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In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These `open Markov processes' serve as the building blocks for…
Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain…
Colloidal particles moving in a fluid interact via the induced velocity field. The collective dynamic state for a class of actively forced colloids, driven by harmonic potentials via a rule that couples forces to configurations, to perform…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
The Master Stability Function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
This paper is concerned with a compositional approach for constructing finite Markov decision processes of interconnected discrete-time stochastic control systems. The proposed approach leverages the interconnection topology and a notion of…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…