Short history of iterated prisoner’s dilemma tournaments

Nineteen Eighty — if I had to pick the year that computational modeling invaded evolutionary game theory then that would be it. In March, 1980 — exactly thirty-five years ago — was when Robert Axelrod, a professor of political science at University of Michigan, published the results of his first tournament for iterated prisoner’s dilemma in the Journal of Conflict Resolution. Game theory experts, especially those specializing in Prisoner’s dilemma, from the disciplines of psychology, political science, economics, sociology, and mathematics submitted 14 FORTRAN programs to compete in a round-robin tournament coded by Axelrod and his research assistant Jeff Pynnonen. If you want to relive these early days of evolutionary game theory but have forgotten FORTRAN and only speak Python then I recommend submitting a strategy to an analogous tournament by Vincent Knight on GitHub. But before I tell you more about submitting, dear reader, I want to celebrate the anniversary of Axelrod’s paper by sharing more about the original tournament.

Maybe it will give you some ideas for strategies.
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False memories and journalism

We like to think of ourselves as a collection of our memories, and of each memory as a snapshot of an event in our lives. Sure, we all know that our minds aren’t as sturdy as our computer’s hard-drive, so these snapshots decay over time, especially the boring ones — that’s why most of us can’t remember what we had for breakfast 12 years ago. We are even familiar with old snapshots rearranging their order and losing context, but we don’t expect to generate vivid and certain memories of events that didn’t occur. How could we have a snapshot of something that didn’t happen?

This view of memory is what makes Brian Williams’ recent fib about being on board a helicopter that was hit by two rockets and small arms fire in Iraq 12 years ago, so hard to believe. There was indeed a helicopter that was forced to land on that day, but the downed aircraft’s crew reports that Williams was actually on a helicopter about an hour behind the three that came under fire. Williams has apologized for his story, saying he conflated his helicopter with the downed one. To this, Erik Wemple voices the popular skepticism that “‘conflating’ the experience of taking incoming fire with the experience of not taking incoming fire seems verily impossible.”

But research into false memories suggests that such constructed memories as Williams’ do occur. In this post, I want to discuss these sort of false memories, share a particularly interesting example, and then discuss what this might mean for journalism.

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An approach towards ethics: primate sociality

Moral decision making is one of the major torrents in human behavior. It often overrides other ways of making judgments, it generates conflicting sets of cultural values and is reinforced by them. Such conflicts might even occur in the head of some unfortunate individual, which makes the process really creative. On the other hand ethical behavior is the necessary social glue and the way people prioritize prosocial practices.

In the comments to his G+ post about Michael Sandel’s Justice course, Artem Kaznatcheev invited me to have a take on moral judgment and social emotions based on what I gathered through my readings in the recent couple of years. I’m by no means an expert in any of the fields that I touch upon in the following considerations, but I’ve been purposefully struggling with the topic due to my interest in behavioral sciences trying to come up with a lucid framework to think about the subject. Not everything I write here is backed up very well by research, mainly because I step up a little and try to see what might come next, but I’ll definitely do my best to leave my general understanding distinct from concepts prevailing in the studies I have encountered. It is not an essay on ethics per se, but rather where I am now in understanding how moral sentiments work. A remark to make is that for the purposes of that text I understand behavior broadly, e.g. thinking is a behavior.

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Diversity working together: cancer, immune system, and microbiome

After a much needed few weeks of recovery, I’ve found some time to post about our annual IMO workshop held this year on the topic of viruses in cancer. Our group had the challenge of learning about all of the complexities of the human microbiome and its interactions with a cancerous lesion. The human microbiome, in a nutshell, is the ecological community of commensal, symbiotic, and pathogenic microorganisms that live on our inner and outer surfaces including bacteria, fungi, and viruses. The number of cells in the human microbiome is more than 10 times the amount of cells in our bodes (Costello et al., 2009), which means that 2-6 pounds of us is made of, not exactly us, but microorganisms. The microbiome has become a popular topic as of recent, with more than just human-centric studies sparking interest (see links for kittens, seagrass, the University of Chicago’s hospital, and the earth). See the video below for a nice introduction to the microbiome (and the cutest depiction of a colon you will ever see):

