Below are a set of projects that I am currently involved in. If you are an interested student, please contact me as some of these projects are more active than others.

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Geometry and Control of Time-Varying Networks
This research focuses on the broad concept of developing geometric techniques to control dynamical systems often represented, at a high-level, as weighted graphs that evolve over time. While the focus of this research is focused on developing underlying theory, the applications are wide spread and overlap with projects below. This said, we are interested in developing broad techniques applicable to biological, power, cyber, social, and financial systems.

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Waterbed Effects and Drug Resistance in Targeted Therapy
This research focuses on understanding and exploiting mechanisms of resistance that can be attributed to failures in cancer targeted therapy as well as broader biological systems (e.g., bacterial resistant strains). From a control perspective, this closely resembles waterbed theory whereby the system observation that when a complex behavior is “pushed” down, the invariable effect of complexity causes for that behavior to “pop-up” elsewhere.

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Contagion Dynamics and Risk Modeling
This project focuses on developing models of risk based models that are able to effectively understand and manage potential “black swan” events whereby the onset of a failure of a given agent leads to a cascade effect of catastrophic system failure. Here, we seek to develop biological inspired dynamic models that can develop prescriptions to manage the spread of virus (contagions) of social, biological and financial systems (e.g., develop a heterogenous social system that is more “cancer-like” in order to disrupt effect of misinformation).

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Control Active Vision
This research focuses on develop control based computational vision approaches to a variety of real-time systems. Here, we employ feedback control towards image sensors to extract necessary signatures and estimate dynamics of the intended system. Recently, such work in this area has included the usage of developing control-theoretic principles to allow for human user computer interaction as well as interactive machine learning. Applications of this research span several areas that include shape reconstruction and visual tracking.

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2D3D Imaging and Vision
This research focuses on the broad concept of developing mathematical approaches that are able to fuse 2D information with its 3D counterpart (and vice versa). In many vision tasks such as image segmentation, object recognition, learning, or tracking, one often tacitly ignores the 3D domain and focuses algorithmic development solely on the 2D domain. Here, we are interested in developing geometric (projective/differential) models and techniques capable of simultaneously including 3D information for 2D tasks (and vice versa)

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Cellular Differentiation and Heterogeneity
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 mostly interested in developing broad biological models as opposed disease specific protocols.

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Optimal Mass Transport and Applications
This research focuses on the mathematical topic of optimal mass transport and exploiting Wasserstein geometry for a variety of network and imaging applications. Mass transport in the broad sense can be regarded as developing optimal plans to transfer resources from one domain to another. Here, we are interested in how Wasserstein geometry allows for the uncovering of interesting mathematical structures that play a role in a variety of problems ranging from power spectral density, quantum mechanics, optimal, and stochastic control.

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Computer Graphics, Shape Metrics
This project focuses on developing shape metrics and analysis techniques that can be employed towards learning. One of the major challenges in longitudinal studies of medical shapes is the ability to detect and classify an anomalies that be associated with disease (combined with genetic markers). This is due to the difficulty of defining similarity measures between arbitrary shapes that live on some non-euclidean manifold. Here, we interested in various approaches to accomplish this task.

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