There is a growing recognition that ecological systems can spend extended periods of time
far away from an asymptotic state, and that ecological understanding will therefore require a …

The global steady state of a system in thermal equilibrium exponentially favors
configurations with lesser energy. This principle is a powerful explanation of self …

We introduce a new information-geometric structure associated with the dynamics on
discrete objects such as graphs and hypergraphs. The presented setup consists of two …

Disentangling irreversible and reversible forces from random fluctuations is a challenging
problem in the analysis of stochastic trajectories measured from real-world dynamical …

A stochastic process is at thermodynamic equilibrium if it obeys time-reversal symmetry;
forward and reverse time are statistically indistinguishable at steady state. Non-equilibrium …

Granger causality can uncover the cause-and-effect relationships in financial networks.
However, such networks can be convoluted and difficult to interpret, but the Helmholtz …

Health care delivery is a collaborative process, requiring close coordination among
networks of providers with specialized expertise. Yet in the United States, care is often …

We analyze the correlation between randomly chosen edge weights on neighboring edges
in a directed graph. This shared-endpoint correlation controls the expected organization of …

Stochastic ecological dynamics result from both transient and asymptotic features of the
underlying system, yet explanations for observed patterns often emphasize asymptotics. For …

While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world
systems are predominantly hierarchical. We demonstrate and extend a mechanism for …