Alexander Kim

Alexander Strang, David SeWell, Alexander Kim et al.

How are the advantage relations between a set of agents playing a game organized and how do they reflect the structure of the game? In this paper, we illustrate "Principal Trade-off Analysis" (PTA), a decomposition method that embeds games into a low-dimensional feature space. We argue that the embeddings are more revealing than previously demonstrated by developing an analogy to Principal Component Analysis (PCA). PTA represents an arbitrary two-player zero-sum game as the weighted sum of pairs of orthogonal 2D feature planes. We show that the feature planes represent unique strategic trade-offs and truncation of the sequence provides insightful model reduction. We demonstrate the validity of PTA on a quartet of games (Kuhn poker, RPS+2, Blotto, and Pokemon). In Kuhn poker, PTA clearly identifies the trade-off between bluffing and calling. In Blotto, PTA identifies game symmetries, and specifies strategic trade-offs associated with distinct win conditions. These symmetries reveal limitations of PTA unaddressed in previous work. For Pokemon, PTA recovers clusters that naturally correspond to Pokemon types, correctly identifies the designed trade-off between those types, and discovers a rock-paper-scissor (RPS) cycle in the Pokemon generation type - all absent any specific information except game outcomes.

Aditya Gupta, Samarth Chitgopekar, Alexander Kim et al.

We present our work on electric bicycles (e-bikes) and their implications for policymakers in the United States. E-bikes have gained significant popularity as a fast and eco-friendly transportation option. As we strive for a sustainable energy plan, understanding the growth and impact of e-bikes is crucial for policymakers. Our mathematical modeling offers insights into the value of e-bikes and their role in the future. Using an ARIMA model, a supervised machine-learning algorithm, we predicted the growth of e-bike sales in the U.S. Our model, trained on historical sales data from January 2006 to December 2022, projected sales of 1.3 million units in 2025 and 2.113 million units in 2028. To assess the factors contributing to e-bike usage, we employed a Random Forest regression model. The most significant factors influencing e-bike sales growth were disposable personal income and popularity. Furthermore, we examined the environmental and health impacts of e-bikes. Through Monte Carlo simulations, we estimated the reduction in carbon emissions due to e-bike use and the calories burned through e-biking. Our findings revealed that e-bike usage in the U.S. resulted in a reduction of 15,737.82 kilograms of CO2 emissions in 2022. Additionally, e-bike users burned approximately 716,630.727 kilocalories through their activities in the same year. Our research provides valuable insights for policymakers, emphasizing the potential of e-bikes as a sustainable transportation solution. By understanding the growth factors and quantifying the environmental and health benefits, policymakers can make informed decisions about integrating e-bikes into future energy and transportation strategies.

Alexander Kim, Ryan Kim

The accurate classification of white blood cells and related blood components is crucial for medical diagnoses. While traditional manual examinations and automated hematology analyzers have been widely used, they are often slow and prone to errors. Recent advancements in deep learning have shown promise for addressing these limitations. Earlier studies have demonstrated the viability of convolutional neural networks such as DenseNet, ResNet, and VGGNet for this task. Building on these foundations, our work employs more recent and efficient models to achieve rapid and accurate results. Specifically, this study used state-of-the-art architectures, including MaxVit, EfficientVit, EfficientNet, EfficientNetV2, and MobileNetV3. This study aimed to evaluate the performance of these models in WBC classification, potentially offering a more efficient and reliable alternative to current methods. Our approach not only addresses the speed and accuracy concerns of traditional techniques but also explores the applicability of innovative deep learning models in hematological analysis.