Presenter
Professor Jeff Sanders, African Institute for Mathematical Sciences, South Africa
Problem statement
Can we design a distributed (i.e. de-centralised) system to manage personal medical history?
People expect to be, and are in normal years, far more mobile than ever before. Mobile phones and the web provide the communications and information they need, but national border control, personal ID and health systems remain resiliently conventional in spite of being essential for travel. By comparison currency has been potentially liberated, with the advent of Bitcoin.
Can we do the same for personal health records?
If you're stung by a jellyfish on holiday in northern Queensland, break a leg skiing in the Alps, or catch a virus whilst working in Wuhan, immediate treatment requires knowledge of your medical history, allergies and insurance. Record books are unreliable, easy to lose and to keep with you at all times. Is there some distributed system which allows access to your personal medical information from anywhere in the world? What functionality should it support? What are the ethical requirements of such a design?
- This project begins with a brief survey of centralised versus distributed systems, emphasising the local thinking needed to design a distributed protocol which achieves some global property.
- It then considers the features and functionality desired of a distributed personal medical system, emphasising those not achievable in a conventional system (for instance exploitation of data analytics). Ethics, accountability, and intrusion are important considerations that participants may not be used to addressing.
- A system is designed which incorporates the desired features. Coding is not required, but reasoning about correctness of behaviour of our design is.
A distributed system will be thought of as a `data structure' i.e. as consisting of state on which certain operations are defined, like `Update a record', and `Query a record'. We must decide what `state' the system has in order to be able to express its operations accurately. The first step is to under stand what exactly is a `data structure' and how to describe it using discrete mathematics in the Z notation.
A typical industrial problem requires a solution which optimises some quantity. When an optimal solution is unrealistic an acceptably efficient one is sought. It might be: what standard length of aluminium minimises wasteage over various uses. Or what treatment of the residue of sugar cane, for use in generating electricity all-year round, minimises use of energy. The solution is typically described by differential equations and then constraints are imposed to optimise the solution.
This project is an example of an important family of contemporary problems whichfit that paradigm, but whose solution is, instead of a solution to a differential equation, a design (of optimal or acceptable efficiency). Ingenuity is required to invent the design and mathematics is needed to express it and to show that it functions as desired. The design might enable several robots to coordinate in exploring a mine. It might be for a secure electronic voting system. Or it might be for on-line sales featuring specials that benefit from market data. The mathematics is discrete and straightforward though perhaps unfamiliar.
An implementation (i.e. code) is not sought. Indeed our time will be spent on deciding then expressing features and reasoning about how they would be captured in a design.
Presentation
Modelling Camp 2022 Problem 1 Presentation
Report-back presentation
Graduate Modelling Camp Problem 1 Report-back Presentation
Written report
