## 汤迎

### Path Integral Approach to Study Stochastic Process: Geometric Brownian Motion

We study the geometric Brownian motion by path integral approach. We find that in this stochastic dynamical process, integral Ito’s formula should be applied to calculate the action. Integral Ito’s formula provides the normalized factor in OU process. Thus, path integral is naturally normalized through our consistent treatment.

## 毛晓军

### Glasso, CLIME and some neuronal results

1：介绍Glasso问题及其算法
2：介绍CLIME算法并且比较它跟Glasso的算法的好坏
3：介绍IF model及其神经网络的稀疏性

## 刘子卓

### Free-carrier absorption in quantum wells at mid-infrared and terahertz wavelengths

In this report, I will present my calculation results about the electron-photon Hamiltonians and the transition probabilities.

## 洪翔

### Solving modified Helmholtz equations using random walk method

A Intruduction to solving modified Helmholtz equation with random walk method based on Feynmanp-Kac formula, and using an acceleration method, walk on sphere, to reduce time cost for simulating random walk.

## 韩崔泽

### Sum of Squares Thresholding(SSTHD): asymptotic properties, random simulation results and application to real data

1.Briefly talk about the rigorous proof of SSTHD’s convergence rate;
2.Compare the result of random simulation about multi-matrices loss of SSTHD&ITHD(Independent one-by-one hard Thresholding);
3.apply it to multi-population classification problem:random simulation and real data

## 黄金紫

1. The design of Three-link Swimmer Type II;
2. The experiment based on Three-link Swimmer Type II;
3. An introduction to the Stokeslets method;
4. Present Three-link Swimmer Type III

## 张国栋

### A cold-trap Residual Gas Analyzer based highly sensitive method for krypton detection

In a liquid xenon dark matter detector, the concentration of krypton plays a vital part in the detection results, since the isotope of which will generate an overwhelming background. The limit for krypton will be 10e-12 mol/mol, which is far beyond the limit of current commercial detector. We now here want to research and develop a highly sensitive and low-cost system to detect the impurities, especially krypton in xenon. The core part are Residual Gas Analyzer (RGA) and a cold-trap. We expect to improve the limit of the RGA from 10e-6 to five or six magnitude of order higher so that it can be applied to dark matter detection.

## 归斌

### A Brief Introduction to Type II1 Factors

wenku.baidu.com/view/dd7f86f84693daef5ef73de5.html?st=1

## 孟昭仪

### Non-uniform Discrete Fourier Transform Report II

1. Eliminating Aliasing effect by non-uniform periodogram.
2. Unbiased Spectrum Estimators
3. Optimal sampling
4. Reduction of noise–Filter & other technique

## 毛晓军

### band and threshold

1.Introduce band method and its numerical results.
2.Introduce generalized threshold operators and adaptive lasso threshold.

## 魏传豪

### Exploring Generalizations of Riemann-Roch Theorem

A brief introduction to complex geometry and Riemann-Roch problem.

## 汤迎

### Path Integral Approach to Study Stochastic Process: Starting from the Ornstein-Uhlenbeck Process

The path integral is a powerful tool to study stochastic process modeled by the Langevin equations. In this work, we implement the path integral formalization from the one dimensional Langevin equation with multiplicative noise for the general $\alpha$-interpretation. We realize the non-equivalence of $\alpha$-interpretation on time and space coordinates, and then illustrate such non-equivalence by the classical Ornstein-Uhlenbeck (OU) process. We then discover the popular space $\alpha$-interpretation violate the probability conservation, leading to a symmetry broken, while the time $\alpha$-interpretation does not have the undesired symmetry broken problem. We obtain the Fokker-Planck equation from the two different conditional probabilities. We also apply the path integral in one dimensional OU process with an external force, showing only the work definition with the force as a control parameter leads to the Jarzynski equality.

## 卢艺舟

### THz量子阱探测器的设计与优化

THz器件的简要介绍和三组数据的测量与分析

## 刘子卓

### Free-carrier absorption in quantum wells at mid-infrared and terahertz wavelengths

In this report, I will present the basic wave functions and Hamiltonians I will use in the calculations of the scaterring probilities in the Fermi’s Golden Rule.

## 孟昭仪

### Non-uniform Discrete Fourier Transform Report I

1. Review of earlier work
2. Proof of the Gaussian distribution
3. Proof and Numerical experiment of the theorem on periodogram
4. Lomb-Scargle Periodogram
5. Non-uniform sampling and Aliasing

## 张国栋

### 基于“冷井和残余气体分析仪”的氙气纯度测量

In a liquid xenon dark matter detector, the concentration of krypton plays a vital part in the detection results, since the isotope of which will generate an overwhelming background. The limit for krypton will be 10e-12 mol/mol, which is far beyond the limit of current commercial detector. We now here want to research and develop a highly sensitive and low-cost system to detect the impurities, especially krypton in xenon. The core part are Residual Gas Analyzer (RGA) and a cold-trap. We expect to improve the limit of the RGA from 10e-6 to five or six magnitude of order higher so that it can be applied to dark matter detection.

## 归斌

### Von Neumann algebras and crossed products

I will give the definitions of some basic and important concepts, including von Neumann algebras, the important topologies related to them. Then I will give some examples and constructions of von Neumann algebras. They are essential for me to introduce the most important concept: crossed products, which are the von Neumann algebras constructed by the group action on measure spaces. My task in the graduation project is to study the relation between the group action on measure spaces and the corresponding crossed products.

## 葛灏

### 太赫兹器件的探究

Thz器件在未来各方面领域有着极大的发展潜力，这里主要介绍了Thz量子阱探测器（QWIP）的工作原理。能带结构对Thz量子阱探测器的使用起到至关重要的作用，能带计算时，在薛定谔方程中，除了要考虑量子阱的周期势能，还需要考虑哈特利势和由多体效应引起的交换关联势。另外，我还介绍了与计算相关的一些物理关系。