Deploying vaccines: my research report.

topRight now covid-19 tests are going to important people more than others — because those important people are scared and we do not really have a strategy. When vaccines become available, if we do not have a science-based strategy, the strategy may well turn out to be “Vaccinate the rich!”. This post takes you through the initial stages of a research project on making plans for vaccine deployment, including some speed-bumps we hit. It may give you a sense of how computational research goes and why it has a good chance of success.

In an earlier post, Occupy Math talked about vaccine deployment strategies. Occupy Math is now part of a deployment strategy project, funded through St. Francis Xavier University in Nova Scotia. The project is led by Professor James Hughes at StFX University. Professor Sheridan Houghten at Brock University is also collaborating. We are old friends and have been collaborating for years. This post is about some of the results we have gotten so far and how the results changed the project. The picture at the top is a bit whimsical as the research we are doing is in three rooms in our houses with our computers. Six rooms if you include students currently in or joining the project.

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John Horton Conway, Requiescat in Pace

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John Conway was a character, a genius, an eccentric, and one of the greatest mathematicians in history. He died on Saturday April 11th of the coronavirus at the age of 82. He was a professor at Princeton and worked in games, abstract algebra, combinatorics, the theory of computing, and many other fields. Occupy Math has attended lectures by this great man and will recount the experience with one of them in the post. Fair warning: Occupy Math is going to cover three of Professor Conway’s many achievements and they are pretty deep. To combat this, there are lots of pictures, some tales of Conway’s personal eccentricity, and the story of Conway’s part in solving a single problem that took over a century to complete. One of Occupy Math’s most useful ideas was based on one of Conway’s algorithms — used in a way that would probably have appalled the professor.

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Vaccine Deployment Strategies

topIn Canada, the country and all ten of our provinces have a Department of Public Health and the picture at the top of the post shows many of the leaders of these departments. These are the people who are trying to keep us healthy, in Canada, long enough for treatments and vaccines to be developed. Occupy Math is working with a group that is going to try and build a tool to help these officials; that tool figures out how to best deploy vaccines as they become available. The idea is to look at the network of contacts among people and deploy vaccines so that they do the most to stop the novel corona virus.

This post will look at some standard vaccination strategies and take a shot at explaining how to combine them into a master strategy that can adapt to changing conditions. Occupy Math keeps saying that being mathematically informed makes things better for you and for others. In this post we are explaining a fairly complex mathematical situation with a metaphor — the contact network of people — that will help you think about the situation and deal with it more effectively.

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An AI artist?

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This week Occupy Math returns to the topic of a post on both digital evolution and computer art: Evolution can do math that people can’t. In this post we will look at shaping the digital art with a technique inspired by the human immune system. These artificial immune systems are another nature-inspired algorithmic technology, like digital evolutionJulie Greensmith taught Occupy Math about these techniques.

Normally an immune system fights disease. The way you use artificial immune systems is to declare something you do not like to be a disease. This is, of course, a bit arbitrary and much simpler than a real biological immune system. The action principle of the artificial immune system is negative selection, the process of removing things we do not like. This post is about some recent work where we used negative selection to pick which sorts of images our computer art system finds by removing the others. One of the pictures generated by the original code, before we added the artificial immune system, appears at the top of the post.

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Guess My Number — An Introduction to Algorithms

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Occupy Math just got back from Schloss Dagstuhl, a castle in the woods in Germany not too far from Luxembourg, where there are week-long research meetings. This meeting was on using artificial intelligence for games. One of the outcomes of this meeting was a simple game used to explore cooperation between humans and artificial intelligence — which Occupy Math thought had potential as an activity to introduce the mind set for programming. This activity is in today’s post. One of the groups was looking at making artificial intelligence to cooperate with human beings. They invented what they thought was the simplest possible coordination game. The game works like this.

