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Full-Text Articles in Physical Sciences and Mathematics
U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli
U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli
Department of Computer Science Faculty Publications
Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data …
Matching Phosphorylation Response Patterns Of Antigen-Receptor-Stimulated T Cells Via Flow Cytometry, Ariful Azad, Saumyadipta Pyne, Alex Pothen
Matching Phosphorylation Response Patterns Of Antigen-Receptor-Stimulated T Cells Via Flow Cytometry, Ariful Azad, Saumyadipta Pyne, Alex Pothen
Department of Computer Science Faculty Publications
Background
When flow cytometric data on mixtures of cell populations are collected from samples under different experimental conditions, computational methods are needed (a) to classify the samples into similar groups, and (b) to characterize the changes within the corresponding populations due to the different conditions. Manual inspection has been used in the past to study such changes, but high-dimensional experiments necessitate developing new computational approaches to this problem. A robust solution to this problem is to construct distinct templates to summarize all samples from a class, and then to compare these templates to study the changes across classes or conditions. …
Two Approximate Minkowski Sum Algorithms, Victor Milenkovic, Elisha P. Sacks
Two Approximate Minkowski Sum Algorithms, Victor Milenkovic, Elisha P. Sacks
Department of Computer Science Faculty Publications
We present two approximate Minkowski sum algorithms for planar regions bounded by line and circle segments. Both algorithms form a convolution curve, construct its arrangement, and use winding numbers to identify sum cells. The first uses the kinetic convolution and the second uses our monotonic convolution. The asymptotic running times of the exact algorithms are increased by kmlogm with m the number of segments in the convolution and with k the number of segment triples that are in cyclic vertical order due to approximate segment intersection. The approximate Minkowski sum is close to the exact sum of perturbation regions that …
Controlled Linear Perturbation, Elisha P. Sacks, Victor Milenkovic, Min-Ho Kyung
Controlled Linear Perturbation, Elisha P. Sacks, Victor Milenkovic, Min-Ho Kyung
Department of Computer Science Faculty Publications
We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires …