Research Projects & Interests

Below are a set of projects spanning and overlapping interests in intelligent systems.

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Robotic 2D3D Image-Based Vision (Human-Machine Hybrid System)
This research focuses on developing image-based guidance to make actionable real world insights such as pose estimation, tracking, avoidance, and attitude determination. To do so, this project concerns itself in developing passive image-based sensors that are reliant on underlying areas of geometry, control, and general signal processing. We are particularly interested in imagery that is low resolution high altitude noisy environments where traditional signal processing (edge) features are not prevalent. Applications of this research span several areas with a primary focus on autonomous systems.

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GPS Denied Navigation and Autonomous Model Verification
This research focuses on the broad concept of developing not only solutions to overcome 2D and 3D localization in GPS denied environments, but the ability to verify the subsequent models developed for such situations. In particular, the focus areas include both imaging as well as network theory to estimate reliability of single and/or multiple agents that are able to collaborate in environments where traditional active sensing is not allowed or becomes unreliable. Applications of this research span several areas that with a primary focus on imaging-based autonomous systems.

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Graph Theory and Multi-Agent Geometric Aspects in Learning
This research focus on graph theory and machine learning with a particular interest in computational and network geometry with connections to dynamical systems. This includes varying discrete mathematics and discretizations over general metric spaces. Recent interests are focus on discrete geometry (namely, curvature) along with connections to Wasserstein geometry, entropy, and spectral graph theory. With no targeted application, we are interested in developing an understanding of network functionality not only “2D” graphs, but those of hypergraphs and multi-graphs as well as areas of distributed reinforcement learning over networks.

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Systems Biology & Mathematical Oncology
This research focuses on notion of robustness, heterogeneity, cellular organization, and phase changes which are ubiquitous concepts that are of significance in order to understand dynamical biological systems. In particular, feedback loops are essential to the function of biological mechanisms and systems that arise from deliberate Darwinian-like principles. This leads one to heterogeneity of cellular population. Here, we are interested in developing underlying biological theory and fundamental “laws” of cancer.

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