  1. Both players pick a number from 1-100 and write the numbers down secretly.
  2. The numbers are revealed. If they are the same, the game is done.
  3. If the number are not the same, the players write numbers again and repeat step 2.
  4. Other than revealing numbers, the players are not allowed to communicate.

The goal of the game is to coordinate — get to the same number — in the smallest number of steps. A play of the game that takes 8 steps is shown at the top of the post. In the rest of the post, we give a couple of ways to use this game as an activity, and we also explain why the researchers do not think, after having people play it, that this game is simple.

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Profit Mad Publishers Poisoning Math Instruction!

topIn this post we look at several ways traditional textbook publishers are poisoning math instruction — charging insane prices for books, writing lectures for professors (bad ones), and doing a bad job of generating problems for practice, homework, and examinations. We begin with the price issue. A while back, Occupy Math announced he had written a calculus book, Fast Start Calculus for Integrated Physics. The material from the book is being republished as the three books pictured at the top of the post. This is part of Occupy Math’s war on outrageous textbook prices. These books are distributed at low cost to a university and zero cost to students at participating universities.

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Generating Complex Ecologies in a Computer

topThis post is about some of Occupy Math’s current research. The picture at the left represents a 200×200 cell “ecology”. Each cell in the grid is occupied by one type of simulated critter. The critters compete with one another to take over cells (the rules for this are lower down in the post). The simulation is run for 1,000 seasons and one of the 40,000 creatures is mutated each season to create a new type of critter. We start with ten types of critters, but mutation sometimes drives the number of types of critters into the hundreds by season 1,000. The picture above is the state of the simulation, with different colors representing different critters, in the thousandth season. This project is generating a diverse collection of these small, complex artificial ecologies.

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Humans and Computers Collaborating on Art

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Occupy Math works with digital evolution on a number of projects including evolving parameters that generate interesting fractals. The advantage to doing this with a computer, assuming you can come up with an automatic function that at least sort of measures “this looks good”, is that you can sort through billions of fractals per hour. One of these is shown at the top of the page. The disadvantage is that people are much better than any of the automatic functions we have found so far at spotting cool fractals. If we use people, though, they burn out way before looking a even a paltry million fractals. This is the phenomenon of user fatigue. This post is about a way to let computers and people collaborate on a project, drawing on the strengths of each. Computers can evaluate huge numbers of fractals to find ones that might look good. Humans have a much better ability to judge which fractals are actually beautiful.

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NEWT: Fractals for everyone!

NEWTwithbkgdThe moment none of you knew you were waiting for is here: Occupy Math is making fractals available to all — not just pictures but an app, Newt, for making your own. Our mascot, Newt, is part of one of the fractals (except for the eyes) and is named after the type of fractal he is — a Newton’s method fractal. One of the perennial topics in Occupy Math is fractals. There are a lot of different types of fractals. One of the less well-explored types is the Newton’s method fractal. Occupy Math Productions is now asking for beta-testers for a new Android app that lets you make your own Newton’s method fractals. If you are interested in beta-testing this app, send a request to occupymathwendy@gmail.com and include your gmail address (they are easy to get if you do not have one already). We are looking for one hundred beta-testers and would really like to hear from you — if you have an android phone or device. Tablets are fine.

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What do senior research students do all day.

topThis post is the second half of Occupy Math’s report on the last academic year. It focuses on the four senior research projects Occupy Math supervised this year. The “senior research project” is a double-credit course that lets students dip their toes in the pool of research to see if it works for them. One of the students took the course in the fall, three in the winter semester, the semester that just wrapped up. Two of the projects were on very different ways to generate maps, one was on the generation of a new class of mathematical puzzles, and the last was a project in bioinformatics that sought to tune the parameters of an algorithm that generates features for identifying different type of genetic sequences. Three of the students were computer science majors, something that will be happening a lot more as the computer science program at Occupy Math’s home university is expanding. Two of the students are going to start masters degree programs in the fall, one in math, one in computer science.

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