Everyone by now knows about this paper I wrote a few months ago: http://arxiv.org/abs/1604.05266 Using data science / machine learning methodologies, it basically showed that the most important factors in characterizing a team’s playoff eligibility are the opponent field goal percentage and the opponent points per game. This seems to suggest that defensive factors as […]
In a previous post, I showed how given random positions of 5 players on the court that they could “fill” the triangle. The main geometric constraint is that 5 players can form 3 triangles on the court, and that due to spacing requirements, these triangles are “optimal” if they are equilateral triangles. Given that we […]
Most people when talking about cosmology typically talk about the universe in one context, that is, as a particular solution to the Einstein field equations. Part of my research in mathematical cosmology is to try to determine whether the present-day universe which we observe to be very close to spatially flat and homogeneous, and very […]
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 […]
Here is a really quick derivation of the Cauchy-Riemann equations of complex analysis. Consider a function of a complex variable, , where , such that: , where and are real-valued functions. An analytic function is one that is expressible as a power series in . That is, . Then, . We formally differentiate this equation […]
As I write this, Cleveland just won the series 4-3. What was behind each team’s wins and losses in this series? First, Golden State: A correlation plot of their per game predictor variables versus the binary win/loss outcome is as follows: The key information is in the last column of this matrix: Evidently, the most […]
I’ve been fascinated by the triangle offense for a long time. I think it is a beautiful way to play basketball, and the right way to play basketball, in the half-court, a “system-based” way to play. For those of you that are interested, I highly recommend Tex Winter’s classic book on the topic. There is […]
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 […]
Using my live tracking app combined with the relevant factors based on this previous work, here is my breakdown of what contributed to the Warriors win in Game 1 of the NBA Finals. First, here is the time series graph of several predictor variables: Breaking this down a bit further, we have: Computing the correlations, […]
Here is the collection of time series of relevant predictor variables captured live during Game 7 of the Western Conference Finals between The Oklahoma City Thunder and The Golden State Warriors: Another video animation: https://twitter.com/dr_ikjyotsinghk/status/737694089437716480 Many commentators are making a point to mention how many three point shots The Warriors made, suggesting that that was […]
Relativity Digest 