Related papers: Hidden Order of Boolean Networks
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
Real-world networks have high-order relationships among objects and they evolve over time. To capture such dynamics, many works have been studied in a range of fields. Via an in-depth preliminary analysis, we observe two important…
Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean…
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current…
In the sequential learning problem, agents in a network attempt to predict a binary ground truth, informed by both a noisy private signal and the predictions of neighboring agents before them. It is well known that social learning in this…
In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts…
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…
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…
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node's importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e.…
Modeling complex networks has been the focus of much research for over a decade. Preferential attachment (PA) is considered a common explanation to the self organization of evolving networks, suggesting that new nodes prefer to attach to…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016),…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…
We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a fully understanding of the genesis of…
Network structure has a large impact on constant-selection evolutionary dynamics, with which multiple types of fitness (i.e., strength) compete on the network. Here we study constant-selection dynamics on two-layer networks in which the…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…
The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability $p$. In order to discriminate the better and…