge ideals*.
Advances in applied mathematics,
50 (2013) 3, p. 409-414Bibtex [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. 161-179Bibtex [DOI]

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

Ay, N.
and W. Wenzel:
*On solution sets of information inequalities*.
Kybernetika,
48 (2012) 5, p. 845-864Bibtex 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. 1-31Bibtex [DOI]

Kahle, T.
:
*Erratum to 'Neighborliness of marginal polytopes'*.
Beiträge zur Algebra und Geometrie,
53 (2012) 1, p. 295-295Bibtex [DOI]

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

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

Martius, G.
and J.
M.
Herrmann:
*Variants of guided self-organization for robot control*.
Theory in biosciences,
131 (2012) 3, p. 129-137Bibtex [DOI]

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

Moritz, P.
; Reichardt, J.
and N. Ay:
*A new common cause principle for bayesian networks*.
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. 149-162Bibtex[FREELINK]

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

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

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

Ay, N.
; Olbrich, E.
; Bertschinger, N.
and J.
Jost:
*A geometric approach to complexity*.
Chaos,
21 (2011) 3, 037103Bibtex 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]

Martius, G.
and J.
M.
Herrmann:
*Tipping the scales : guidance and intrinsically motivated behavior*.
Advances in Artificial Life, ECAL 2011 : Proceedings of the Eleventh European Conference
on the Synthesis and Simulation of Living Systems / T.
Lenarts (ed.). MIT Press, 2011. - P. 506-513Bibtex

Matus, 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. 903-907Bibtex [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. 1306-1319Bibtex MIS-Preprint: 23/2010 [DOI]

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 / J. Shawe-Taylor (ed.). Neural Information Processing Systems, 2011. - P. 1-9Bibtex MIS-Preprint: 27/2011 [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. 3211-3233Bibtex 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. 3236-3247Bibtex MIS-Preprint: 82/2009 [DOI] [ARXIV]

Rauh, J.
:
*Finding the maximizers of the information divergence from an exponential family*.
Dissertation, Universität Leipzig, 2011Bibtex[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. 613-626Bibtex 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. 4593-4607Bibtex [DOI] [ARXIV]

Boldhaus, G.
; Bertschinger, N.
; Rauh, J.
; Olbrich, E.
and K.
Klemm:
*Robustness of boolean dynamics under knockouts*.
Physical review / E,
82 (2010) 2, 021916Bibtex [DOI] [ARXIV]

Daniusis, P.
; Janzing, D.
; Mooij, J.
; Zscheischler, J.
; Steudel, B.
; Zhang, K.
and B.
Schoelkopf:
*Inferring deterministic causal relations*.
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence : UAI
2010, June 8-11, 2010, Avalon, CA / P.
Grünwald... (eds.). AUAI Press, 2010. - P. 143-150Bibtex[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. 338-355Bibtex [DOI] [ARXIV]

Güttler, F.
; Rabe, W.
; Hoffmann, J.
; Bogdan, M.
and R. Der:
*Transposing simulated self-organizing robots into reality using the plug &
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. 350-357Bibtex [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. 317-333Bibtex [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. 189-212Bibtex [DOI] [ARXIV]

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

Kahle, T.
:
*Decompositions of binomial ideals*.
Annals of the institute of statistical mathematics,
62 (2010) 4, p. 727-745Bibtex [DOI]

Kahle, T.
:
*On boundaries of statistical models*.
Dissertation, Universität Leipzig, 2010Bibtex[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. 255-268Bibtex [DOI]

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

Montúfar, G.
:
*Mixture models and representational power of RBM's, DBN's, and DBM's*.
Deep Learning and Unsupervised Feature Learning Workshop : NIPS 2010 ; December 19,
2010, Hilton, Vancouver, CanadaBibtex[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, 072203Bibtex 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. 239-247Bibtex 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, P11025Bibtex [DOI]

Steudel, B.
; Janzing, D.
and B.
Schoelkopf:
*Causal Markov condition for submodular information measures*.
COLT 2010 : Proceedings of the 23rd Annual Conference on Learning Theory, Haifa, Israel
June 27-29, 2010 / A.
T.
Kalai... (eds.). Association for Computing Machinery, 2010. - P. 464-476Bibtex[ARXIV]

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

Der, R.
:
*Artificial life from the principle of homeokinesis*.
Proceedings of the 8th German Workshop on Artificial Life, July 30 - August 1, 2008,
Leipzig, Germany / K.
Klemm... (eds.). Akademische Verlagsgesellschaft, 2009. - P. 125-136Bibtex

