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The Cartesian Cafe — Mathematics
The Cartesian Cafe

The Cartesian Cafe is the podcast where an expert guest and Timothy Nguyen map out scientific and mathematical subjects in detail. This collaborative journey with other experts will have us writing down formulas, drawing pictures, and reasoning about them together on a whiteboard. If you’ve been longing for a deeper dive into the intricacies of scientific subjects, then this is the podcast for you. Topics covered include mathematics, physics, computer science, machine learning, and artificial intelligence.

Content also viewable on YouTube: www.youtube.com/timothynguyen and Spotify.

Timothy Nguyen is a mathematician and AI researcher working in industry. Homepage: www.timothynguyen.com, Twitter: @IAmTimNguyen

Patreon: www.patreon.com/timothynguyen

Copyright: © Copyright 2022 All rights reserved.

Latest Episodes:

Po-Shen Loh | The Mathematics of COVID-19 Contact Tracing Aug 19, 2022

Show notes

Po-Shen Loh is a professor at Carnegie Mellon University and a coach for the US Math Olympiad. He is also a social entrepreneur where he has his used his passion and expertise in mathematics in the service of education (expii.com) and epidemiology (novid.org).

In this episode, we discuss the mathematics behind Loh's novel approach to contact tracing in the fight against COVID, which involves a beautiful blend of graph theory and computer science.

Originally published on March 3, 2022 on Youtube: https://youtu.be/8CLxLBMGxLE

Patreon: https://www.patreon.com/timothynguyen

Timestamps:

00:00:00 : Introduction
00:01:11 : About Po-Shen Loh
00:03:49 : NOVID app
00:04:47 : Graph theory and quarantining
00:08:39 : Graph adjacency definition for contact tracing
00:16:01 : Six degrees of separation away from anyone?
00:21:13 : Getting the game theory and incentives right
00:30:40 : Conventional approach to contact tracing
00:34:47 : Comparison with big tech
00:39:19 : Neighbor search complexity
00:45:15 : Watts-Strogatz small networks phenomenon
00:48:37 : Storing neighborhood information
00:57:00 : Random hashing to reduce computational burden
01:05:24 : Logarithmic probing of sparsity
01:09:56 : Two math PhDs struggle to do division
01:11:17 : Bitwise-or for union of bounded sets
01:16:21 : Step back and recap
01:26:15 : Tradeoff between number of hash bins and sparsity
01:29:12 : Conclusion

Further reading:

Po-Shen Loh. "Flipping the Perspective in Contact Tracing" https://arxiv.org/abs/2010.03806

Introduction Aug 17, 2022

Show notes

Hello everyone, this is Tim Nguyen and welcome to The Cartesian Cafe. On this podcast we embark on a collaborative journey with other experts, to discuss mathematical and scientific topics in faithful detail, which means writing down formulas, drawing pictures, and reasoning about them together on a whiteboard. If you’ve been longing for a deeper dive into the intricacies of scientific subjects, then this is the podcast for you. Welcome to The Cartesian Cafe.

Patreon: https://www.patreon.com/timothynguyen

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