Day 23, Mat115H

• Can anyone attend? I have class at this time:

  CINSAM Seminar Series

  Thusday, 12:30-1:30 p.m., Griffin Hall 250

  CINSAM Seminar Series presents "Exploring soil contamination in Newport, KY: Environmental Science & Journalism students dig deep to uncover the source." Interested in environmental science? Journalism? Science communication? Local issues? Come hear about how NKU faculty and students from different departments have worked together to learn more about the soil contamination problems in Newport, and what've been doing to inform the community.

  I'll give you a "get out of homework free" card if you attend, and will write a report to the class.

• You have a homework due today: your proposals for the survey. We'll take a look at your suggestions on Friday, and have the break to reflect on them a bit.
• Your graph homework....
  • Sorry - I forgot to include a loop on III.
  • You need to write the equations, so that I know what you're doing!
  • Some of you thought that there were "unsteady states" in the dynamics, but there are none: they're all (eventually) steady.
  • If your adjacency matrices are unsymmetric, for these undirected graphs, you have a problem.
  • Rook's adjacency shouldn't have more ones than Queen's adjacency.
  • What about Newport? How many tracts?

Question of the Day:

• Last time we talked about using Pascal's triangle to find all simple graphs on labelled vertices.

  The graph of Newport census tracts is a simple graph, and just one of many with seven vertices (one for each of the tracts 501, 504, 505, 506, 532, 524, and 525).

  Here's the adjacency matrix (rook) that I get using my maps, and these 7 tracts of Newport:

  	501	504	505	506	524	525	532
  501	0	0	0	1	0	0	1
  504	0	0	1	0	1	0	1
  505	0	1	0	1	1	1	1
  506	1	0	1	0	0	1	0
  524	0	1	1	0	0	1	0
  525	0	0	1	1	1	0	0
  532	1	1	1	0	0	0	0

• Today we're going to continue talking spatial statistics, and how they are used and defined. In particular, I'd like you to play my "spatial autocorrelation game".

  As a focal point, connecting the issues of social deprivations and lead contamination (and poisoning), I present the case of Woburn, MA (depicted in the film A Civil Action).

  There is another type of analysis we will do with lead (spatial interpolation) yet to come. But today we focus on the use of adjacency matrices in the creation of these spatial statistics. But perhaps we focus instead, today, on why we need them....

  Many years ago I created a short history of the Woburn, MA case of cancer clusters.

  • A more extensive exploration of the situation is at this website. I'd like you to explore this website for class discussion on Friday.

  • At the outset, it was a cluster of cases that tipped off residents that there was a cancer problem in their town, and in a particular part of town.

    In the end, this clustering tipped off authorities to the legacy of toxic pollution left by the heavy industrialization of the town.

  • Some spatial statistics are used to measure clustering: Spatial Autocorrelation game

  • What is Moran's I (we can get there via the Stat Advisor)?
    • The objective of Moran's I is to detect departures from spatial randomness.
    • From the example: "In the absence of more detailed knowledge areas are often connected based on geographic adjacency. Two areas, i and j, are assigned a weight of 1 when they share a common border. Otherwise they are assigned a weight of 0. The alternative spatial model under this simple scheme states that rates in spatially contiguous areas are correlated. This is a reasonable model to use when you are interested in detecting contiguous areas with similar disease rates."
    • If the populations of the census tracts are considerably different, we might consider using Ipop, which is Moran's I fine-tuned for a case where the population sizes are vastly different.

• Links:
  • Census info for Newport, KY
  • NHGIS data from the U.S. Census