Research

I am an applied mathematician. My research interests lie broadly in Computational Neuroscience, Math Biology Modeling, and Machine Learning. 

• Computational Neuroscience

  Most of my work is inspired by neuroscience. One theme of this research is to modeling how stress can affect human cognitive functions and seizure dynamics. My concentration in the computational part is modeling neuronal synaptic plasticity. Synaptic plasticity is one of the most important neuroscience foundations for human cognitive function. We have developed techniques for approximating the plasticity outcome based on different types of stress that allow multi-spikes input. The other theme of the research is to investigating the dynamics of seizure activities by different models.

• Math Biology Modeling

  Most of the research works in this area were based on the undergraduate projects I supervised in Evansville. The theme of this research is to apply dierent techniques to a number of nonlinear ecology problems. For example, we provides a mathematical study for analyzing the dynamics of smoking with health education campaigns involved. The method of next generation matrix is used to derive the basic reproduction number R0. We prove that the smoking-free equilibrium is both locally and globally asymptotically stable if the reproduction number is less than 1; and the smoking-present equilibrium is globally asymptotically stable if it's greater than1. By comparing with smoking dynamics without health education involved, we conclude that health education can decrease smoking population. Numerical simulations are used to support our conclusions.

• Machine Learning

  Most of the research works in this section are focused on data analytic and machine learning applications. As a typical model of deep learning, convolutional neural networks (CNN) has a state of art result on the large-scale images classication. However, with the constantly increasing of digit images, there contains more and more redundant, relevant and noisy samples which cause CNN running slowly and its classication accuracy also decreasing at the same time. In this research, we provide an eective sample selection method for large-scale images based on the improved condensed nearest neighbor rule (called Condensed NN) by the k-means clustering algorithm. Experimental results show that the proposed method can eectively reduce most of useless samples and has a better generalization performance.

• Current Undergraduate Research Projects

1.  Epidemiological Modeling of MisInformation Diffusion on social network (Jan Strydom, Jesse Todd): Characterizing the misinformation diffusion on social networks enables us to understand the properties of underlying media and model communication patterns. In this research project, we will use epidemiological modeling to study the spread of misinformation(rumors).
2. Modeling the Effect of Education on E-Cigarette use Behavior From Youth to  Youth Adult (Sydney Chittarath, Nick Vincent, Aria Mokhtari): E-cigarettes are the most used tobacco product among youth in the US. In 2018, more than 3.6 million US youth, including 1 in 5 high school students and 1 in 20 middle school students, use e-cigarettes. Among many control policies, health education campaigns play an important role. In this project, we will conduct a mathematical study to analyze the transition dynamics of E-cigarette use from youth to young adults with an educational effect. A compartmental model for smoking behavior transmission will be built for the dynamical system analysis. National Youth Tobacco Survey (NYTS) and National Adult Tobacco Survey (NATS) from the Centers for Disease Control and Prevention (CDC) will be used to estimate the parameters in this model.

 

 

Here are my Google Scholar page and Researchgate page.