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Tuorui "v1ncent19" Peng

En voyage dans l'espace de Hilbert.

Blog

Study notes and half-formed ideas alongside recipes and the occasional travel log. Posts are indexed here in the language they were written in.

37Posts
3Categories
Feb 2025Latest
Showing 37 of 37 posts
Cuisine·≈ 2 min read

芝士焗饭

好久没有更新美食栏目了，事实上在刚刚过去的冬天还是扩展了很多菜谱的。本次的内容是芝士焗饭，具体来说是番茄牛肉芝士焗饭，提供了一个大致的操作手法，我觉得应该也会能适用于其他口味的焗饭。

中文Read
Documentation·≈ 12 min read

日本語

事实上日语中虽然有大量的汉字词，但事实上写法并不完全相同，导致其实直接在某个文本环境中键入时其实很多汉字打出的是中文的字形。有些字尚且还是“本质上不同的字”（占据不同的编码），有些则是根本是同一个编码，只是在中文环境/日文环境下显示的字形不同。下面是一些具体的例子：

中文Read
Cuisine·≈ 2 min read

Clam Chowder

自从暑假去了趟Boston玩之后一直十分回味新英格兰奶油蛤蜊汤，xhs攻略了一波发现并不是很困难，自己复刻了几次感觉味道已经比较接近良好了。

中文Read
Cuisine·≈ 2 min read

蛋炒饭

按道理说炒饭这个东西应该有很多种炒法，而大家都会认为自己的炒法是最正宗的（笑）。这个假期我在家尝试了若干次，在此提供一下实验成果和相关的炒饭哲学。

中文Read
Cuisine·≈ 10 min read

France 2024 巴黎餐馆简评

2024年春假期间去了趟西欧，品鉴了不少当地餐馆，主要在巴黎，部分在周边城市。这里简评一下吃过的饭馆。

中文Read
Cuisine·≈ 3 min read

青椒炒鸡

我最开始想做这个的原因是想起来上次去 88mart 买的青椒和上周去缺德舅买的甜椒都要坏了，所以不得已想想办法一起解决了。我也不会做川湘菜啊，我只会吃，只能凭感觉做做这样子（紫四呜呜我的紫四，想念华子的食堂）。

中文Read
Cuisine·≈ 1 min read

广式炖牛腩

我也不知道是不是什么所谓的“广式炖牛腩”啊，我只是感觉我妈自古以来都是这么做的，偷师了一下。

中文Read
Cuisine·≈ 1 min read

Mousse au Chocolat

还记得以前每次去开会都逮着茶歇小蛋糕猛吃，现在能自己做乐坏我了。

中文Read
Cuisine·≈ 4 min read

豉汁排骨

完全成功，几乎符合我记忆中豉汁排骨的味道。

中文Read
Cuisine·≈ 2 min read

Ragù alla Bolognese

My favourite sauce for pasta! 以前在家做的时候总感觉酱的口感不对劲，自己来这边薅了两次能做出来了，感觉还不错。

中文Read
Cuisine·≈ 1 min read

Carbonara

经典的蛋黄意面，有点难搞，我经常把蛋莫名其妙就弄熟了。

中文Read
Cuisine·≈ 2 min read

辛拉面配香煎鸡排

理论上说大家把方便面定义为不健康食品，但是仔细一想稍微搭配一下就可以包含肉蛋蔬菜碳水，而且还很好吃，so why not?

中文Read
Documentation·≈ 6 min read

LaTeX VSCode Snippets

My VSCode Snippet Settings (the json file) for LaTeX. The Snippets allow me to quickly input some common LaTeX commands.

EnglishRead
Cuisine·≈ 1 min read

Steak

一开始我买了条温针，后面煎多了按按就知道熟度了。

中文Read
Cuisine·≈ 2 min read

奶汁烩菜

我还挺喜欢奶汁烩菜的，但是它真的有点腻，腻得不行。我的一位好友说他们学校食堂全是奶汁烩菜，吃的他腻得反胃（乐）。

中文Read
Mathematics & Statistics·≈ 4 min read

RKHS in a Dual Space delta function Perspective

Recently I was introduced a new point of view of RKHS by my advisor. I think it's quite interesting and worth sharing. It provides a new understanding of how RKHS is constructed and, it's

中文Read
Documentation·≈ 2 min read

Other Activities

I was awarded five-star Zijing volunteer @ Tsinghua Univ in 2023.

EnglishRead
Documentation·≈ 4 min read

Joke Collection

工程师的罐头打开了，纸跟笔没有动，但墙上有很多印。原来工程师把罐头丢到墙上，试验了很多次，终于找到了合适的角度磕开了罐头。 物理学家的罐头也被打开了，他的纸上密密麻麻地满了公式和数字，但墙上只有一个印。原来物理学家经过计算找到了完美的角度，一下子就磕开了罐头。

中文Read
Documentation·≈ 2 min read

Λέξεις και Φράσεις

Here are the words and phrases I learnt when attending a second foreign language course of Greek.

