Jul 17, 2025
According to the central limit theorem, the sum of some i.i.d. samples is normally distributed in the limit of large sample size. This fact can be used to implement a multi-pass Gaussian blur filter, where the total number of passes is equal to the number of samples used in the averaging. Through this, we can also see a nice relation to the heat equation, which is not surprising since the heat kernel is a Gaussian function.
Jun 22, 2025
There is a gradually-accelerating buildup kickroll at 1:18 in the song Time to beat the odds by 影虎。. In order to know the details of this rhythm, I have to analyze the sample using Python.
Apr 11, 2025
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called θ. The limiting cases of a disk and a circle are discussed.
Mar 3, 2025
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
Jan 9, 2025
It is common for school courses to require students to submit their homework using GitHub. However, this is usually a bad idea for several reasons.