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Model of Feedback-Mediated Dynamics in Coupled Nephrons with Compliant Thick Ascending Limbs
Irregular flow and pressure have been observed in the nephrons of spontaneously hypertensive rats (SHR). Coupling of nephrons through their tubuloglomerular feedback (TGF) systems may be one of the factors involved in this ...
Classification of Legendrian Knots and Links
We write a program in Java to generate all grid diagrams of up to size 10. Using equivalence between grid diagrams modulo a set of Cromwell moves and classification of Legendrian links up to Legendrian isotopy, together ...
Multiscale Estimation of Intrinsic Dimensionality of Point Cloud Data and Multiscale Analysis of Dynamic Graphs
In the first part of the thesis, we study the problem of estimating the intrinsic dimension of point cloud data sampled from a noisy manifold. We show that a multiscale algorithm succeeds with high probability. The second ...
Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface
Thin layers of slow-moving, viscous fluid which coat hydrophobic surfaces are shaped by the competing forces of disjoining pressure and surface tension. These forces form the fluid layer into an array of discrete droplets ...