Publications

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:
*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]

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]

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Ay, N.
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Ay, N.
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Bertschinger, N.
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*Information and closure in systems theory*.
Explorations in the complexity of possible life : abstracting and synthesizing the
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