Topic: networks

Richard Montgomery explores graph theory as the mathematics underlying networks, from infrastructure to biological connections. He discusses his contribution to the proof of Ringel’s conjecture and why extremal questions about graphs are mathematically productive. The interview follows recognition of his work with an EMS Prize.

A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose to infer networks of causal relations via pairwise edge measure (PEMs) that one can easily compute from lagged correlation matrices. Motivated by contributions of process motifs to covariance and lagged variance, we formulate two PEMs that correct for confounding factors and for reverse causation. To demonstrate the performance of our PEMs, we consider netwo

We consider new measures of centrality in networks which take into account parameters of nodes and group influence of nodes to nodes. Several examples are discussed.

In our everyday lives, we form connections and build up social networks that allow us to function successfully as individuals and as a society. Our social networks tend to include well-connected individuals who link us to other groups of people that we might otherwise have limited access to. In addition, we are more likely to befriend individuals who a) live nearby and b) have mutual friends. Interestingly, neurons tend to do the same…until development is perturbed. Just like social networks, neuronal networks require highly connected hubs to elicit efficient communication at minimal cost (you

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. In this talk, I will show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget. Our strategy is based on an open-loop control scheme and alludes to a fundament

Both computational and experimental results in single neurons and small networks demonstrate that very similar network function can result from quite disparate sets of neuronal and network parameters. Using the crustacean stomatogastric nervous system, we study the influence of these differences in underlying structure on differential resilience of individuals to a variety of environmental perturbations, including changes in temperature, pH, potassium concentration and neuromodulation. We show that neurons with many different kinds of ion channels can smoothly move through different mechanisms

Both computational and experimental results in single neurons and small networks demonstrate that very similar network function can result from quite disparate sets of neuronal and network parameters. Using the crustacean stomatogastric nervous system, we study the influence of these differences in underlying structure on differential resilience of individuals to a variety of environmental perturbations, including changes in temperature, pH, potassium concentration and neuromodulation. We show that neurons with many different kinds of ion channels can smoothly move through different mechanisms