<p dir="ltr">In my thesis, I propose a Graph Regularized-Attention-Based Diffusion Transformer (GRAD-T) model, which uses kernel temporal attention and a regularized sparse graph method to analyze model general diffusion processes over networks. The proposed model uses the spatiotemporal nature of data generated from diffusion processes over networks to examine phenomena that vary across different locations and time, such as disease outbreaks, climate patterns, ecological changes, information flows, news contagion, transportation flows or information and sentiment contagion over social networks. The kernel attention models the temporal dependence of diffusion processes within locations, and the regularized spatial attention mechanism accounts for the spatial diffusion process. The proposed regularization using a combination of penalized matrix estimation and a resampling approach helps in modeling high-dimensional data from large graphical networks, and identify the dominant diffusion pathways. I use the model to predict how emotions spread across sparse networks. I applied the model to a unique dataset of COVID-19 tweets that I curated, spanning April to July 2020 across various U.S. locations. I used model parameters (attention measures) to create indices for comparing emotion diffusion potential within and between nodes. Our findings show that negative emotions like fear, anger, and disgust demonstrate substantial potential for temporal and spatial diffusion. Using the dataset and the proposed method we demonstrate that different types of emotions exhibit different patters of temporal and spatial diffusion. I show that the proposed model improves prediction accuracy of emotion diffusion over social medial networks over standard models such as LSTM and CNN methods. Our key contribution is the regularized graph transformer using a penalty and a resampling approach to enhance the robustness, interpretability, and scalability of sparse graph learning.</p>

This study analyzes snow maintenance data of Borlänge municipality of Sweden based on the data of 2017 to 2018. The goal of this study is to reduce operational overhead of snow maintenance, for example, fuel and time consumption of the snow maintenance vehicles, work hour of dedicated personnel, etc. Borlänge Energy equipped the snow maintenance vehicles with GPS devices which stored the record of the snow maintenance activities. The initial part of this study obtained insights out of the GPS data by using spatiotemporal data analysis. Derivation of the different snow maintenance treatments (plowing, sanding and salting) as well as the efficiency of the sub-contractors (companies which are responsible for snow maintenance) and inspectors (personnel who are liable to call the subcontractors if they think it is time for snow maintenance) are performed in the beginning of this study. The efficiency of the subcontractors and inspectors are measured to compare their performance with each other. The latter part of this study discusses a simulated annealing-based heuristics technique to find out optimal location for dispatching snow maintenance vehicles. In the existing system of snow maintenance, drivers of the maintenance vehicles decide to start location of maintenance work based on their experience and intuition, which might vary from one driver to another driver. The vehicle dispatch locations are calculated based on the availability of the vehicles. For example, if a subcontractor has three vehicles to perform snow maintenance on a specific road map, the proposed solution would suggest three locations to dispatch those vehicles. The purpose of finding the optimal dispatch location is to reduce the total travel distance of the maintenance vehicles, which yield less fuel and time consumption. The study result shows the average travel distance for 1, 3, and 5 vehicles on 15 road networks. The proposed solution would yield 18% less travel than the existing system of snow maintenance.