## Hamiltonian systems and closed orbits in replicator dynamics of cancer

June 24, 2016 2 Comments

Last month, I classified the possible dynamic regimes of our model of acidity and vasculature as linear goods in cancer. In one of those dynamic regimes, there is an internal fixed point and I claimed closed orbits around that point. However, I did not justify or illustrate this claim. In this post, I will sketch how to prove that those orbits are indeed closed, and show some examples. In the process, we’ll see how to transform our replicator dynamics into a Hamiltonian system and use standard tricks from classical mechanics to our advantage. As before, my tricks will draw heavily from Hauert et al. (2002) analysis of the optional public good game. Studying this classic paper closely is useful for us because of an analogy that Robert Vander Velde found between the linear version of our double goods model for the Warburg effect and the optional public good game.

The post will mostly be about the mathematics. However, at the end, I will consider an example of how these sort of cyclic dynamics can matter for treatment. In particular, I will consider what happens if we target aerobic glycolysis with a drug like lonidamine but stop the treatment too early.

## Computational kindness and the revelation principle

June 30, 2016 by Artem Kaznatcheev 8 Comments

In EWD1300, Edsger W. Dijkstra wrote:

He wrote this as the justification for the mathematical notations that he introduced and as an ode to the art of definition. But any writer should heed this aphorism.

^{[1]}Recently, I finished readingAlgorithms to Live Byby Brian Christian and Tom Griffiths.^{[2]}In the conclusion of their book, they gave a unifying name to the sentiment that Dijkstra expresses above:computational kindness.As computer scientists, we recognise that computation is costly. Processing time is a limited resource. Whenever we interact with others, we are sharing in a joint computational process, and we need to be mindful of when we are not carrying our part of the processing burden. Or worse yet, when we are needlessly increasing that burden and imposing it on our interlocutor. If you are computationally kind then you will be respectful of the cognitive problems that you force others to solve.

I think this is a great observation by Christian and Griffiths. In this post, I want to share with you some examples of how certain systems — at the level of the individual, small group, and society — are computationally kind. And how some are cruel. I will draw on examples from their book, and some of my own. They will include, language, bus stops, and the revelation principle in algorithmic game theory.

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Filed under Books, Commentary, Reviews Tagged with algorithmic philosophy, ethics and morality, philosophy of mind