Zachary Zhang

The Ricci curvature was very important on geometric analysis. I prove two results characterizing the graphs with positive Ricci curvature with the definition of Ricci curvature provided by Lin-Lu-Yau.

In order to determine which households are prepared to own a pet.We conducted a diverse nationwide questionnaires, and warmed up by developing a mathematical model to evaluate a household’s readiness for cat ownership.After data cleaning, we delved deeply into the dataset focusing on core dimensions such as living environment conditions, lifestyle, and economic time investment, extracting 17 secondary indicators which were further integrated into seven primary evaluation criteria, thus forming a comprehensive assessment system for pet ownership. We applied the K-means++ clustering algorithm to classify the samples, determining the optimal number of clusters as three through the CH criterion.

In order to evaluate different measures implemented by a production plant to reduce CO2 emissions, we manually sorted data from 20 different electronic manufacturing companies and focused on the impact of multiple factors on carbon dioxide emissions such as company revenue, labor, total energy consumption, and recycled materials. By applying the linear, ridge, and lasso regression models generated from datasets of these factors, our comprehensive study reveals a complex dynamic relationship between operational adjustments in electronic equipment manufacturing plants and the effects of research factors on CO2 emissions.

In order to identify player’s performance better at a given time of the match, we developed a model to explore how momentum affects match results and uses machine learning to predict them.Three different machine learning models—KSVM, Random Forest (RF), and XGBoost—are employed across two different time scales, with 5-fold cross-validation to assess model performance. Metrics such as AUC value, Micro-F1, and Macro-F1 are introduced to evaluate model accuracy.The model also undergoes validation through application to various matches and moving average processing. The Autocorrelation Function (ACF) test is used to examine randomness within a single series, while the Cross-Correlation Function (CCF) test observes the correlation between win rates and momentum. In tackling the third problem, a sensitivity analysis of the four feature indicators is conducted,with three-dimensional graphs created to visualize the relationship between different indicators and momentum.

In order to research the diffusion and evolution process of dandelion,and analyse its characteristics and the harm it inflicts on environment.Our analysis considered relevant indicators of species growth and environmental factors, including the impact of invasive species on ecology, economy, and agriculture.Among the selected five factors, we utilized the XGBoost algorithm to measure the proportion of each impact factor in calculating species invasion. Through a weighted combination approach, we derived the final invasion impact factors for dandelion species, ensuring representative results. Using the established biological invasion impact factor model, we calculated the impact factor scores for dandelion, providing valuable insights into its growth, reproduction, and invasion factors.

China’s national volume-based drug procurement policy is a big reform in pharmaceutical industry. The influenced drugs had an average reduction of around 50%, and the maximum reduction exceeding 90%. I built the multi-period DID model to study the impact of the policy on listed pharmaceutical companies’ innovation. The empirical results revealed that the policy significantly promotes the pharmaceutical companies’ R&D investment intensity  and the quality of invention patents under the survival pressure. It also helped me to end the debate about the effectiveness of the policy between my father, a doctor and my mother, an investor.

In order to research the relationship between temperature and CO2 and predict future land-ocean temperatures changes.We developed three modeling approaches to investigate CO2 concentrations-linear model, ARIMA model, RNN model.We analyzed the advantages and disadvantages of the model and wrote a note to the relevant institutions to elaborate our study in the future.

American Invitational Mathematics Examination top1, perfect score