Friday, January 19, 2018
Monday, January 15, 2018
Friday, January 12, 2018
Title: Synergistic Effects in Threshold Models on Networks
Authors: Jonas S. Juul, and Mason A. Porter
Abstract: Network structure can have a significant impact on the propagation of diseases, memes, and information on social networks. Different types of spreading processes (and other dynamical processes) are affected by network architecture in different ways, and it is important to develop tractable models of spreading processes on networks to explore such issues. In this paper, we incorporate the idea of synergy into a two-state ("active" or "passive") threshold model of social influence on networks. Our model’s update rule is deterministic, and the influence of each meme-carrying (i.e., active) neighbor can—depending on a parameter—either be enhanced or inhibited by an amount that depends on the number of active neighbors of a node. Such a synergistic system models social behavior in which the willingness to adopt either accelerates or saturates in a way that depends on the number of neighbors who have adopted that behavior. We illustrate that our model’s synergy parameter has a crucial effect on system dynamics, as it determines whether degree-k nodes are possible or impossible to activate. We simulate synergistic meme spreading on both random-graph models and networks constructed from empirical data. Using a heterogeneous mean-field approximation, which we derive under the assumption that a network is locally treelike, we are able to determine which synergy-parameter values allow degree-k nodes to be activated for many networks and for a broad family of synergistic models.
Thursday, January 11, 2018
Tuesday, January 09, 2018
What Happens at the Joint Mathematics Meetings Stays at the Joint Mathematics Meetings (2018 Edition)
Update: Here is a short video of some nice scenery during my train ride from Los Angeles to San Diego. Below is a still shot that I took just before the video and also a picture of me and a statue of the late, great Tony Gwynn.
And, finally, here is my tweet after I arrived.
I made it to the 2018 Joint Math Meetings (@JointMath)! #JMM2018— Mason Porter (@masonporter) January 10, 2018
I'll try not to get booed during my talk this year, like I was in 2005. (With people from an impending on-campus faculty interview in the audience.)
You know you've made it when you're booed at a math conference.