Ghazi-Zahedi, K.
:
*Self-regulating neurons : a model for synaptic plasticity in artificial recurrent
neural networks*.
Dissertation, Universität Osnabrück, 2009Bibtex[FREELINK]

Hesse, F.
; Der, R.
and J.
M.
Herrmann:
*Modulated exploratory dynamics can shape self-organized behavior*.
Advances in complex systems,
12 (2009) 3, p. 273-291Bibtex [DOI]

Kahle, T.
; Olbrich, E.
; Jost, J.
and N. Ay:
*Complexity measures from interaction structures*.
Physical review / E,
79 (2009) 2, pt. 2, 026201Bibtex 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. 189-207Bibtex MIS-Preprint: 30/2008 [ARXIV] [FREELINK]

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

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

Müller, M.
:
*Convex trace functions on quantum channels and the additivity conjecture*.
Physical review / A,
79 (2009) 5, 052332Bibtex [DOI] [ARXIV]

Müller, M.
:
*Does probability become fuzzy in small regions of spacetime?*.
Physics Letters / B,
673 (2009) 2, p. 166-167Bibtex [DOI]

Müller, M.
:
*On the quantum Kolmogorov complexity of classical strings*.
International journal of quantum information,
7 (2009) 4, p. 701-711Bibtex [DOI]

Müller, M.
; Rogers, C.
and R.
Nagarajan:
*Lossless quantum prefix compression for communication channels that are always open*.
Physical review / A,
79 (2009) 1, 012302Bibtex [DOI] [ARXIV]

Nussbaum, M.
and A. Szkoła:
*The Chernoff lower bound for symmetric quantum hypothesis testing*.
The annals of statistics,
37 (2009) 2, p. 1040-1057Bibtex 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. 251-283Bibtex 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. 329-339Bibtex [DOI]

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

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

Bjelakovic, I.
; Deuschel, J.
; Krüger, T.
; Seiler, R.
; Siegmund-Schultze, R.
and A. Szkoła:
*Typical support and Sanov large deviations of correlated states*.
Communications in mathematical physics,
279 (2008) 2, p. 559-584Bibtex MIS-Preprint: 33/2007 [DOI] [ARXIV]

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. 166-172Bibtex

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]

Müller, M.
and C.
Rogers:
*Quantum bit strings and prefix-free Hilbert spaces*.
Proceedings of the 2008 International Conference on Information Theory and Statistical
Learning : ITSL 2008, Las Vegas, Nevada, USA, July 14 - 17, 2008 / M.
Dehmer... (eds.). CSREA Press, 2008. - P. 106-111Bibtex[ARXIV]

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. 407-415Bibtex [DOI]

Atay, F.
M. and D. J. Albers:
*Entropy, dimension, and state mixing in a class of time-delayed dynamical systems*.
Bibtex MIS-Preprint: 83/2007 [ARXIV]

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. 441-447Bibtex [DOI]

Ay, N.
and D.
C. Krakauer:
*Geometric robustness theory and biological networks*.
Theory in biosciences,
125 (2007) 2, p. 93-121Bibtex 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 statisitical
dependencies between subsystems*.
Physica / A,
378 (2007) 1, p. 1-10Bibtex [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. 190-197Bibtex [DOI]

Albers, D.
J. and J. C. Sprott:
*Probability of local bifurcation type from a fixed point: a random matrix perspective*.
Journal of statistical physics,
125 (2006) 4, p. 889-925Bibtex MIS-Preprint: 94/2005 [DOI]

Albers, D.
J. and J. C. Sprott:
*Routes to chaos in high-dimensional dynamical systems : a qualitative numerical study*.
Physica / D,
223 (2006) 2, p. 194-207Bibtex MIS-Preprint: 92/2005 [DOI]

Albers, D.
J. and J. C. Sprott:
*Structural stability and hyperbolicity violation in high-dimensional dynamical systems*.
Nonlinearity,
19 (2006) 8, p. 1801-1847Bibtex MIS-Preprint: 93/2005 [DOI]

Albers, D.
J. ; Sprott, J. C. and J. P. Crutchfield:
*Persistent chaos in high dimensions*.
Physical review / E,
74 (2006) 5, 057201Bibtex MIS-Preprint: 95/2005 [DOI]

Ay, N.
and A.
Knauf:
*Maximizing multi-information*.
Kybernetika,
42 (2006) 5, p. 517-538Bibtex 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. 80-80Bibtex[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.). Aka, 2006. - P. 9-19Bibtex

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. 52-61Bibtex MIS-Preprint: 94/2006 [FREELINK]