M. Nussbaum, A. Szkoła, An asymptotic error bound for testing multiple quantum hypotheses. Annals of Statistics (accepted), MIS Preprint 54/2011 [pdf]

T. Kahle, J. Rauh, S. Sullivant, Positive margins and primary decomposition. Max Planck Institute for Mathematics in the Sciences, (2012) Arxiv 1201.2591 [pdf]

W. Löhr, A. Szkoła, N. Ay, Process dimension of classical and non-commutative processes. Open systems and information dynamics (2012) 19:1, pp: 1250007 Arxiv 1108.3984 [pdf]

G. Montufar, Discrete mixture models, restricted Boltzmann machines, deep belief networks : a unified mathematical treatment. Universität Leipzig. PhD Thesis. (2012)

N. Ay, G. Montufar, J. Rauh, Selection criteria for neuromanifolds of stochastic dynamics. Advances in cognitive neurodynamics III, (2012). MIS-Preprint 15/2011 [pdf]

S. Weis, Continuous maximum-entropy inference and open quantum channels in finite dimensions. (2012) Arxiv 1202.3116 [pdf] MIS-Preprint 6/2012 [pdf]

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

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

N. Ay, K. Zahedi, An Information Theoretic Approach to Intention and Deliberative Decision-Making of Embodied Systems. Advances in cognitive neurodynamics III, (2012). MIS Preprint 2011/22 [pdf]

M. Nussbaum, A. Szkoła, Asymptotic optimal discrimination between pure quantum states. Theory of Quantum Computation, Communication and Cryptography, 5th Conference, TQC 2010, Leeds, UK, Lecture Notes in Computer Science, pp: 1-8 (2011). MIS Preprint 1/2010 [pdf]

J. Rauh, Finding the Maximizers of the Information Divergence from an Exponential Family. IEEE Transactions on Information Theory (2011) 57:6, pp: 3236-3247 [pdf] Arxiv 0912.4660 [pdf] MIS-Preprint 82/2009 [pdf]

N. Ay, M. Müller, A. Szkoła, Effective Complexity of Stationary Process Realizations. Entropy (2011) 13, pp: 1200-1211 [pdf] Santa Fe Working Paper 11-04-014 [pdf]

N. Ay, W. Wenzel, On solution sets of information inequalities. (2011) MIS-Preprint 16/2011 [pdf]

D. C. Krakauer, J. C. Flack, N. Ay, Probabilistic design principles for robust multimodal communication networks. Modeling Perception with Artificial Neural Networks, pp: 255-268 (2011).

F. Matus, 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, pp: 903-907 (2011). [pdf]

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

I. Bengtsson, S. Weis, K. Zyczkowski, Geometry of the set of mixed quantum states : an apophatic approach. XXX Workshop on Geometric Methods in Physics : 26 June-2 July 2011, Bialowieza, Poland, (2011). Arxiv 1112.2347 [pdf] MIS-Preprint 83/2011 [pdf]

J. Rauh, T. Kahle, N. Ay, Support sets in exponential families and oriented matroid theory. International Journal of Approximate Reasoning (2011) 52:5, pp: 613-626 Arxiv 0906.5462 [pdf] Article [pdf] MIS-Preprint 28/2009 [pdf]

D. C. Krakauer, J. C. Flack, N. Ay, Probabilistic design principles for robust multimodal communication networks. Modelling perception with artificial neural networks, pp: 255-268 (2011). [pdf]

J. Rauh, Finding the Maximizers of the Information Divergence from an Exponential Family. University of Leipzig. PhD Thesis. (2011)

R. Der, G. Martius, The playful machine : theoretical foundation and practical realization of self-organizing robots. Springer, (2011)

G. Montúfar, J. Rauh, 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, (2011). [pdf] MIS Preprint 27/2011 [pdf]

J. Rauh, Optimally approximating exponential families. MIS Preprint (2011), Arxiv 1111.0483 [pdf] MIS-Preprint 73/2011 [pdf]

G. Montúfar, N. Ay, Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines. Neural Computation (2011) 23:5, pp: 1306-1319 [pdf] MIS-Preprint 23/2010 [pdf]

J. Rauh, N. Ay, Robustness and Conditional Independence Ideals. arXiv (2011), Arxiv 1110.1338 [pdf] MIS-Preprint 63/2011 [pdf]

