comp-top-project-2/report.typ at main · Gabriel-R-Parra/comp-top-project-2 · GitHub

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#set page(
  paper: "us-letter"
)

#set text(
  size: 11pt
)

#align(center, [
= Project 2
Gabriel Parra

#show link: set text(fill: blue)
Project available at: #link("https://github.com/Gabriel-R-Parra/comp-top-project-2")
])


= Part 1

#figure(image("jupyter/figure-1.svg"), caption: [
  T_A CD8 (Orange), T_A FoxP3 (Sky Blue), and T_A CD68 (Purple) point clouds.
])
#figure(image("jupyter/figure-2.svg"), caption: [
  T_A CD8 (Orange) and T_A FoxP3 (Sky Blue) point cloud.
])

Individual point clouds for T_A CD8 and T_A FoxP3, as well as a point cloud that includes both of them are available with the additional files attached with this projects submission.

= Part 2

#figure(image("jupyter/six-pack.svg"), caption: [Six-pack persistence diagrams computed on point cloud containing T_A CD8 and T_A FoxP3.])

== Results

In these persistence diagrams T_A CD8 is mapped (union) onto T_A FoxP3.

=== Kernel
The kernel shows when the FoxP3 points begin to fill a cycle made by the CD8. By inspecting the plot, we can tell that there are lots of connected components that die earlier than the holes that are filled. I interpret this as lots of very dense regions of both CD8 and FoxP3, accompanied by larger pockets of CD8 that are filled with FoxP3.

=== Cokernel
The cokernel tells us that there are lots of dense regions of FoxP3 that don't contain CD8. Additionally, it indicates that there are larger pockets of FoxP3 that aren't filled with CD8. Paired with the kernel results, I interpret this to mean that FoxP3 is usually surrounded by CD8, and not the other way around.

=== Image
The image builds upon the relationship previously mentioned in the Cokernel section. It indicates that a large chunk (green) of the dense CD8 regions die quickly when introducing FoxP3 into them, but the loops (blue) survive longer when the CD8 does not surround FoxP3. My final interpretation of this is that there are many dense regions of CD8 and pockets of CD8, and that FoxP3 is usually found within the dense regions CD8, or surrounded by CD8. I believe that this means CD8 is more likely to have pockets where no FoxP3 is surrounding it and it is also more likely to have pockets that completely surround FoxP3. In the greater context of the data, this tells me that the CD8 is seeking out the FoxP3 and surrounding it. Pretty neat.