Mathematics and Statistics

Applied Mathematics, Geometry and Topology, Analysis, Mathematical Modeling, Statistical Modeling, Game Theory, Operations, Biostatistics, Epidemiology, GIS, Image Processing

Just A Blink

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
When you’re in school, it seems like everything you’re learning is super important. You might even get the impression that you will definitely use what you learn forever. Here’s the deal: that’s almost certainly not true. No matter how sophisticated the material you’re learning is, there’s a decent chance that the only time you will “apply” it in your life is during your studies. After that, you might get a career in a totally different…

Continue reading

Mathematics for Enjoyment

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
The title of this post may not be words you are used to seeing together. Sure, you might think that mathematics is powerful, but does anyone actually do mathematics just because they enjoy it? If you ask someone other than a mathematician, you might expect the answer to be “no”. If you ask someone if they enjoy mathematics, there tend to be two possible answers that are given. The least common answer is, “Yes, I’m…

Continue reading

Fitness distributions versus fitness as a summary statistic: algorithmic Darwinism and supply-driven evolution

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
For simplicity, especially in the fitness landscape literature, fitness is often treated as a scalar — usually a real number. If our fitness landscape is on genotypes then each genotype has an associated scalar value of fitness. If our fitness landscape is on phenotypes then each phenotype has an associated scalar value of fitness. But this is a little strange. After all, two organisms with the same genotype or phenotype don’t necessarily have the same…

Continue reading

Not Everyone Thinks The Same

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
It’s tempting to imagine that if you see something, everyone else does too. After all, in our interconnected world, we tend to be reminded every day just how good other people are. This makes it easy to imagine that any supposed “insight” you may have has already been thought of before. Without the right mindset, this can create a situation in which you do almost no creative work, since you’re worried about wasting time on…

Continue reading

End of the Treadmill

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
Staying there isn’t easy. It’s not that the back of the treadmill is any different from the front. It’s the same spinning belt, going the same speed as the front. And yet, there’s something else about the back of the treadmill. The difference is psychological, because you know that you’re almost out of room. One wrong or slow step, and you will come crashing down. Suffice to say, the end of the treadmill is not…

Continue reading

Quick introduction: Generalizing the NK-model of fitness landscapes

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
As regular readers of TheEGG know, I’ve been interested in fitness landscapes for many years. At their most basic, a fitness landscape is an almost unworkably vague idea: it is just a mapping from some description of organisms (usually a string corresponding to a genotype or phenotype) to fitness, alongside some notion of locality — i.e. some descriptions being closer to each other than to some other descriptions. Usually, fitness landscapes are studied over combinatorially…

Continue reading

Derailing an Explanation

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
I think a lot about the process of learning, both in my experience and when I am teaching others. I find learning to be a fascinating topic, because it’s what lets us improve and become better at a variety of tasks, skills, and subjects. I’m also interested in the difficulties that are present when learning. In particular, are there things we should do or avoid while trying to learn? One of the most frustrating things…

Continue reading

Equations as Constraints

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
Can you construct a right cone that has a height of 4, a radius of 3, and a slant height of 6? This question has an easy answer, but only if you know what to look for. The reason is that the question is posed in a way that requires a “yes” or “no” answer. If your answer is “yes”, then you have to prove it by giving me a cone that has the desired…

Continue reading

Quick introduction: Evolutionary game assay in Python

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
It’s been a while since I’ve shared or discussed code on TheEGG. So to avoid always being too vague and theoretical, I want to use this post to explain how one would write some Python code to measure evolutionary games. This will be an annotated sketch of the game assay from our recent work on measuring evolutionary games in non-small cell lung cancer (Kaznatcheev et al., 2019). The motivation for this post came about a…

Continue reading

Going After The Average

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
When making work that’s important to you, it’s tempting to focus on improving your best work. After all, when you think of your work, that’s what first comes to mind. (You don’t think about the mediocre work.) Therefore, it makes sense to focus on that. By definition, this should be scarce. It’s not that you decide to sometimes do great work. Rather, it’s a simple consequence of looking at many pieces. Some will jump out…

Continue reading