Our new paper examining the dynamics of an asymmetric Hawk-Dove game was published in The International Journal of Differential Equations:
As usual, Phil Jackson made another interesting tweet today:
And, as usual received many criticisms from “Experts”, who just looked at the raw numbers from each players, and saw that there is just no way such a statement is justified, but it is not that simple!
When you compare two players (or two objects) who have very different data feature values, it is not that they can’t be compared, you must effectively normalize the data somehow to make the sets comparable.
In this case, I used the data from Basketball-Reference.com to compare Chris Jackson’s 6 seasons in Denver to Stephen Curry’s last 6 seasons (including this one) and took into account 45 different statistical measures, and came up with the following correlation matrix/similarity matrix plot:
What would be of interest in an analysis like this is to examine the diagonal of this matrix, which offers a direct comparison between the two players:
Therefore, it is true that Stephen Curry and Chris Jackson do in fact share many strong similarities!
A short post by me today. I wanted to look at the which states are important in winning the national election. Looking at the last 14 presidential elections, I generated the following correlation plot:
For those not familiar with how correlation plots work, the number bar on the right-hand-side of the graph indicates the correlation between a state on the left side with a state at the top, with the last row and column respectively indicating the national presidential election winner. Dark blue circles representing a correlation close to 1, indicate a strong relationship between the two variables, while orange-to-red circles representing a correlation close to -1 indicate a strong anti-correlation between the two variables, while almost white circles indicate no correlation between the two variables.
For example, one can see there is a very strong correlation between who wins Nevada and the winner of the national election. Indeed, Nevada has picked the last 13 of 14 U.S. Presidents. Darker blue circles indicate a strong correlation, while lighter orange-red circles indicate a weak correlation. This also shows the correlation between winning states. For example, from the plot above, candidates who win Alabama have a good chance of winning Mississippi or Wyoming, but virtually no chance of winning California.
This could serve as a potential guide in determining which states are extremely important to win during the election season!
A recent lecture and a series of interviews has been posted online where cosmologist George F.R. Ellis discusses the issue of fine-tuning in biology at considerable length and in considerable detail. Of course, the larger theme here is that to discuss and understand things like Darwinian evolution properly, one needs to have an understanding of the underlying physics, as it is laws of physics that allow life to emerge and for Darwinian evolution to occur in the first place. Here are the lectures:
A big part of my research involves dynamical systems theory. A lot of people don’t know what this is, at least, they don’t have a very good idea. It has not helped that the vast majority of Canadian university physics programs have deemphasized classical mechanics and differential equations, but that is an another story!
Anyways, here are some notes describing what they are and how they work.
Since I expect the concept of gravitational waves to once become very popular in the next few days, I wrote some quick notes on them, I.e., where they come from. They are handwritten, as I didn’t have time to LaTeX them, but, hopefully, they’ll be useful to interested readers!
Also note that, gravitational waves are not necessarily evidence of inflation. I wrote a paper a few years ago, describing a anisotropic early universe that had an epoch of plane waves that isotropized to our present-day universe. It can be seen here. It was subsequently published in Physical Review D.
Anyways, here are the notes (Interested readers should see the classic texts by Misner, Thorne, Wheeler, Landau and Lifshitz, or Stephani for more details).
One of my earliest works was deriving equations which themselves were forms of Einstein’s field equations that described the state of the early universe, which may have had dominant viscous effects. I was delighted to learn that these equations were published in Springer’s Handbook of Spacetime Cosmology textbook.
Here is a snapshot of the textbook page citing these equations: