Phil 8.1.18

7:00 – 6:00 ASRC MKT

  • I need to add some things to both talks
    • Use Stephens to show how we can build vectors out of ‘positions’ in high dimension space, and then measure distances (hypotenuse, cosine similarity, etc). Also, how the use of stories show alignment over time and create a trajectory – done
    • Add slide that shows the spectrum from low-dimensional social space to high-dimensional environmental space.
      • Aligning in social spaces is easier because we negotiate the terrain we interact on
      • Aligning in environmental spaces is harder because there is no negotiation
    • Add slides for each of the main parts
      • Social influence
      • Dimension Reduction
      • Heading
      • Velocity
      • State (what we tend to think about)
    • Add demo slide that walks through each part of the demo – done
      • Single population with different SIH
      • Small explorer population interacting with stampeding groups
      • Adversarial Herding
      • Opposed AH
      • Map building
  • Capturing the interplay of dynamics and networks through parameterizations of Laplacian operators
    • We study the interplay between a dynamical process and the structure of the network on which it unfolds using the parameterized Laplacian framework. This framework allows for defining and characterizing an ensemble of dynamical processes on a network beyond what the traditional Laplacian is capable of modeling. This, in turn, allows for studying the impact of the interaction between dynamics and network topology on the quality-measure of network clusters and centrality, in order to effectively identify important vertices and communities in the network. Specifically, for each dynamical process in this framework, we define a centrality measure that captures a vertex’s participation in the dynamical process on a given network and also define a function that measures the quality of every subset of vertices as a potential cluster (or community) with respect to this process. We show that the subset-quality function generalizes the traditional conductance measure for graph partitioning. We partially justify our choice of the quality function by showing that the classic Cheeger’s inequality, which relates the conductance of the best cluster in a network with a spectral quantity of its Laplacian matrix, can be extended to the parameterized Laplacian. The parameterized Laplacian framework brings under the same umbrella a surprising variety of dynamical processes and allows us to systematically compare the different perspectives they create on network structure.

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