N. Ay, R. Der, M. Prokopenko, Information Driven Self-Organization: The Dynamical System Approach to Autonomous Robot Behavior. Theory in Biosciences (2011), [pdf] Santa Fe Working Paper 10-09-018 [pdf]

S. Weis, Information topologies on non-commutative state spaces. (2011) Arxiv 1003.5671 [pdf] MIS-Preprint 75/2011 [pdf]

S. Weis, Duality of non-exposed faces. Max Planck Institute for Mathematics in the Sciences, (2011) Arxiv 1107.2319 [pdf] MIS-Preprint 76/2011 [pdf]

T. Krüger, G. Montufar, R. Seiler, R. Siegmund-Schultze, Universally typical sets for ergodic sources of multidimensional data. (2011) Arxiv 1105.0393 [pdf] MIS-Preprint 20/2011 [pdf]

A. Knauf, S. Weis, Entropy distance : new quantum Phenomena. Max Planck Institute for Mathematics in the Sciences, (2011) MIS-Preprint 72/2011 [pdf]

E. Olbrich, T. Kahle, N. Bertschinger, N. Ay, J. Jost, Quantifying structure in networks. The European Physical Journal B - Condensed Matter and Complex Systems (2010) 77, pp: 239-247 Arxiv 0912.4450 [pdf] MIS-Preprint 81/2009 [pdf] [pdf]

M. Nussbaum, A. Szkoła, Exponential error rates in multiple state discrimination on a quantum spin chain. Journal of Mathematical Physics (2010) 51:7, pp: 072203 [pdf] [pdf] MIS-Preprint 3/2010 [pdf]

B. Steudel, D. Janzing, B. Schoelkopf, Causal Markov condition for submodular information measures. Proceedings of the Conference on Learning Theory (COLT 2010), pp: 464-476 (2010). Arxiv 1002.4020 [pdf]

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

P. Daniusis, D. Janzing, J. Mooij, J. Zscheischler, B. Steudel, K. Zhang, B. Schoelkopf, Inferring deterministic causal relations. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence : UAI 2010, June 8-11, 2010, Avalon, CA, pp: 143-150 (2010). [pdf]

B. Steudel, N. Ay, Information-theoretic inference of common ancestors. (2010) Arxiv 1010.5720 [pdf]

T. Kahle, Decompositions of binomial ideals. Annals of the Institute of Statistical Mathematics (2010) 62, pp: 727-745 [pdf]

W. Löhr, Models of Discrete-Time Stochastic Processes and Associated Complexity Measures. University of Leipzig. PhD Thesis. (2010) [pdf]

F. Güttler, W. Rabe, J.\"} Hoffmann, M. Bogdan, 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, pp: 350-357 (2010).

G. Boldhaus, N. Bertschinger, J. Rauh, E. Olbrich, K. Klemm, Robustness of boolean dynamics under knockouts. Physical review / E (2010) 82:2, pp: 021916 Arxiv 1003.0104 [pdf]

J. Herzog, T. Hibi, F. Hreinsdóttir, T. Kahle, J. Rauh, Binomial edge ideals and conditional independence statements. Advances in Applied Mathematics (2010) 45:3, pp: 317-333 [pdf]

K. Zahedi, N. Ay, R. Der, Higher coordination with less control -- A result of information maximization in the sensori-motor loop. Adaptive Behavior (2010) 18:3--4, pp: 338-355 [pdf]

N. Ay, M. Müller, A. Szkoła, Effective Complexity and Its Relation to Logical Depth. Information Theory, IEEE Transactions on (2010) 56:9, pp: 4593-4607 Arxiv 0810.5663 [pdf] Santa Fe Working Paper 08-12-046 [pdf]

T. Kahle, On Boundaries of Statistical Models. University of Leipzig. PhD Thesis. (2010) [pdf]

D. Janzing, B. Steudel, Justifying additive-noise-based causal discovery via algorithmic information theory. Open Systems and Information Dynamics (2010) 17:2, pp: 189-212

M. Müller, Stationary algorithmic probability. Theoretical Computer Science (2010) 411, pp: 113-130 Arxiv 0608095 [pdf]

G. Montúfar, Mixture Decomposition of Distributions using a Decomposition of the Sample Space. Kybernetika (2010), Arxiv 1008.0204 [pdf] MIS-Preprint 2010/39 [pdf]

