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Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
An accessibility graph of a network contains a link, wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding…
We prove that the fully asynchronous dynamics of a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very specific way, by a monotone Boolean network with $2n$ components. We then use this result to…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
Reachability analysis is a fundamental program analysis with a wide variety of applications. We present FlowCFL, a framework for type-based reachability analysis in the presence of mutable data. Interestingly, the underlying semantics of…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
In this paper we propose a causal analog to the purely observational Dynamic Bayesian Networks, which we call Dynamic Causal Networks. We provide a sound and complete algorithm for identification of Dynamic Causal Net- works, namely, for…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the…
The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
Cellular phenotypes are determined by the dynamical activity of networks of co-regulated genes. Elucidating such networks is crucial for the understanding of normal cell physiology as well as for the dissection of complex pathologic…
Many real-world networks such as social networks consist of strategic agents. The topology of these networks often plays a crucial role in determining the ease and speed with which certain information driven tasks can be accomplished.…
The mutations of a complex systemic disease like cancer can be modeled as stuck-at faults in the Boolean system paradigm. For a class of multiple faults, the fault identification is exceptionally significant under the incomplete access of…
In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different…