A year in books: Neanderthals to the National Cancer Act to now

A tradition I started a couple of years ago is to read at least one non-fiction book per month and then to share my thoughts on the reading at the start of the following year. Last year, my dozen books were mostly on philosophy, psychology, and political economy. My brief comments on them ended up running a long 3.2 thousand words. This time the list had expanded to around 19 books. So I will divide the summaries into thematic sets. For the first theme, I will start with a subject that is new for my idle reading: cancer.

As a new researcher in mathematical oncology — and even though I am located in a cancer hospital — my experience with cancer has been mostly confined to the remote distance of replicator dynamics. So above all else these three books — Nelson’s (2013) Anarchy in the Organism, Mukherjee’s (2010) The Emperor of All Maladies, and Leaf’s (2014) The Truth in Small Doses — have provided me with insights into the personal experiences of the patient and doctor.

I hope that based on these reviews and the ones to follow, you can suggest more books for me to read in 2016. Better yet, maybe my comments will help you choose your next book. Much of what I read in 2015 came from suggestions made by my friends and readers, as well as articles, blogs, and reviews I’ve stumbled across.[1] In fact, each of these cancer books was picked for me by someone else.

If you’ve been to a restaurant with me then you know that I hate choosing between close-to-equivalent options. To avoid such discomfort, I outsourced the choosing of my February book to G+ and Nelson’s Anarchy in the Organism beat out Problems of the Self by a narrow margin to claim a spot on the reading list. As I was finishing up Nelson’s book — which I will review last in this post — David Basanta dropped off The Emperor of All Maladies on my desk. So I continued my reading on cancer. Finally, Leaf’s book came towards the end of the year based on a recommendation from Jacob Scott. It helped reinvigorate me after a summer away from the Moffitt Cancer Center.
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Double public goods games and acid-mediated tumor invasion

Although I’ve spent more time thinking about pairwise games, I’ve recently expanded my horizons to more serious considerations of public-goods games. They crop up frequently when we are modeling agents at the cellular level, since interacts are often indirect through production of some sort of common extra-cellular signal. Unlike the trivial to characterize two strategy pairwise games, two strategy public-goods have a more sophisticated range of possible dynamics. However, through a nice trick using the properties of Bernstein polynomials, Archetti (2013,2014) and Peña et al. (2014a) have greatly increased our understanding of the public good, and I will be borrowing heavily from the toolbag and extending it slightly in this post. I will discuss the obvious continuation of this work by considering more than two strategies and several public goods together. Unfortunately, the use of public goods games here — and of evolutionary game theory (EGT) more generally — is not without controversy. This extension is not meant to address the controversy of spatial structure (although for progress on this, see Peña et al., 2014b), but the rigorous qualitative analysis that I’ll use (mostly in a the next post on this project) will allow me to side-step much of the parameter-fitting issues.

Of course, having two public goods games is only interesting if we couple them to each other. In this case, we will have one public good from which everyone benefits, but the second good is anti-correlated in the sense that only those that don’t contribute to the first can benefit from the second. A more general analysis of all possible ways to correlate two public-goods game might be a fun future direction, but at this point it is not clear what other correlations would be useful for modeling; at least in mathematical oncology.

By the way, if you are curious what mathematical oncology research looks like, it is often just scribbles like this emailed back and forth:


I’ll use the rest of this post to guide you through the ideas behind the above sketch, and thus introduce you to the joint project that I am working on with Robert Vander Velde, David Basanta, and Jacob Scott. Treat this as a page from my open research notebook.

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A year in books: philosophy, psychology, and political economy

If you follow the Julian calendar — which I do when I need a two week extension on overdue work — then today is the first day of 2015.

Happy Old New Year!

This also means that this is my last day to be timely with a yet another year-in-review post; although I guess I could also celebrate the Lunar New Year on February 19th. Last year, I made a resolution to read one not-directly-work-related book a month, and only satisfied it in an amortized analysis; I am repeating the resolution this year. Since I only needed two posts to catalog the practical and philosophical articles on TheEGG, I will try something new with this one: a list and mini-review of the books I read last year to meet my resolution. I hope that based on this, you can suggest some books for me to read in 2015; or maybe my comments will help you choose your next book to read. I know that articles and blogs I’ve stumbled across have helped guide my selection. If you want to support TheEGG directly and help me select the books that I will read this year then consider donating something from TheEGG wishlist.

