Complex Systems

We are studying complex dynamical systems for understanding fundamental principles governing living systems at various scales of organization. Our work has focused on:

  • the relationships between the structure of such systems and their dynamics;
  • the ability to balance robustness with adaptability in an uncertain and variable environment while making decisions in response to information in the environment;
    • this includes work on phase transitions and criticality
  • the coordination of complex behaviors, computation, and memory;
  • and the emergence of diversity.

We are exploring information-theoretic approaches to tackle these questions, using mathematical and statistical modeling, computer simulations, and large-scale biological measurements.

I. Shmulevich, “On the Lyapunov Exponent of Monotone Boolean Networks,” Mathematics, Vol. 8, 1035, 2020.

M. Echlin, B. Aguilar, M. Notarangelo, D. L. Gibbs, I. Shmulevich, “Flexibility of Boolean Network Reservoir Computers in Approximating Arbitrary Recursive and Non-Recursive Binary Filters,” Entropy, Vol. 20, No. 12, 954, 2018.

C. Kang, B. Aguilar and I. Shmulevich, “Emergence of diversity in homogeneous coupled Boolean networks“, Physical Review E, Vol. 97, No. 5, 2018.

A. Sadot, S. Sarbu, J. Kesseli, H. Amir-Kroll, W. Zhang, M. Nykter, I. Shmulevich, “Information-Theoretic Analysis of the Dynamics of an Executable Biological Model,” PLoS ONE, Vol. 8, No. 3, e59303, 2013.

A. V. Ratushny, I. Shmulevich, J. D. Aitchison, “Trade-off between responsiveness and noise suppression in biomolecular system responses to environmental cues,” PLoS Computational Biology, Vol. 7, No. 6, e1002091, 2011.

D. J. Galas, M. Nykter, G. W. Carter, N. D. Price, I. Shmulevich, “Biological information as set-based complexity,” IEEE Transactions on Information Theory, Vol. 56, No. 2, pp. 667-677, 2010.

M. Nykter, J. Kesseli, and I. Shmulevich, “Dynamical systems analysis of stack filters,” in I. Tabus, K. Egiazarian, and M. Gabbouj, editors, Festschrift in honor of Jaakko Astola on the occasion of his 60th Birthday, pp. 169-181, Tampere International Center of Signal Processing, 2009.

E. Balleza, E. Alvarez-Buylla, A. Chaos, S. A. Kauffman, I. Shmulevich, M. Aldana, “Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms,” PLoS ONE, Vol. 3, No. 6, e2456, 2008.

M. Nykter, N. D. Price, A. Larjo, T. Aho, S. A. Kauffman, O. Yli-Harja, I. Shmulevich, “Critical networks exhibit maximal information diversity in structure-dynamics relationships,” Physical Review Letters, Vol. 100, 058702, 2008.

M. Nykter, N. D. Price , M. Aldana, S. A. Ramsey, S. A. Kauffman, L. Hood, O. Yli-Harja, I. Shmulevich, “Gene Expression Dynamics in the Macrophage Exhibit Criticality,” Proceedings of the National Academy of Sciences of the USA, Vol. 105, No. 6, pp. 1897-1900, 2008.

S. A. Kauffman, R. K. Logan, R. Este, R. Goebel, D. Hobill, I. Shmulevich, “Propagating Organization: An Enquiry,Biology and Philosophy, Vol. 23, No. 1, pp. 27-45, 2007.

P. Krawitz, I. Shmulevich, “Entropy of complex relevant components in Boolean networks,” Physical Review E, Vol. 76, 036115, 2007.

P. Krawitz, I. Shmulevich, “Basin Entropy in Boolean Network Ensembles,” Physical Review Letters, Vol. 98, No. 15, pp. 158701, 2007.

C. Gershenson, S. A. Kauffman, and I. Shmulevich, “The Role of Redundancy in the Robustness of Random Boolean Networks,” in Rocha, L. M., L. S. Yaeger, M. A. Bedau, D. Floreano, R. L. Goldstone, and A. Vespignani (Eds.), Artificial Life X, Proceedings of the Tenth International Conference on the Simulation and Synthesis of Living Systems, pp. 35-42. MIT Press, 2006.

T. Toulouse, P. Ao, I. Shmulevich, S. A. Kauffman, “Noise in a Small Genetic Circuit that Undergoes Bifurcation,” Complexity, Vol. 11, No. 1, pp. 45-51, 2005.

I. Shmulevich, S. A. Kauffman, M. Aldana, “Eukaryotic cells are dynamically ordered or critical but not chaotic,” Proceedings of the National Academy of Sciences of the USA, Vol. 102, No. 38, pp. 13439-13444, 2005.

W. Just, I. Shmulevich, J. Konvalina, “The number and probability of canalizing functions,” Physica D, Vol. 197, pp. 211-221, 2004.

I. Shmulevich, H. Lähdesmäki, and K. Egiazarian “Spectral Methods for Testing Membership in Certain Post Classes and the Class of Forcing Functions,” IEEE Signal Processing Letters, Vol. 11, No. 2, pp. 289-292, 2004.

I. Shmulevich, S. A. Kauffman, “Activities and Sensitivities in Boolean Network Models,Physical Review Letters, Vol. 93, No. 4, pp. 048701(1-4), 2004.

I. Shmulevich, H. Lähdesmäki, E. R. Dougherty, J. Astola, W. Zhang, “The role of certain Post classes in Boolean network models of genetic networks,” Proceedings of the National Academy of Sciences of the USA, Vol. 100, No. 19, pp. 10734-10739, 2003.