## Table of Contents

- 1. Stephen Wolfram: Brainstorming about Digital Contact Tracing
- 2. Notes
- 2.1. Reviewing phone-to-phone encounter protocol from http://covid-watch.org/article [18:00]
- 2.2. Delayed tracing [26:00]
- 2.3. Example encounter graph [42:00]
- 2.4. Custering discussion [52:00]
- 2.5. Possible common ways of infection [1:00:00]
- 2.6. Discussion about graph communities [1:10:00]
- 2.7. False-positives [1:18:00]
- 2.8. Model for length of interaction [1:32:00]
- 2.9. In-between summary

## 1 Stephen Wolfram: Brainstorming about Digital Contact Tracing

My notes of the video https://youtu.be/wjQfteOMHj4?list=PLxn-kpJHbPx1ehn1vcYZ4FqVQ37CkkWNp, a session of Stephen Wolfram (of Wolfram Alpha) having a brainstorming session about digital contact tracing.

At 1:49:00 I ran out of time, the discussion was moving towards the topic of how exchange of data with a central authority could work. I recommend to watch the video at 1.25 - 1.5 speed.

The discussion was interesting for me because:

- There are technical problems, but also problems how to create a model that represents the real-world, as not all data is easily available.
- Also the discussion of what data would be useful vs. what could be realistically extracted. Some data requires user cooperation that might just not happen or some data raises privacy concerns, especially if it's shared with a central authority.
- I have my doubts that the people discussing were right on every point they raised, but the session was a brainstorming session anyway, so it's sometimes useful to start with only vague ideas.
- I liked the description of "<something> being a proxy for <some other concept>". That is a good description of what's happening.

## 2 Notes

### 2.1 Reviewing phone-to-phone encounter protocol from http://covid-watch.org/article [18:00]

- Each phone generates a UUID, every x time interval.
- Keep track of seen UUIDs via bluetooth.
- If phone gets infected, notify people in the list.
- How to notify people in the list?
- Use push notifications, send out infected ids to everyone and app checks if id is in "seen" list.
- "Encountered phones" is a proxy of being the same place.

### 2.2 Delayed tracing [26:00]

- Store BLE (Bluetooth low energy) env in a hash?
- Perceptual hashing used in image comparision, since BLE is transient/changing over time.
- Can perceptual hashing be cryptograhically secure? Note two different kinds of cryptograhicall secure: pre-image attack and collisions.
- Question that can be answered using BLE: "Have I been in the same env as infected phone within certain timeframe?"

### 2.3 Example encounter graph [42:00]

- Important way to check if I might be infected: same place as infected phone within certain timeframe.
- Nodes in the graph can also be objects (like BLE beacons) not only phones/persons.
- Note the partial ordering possible in the graph based on time.
- Is it possible to deduce spatial structure from this phone encounter data? [47:00]
- BLE as proxy for location in space. [50:00]
- Inform people with overlap in BLE env that they might be at risk.

### 2.4 Custering discussion [52:00]

- A population study can be done: assuming significant number of infections, then trace it back (helpful to find source of infection).
- On the Graph of phone-to-phone connections we can do reachability computations.
- Partial order, since we can't infect in the past.
- Determing the location equal to clustering [53:00]
- But algorithm should not depend on idea of cluster, since cluster is constantly changing by ppl coming/leaving the cluster.

### 2.5 Possible common ways of infection [1:00:00]

- Question for this session: Besides "pure instantaneous phone interactions", is there a way to find delayed tranmissions? [1:02:00]

[ This part contains a discussion about the most common way to get infected, but I largely skipped that since there is no conclusion due to lack of data at that point in time. ]

### 2.6 Discussion about graph communities [1:10:00]

[ This part they discuss about the properties and suitability of graph communities, but I skipped that since it was hard to follow. ]

### 2.7 False-positives [1:18:00]

- False positives could be reduced if people provide additional data, like are they wearing a mask.
- But realistically only a 0-effort app would work, if too much user interaction is required, people won't do it.
- What is the actual false-positive rate? If R0 is the number of people infected by infected person (on average), if you see 1000 phones in a certain timeframe, then you infect on average 1/1000, but we need to notify all of them to be quarantained?
- It really depends on how much phones you encounter.
- Is it possible to filter BLE on decibel strength?
- What happens in an environment with a large number of people in BLE range, like a stadium? [1:27:00]
- Singapore traces everybody on a plane if one person gets infected, that is, a few hundred.
- Can we return a confidence level to quantify possible infection? But what do people do with that?
- This confidence level could get more accurate over time due to a learning effect.
- Differential equation models assume well-mixed interactions with strangers. [1:30:00]
- Network models assume interactions within a fixed network, which might be closer to a lockdown situation.

### 2.8 Model for length of interaction [1:32:00]

- Length of time spent together might be critical parameter for probability of infection. [1:33:00]
- Question is: can contact tracing work if false-positives are high. Meta claim: meeting on passing by on the street is different than spending 2 hrs together. Does this matter or not?
- Is contact time linear relation to risk of infection? [1:37:00]
- Might be able to get more data on this using contact tracing.

### 2.9 In-between summary

Can we do better than instantaneous contacts? Yes, use BLE info, use gaph of instantaneous contacts, but comes at cost of privacy. [1:49:00]