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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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Evolution as a risk-averse investor

DanielBernoulliI don’t know about you, but most of my money is in my savings account and not in more volatile assets like property, bonds, or stocks. This is a consequence of either laziness to explore my options, or — the more comforting alternative — extreme risk-aversion. Although it would be nice to have a few thousand dollars more to my name, it would be devastating to have a few thousand dollars less. As such if I was given a lottery where I had a 50% chance of loosing $990 or a 50% chance of winning $1000 then I would probably choose not to play, even though there is an expected gain of $10; I am risk averse, the extra variance of the bet versus the certainty of maintaining my current holdings is not worth $10 for me. I most cases, so are most investors, although the degree of expected profit to variance trade-off differs between agents.

Daniel Bernoulli (8 February 1700 – 17 March 1782) was one of the mathematicians in the famous Bernoulli family of Basal, Switzerland, and contemporary and friend of Euler and Goldbach. He is probably most famous for Bernoulli’s principle in hydrodynamics that his hyper-competitive father Johann publishing in a book he pre-dated by ten years to try and claim credit. One of Daniel’s most productive times was working alongside Euler and Goldbach in the golden days (1724-1732) of the St. Petersburg Academy. It was in Russia that he developed his solution to the St. Petersburg paradox by introducing risk-aversion, and made his contribution to probability, finance, and — as we will see — evolution.
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Liquidity hoarding and systemic failure in the ecology of banks

As you might have guessed from my recent posts, I am cautious in trying to use mathematics to build insilications for predicting, profiting from, or controlling financial markets. However, I realize the wealth of data available on financial networks and interactions (compared to similar resources in ecology, for example) and the myriad of interesting questions about both economics and humans (and their institutions) more generally that understanding finance can answer. As such, I am more than happy to look at heuristics and other toy models in order to learn about financial systems. I am particularly interested in understanding the interplay between individual versus systemic risk because of analogies to social dilemmas in evolutionary game theory (and the related discussions of individual vs. inclusive vs. group fitness) and recently developed connections with modeling in ecology.

Three-month Libor-overnight Interest Swap based on data from Bloomberg and figure 1 of Domanski & Turner (2011). The vertical line marks 15 September 2008 -- the day Lehman Brothers filed for bankruptcy.

Three-month Libor-overnight Interest Swap based on data from Bloomberg and figure 1 of Domanski & Turner (2011). The vertical line marks 15 September 2008 — the day Lehman Brothers filed for bankruptcy.

A particular interesting phenomenon to understand is the sudden liquidity freeze during the recent financial crisis — interbank lending beyond very short maturities virtually disappeared, three-month Libor (a key benchmarks for interest rates on interbank loans) skyrocketed, and the world banking system ground to a halt. The proximate cause for this phase transition was the bankruptcy of Lehman Brothers — the fourth largest investment bank in the US — at 1:45 am on 15 September 2008, but the real culprit lay in build up of unchecked systemic risk (Ivashina & Scharfstein, 2010; Domanski & Turner, 2011; Gorton & Metrick, 2012). Since I am no economist, banker, or trader, the connections and simple mathematical models that Robert May has been advocating (e.g. May, Levin, & Sugihara (2008)) serve as my window into this foreign land. The idea of a good heuristic model is to cut away all non-essential features and try to capture the essence of the complicated phenomena needed for our insight. In this case, we need to keep around an idealized version of banks, their loan network, some external assets with which to trigger an initial failure, and a way to represent confidence. The question then becomes: under what conditions is the initial failure contained to one or a few banks, and when does it paralyze or — without intervention — destroy the whole financial system?
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Cooperation through useful delusions: quasi-magical thinking and subjective utility

GoBoardEconomists that take bounded rationality seriously treat their research like a chess game and follow the reductive approach: start with all the pieces — a fully rational agent — and kill/capture/remove pieces until the game ends, i.e. see what sort of restrictions can be placed on the agents to deviate from rationality and better reflect human behavior. Sometimes these restrictions can be linked to evolution, but usually the models are independent of evolutionary arguments. In contrast, evolutionary game theory has traditionally played Go and concerned itself with the simplest agents that are only capable of behaving according to a fixed strategy specified by their genes — no learning, no reasoning, no built in rationality. If egtheorists want to approximate human behavior then they have to play new stones and take a constructuve approach: start with genetically predetermined agents and build them up to better reflect the richness and variety of human (or even other animal) behaviors (McNamara, 2013). I’ve always preferred Go over chess, and so I am partial to the constructive approach toward rationality. I like to start with replicator dynamics and work my way up, add agency, perception and deception, ethnocentrism, or emotional profiles and general condition behavior.