The first thing that I learned about the human microbiome is the extreme diversity of the bacterial communities. We have quite unique microbiomes, though they are shared through kissing, similar diets, and among families and pets (Song et al., 2013; Kort et al., 2014)! Further, there are huge discrepancies of the microbial communities that live in our hair, nose, ear, gut and foot (Human Microbiome Project Consortium, 2012). So the challenge to find a project that would address this diverse microbiome and its interaction with cancer in a way that we could test with real data to BOTH answer a clinically-relevant question AND be mathematically modeled in 4 days (what!?) was a little daunting. Good thing we had an epidemiologist and expert in the microbiome (Christine Pierce Campbell), a medical oncologist specializing in head and neck cancers (Jeffery Russell), and an excellent team of biologists, mathematicians, computer scientists, and biophysicists (#teamFecal) ready to rumble.

TeamMicroB
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Memes, compound strategies, and factoring the replicator equation

When you work with evolutionary game theory for a while, you end up accumulating an arsenal of cute tools and tricks. A lot of them are obvious once you’ve seen them, but you usually wouldn’t bother looking for them if you hadn’t know they existed. In particular, you become very good friends with the replicator equation. A trick that I find useful at times — and that has come up recently in my on-going project with Robert Vander Veldge, David Basanta, and Jacob Scott — is nesting replicator dynamics (or the dual notion of factoring the replicator equation). I wanted to share a relatively general version of this trick with you, and provide an interpretation of it that is of interest to people — like me — who care about the interaction of evolution in learning. In particular, we will consider a world of evolving agents where each agent is complex enough to learn through reinforcement and pass its knowledge to its offspring. We will see that in this setting, the dynamics of the basic ideas — or memes — that the agents consider can be studied in a world of selfish memes independent of the agents that host them.
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Helicobacter pylori and stem cells in the gastric crypt

IMO2014Group

Last Friday, the 4th Integrated Mathematical Oncology Workshop finished here at Moffitt. The event drew a variety of internal and external participants — you can see a blurry photo of many of them above — and was structured as a competition between four teams specializing in four different domains: Microbiome, Hepatitis C, Human papillomavirus, and Helicobacter pylori. The goal of each team was to build mathematical models of a specific problem in their domain that were well integrated with existing clinical and biological resources, the reward was a start-up grant to the project that seemed most promising to the team of judges. As I mentioned earlier in the week, I was on team H. Pylori — lead by Heiko Enderling with clinical insights from Domenico Coppola and Jose M. Pimiento. To get a feeling for the atmosphere of this workshop, I recommend a video summary of 2013’s workshop made by Parmvir Bahia, David Basanta, and Arturo Araujo:

I want to use this post to summarize some of the modeling that we did for the interaction of H. Pylori and gastric cancer. This is a brief outline — a reminder of sorts — and concentrates only on the parts that I was closely involved in. Unfortunately, this means that I won’t cover all the perspectives that our team offered, nor all the great work that they did. I apologize for the content I omitted. Hopefully, I can convince some other team members to blog about their experience to give a more balanced perspective.

This post also won’t cover all that you might want to know about bacteria and gastric cancer. As we saw earlier, fun questions about H. Pylori span many length and temporal scales and it was difficult to pick one to focus on. Domenico pointed us toward Houghton et al.’s (2004) work on the effect of H. Pylori on stem cell recruitment (for a recent survey, see Bessede et al., 2014), and suggested we aim our modeling at a level where we can discuss stem cells quantitatively. The hope is to use the abundance of stem cells as a new marker for disease progression. In the few days of the workshop, we ended up building and partially integrating two complimentary models; one agent-based and one based purely on ODEs. In the future, we hope to refine and parametrize these models based on patient data from Moffitt for the non-H. Pylori related gastric cancers, and from our partners in Cali, Colombia for H. Pylori related disease.
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Critical thinking and philosophy

Regular readers of TheEGG might have noticed that I have a pretty positive disposition toward philosophy. I wound’t call myself a philosopher — at least not a professional one, since I don’t think I get paid to sit around loving wisdom — but I definitely greatly enjoy philosophy and think it is a worthwhile pursuit. As a mathematician or theoretical computer scientists, I am also a fan of rational argument. You could even say I am a proponent of critical thinking. At the very least, this blog offers a lot of — sometimes too much — criticism; although that isn’t what is really meant by ‘critical thinking’, but I’ll get back to that can of worms later. As such, you might expect that I would be supportive of Olly’s (of Philosophy Tube) recent episode on ‘Why We Need Philosophy’. I’ll let you watch:

I am in complete support of defending philosophy, but I am less keen on limiting or boxing philosophy into a simple category. I think the biggest issue with Olly’s defense is that he equates philosophy to critical thinking. I don’t think this is a justified identity and false in both directions. There is philosophy that doesn’t fall under critical thinking, and there is critical thinking that is not philosophy. As such, I wanted to unpack some of these concepts with a series of annotated links.

