Abstract: Cellular behaviors, governed by various interaction networks among biomolecules, are often modeled using Boolean networks, where the future state of a node is determined by a logic function of the current states of its regulator nodes. Dynamic simulations of the system's trajectory in state space and methods that link the structure and the dynamics of the network have proven insightful. For example, stable motifs by Zanudo et. al. determine the steady states of the system. Here we propose a complementary method, namely the identification and representation of the backbone logical structure of a network, based on categorizing edges as sufficient or necessary. A sufficient activating (inhibitory) relationship means that the ON state of the regulator implies the ON (OFF) state of the target. A necessary activating (inhibitory) relationship means that the OFF state of the regulator implies the OFF (ON) state of the target. We identify (complex) subnetworks distillable into a causal relationship. This way, we represent a signal transduction network as a backbone network of external signals, stable motifs, and the output nodes. Furthermore, we use this framework to identify crucial nodes that can drive the system from one steady state to another.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).