Ulysses' trip

Latest post

A hand holding a Wacom pen with pen grip.

Oct 29, 2025, 23:18:50

Ever since I installed the pen holder grip on my #Wacom pen, the pain in my right thumb disappeared. Very nice.

Articles

Sep 8, 2023
I created Sunniesnow, a rhythm game similar to Lyrica

In order to build a better player community for the rhythm game Lyrica, I created a new rhythm game called Sunniesnow. Learn more about Sunniesnow by joining our Discord server.
- Categories: update
- Tags: update, rhythm game, web
May 9, 2023
The distribution when indistinguishable balls are put into boxes

Suppose there are $n$ distinguishable boxes and $k$ indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains $m$ balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit $n,k\to\infty$ with $k/n$ fixed, the distribution tends to be a geometric distribution.
- Categories: math
- Tags: probability, combinatorics, ruby
May 7, 2023
Labeled break, next, and redo in Ruby

Many languages support breaking out of nested loops, such as Perl, Java, JavaScript, C#, etc. Languages that have goto can also do this easily. However, in most other languages, it is not easy to break out of nested loops. I want to introduce a way to do this in Ruby.
- Categories: programming
- Tags: meta programming, ruby
May 1, 2023
Free trade (single good case)

I set up a simple model to determine the production and consumption in free trade between nations.
- Categories: economics
- Tags: global economy, from zhihu
May 1, 2023
A measure-theoretic formulation of statistical ensembles (part 2)

For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.
- Categories: physics
- Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper
Apr 5, 2023
Summarizing my methods for studying

I summarized my methods for studying. This can be served as a guide for those who have started learning math and science.
- Categories: misc
- Tags: chinese, school
Mar 30, 2023
A measure-theoretic formulation of statistical ensembles (part 1)

For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.
- Categories: physics
- Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper
Mar 25, 2023
The core of a voting system is the intersection of Pareto sets

There is a very neat relation between the core (the set of proposals that defeats every proposal) of a voting system and the Pareto sets of the voters. Suppose there is a voting system of quota $q$ , then the core is the intersection of all such sets: the Pareto set of $q$ of the voters.
- Categories: economics
- Tags: voting system, preference relation, pareto efficiency
Feb 6, 2023
Relationship between the Gini coefficient and the variance

Both the Gini coefficient and the variance are measures of statistical dispersion. We are then motivated to find the relationship between them. It turns out that there is a neat mathematical relationship between them.
- Categories: economics
- Tags: from zhihu, calculus, probability
Feb 4, 2023
Distinguishing all the letters in handwritten math/physics notes

Personally, I have the demand of handwriting math/physics notes, but an annoying fact about this is that I usually cannot distinguish every letter that may be possibly used well enough. In this article, I will try to settle this problem.
- Categories: misc
- Tags: from zhihu, font, tex, handwriting, long paper