EnglishRead
Mathematics & Statistics·≈ 2 min read

Brownian Bridge and Basel Problem

This blog originates from a question in the final exam of Applied Stochastic Process this semester. The question focused on the Karhunen-Loève expansion of Brownian Bridge. Soon I was surprised to

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Mathematics & Statistics·≈ 2 min read

Derivation of Poisson Distribution

Here I record two ways to derive Poisson distribution. A Poisson process is the number of events {N(t),t≥0}\{N(t),t\geq 0\} in some given time [0,t][0,t], with the following property:

EnglishRead
Mathematics & Statistics·≈ 10 min read

Reading Notes of Replica Symmetric Breaking

Here is my reading note for the book 'Statistical Physics of Spin Glasses and Information Processing: An Introduction' by Hidetoshi Nishimori. I am still not quite clear about this field so please

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Documentation·≈ 1 min read

R Package File

The file is written in package.r and called by command source('package.r')

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Mathematics & Statistics·≈ 2 min read

Variance of Odds Ratio in Contingency Table

Odds ratio of the contingency table below is an important statistics

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Documentation·≈ 6 min read

LaTeX Head File

Here I document two LaTeX head files I frequently use. By replacing all CAPITALIZED CONTENTS to what you need and compile with xelatex you could obtain a well pre-designed LaTeX document. For help

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Mathematics & Statistics·≈ 1 min read

Best Linear Estimator

Theoretically best linear estimator is crucial in definition of Partial Autocorrelation in time series. It provides an estimation with correlated variable considered.

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Mathematics & Statistics·≈ 6 min read

Theory of Reproducing Kernel Hilbert Space (RKHS) and Application

Before the rise of (deep) neural network, Kernel trick is an important approach used in feature engineering to 'define similarity' and thus is powerful in extracting feature. Based on Reproducing

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Mathematics & Statistics·≈ 2 min read

Basic Constrained Optimize Theory

For optimize problem in convex set X\mathcal{X}

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Mathematics & Statistics·≈ 3 min read

Cochran Theorem for Variance Decomposition

Cochran's Theorem is the basis of variance composition in ANOVA. Here is a proof that could be understood intuitively, and an linear regression example of how Cochran's thm. is used in ANOVA.

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Mathematics & Statistics·≈ 5 min read

Expectation-Maximization Algorithm in Gaussian Mixture Model

Expectation-Maximization is used in MLE to estimate some model parameter θ\theta for model {xi}\{x_i\} i.i.d. ∼f(x∣θ)\sim f(x\vert \theta ).

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Mathematics & Statistics·≈ 1 min read

Convergence Order 1.618 of Secant Interpolation Rooting

For some iteration algorithm x(t+1)=g(x(t))x^{(t+1)}=g\left( x^{(t)} \right) with final solution denoted x∗x^*, error ε(t):=x(t)−x∗\varepsilon ^{(t)}:=x^{(t)}-x^*, its convergence order α\alpha and converngence rate cc:

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Mathematics & Statistics·≈ 2 min read

Positive-Definition of Diagonal Dominant Matrix

Positive semi-definition of Diagonal Dominant Matrix (with non-negative diagonal) is an important property in numeric linear algebra. Here I record two prooves, one following the idea of Gershgorin

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Mathematics & Statistics·≈ 1 min read

Box-Cox Transformation

Usually transformation to numeric data D={Xi,Yi}i=1n\mathcal{D}=\{X_i,Y_i\}_{i=1}^n is necessary in regression analysis, usually to stablize variance. Box-Cox is the most important method.

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Mathematics & Statistics·≈ 3 min read

Residuals for Influential Diagnosis in Linear Regression

In linear regression, influential diagnosis is important to obtain better model fit and performance. Usually such diagnosis is based on residuals. Here are some important residuals that help locate

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Mathematics & Statistics·≈ 2 min read

Liénard–Wiechert Potential

In dealing with electro-magnetic field of moving charged particle qq at r⃗0(t)\vec{r}_0(t) with velocity v⃗0(t)\vec{v}_0(t):

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Mathematics & Statistics·≈ 2 min read

Proof Two Properties of Log-Likelihood

Given data D={x}i=1N\mathcal{D}=\{x\}_{i=1}^N and statistics model X∼F={f(x;θ):θ∈Θ}X\sim \mathscr{F} = \{ f(x;\theta ):\theta \in\Theta \}. Maximum Likelihood Estimation (MLE) is an important approach to estimation of θ\theta

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Mathematics & Statistics·≈ 1 min read

Indepency between Xˉ\bar{X} and S2S^2

Data is given as D={Xi}i=1n\mathcal{D}=\{X_i\}_{i=1}^n, with XiX_i i.i.d. ∼N(μ,σ2)\sim N(\mu ,\sigma ^2). Two crucial statistics are mean value Xˉ\bar{X} and variance SX2S^2_X:

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