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Personification and pseudoscience

If you study the philosophy of science — and sometimes even if you just study science — then at some point you might get the urge to figure out what you mean when you say ‘science’. Can you distinguish the scientific from the non-scientific or the pseudoscientific? If you can then how? Does science have a defining method? If it does, then does following the steps of that method guarantee science, or are some cases just rhetorical performances? If you cannot distinguish science and pseudoscience then why do some fields seem clearly scientific and others clearly non-scientific? If you believe that these questions have simple answers then I would wager that you have not thought carefully enough about them.

Karl Popper did think very carefully about these questions, and in the process introduced the problem of demarcation:

The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as ‘metaphysical’ systems on the the other

Popper believed that his falsification criterion solved (or was an important step toward solving) this problem. Unfortunately due to Popper’s discussion of Freud and Marx as examples of non-scientific, many now misread the demarcation problem as a quest to separate epistemologically justifiable science from the epistemologically non-justifiable pseudoscience. With a moral judgement of Good associated with the former and Bad with the latter. Toward this goal, I don’t think falsifiability makes much headway. In this (mis)reading, falsifiability excludes too many reasonable perspectives like mathematics or even non-mathematical beliefs like Gandy’s variant of the Church-Turing thesis, while including much of in-principle-testable pseudoscience. Hence — on this version of the demarcation problem — I would side with Feyerabend and argue that a clear seperation between science and pseudoscience is impossible.

However, this does not mean that I don’t find certain traditions of thought to be pseudoscientific. In fact, I think there is a lot to be learned from thinking about features of pseudoscience. A particular question that struck me as interesting was: What makes people easily subscribe to pseudoscientific theories? Why are some kinds of pseudoscience so much easier or more tempting to believe than science? I think that answering these questions can teach us something not only about culture and the human mind, but also about how to do good science. Here, I will repost (with some expansions) my answer to this question.
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Limits of prediction: stochasticity, chaos, and computation

Some of my favorite conversations are about prediction and its limits. For some, this is purely a practical topic, but for me it is a deeply philosophical discussion. Understanding the limits of prediction can inform the philosophies of science and mind, and even questions of free-will. As such, I wanted to share with you a World Science Festival video that THEREALDLB recently posted on /r/math. This is a selected five minute clip called “What Can’t We Predict With Math?” from a longer one and a half hour discussion called “Your Life By The Numbers: ‘Go Figure'” between Steven Strogatz, Seth Lloyd, Andrew Lo, and James Fowler. My post can be read without watching the panel discussion or even the clip, but watching the clip does make my writing slightly less incoherent.

I want to give you a summary of the clip that focuses on some specific points, bring in some of discussions from elsewhere in the panel, and add some of my commentary. My intention is to be relevant to metamodeling and the philosophy of science, but I will touch on the philosophy of mind and free-will in the last two paragraphs. This is not meant as a comprehensive overview of the limits of prediction, but just some points to get you as excited as I am about this conversation.

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Experimental and comparative oncology: zebrafish, dogs, elephants

One of the exciting things about mathematical oncology is that thinking about cancer often forces me to leave my comfortable arm-chair and look at some actually data. No matter how much I advocate for the merits of heuristic modeling, when it comes to cancer, data-agnostic models take second stage to data-rich modeling. This close relationship between theory and experiment is of great importance to the health of a discipline, and the MBI Workshop on the Ecology and Evolution of Cancer highlights the health of mathematical oncology: mathematicians are sitting side-by-side with clinicians, biologists with computer scientists, and physicists next to ecologists. This means that the most novel talks for me have been the ones highlighting the great variety of experiments that are being done and how they inform theory.In this post I want to highlight some of these talks, with a particular emphasis on using the study of cancer in non-humans to inform human medicine.
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