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We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T = 1 this approach recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, thereby enabling us to explain certain features of the likelihood landscape of this popular generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a time-scale T >> 1 is essential, using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.
Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block mod
The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules.We present a method to obtain path ensemble averages of a perturbed dynamics fro
As new instances of nested organization --beyond ecological networks-- are discovered, scholars are debating around the co-existence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being
Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies a
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dyna