M. Prokopenko, N. Ay, O. Obst, D. Polani, Phase transitions in least-effort communications. Journal of Statistical Mechanics (2010) P11025, [pdf]

G. Montufar, 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, Canada, (2010). [pdf]

T. Kahle, Neighborliness of Marginal Polytopes. Contributions to Algebra and Geometry (2010) 51:1, pp: 45-56 Arxiv 0809.0786 [pdf] MIS-Preprint 57/2008 [pdf]

W. Löhr, N. Ay, On the Generative Nature of Prediction. Advances in Complex Systems (2009) 12, pp: 169-194 [pdf] Santa Fe Working Paper 08-02-004 [pdf] MIS-Preprint 8/2008 [pdf]

N. Ay, A refinement of the common cause principle. Discrete Appl. Math. (2009) 157, pp: 2439-2457 [pdf] Santa Fe Working Paper 08-01-001 [pdf]

W. Löhr, Properties of the Statistical Complexity Functional and Partially Deterministic HMMs. Entropy (2009) 11:3, pp: 385-401 [pdf] [pdf] MIS-Preprint 24/2009 [pdf]

M. Müller, C. Rogers, R. Nagarajan, Lossless quantum prefix compression for communication channels that are always open. Physical review / A (2009) 79:1, pp: 012302 Arxiv 0808.2003 [pdf]

T. Kahle, W. Wenzel, N. Ay, Hierarchical models, marginal polytopes, and linear codes. Kybernetika (2009) 45:2, pp: 189-207 Santa Fe Working Paper 09-01-001 [pdf] MIS-Preprint 30/2008 [pdf]

W. Löhr, 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, (2009). [pdf]

K. M. Ghazi-Zahedi, Self-Regulating Neurons. A model for synaptic plasticity in artificial recurrent neural networks. University of Osnabrück. PhD Thesis. (2009) [pdf]

J. Rauh, T. Kahle, N. Ay, Support Sets in Exponential Families and Oriented Matroid Theory. Proceedings of WUPES'09, (2009). Arxiv 0906.5462 [pdf]

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

T. Kahle, E. Olbrich, J. Jost, N. Ay, Complexity measures from interaction structures. Physical Review / E (2009) 79:2, pp: 026201 Arxiv 0806.2552 [pdf]

M. Müller, Convex trace functions on quantum channels and the additivity conjecture. Physical review / A (2009) 79:5, pp: 052332 Arxiv 0809.4060 [pdf]

N. Ay, Multi-Information as Guiding Scheme for Complexity Theory. Friedreich-Alexander University Erlangen-Nuremberg. Habilitation Thesis. (2009)

K. M. R. Audenaert, M. Nussbaum, A. Szkoła, F. Verstraete, Asymptotic Error Rates in Quantum Hypothesis Testing. Communications in Mathematical Physics (2009) 279:1, pp: 251-283 [pdf] MIS-Preprint 84/2007 [pdf]

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

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

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

R. Der, F. Güttler, 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, pp: 166-172 (2008). [pdf]

K. Zahedi, A. V. Twickel, F. Pasemann, YARS: A Physical 3D Simulator for Evolving Controllers for Real Robots. SIMPAR 2008, pp: 71-82 (2008). [pdf]

I. Bjelaković, J.D. Deuschel, T. Krüger, R. Seiler, R. Siegmund-Schultze, A. Szkoła, Typical Support and Sanov Large Deviations of Correlated States. Communications in Mathematical Physics (2008) 279, pp: 559-584 [pdf] Arxiv 0703772 [pdf] MIS-Preprint 33/2007 [pdf]

N. Bertschinger, E. Olbrich, N. Ay, J. Jost, Autonomy: An information theoretic perspective. Biosystems (2008) 91:2, pp: 331-345 [pdf]

N. Ay, D. Polani, Information Flows in Causal Networks. Advances in Complex Systems (2008) 11:1, pp: 17-41 [pdf] MIS-Preprint 47/2006 [pdf]

M. Müller, 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, pp: 106-111 (2008). Arxiv 0804.0022 [pdf]

M. Müller, Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity. IEEE Transactions on Information Theory (2008) 54:2, pp: 763-780 Arxiv 0605030 [pdf]

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

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

N. Ay, D. C. Krakauer, Geometric robustness theory and biological networks. Theory in Biosciences (2007), pp: 93-121 [pdf] MIS-Preprint 14/2006 [pdf]