Most recently, my colleagues and I have been interested in the relationship between evolution and learning, both individual and social. A key realization has been that evolution takes cues from an external reality, while learning is guided by a subjective utility, and there is no a priori reason for those two incentives to align. As such, we can have agents acting rationally on their genetically specified subjective perception of the objective game. To avoid making assumptions about how agents might deal with risk, we want them to know a probability that others will cooperate with them. However, this depends on the agent’s history and local environment, so each agent should learn these probabilities for itself. In our previous presentation of results we concentrated on the case where the agents were rational Bayesian learners, but we know that this is an assumption not justified by evolutionary models or observations of human behavior. Hence, in this post we will explore the possibility that agents can have learning peculiarities like quasi-magical thinking, and how these peculiarities can co-evolve with subjective utilities.
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Mathematics in finance and hiding lies in complexity

Sir Andrew Wiles

Sir Andrew Wiles

Mathematics has a deep and rich history, extending well beyond the 16th century start of the scientific revolution. Much like literature, mathematics has a timeless quality; although its trends wax and wane, no part of it becomes out-dated or wrong. What Diophantus of Alexandria wrote on solving algebraic equations in the 3rd century was still as true in the 16th, 17th, or today. In fact, it was in 1637 in the margins of Diophantus’ Arithmetica that Pierre de Fermat scribbled the statement of his Last Theorem. that the margin was too narrow to contain[1]. In modern notation it is probably one of the most famous Diophantine equations a^n + b^n = c^n with the assertion that it has no solutions for n > 2 and a,b,c as positive integers. A statement that almost anybody can understand, but one that is far from easy to prove or even approach[2].
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Bounded rationality: systematic mistakes and conflicting agents of mind

Before her mother convinced her to be a doctor, my mother was a ballerina. As a result, whenever I tried to blame some external factor for my failures, I was met with my mother’s favorite aphorism: a bad dancer’s shoes are always too tight.

“Ahh, another idiosyncratic story about the human side of research,” you note, “why so many?”

Partially these stories are to broaden TheEGG blog’s appeal, and to lull you into a false sense of security before overrunning you with mathematics. Partially it is a homage to the blogs that inspired me to write, such as Lipton and Regan’s “Godel’s Lost Letters and P = NP”. Mostly, however, it is to show that science — like everything else — is a human endeavour with human roots and subject to all the excitement, disappointments, insights, and biases that this entails. Although science is a human narrative, unlike the similar story of pseudoscience, she tries to overcome or recognize her biases when they hinder her development.


The self-serving bias has been particularily thorny in decision sciences. Humans, especially individuals with low self-esteem, tend to attribute their success to personal skill, while blaming their failures on external factors. As you can guess from my mother’s words, I struggle with this all the time. When I try to explain the importance of worst-case analysis, algorithmic thinking, or rigorous modeling to biologist and fail, my first instinct is to blame it on the structural differences between the biological and mathematical community, or biologists’ discomfort with mathematics. In reality, the blame is with my inability to articulate the merits of my stance, or provide strong evidence that I can offer any practical biological results. Even more depressing, I might be suffering from a case of interdisciplinitis and promoting a meritless idea while completely failing to connect to the central questions in biology. However, I must maintain my self-esteem, and even from my language here, you can tell that I am unwilling to fully entertain the latter possibility. Interestingly, this sort of bias can propagate from individual researchers into their theories.

One of the difficulties for biologists, economists, and other decision scientists has been coming to grips with observed irrationality in humans and other animals. Why wouldn’t there be a constant pressure toward more rational animals that maximize their fitness? Who is to blame for this irrational behavior? In line with the self-serving bias, it must be that crack in the sidewalk! Or maybe some other feature of the environment.
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Evolving useful delusions to promote cooperation

This joint work with Marcel Montrey and Thomas Shultz combines — to be consistent with the interdisciplinary theme of this symposium — ideas from biology, economics, a little bit of cognitive science, and the approach is through applied mathematics. This post is a transcript of a presentation I gave on March 27th and covers part of my presentation today at Swarmfest.
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