Hello everyone, I am currently a graduate student interested in computational topology. The topic I'd like to work on is related to my project and I would love help with visualizations/video editing.
Quick Summary
The topic in question is based on a paper called Evasion Paths in Mobile Sensor Networks (links bellow). At a high level, you can imagine a network of sensors with sensing radius r sweeping a bounded 2D domain to determine if an invader may be present. If we allow the sensors to know their positions (say through GPS) then the problem is relatively easy and you may use computational geometry to calculate the area of the union of the sensing balls. However, we can reduce this problem to only using local information (say sensors have no GPS but can detect other sensors within their sensing radius) to solve the global problem of the possibility of the existence of an invader in the domain.
The beauty of this problem is that it introduces an important idea from Topology which is extracting global information from local properties. The actual elements in question can also be interpreted as physical objects so students who may not have an advanced background can still follow along with the questions that are posed.
Target medium
(Are you hoping for your idea to be produced into a video? An illustrated/interactive article? What skillsets are you looking for in a collaborator?)
I would like the idea to made into a video and I'm looking for someone with video editing skills and experience with programatic animation for the sensor networks themselves. If time permits, I have some code for an old project to perhaps allow for a web-interactive as well!
I did a talk on this problem about 6 months ago were I introduced the problem so I will be following the structure of introducing the following concepts:
The Evasion Path Problem (stationary)
Cech complex
Allowing for Mobile Sensors
Voronoi Diagrams
Alpha Complex
Boundary Cycles
Atomic changes
Dependence on Embedding and final thoughts
Contact details
(What's the best way for people to contact you?)
If you're interested in learning more or want to collaborate, feel free to e-mail me at:
marco.campos24@utexas.edu
About the author
Hello everyone, I am currently a graduate student interested in computational topology. The topic I'd like to work on is related to my project and I would love help with visualizations/video editing.
Quick Summary
The topic in question is based on a paper called Evasion Paths in Mobile Sensor Networks (links bellow). At a high level, you can imagine a network of sensors with sensing radius r sweeping a bounded 2D domain to determine if an invader may be present. If we allow the sensors to know their positions (say through GPS) then the problem is relatively easy and you may use computational geometry to calculate the area of the union of the sensing balls. However, we can reduce this problem to only using local information (say sensors have no GPS but can detect other sensors within their sensing radius) to solve the global problem of the possibility of the existence of an invader in the domain.
The beauty of this problem is that it introduces an important idea from Topology which is extracting global information from local properties. The actual elements in question can also be interpreted as physical objects so students who may not have an advanced background can still follow along with the questions that are posed.
Target medium
(Are you hoping for your idea to be produced into a video? An illustrated/interactive article? What skillsets are you looking for in a collaborator?)
I would like the idea to made into a video and I'm looking for someone with video editing skills and experience with programatic animation for the sensor networks themselves. If time permits, I have some code for an old project to perhaps allow for a web-interactive as well!
More details
Links:
Evasion Paths in Mobile Sensor Networks https://arxiv.org/abs/1308.3536
This paper: https://arxiv.org/pdf/2101.09813.pdf gives an overview of the algorithms as well as some experiments that have been carried out.
Here is a slideshow from Henry Adams about the problem: https://www.math.colostate.edu/~adams/talks/EvasionProblemSlides-CutForJMM2021.pdf
Some talks on the problem: https://www.youtube.com/watch?v=p0T4OPFvTt0&list=PL4kY-dS_mSmLFh9BpI3LqIQnw6KMg0jlt&index=24&ab_channel=AppliedAlgebraicTopologyNetwork
Outline:
I did a talk on this problem about 6 months ago were I introduced the problem so I will be following the structure of introducing the following concepts:
Contact details
(What's the best way for people to contact you?)
If you're interested in learning more or want to collaborate, feel free to e-mail me at: marco.campos24@utexas.edu