How to derive the volume of an n-dimensional hypersphere (the long version) Dr. Quark 2012-02-17 | I was trying to get a better intuition for "the curse of dimensionality" in machine learning, and needed to know the volume of a unit n-sphere -- so I remembered how to derive it. This derivation is quick, easy, and cool, and I want to share it with the world :) This is the detailed version of my 3-minute derivation (http://youtu.be/QkMn_5QpsX8)
Integrating the Dirichlet probability distribution, for great justice Dr. Quark 2012-05-27 | This video show a neat trick that allows to take the integrals that come up in Bayesian inference when Dirichlet priors are used.
The Fourier transform of Salsa Dr. Quark 2012-03-16 | Following up on my Fourier transform of Lindy Hop videos (check them out at http://www.youtube.com/watch?v=2P2WZZvpogM), here are the acceleration/angular velocity plots for Salsa, featuring Andrea Vacca and Jenny Chen. Notice that in contrast to swing, Salsa steps do not register on the frequency plot! This suggests that the basic motion of Salsa is smoother, and that the hips/upper body are in a sense isolated from the rhythm of the steps. The frequency spike at 25 bpm likely corresponds to the frequency of 8-counts in a 200 bpm song. Notice that the gyroscope data for the lead is not very clean and cross-couples to acceleration. In addition, the video stream drifts behind the data stream by 1.2 seconds towards the end of the video. We hope to have better data in the future :)
Swing dancing and Fourier transforms, Part II Dr. Quark 2012-03-08 | Lindy hop + accelerometer + gyroscope data == pure fun. Lead's traces are blue, follow's traces are red. Top plot: acceleration (magnitude) over the last 8 seconds of the dance. Middle, (left): frequency spectrum of the 8-second acceleration window; middle (right): frequency spectrum of all the data up to this point in the dance. Bottom: angular velocity around the vertical axis (available for the follow only). Positive values correspond to counterclockwise rotation, negative values give clockwise rotation.Check out http://dnquark.com/blog/lindy-science for more!
Swing dancing and Fourier transforms Dr. Quark 2012-03-02 | Pulse and bounce are key characteristics of lindy hop movement. But how do you know that you are pulsing enough? Easy: measure acceleration and take the Fourier transform. In these diagrams, the top trace gives the magnitude of acceleration, the middle is the Fourier transform of the last 8 seconds of acceleration (what you see in the top trace), and the bottom trace is the transform of all the data accumulated up to that point. The horizontal scale on the frequency plots is beats per minute, and the big peak is at 161 bpm, the tempo of the song. Thanks to Jennifer for dancing, Tao for filming, and Becca for DJing! Stay tuned for more lindy hop science! For more info on the data collection and analysis visit http://dnquark.com/blog/lindy-science
How to derive the volume of an n-dimensional hypersphere in 3 minutes. Dr. Quark 2012-02-17 | I was trying to get a better intuition for "the curse of dimensionality" in machine learning, and needed to know the volume of a unit n-sphere -- so I remembered how to derive it. This derivation is quick, easy, and cool, and I want to share it with the world :) There is a long version of this derivation where I fill in the details that didn't fit into the 3 minute time frame, you can see it at http://youtu.be/eEJtMFdkzzU.
Hyperbolic metamaterials explained in 5 minutes Dr. Quark 2012-01-18 | Hyperbolic metamaterials are an exciting recent development in the field of nanophotonics. They combine the properties of metals and dielectrics -- an idea so crazy that it just might work!
