Analyzing the narrative of <cite>Kittens Game</cite>
Kittens Game is an incremental game that has very few narrative sentences presented in the game. However, it tells a very rich story in its own unique way through the interaction with the player.
Ulysses’ trip
Here we are at the awesome (awful) blog written by UlyssesZhan!
Latest posts
Text-based visual art in LaTeX
Using the verbatimbox package, one can include a text-based visual art in a figure in a document generated by LaTeX.
Ways of reducing mass rebuilds in Nix without changing Nix
One serious problem with Nix is the amount of mass rebuilds happening in Nixpkgs every time some package with many dependents gets an update. I thought about three ideas to reduce mass rebuilds: store path replacements, separating compiling and linking, and ditching check phases. Each of them has some degree of impracticality.
Determining the stabilizability of the abelian sandpile model
The abelian sandpile model is a cellular automaton where each cell is a sandpile that can topple to put grains on neighboring cells when having enough grains. It is stable if none of the sandpiles can topple. A natural question to ask is whether it can become stable eventually. In this article, I will show that one can determine the stabilizibility usiung integer linear programming for the abelian…
From Picard iteration to Feynman path integral
The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit.
Imperative programming in Nix language
Nix is a functional programming language primarily used for package management and system configuration. However, it may be interesting to emulate imperative programming constructs within Nix. This post explores how to achieve imperative-style programming in Nix, ipmlementing control flow, exception handling, and interactive IO.
Multi-pass Gaussian blur filter
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…
The buildup kickroll in <cite>Time to beat the odds</cite>
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. The main method is to do a short-time Fourier transform and to find the peaks in the high-frequency region of the spectrogram. A linear regression shows that the time intervals decay geometrically.
Eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition
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 \tht . The limiting cases of a disk and a circle are discussed.
The role of particle indistinguishability in statistical mechanics
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
Why it is a bad idea to use GitHub for submiting school homework
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, potentially including TOS violation, community degradation, and reliability.
How to use JavaScript in GitHub Actions without committing <code>node_modules</code>
I was creating my first GitHub Action. According to the official documentation, I should commit the node_modules to the repo or generate a script that bundles the whole node_modules if I want to create a JavaScript action. I think this is not good practice, so I try to find another way: manually managing the caches for the dependencies in node_modules .
Some understanding of Grassmann numbers out of intuition
I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question.
The notational convenience of imaginary time in the derivation of the metric in Poincaré coordinates
In general relativity, people usually choose one of the two major metric signatures. However, in certain cases, the imaginary time convention can be more convenient. Here is one of such cases: the derivation of the metric in Poincaré coordinates for the anti-de Sitter space.
The smallest wave packet in the lowest Landau level
The smallest wave packet in the lowest Landau level exists, and is a Gaussian wave packet. This turns out to be related to the coherent state of the harmonic oscillator.
Regularizing the partition function of a hydrogen atom
The partition function of a hydrogen atom diverges (only considering bound states). However, we can regularize it to get finite answers. Different regularizations give the same result. They largely agree with the physical arguments for the case of the hydrogen atom at room or cold temperature, but this should be considered a mere coincidence. The results from regularized partition functions cannot…
Letting people know when you are asleep
While I am asleep, the sleeping state is indicated on my Discord and GitHub user status. I achieve this by using MacroDroid.
Using nmcli to connect to eduroam in UCSB
Use nmcli to connect to eduroam in UCSB without using the configuration assistant tool provided by eduroam.
The duality between two plane trajectories related by a conformal map
The conformal map w ( z ) \fc wz transforms the trajectory with energy − B -B in potential U ( z ) ≔ A ∣ d w / d z ∣ 2 \fc Uz\ceq A\v{\d w/\d z}^2 into the trajectory with energy − A -A in potential V ( w ) ≔ B ∣ d z / d w ∣ 2 \fc Vw\ceq B\v{\d z/\d w}^2 . I will prove this beautiful result and show some implications of it.
Embed the latest Mastodon post in my website
I show the latest Mastodon post in my website hosted on GitHub Pages, and it does not require JavaScript on the client side. How do I do that?