A beautiful mind.

Goodbye John Nash

As most of you know (and I re-posted a couple of days ago) John Forbes Nash ceased to be. A tragic traffic accident means that he died at 86 and not of old age.

Nash was awarded a Nobel prize in economics in 1994 and was just returning from a trip to Oslo to receive the Abel prize for his work on non-linear partial differential equations. Those qualities would be enough to make him one of the most famous mathematicians in the world but most of us remember him from the movie A beautiful mind.

Despite of all these accolades and his work on PDEs, mathematically Nash will be remembered for the Nash equilibrium. This is a key concept in Game Theory as it allows us to figure out a set of strategies such that the players involved in the game will not have any incentive to change them. This can lead to some paradoxical outcomes like in prisoners dilemma where the Nash equilibrium is the one in which both players cheat each other resulting in a suboptimal outcome for both of them.

For people following this blog the interesting part about Nash equilibrium is that the equivalent in Evolutionary GT, the Evolutionary Stable Strategy, can be used to understand if a given mutation could spread in a population in equilibrium. The canonical example is the Hawk-Dove game, which does not look anything like this:


With this game you assume a population in some sort of equilibrium and study whether in that population a mutation conferring aggressiveness (hawks) or meekness (doves) could emerge and spread. Assuming that dovish individuals do not pursue their goals aggressively but also are not likely to get into dangerous fights then the ESS will show that any given population will have not one type or the other but a mixture of both types of behaviours.

Cancers are very dynamic but, although not in every case, they can take decades to grow and acquire mutations that expand in a clonal fashion. If we know the key driver phenotypes (and we can make educated guesses about that), we can see what potential phenotype will emerge next and how will it drive tumour heterogeneity (which can be correlated to resistance to treatment). Also we can design novel treatments that will impact the rules of the game instead of trying to kill tumour cells indiscriminately.

So thanks Dr. Nash and rest in equilibrium.


Are algorithms too complex?

It is no news that algorithms and mathematical models have become a force that shapes (and sometimes drives) our choices these days. From the results from your favourite search engine, the models that are responsible for most of the transactions in the stock markets, the pricing in airlines and uber or our suggestions at Netflix or Amazon, algorithms are everywhere.

If you like TED talks and you like podcasts then, first check Pint of Science. Our podcasts are more about science and less about entertainment and design (maybe more T and little ED). But if you have spare time then check the TED podcasts at NPR. One of the more recent ones is called Solve for X and includes excerpts of a talk by Kevin Slavin warning us about the increase in the complexity of the algorithms that shape (and will soon rule) our lives.


And here is the thing: as a computer scientist and mathematical modeller I believe in the potential that these algorithms have to change our lives for the better. But I am also quite concerned about increasing the complexity of certain algorithms when they are effectively black boxes. As an example of this problem, Slavin refers to a recent and massive market crash at the NYSE that was caused by one of these algorithms. Having a complex algorithm in charge of, say, Netflix recommendations is not a big deal: it is not the end of the world if some of us get recommended Wolf of Wall Street when we would rather watch Margin Call for instance. It is a different matter when an algorithm can make billions of dollars disappear from the stock market or, closer to home, determine (or guide) the clinical strategy for a patient at Moffitt. In those situations we need algorithms and models whose complexity can be understood so that when something wrong happens (as it is bound to happen) then we can learn and adapt the algorithm accordingly. Modelling is not about capturing all the complexity of a system (be it the stock market, our your taste in movies and music) but about having a framework in which to place all the key variables. This allows us to get not only predictions but also understanding which is a lot more powerful.


The similarities between prostate and breast cancer

Mathematical biologists deal with spherical cows, that is, we look for patterns in nature. That means abstracting some details so that we can concentrate our attention on the key features that are relevant to our question.

That is why, as a mathematical modeller working on prostate cancer I was always interested in breast cancer.  The first is one of the most common cancers in men whereas the latter is one of the most common in women (although men can also have breast cancer). Both are cancers that initiate in the epithelial cells that form the glands that characterize prostate and breast. Both are usually quite treatable and most patients survive. When things take a wrong turn, both prostate and breast cancer usually metastasise to the bone. Surely there are substantial differences between the two cancers but there are also enough similarities that I was not too surprised with recent findings showing that genes that are usually mutated in breast cancer are found to be mutated in prostate cancer too (a fifth of prostate cancer patients have mutations in BRCA1 and 2). The study has been labeled the Rosetta stone of prostate cancer. One of the take-home messages is that 90% of metastatic tumours are dominated by cells with mutations for which we have treatment. This is a rather optimistic point of view though, as we know that these metastases are heterogeneous and that thus, emergence is likely to emerge.

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Del Desayuno a la pinta: Ya llega Pint Of Science

For those of you that can read in Spanish, here is a post about the sister organization to Pint of Science in Spain.

Desayuno con fotones

Ya llega Pint of Science, un festival de la ciencia que se celebrará simultáneamente la semana que viene (días 18, 19 y 20 de Mayo) en bares de 8 ciudades de España, y al mismo tiempo en 50 ciudades del mundo. Durante tres días consecutivos, científicos de diferentes laboratorios y Universidades hablarán sobre su trabajo en un ambiente distendido y agradable, propicio para establecer una comunicación de tú a tú entre los investigadores y la gente.

Pint of Science surgió en 2012, cuando dos científicos del Imperial College de Londres, Michael Motskin y Praveen Paul, invitaron a pacientes de Párkinson y de otras enfermedades neurodegenerativas a visitar los laboratorios donde investigaban estas afecciones. La experiencia fue todo un éxito para ambas partes, y entonces pensaron que si la gente estaba interesada en ir a los laboratorios para ver lo que los científicos hacen, ¿por qué no invitar a los…

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