Rachel Leander

Optimal Control of Treatment in a Free Boundary Problem Modeling Multilayered Tumor Growth

Xinyue Evelyn Zhao, Yixiang Wu, Rachel Leander, Wandi Ding et autres

Abstract. We study the optimal control problem of a free boundary PDE model describing the growth of a multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor tissue and …

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Optimal control for a free boundary tumor growth model

Yixiang Wu, Xinyue Evelyn Zhao, Rachel Leander, Wandi Ding

This paper investigates the optimal control of treatment in a free boundary PDE model that describes the growth of a radially symmetric tumor. The optimal control strategy is designed to inhibit tumor growth while minimizing side effects. We establish the well-posedness of …

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Optimal Control for a Free Boundary Tumor Growth Model

Yixiang Wu, Xinyue Evelyn Zhao, Rachel Leander, Wandi Ding

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On solutions to the continuum version of the Kuramoto model with identical oscillators

Anthony P. Krueger, Sathyanarayanan Rengaswami, Rachel Leander

The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to better characterize solution dynamics. In this paper, we combine the method of characteristics with …

Optimal control of continuous systems with impulse controls

Rachel Leander, Suzanne Lenhart, V. Protopopescu

The term For i = 1, …, N, j = 1, …, L above Equation (37) must be replaced with For i = 0, …, N − 1, j = 1, …, L

Correction to: Modulation of the cAMP Response by G$$\alpha _i$$ and G$$\beta \gamma $$: A Computational Study of G Protein Signaling in Immune Cells

Rachel Leander, Alexandra Friedman

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Controlling synchrony in a network of Kuramoto oscillators with time-varying coupling

Rachel Leander, Suzanne Lenhart, V. Protopopescu

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Optimal control of continuous systems with impulse controls

Rachel Leander, Suzanne Lenhart, V. Protopopescu

Impulse control problems, in which a continuously evolving state is modified by discrete control actions, have applications in epidemiology, medicine, and ecology. In this paper, we present a simple method for solving impulse control problems for systems of differential equations. In particular, …

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Derivation and experimental comparison of cell-division probability densities

Rachel Leander, E.J. Allen, Shawn Garbett, Darren R. Tyson et autres

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Modulation of the cAMP Response by G$$\alpha _i$$ and G$$\beta \gamma $$: A Computational Study of G Protein Signaling in Immune Cells

Rachel Leander, Alexandra Friedman

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On the dynamics of radially symmetric granulomas

Avner Friedmen, Chiu‐Yen Kao, Rachel Leander

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A Mathematical Model of CR3/TLR2 Crosstalk in the Context of Francisella tularensis Infection

Rachel Leander, Shipan Dai, Larry S. Schlesinger, Avner Friedman

Complement Receptor 3 (CR3) and Toll-like Receptor 2 (TLR2) are pattern recognition receptors expressed on the surface of human macrophages. Although these receptors are essential components for recognition by the innate immune system, pathogen coordinated crosstalk between them can suppress the production …

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