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This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
This paper presents several conditions to determine strong sign controllability for diffusively-coupled undirected networks. The strong sign controllability is determined by the sign patterns (positive, negative, zero) of the edges. We…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
Network science has experienced unprecedented rapid development in the past two decades. The network perspective has also been widely applied to explore various complex systems in great depth. In the first decade, fundamental…
We study the asymptotic dynamical properties of Boolean networks without local negative cycle. While the properties of Boolean networks without local cycle or without local positive cycle are rather well understood, recent literature raises…
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
The response of complex networks to perturbations is of utmost importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that the perturbation of one node can…
Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
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…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Cells are regulated by networks of controllers having many targets, and targets affected by many controllers, but these "many-to-many" combinatorial control systems are poorly understood. Here we analyze distinct cellular networks…
In this paper, we demonstrate a conflicting relationship between two crucial properties---controllability and robustness---in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes $N$ and…