Publications

Kahle, T.
; Rauh, J.
and S.
Sullivant:
*Algebraic aspects of conditional independence and graphical models*.
Handbook of graphical models / M.
Maathuis... (eds.). CRC Press, 2019. - P. 61-80
(Chapman & Hall/CRC handbooks of modern statistical methods)
Bibtex[ARXIV]

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. 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
(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. 1692-1725Bibtex 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 [DOI] [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.
and N. Ay:
*Dynamical systems induced by canonical divergence in dually flat manifolds*.
Information geometry,
Vol. not yet known, pp. not yet knownBibtex MIS-Preprint: 103/2018 [ARXIV]

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

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. 267-281Bibtex [DOI]

Kohl, F.
; Li, Y.
; Rauh, J.
and R.
Yoshida:
*Semigroups - a computational approach*.
The 50th anniversary of Gröbner bases : proceedings of the 8th Mathematical
Society of Japan Seasonal Institute (MSJ SI 2015) : July 1-10, 2015, at Hotel Nikko
Osaka / T.
Hibi (ed.). Mathematical Society of Japan, 2018. - P. 155-170
(Advanced studies in pure mathematics ; 77)
Bibtex [DOI] [ARXIV]

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. 105-116Bibtex[FREELINK]

Li, W.
and G. Montúfar:
*Natural gradient via optimal transport*.
Information geometry,
1 (2018) 2, p. 181-214Bibtex [DOI] [ARXIV]

Li, W.
and G. Montúfar:
*Ricci curvature for parametric statistics via optimal transport*.
Bibtex[ARXIV]

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, 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. 133-140Bibtex[FREELINK]

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]

Rauh, J.
:
*Secret sharing and shared information [Entropy, 19 (2017) 11, 601]*.
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. 138-149Bibtex [DOI] [ARXIV]

Rauh, J.
; Banerjee, P.
K.
; Olbrich, E.
; Jost, J.
and N.
Bertschinger:
*On extractable shared information [Entropy, 19 (2017) 7, 328]*.
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. 11-20Bibtex [DOI] [ARXIV]

Rauh, J.
; Banerjee, P.
K.
; Olbrich, E.
; Jost, J.
; Bertschinger, N.
and D.
Wolpert:
*Coarse-graining and the Blackwell order [Entropy, 19 (2017) 10, 527]*.
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. 150-160Bibtex [DOI] [ARXIV]

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

Seigal, A.
and G. Montúfar:
*Mixtures and products in two graphical models*.
Journal of algebraic statistics,
9 (2018) 1, p. 1-20Bibtex[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]

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*.
2017 international conference on sampling theory and applications (SampTA) / G.
Anbarjafari... (eds.). IEEE, 2017. - P. 156-159Bibtex[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.
; 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, 2017Bibtex[FREELINK]

Montúfar, G.
and J.
Morton:
*Dimension of marginals of Kronecker product models*.
SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 126-151Bibtex 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.
:
*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.
:
*Geometry of Boltzmann machines*.
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. 25-25Bibtex MIS-Preprint: 87/2018 [ARXIV]

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]

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. 17-17Bibtex

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:
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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. 1-10Bibtex [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.). IOS Press, 2006. - P. 9-19Bibtex

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. 7-12Bibtex

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]