Hello everyone! Welcome to my blog! I’ll be sharing my journey as a PhD student at the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences.

This blog isn’t just about my math research – I’ll also explore topics like economics, finance, and anything else that sparks my interest.

All the cover images on this blog are taken by myself.

If you have any questions or just want to reach out, feel free to email me at wangtuo1020@outlook.com.

The cover image of this article was taken at Sydney Opera House, Sydney, Australia.

Motivation

Let $(X,d)$ be a metric space, $F, F_n: X\to \overline{\mathbb{R}}, n=1,2,\cdots$ be functionals, suppose that $x_n\in X$ minimizes $F_n$ for each $n=1,2,\cdots$, does $\lim\limits_{n\to\infty} x_n$ (if it exists) minimize any functional $F$? And in what sense does $F_n$ converge to $F$ ensure the minimizer of $F_n$ converges to minimizer of $F$?

This is the talk I presented in the Optimization Group Seminar, titled: An Introduction to Optimization over the Space of Probability Measures: From Sampling to Wasserstein Gradient Flow.

Dual Drivers of the Gold and Silver Market

Currency-Driven Factors

The trends in the gold and silver markets are influenced by two major factors: monetary policy and geopolitical risks.

Introduction

Markov Chain

Let $(\Omega,\mathcal{F})$ be a measurable space, $P:\Omega\times \mathcal{F}\to [0,1]$ be a transition kernel, that is,

• for every $x\in \Omega$, $P(x,\cdot)$ is a probability measure on $\mathcal{F}$;
• for every $A\in \mathcal{F}$, $x\mapsto P(x,A)$ is measurable.

In generative modeling, we are given a collection of training samples $\{x_i\}_{i=1}^N$ and wish to generate new samples from the underlying target distribution $\pi$. There are already many established approaches to this problem, including likelihood-based methods, implicit generative models such as GANs, and score-based diffusion models. More recently, the flow matching framework has emerged as another powerful paradigm. In what follows, we introduce the basic ideas of flow matching and explain how works.

This is the talk I presented in the group seminar, titled: Sampling and Diffusion Model.

This is the talk I presented in the group seminar, titled: Analogy between Sampling and Optimization.