J. Jost, N. Bertschinger, E. Olbrich, N. Ay, S. Frankel, An information theoretic approach to system differentiation on the basis of statistical dependencies between subsystems. Physica A: Statistical Mechanics and its Applications (2007) 378:1, pp: 1-10 [pdf]

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

M. Müller, On the Quantum Complexity of Classical Words. ECCS 2007 : proceedings of the European Conference on Complex Systems 2007 ; Dresden, October 1-6, 2007, (2007). [pdf]

A. W. M. Dress, W. Wenzel, Arithmetic and polynomials over fuzzy rings. Max Planck Institute for Mathematics in the Sciences, (2007)

N. Ay, A. Knauf, Maximizing Multi-Information. Kybernetika (2007) 42:5, pp: 517-538 Arxiv 0702002 [pdf] MIS-Preprint 42/2003 [pdf]

F. M. Atay, D. J. Albers, Entropy, dimension, and state mixing in a class of time-delayed dynamical systems. (2007) Arxiv 0710.2626 [pdf] MIS-Preprint 83/2007 [pdf]

N. Ay, J. C. Flack, D. C. Krakauer, Robustness and Complexity Co-constructed in Multi-modal Signaling Networks. Philosophical transactions of the Royal Society of London / B (2007), pp: 441-447 [pdf]

K. Zahedi, F. Pasemann, Adaptive Behavior Control with Self-regulating Neurons. 50 Years of Artificial Intelligence, pp: 196-205 (2007). [pdf]

F. Benatti, T. Krüger, M. Müller, R. Siegmund-Schultze, A. Szkoła, Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem. Communications in Mathematical Physics (2006) 265, pp: 437-461 Arxiv 0506080 [pdf]

Y. Sato, N. Ay, Adaptive Dynamics for Interacting Markovian Processes. (2006) Arxiv 0611032 [pdf]

D.. Albers, J.. Sprott, Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study. Physica / D (2006) 223:2, pp: 194-207 [pdf] MIS-Preprint 92/2005 [pdf]

D. Albers, J. Sprott, Probability of Local Bifurcation Type from a Fixed Point: A Random Matrix Perspective. Journal of Statistical Physics (2006) 125, pp: 885-921 [pdf] MIS-Preprint 94/2005 [pdf]

D. J. Albers, Persistent Chaos in High Dimensions. Physical review / E (2006) 74:5, [pdf] MIS-Preprint 95/2005 [pdf]

T. Kahle, N. Ay, Support Sets of Distributions with given Interaction Order. Proceedings of WUPES'06, pp: 52-61 (2006). [pdf] Santa Fe Working Paper 06-08-027 [pdf] MIS Preprint 2006/94 [pdf]

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

T. Wennekers, N. Ay, A temporal learning rule in recurrent systems supports high spatio-temporal stochastic interactions. Neurocomputing (2006) 69, pp: 1199-1202 [pdf]

N. Ay, E. Olbrich, N. Bertschinger, J. Jost, A Unifying Framework for Complexity Measures of Finite Systems. Proceedings ECCS'06, (2006). Santa Fe Working Paper 06-08-028 [pdf]

N. Bertschinger, E. Olbrich, N. Ay, J. Jost, Information and closure in systems theory. The Proceedings of the 7th German Workshop of Artificial Life, pp: 26-28 (2006). [pdf]

G. Montufar, Discrete mixture models, restricted Boltzmann machines, deep belief networks : a unified mathematical treatment. Universität Leipzig. PhD Thesis. (2012)

J. Rauh, Finding the Maximizers of the Information Divergence from an Exponential Family. University of Leipzig. PhD Thesis. (2011)

W. Löhr, Models of Discrete-Time Stochastic Processes and Associated Complexity Measures. University of Leipzig. PhD Thesis. (2010) [pdf]

T. Kahle, On Boundaries of Statistical Models. University of Leipzig. PhD Thesis. (2010) [pdf]

K. M. Ghazi-Zahedi, Self-Regulating Neurons. A model for synaptic plasticity in artificial recurrent neural networks. University of Osnabrück. PhD Thesis. (2009) [pdf]

N. Ay, Multi-Information as Guiding Scheme for Complexity Theory. Friedreich-Alexander University Erlangen-Nuremberg. Habilitation Thesis. (2009)