Tackling and Evaluating Urban Heat Island (UHI) Effect in Singapore: Greeneries Perspective

Tianyu W., Fengyuan H.

We analyzed how greeneries in general, and how different types of greeneries contribute to the various distribution of Land Surface Temperature (LST) in Singapore. Further, we explored how other factors (e.g. land uses, water bodies) would influence the effectiveness of newly constructed green spaces in reducing the local Land Surface Temperature (LST) in Singapore.

Apr 2022 [Presentation]

Determining the Diversified Portfolio by the Capital Asset Pricing Model (CAPM) Regression

Tianyu W., Jie Han K., Xing Yu W., Choon Leng C., Brian H.

We proposed a diversified portfolio by applying the Capital Asset Pricing Model (CAPM) regression, targeted at typical Japanese individual investors. Moreover, to accomodate with different risk appetites and preferences, we split our CAPM regression into 3 modified portfolios.

Apr 2022 [Report]

Value-at-Risk (VaR) and Its Application in Actuarial Science

Tianyu W.

As an important risk measure in various financial scenarios, I made a detailed introduction to the concept of Value-at-Risk (VaR) under notations commonly used in Actuarial Science. I used Historical Simulation Method (HSM) and Variance-Covariance Method to further explicitly explain its calculation. Furthermore, I applied the axioms of coherent risk measures to verify VaR's properties.

Apr 2022 [Report]

Na-K Model in Neurodynamics

Tianyu W., Samuel Y., Eric Q., Yifu W.

We reviewed the literature to find a suitable dynamic model for the neuron. Then, with the use of Mathematica, we applied computational methods to visualize the system's dynamics evolution, as well as how that evolution would alter under various parameter settings. One specific parameter that we focus on is the electric stimulus I, or the bias current, the manipulable external factor that triggers neural action.

Mar 2021 [Report]

Introduction to Fast Fourier Transform (FFT)

Jinchen Z., Tianyu W., Qianyu P., Huyue Y.

We reviewed the algorithm, fast Fourier Transform (FFT), which is used to compute the discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). We made a complete literature review, methodology, and applications to describe how an FFT can rapidly compute such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.

Dec 2020 [Report]

Pigeonhole Principle and its Applications

Tianyu W.

We reviewed the basic and general version of Pigeonhole Principle (PHP), and provided its corresponding proof. Then we extended this classical principle to its useful applications in proof of perplex theorems, including Erdős-Szekeres Theorem and Dirichlet's Approximation Theorem.

Oct 2021 [Presentation]