Publications

Andreotti, E.
; Bazzani, A.
; Remondini, D.
and G.
Servizi:
*On the multiplicity of Laplacian eigenvalues and Fiedler partitions*.
Bibtex[ARXIV]

Ay, N.
; Gibilisco, P.
and F. Matus (eds.):
*Information geometry and its applications : on the Occasion of Shun-ichi Amari's 80th
Birthday, Liblice, Czech Republic, June 2016*.
Springer, 2018 ISBN 978-3-319-97797-3 Bibtex

Ay, N.
; Jost, J.
; Lê, H.
V.
and L.
J. Schwachhöfer:
*Parametrized measure models*.
Bernoulli,
24 (2018) 3, p. 1692-1725Bibtex 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. 141-145Bibtex MIS-Preprint: 73/2017 [ARXIV]

Boege, T.
; D'Ali, A.
; Kahle, T.
and B.
Sturmfels:
*The geometry of Gaussoids*.
Foundations of computational mathematics,
Vol. not yet known, pp. not yet knownBibtex MIS-Preprint: 70/2017 [DOI] [ARXIV]

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

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

Fritz, T.
and P. Perrone:
*Stochastic order on metric spaces and the ordered Kantorovich monad*.
Bibtex MIS-Preprint: 76/2018

Fritz, T.
and P. Perrone:
*A criterion for Kan extensions of lax monoidal functors*.
Bibtex MIS-Preprint: 83/2018 [ARXIV]

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

Lin, A.
T.
; Li, W.
; Osher, S.
and G. Montúfar:
*Wasserstein proximal of GANs*.
Bibtex MIS-Preprint: 88/2018 [FREELINK]

Montúfar, G.
:
*Illustration of maxout layer upper bound*.
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, Liblice, Czech Republic, June 2016 / N.
Ay... (eds.). Springer, 2018Bibtex MIS-Preprint: 87/2018 [ARXIV]

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

Perrone, P.
:
*Categorical probability and stochastic dominance in metric spaces*.
Dissertation, Universität Leipzig, 2018Bibtex[FREELINK]

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

Sokoloski, S.
:
*Implementing Bayesian inference with neural networks*.
Dissertation, Univeristät Leipzig, 2018Bibtex

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... (eds.). 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, 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]

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

Fritz, T.
and P. Perrone:
*A probability monad as the colimit of finite powers*.
Theory and applications of categories,
Vol. not yet known, pp. not yet knownBibtex MIS-Preprint: 77/2017 [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. 464-469Bibtex [DOI] [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]

Kahle, T.
; Rauh, J.
and S.
Sullivant:
*Algebraic aspects of conditional independence and graphical models*.
Bibtex[ARXIV]

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.
:
*Notes on the number of linear regions of deep neural networks*.
Bibtex[FREELINK]

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

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]

Schwachhöfer, L.
J. ; Ay, N.
; Jost, J.
and H.
V.
Lê:
*Congruent families and invariant tensors*.
Bibtex[ARXIV]

Seigal, A.
and G. Montúfar:
*Mixtures and products in two graphical models*.
Journal of algebraic statistics,
Vol. not yet known, pp. not yet knownBibtex[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.
:
*In search for the neural mechanisms of individual development : behavior-driven differential
Hebbian learning*.
Frontiers in robotics and AI,
2 (2016), 37Bibtex [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), 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]

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

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]

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.
and W. Löhr:
*The Umwelt of an embodied agent : a measure-theoretic definition*.
Theory in biosciences,
134 (2015) 3-4, 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) 2, P02008Bibtex [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-E6232Bibtex [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. 70-77Bibtex MIS-Preprint: 21/2015 [DOI] [ARXIV] [FREELINK]

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*.
Third international conference on learning representations - ICLR 2015 : May 7-9 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:
*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. 147-154Bibtex 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. 131-145Bibtex 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]

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. 167-178Bibtex[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. 91-109Bibtex 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]

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.
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*.
Theory in biosciences,
Vol. not yet known, pp. not yet knownBibtex[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*.
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. 2924-2932Bibtex 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. 234-245Bibtex [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*.
Second 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]

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:
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Entropy,
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Rauh, J.
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Ay, N.
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Boldhaus, G.
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Adaptive behavior,
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Montúfar, G.
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*Mixture models and representational power of RBM's, DBN's, and DBM's*.
Deep learning and unsupervised feature learning workshop : NIPS 2010 ; December 19,
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Nussbaum, M.
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Olbrich, E.
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*Quantifying structure in networks*.
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Prokopenko, M.
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Leipzig, Germany / K.
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Ghazi-Zahedi, K.
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*Self-regulating neurons : a model for synaptic plasticity in artificial recurrent
neural networks*.
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Hesse, F.
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Kahle, T.
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79 (2009) 2, pt. 2, 026201Bibtex MIS-Preprint: 44/2008 [DOI] [ARXIV]

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

Löhr, W.
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Entropy,
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Complex sciences : first international conference, Complex 2009, Shanghai, China,
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Müller, M.
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*Does probability become fuzzy in small regions of spacetime?*.
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Müller, M.
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*On the quantum Kolmogorov complexity of classical strings*.
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Müller, M.
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Nussbaum, M.
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Audenaert, K. M. R. ; Nussbaum, M.
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and F.
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Ay, N.
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The European physical journal / B,
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Ay, N.
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Bertschinger, N.
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Biosystems,
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279 (2008) 2, p. 559-584Bibtex MIS-Preprint: 33/2007 [DOI] [ARXIV]

Der, R.
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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.
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*YARS : A physical 3D simulator for evolving controllers for real robots*.
Simulation, modeling, and programming for autonomous robots : first international
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Atay, F.
M. and D. J. Albers:
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Ay, N.
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C. Krakauer:
*Robustness and complexity co-constructed in multimodal signalling networks*.
Philosophical transactions of the Royal Society of London / B,
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Ay, N.
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Jost, J.
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*An information theoretic approach to system differentiation on the basis of statistical
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Physica / A,
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Wennekers, T.
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*High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal
stochastic interactions*.
Biosystems,
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Albers, D.
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Albers, D.
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Nonlinearity,
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Albers, D.
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Ay, N.
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*Maximizing multi-information*.
Kybernetika,
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Ay, N.
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ECCS'06 : proceedings of the European Conference on Complex Systems 2006 ; towards
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Ay, N.
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*Stochastic independence of crosstalk variables in the hopfield model*.
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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
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. 9-19Bibtex

Bertschinger, N.
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Artificial life X : proceedings of the tenth international conference on the synthesis
and simulation of living systems / L.
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Kahle, T.
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*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]