arXiv subjects

Rohit Jammula

Publications and source records attributed to Rohit Jammula.

2 recordsLinked to original sources

arXiv2026

Elastic Curves via Geometric Mechanics

Elastic curves are the mathematical shapes of thin elastic rods in equilibrium, with deep connections to mechanics, geometry, and computer graphics. Traditionally described as stationary points of bending energy under length and torsion constraints, their rich theory admits many equivalent characterizations. We develop a new one from the viewpoint of geometric mechanics. Our main contribution relies on a lesser-known isoperimetric characterization: a curve is elastic if and only if it is a critical point of the length functional under fixed area and volume vectors. We show that these constraints transform naturally under orientation-preserving rigid body motions, identifying them as momentum variables for these symmetries. This structure suggests a new discrete theory. We show that the low-order integral quantities length, area, and volume vectors are all naturally defined for polygonal curves, leaving the same transformation laws exactly satisfied. The resulting definition of discrete elastic curves in terms of the isoperimetric characterization restricted to discrete polygonal curves is variational, structure-preserving, and requires no auxiliary discretizations of curvature or material frames. Finally, the same structure carries the Marsden--Weinstein form, a canonical (pre-)symplectic structure on the space of curves, to polygonal curves. This yields novel approaches to Hamiltonian dynamics on discrete space curves, including tangent, vortex-filament, and modified Korteweg--de Vries flows.

math.DG↗

arXiv2020

Optimal Transfer Learning Model for Binary Classification of Funduscopic Images through Simple Heuristics

Deep learning models have the capacity to fundamentally revolutionize medical imaging analysis, and they have particularly interesting applications in computer-aided diagnosis. We attempt to use deep learning neural networks to diagnose funduscopic images, visual representations of the interior of the eye. Recently, a few robust deep learning approaches have performed binary classification to infer the presence of a specific ocular disease, such as glaucoma or diabetic retinopathy. In an effort to broaden the applications of computer-aided ocular disease diagnosis, we propose a unifying model for disease classification: low-cost inference of a fundus image to determine whether it is healthy or diseased. To achieve this, we use transfer learning techniques, which retain the more overarching capabilities of a pre-trained base architecture but can adapt to another dataset. For comparisons, we then develop a custom heuristic equation and evaluation metric ranking system to determine the optimal base architecture and hyperparameters. The Xception base architecture, Adam optimizer, and mean squared error loss function perform best, achieving 90% accuracy, 94% sensitivity, and 86% specificity. For additional ease of use, we contain the model in a web interface whose file chooser can access the local filesystem, allowing for use on any internet-connected device: mobile, PC, or otherwise.

cs.LG↗