# Andrew BurchillArizona State University | ASU · Center for Social Dynamics and Complexity

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Bachelor of Science
12
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Introduction
Andrew Burchill currently works at the Center for Social Dynamics and Complexity, Arizona State University. Andrew does research in Evolutionary Biology, Entomology and Animal Communications.
Research Experience
Aug 2015 - May 2020
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Research items (12)
Question
To make this situation clear, I'll use a somewhat silly, but conceptually simple example. Imagine I record teams of movers carrying furniture down the block. I measure the furniture's position/speed over time (say every 15 seconds), the size of the furniture (small, medium, or large), and the numbers of people carrying the object at each 15 second time point. People on the teams join in and help transport or let go and step back freely; maybe they join when they feel they could be useful or something, who knows, it just changes.
I record these trips multiple times across different furniture sizes, etc. I now want to determine HOW the number of movers carrying the furniture and the size of furniture affect the speed of transport. If there were only one trip, I think I would use some sort of ARIMAX model and regress the number of movers against their instantaneous speed over the single time-series run (with ARIMA errors). However, I want to make a generalization ACROSS all these recordings and I want to see if the categorical variable of furniture size has an effect as well (or how it interacts with mover number). How in the world do I incorporate all of these recorded trips (many different time-series iterations) in one analysis?
Additionally, imagine I think both the speed and the number of helpers are non-stationary, but in different ways. I think it's likely that the speed increases throughout the trip, and the number of workers increases initially (as they try to get it going, say) and then decreases (once it's moving along, maybe extra movers just get in the way). What would I do in that situation?
Lastly, I'm trying to do this in R. Crazy bonus points if you can explain it using R code!
Ah, I think there was a misunderstanding! I meant, generate all the possible start-to-ending paths possible that will include the animal walking the full path. If there's one "loop de loop," calculate the tortuosity of the path as if the animal goes around the loop CCW and calculate it again as if it went CW, then average these two FULL paths together? I mean, it'll depend on your data. Otherwise, I think your method of calculating chunks weighted by length might be good.
Yeah, what you're referring to is called "rediscretization" and some measures of tortuosity DEPEND on it. If you're using R, check out Jim McLean's "trajr" package. He has a whole package dedicated to this sort of thing:
This document is also really useful for understanding how the package works. Check the "resampling" section first!
Haha, I'm not sure I can add any more info than this... In the end, it's whatever you can convince reviewers to accept!
I think that BiSSE (Binary State Speciation and Extinction model) would be best for you. Hopefully you're using R?
I'd recommend FitzJohn's diversitree package. I think this documentation will be helpful if you know R: http://www.zoology.ubc.ca/~fitzjohn/diversitree.docs/make.bisse.html
Note in the example section where you can use the "constrain()" function to get what you're describing:
lik.bisse.bd <- constrain(lik, lambda1 ~ lambda0, mu1 ~ mu0, q01 ~ 0.01, q10 ~ 0.02)
Oooof, that is gonna be a difficult one. It probably depends on the amount of overlap / loops you have. Does the animal ever cross over its own tracks? If not and you have only one possible trajectory through space (irrespective of time), then it should be easy. Many measures don't need time components.
However, if it DOES cross over its own path, then multiple possible trajectories are possible. I might try computing tortuosity for each path and then averaging/finding the median?
Question
So, I have several directed (multi-edged) networks, and within them each node has been assigned to one of seven categories (based on some *a priori* circumstances). Each category *should* have a higher within-category interaction rate, but I want to test the statistical significance of this.
Since "a set of nodes, densely connected internally" is pretty much the definition of a community, I want to manually impose my community assignments on the nodes in the network and then test whether this assignment is statistically more "community-like" than a random assignment. **In essence, my question is: "Is this given community structure statistically significant?"**
I found [this paper][1] which seems to have a way of measuring the statistical significance of a single community group in the network, but it doesn't seem to apply to a given, entire community structure. I also found [this baby][2], but it seems to only be focused on much smaller, local structures.
There's gotta be a way to do this for directed, multi-edged networks, I just can't seem to find any! (Additionally, I'll have to do this analysis in R, so mega-triple-extra bonus points if you know of an R package that already does this.)