# Tag: science

## Attempts at a General Einstein Equation for an Arbitrary FLRW Cosmology

I tried to derive a general Einstein field equation for an arbitrary FLRW cosmology. That is, one that can handle any of the possible spatial curvatures: hyperbolic, spherical, or flat. Deriving the equation was easy, solving it was not! It ends up being a nonlinear, second-order ODE, with singularities at a=0, which turns out to be the Big Bang singularity, which obviously is of physical significance. Anyways, here’s a log of my notebook, showing the attempts. More to follow!

## Game 2 of CLE vs GSW Breakdown

As usual, here is the post-game breakdown of Game 2 of the NBA Finals between Cleveland and Golden State. Using my live-tracking app to track the relevant factors (as explained in previous posts) here are the live-captured time series:

Computing the correlations between each time series above and the Golden State Warriors point difference, we obtain:

One sees once again that the most relevant factors to GSW’s point difference in the game was CLE’s personal fouls during the game, GSW’s personal fouls during the game, and not far behind, GSW 3-point percentage during the game. What is interesting is that one can see the importance of these variables played out in real time matching the two graphs above.

In fact, looking at the personal fouls vs. GSW point difference in real time (essentially taking a subset of the time series graph above), we obtain:

## New paper published on cosmological singularities

My new paper has now been published in Annalen der Physik, which is a great honour, because 100 years ago, Einstein’s General Theory of Relativity was also published in the same journal.

This paper describes a method by which one is able to determine whether a given spatially flat cosmological model produces finite-time singularities, and also gives some examples of interesting cosmological model configurations.

The paper can be accessed by clicking the image below:

The preprint can be accessed here on the arXiv.

## Making a Cosmological Model

What goes into making a cosmological model? Here is a presentation (that was part of my Ph.D. dissertation) that I have reproduced and embedded here to describe what actually goes into the making of a cosmological model. After describing some general properties, I describe specifically a early-universe model that contains a viscous fluid and a magnetic field.

The background mathematics can be found in this old presentation of mine here:

## Pi Day and Einstein

## Stephen Curry and Mahmoud Abdul-Rauf?

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:

Dark blue circles indicate a strong correlation, while dark red circles indicate a weak correlation between two sets of features.

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:

One can see that there are many features that have strong correlation coefficients.

Therefore, it is true that Stephen Curry and Chris Jackson do in fact share many strong similarities!