School of Science Department of Mathematics 44 Retrieving of Urban Morphology from Satellite Images and Machine Learning Supervisor: FUNG Jimmy Chi Hung / MATH Student: YANG Yuang / DSCT Course: UROP2100, Fall Urban morphology is of great interest to a wide range of fields, including environmental science and city planning. In this project, we aim to deploy machine learning methods and satellite images to allow the retrieval of building height information at a low cost. Following the progress on this project in the Summer of 2021, several things have been tried out to improve the performance of the earlier developed model. Those methods include generating a 3D view of the buildings to obtain more accurate ground truth, trying out alternative satellite images as input, and exploring open-source datasets that can be used in this project in the future. This report describes these methods in detail, along with the results and difficulties encountered. Retrieving of Urban Morphology from Satellite Images and Machine Learning Supervisor: FUNG Jimmy Chi Hung / MATH Student: ZHAO Haoyu / DSCT Course: UROP1100, Fall UROP2100, Spring Urban information plays an important role in various scientific fields. One of the key features of urban information is the dimension information of urban buildings. However, the acquisition of three-dimensional information tends to be difficult and expensive in the past. But with the online map engine and open-source street view images, high-resolution satellite images are available, which provides chances to obtain building information at a low cost. This report will discuss a specific deep-learning method, the U-Net neuron network, and use four satellite image data sets to train a machine-learning model for building detection. After training 20 epochs, the overall accuracy can reach up to 0.7. The feature of data sets and the techniques used in extracting features in images are also discussed. Quantum Groups Supervisor: IP Ivan Chi Ho / MATH Student: CHAN Hong Ming / COSC Course: UROP2100, Fall In paper given by V.G. Turaev, a more general type of link in-variant is constructed which can be reduced to Jones polynomial. This report will show how the reduction to Jones Polynomial is performed. In another two papers given by N.Reshetikhin and V.G. Turaev, further generalized the invariant to coloured ribbon graph in closed oriented connected 3-manifold. This can used to generate a 2-variable Jones-Conway polynomial and an infinite set of 1-variable reductions of the 2-variable Kauffman polynomial according to N.Reshetikhin and V.G. Turaev. In this report, we will show some interesting property of the invariant Pm in V.G. Turaev.