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Special Projects
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Non-Parametric Estimation of Manifolds from Noisy Data
Description:
A common task in many data-driven applications is to find a low dimensional manifold that describes the data accurately. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there is no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples wi...
Creator:
Aizenbud, Yariv (Yale University)
Created:
2021-11-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
Non-Parametric Estimation of Manifolds from Noisy Data
Normalized Antics: Polyhedral Computation in an Irrational Age
Description:
https://www.math.ucdavis.edu/~mkoeppe/art/ima-2019/
Creator:
Koeppe, Matthias (University of California, Davis)
Created:
2019-07-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
Normalized Antics: Polyhedral Computation in an Irrational Age
Not knot
Description:
Knots provide a starting point for several branches of lowdimensional topology. Often, lowdimensional topologists are more interested in the complement of a knot than in the knot itself. Several types of invariants allow to distinguish between knots. In addition, a topological criterion for distinguishing different geometric types of knot comple...
Creator:
Schultens, Jennifer (University of California, Davis)
Created:
2019-06-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
Not knot
Novel CT Data Acquisition and Processing
Description:
While x-ray computed tomography is a mature technology that is used for a wide range of diagnoses, there continue to be new untapped strategies to collect more information and to enable more efficient data collections (e.g. increased image quality and/or lower x-ray exposures). This talk will review new approaches that involve spatial and/or spe...
Creator:
Stayman, Joseph (Johns Hopkins University)
Created:
2019-10-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
Novel CT Data Acquisition and Processing
On Anisotropic Diffusion Equations for Label Propagation
Description:
In many problems in data classification, it is desirable to assign labels to points in a point cloud where a certain number of them is already correctly labeled. In this talk, we propose a microscopic ODE approach, in which information about correct labels propagates to neighboring points. Its dynamics are based on alignment mechanisms, often us...
Creator:
Kreusser, Lisa-Maria (University of Cambridge)
Created:
2020-09-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On Anisotropic Diffusion Equations for Label Propagation
On Multiclass Adversarial Training, Perimeter Minimization, and Multimarginal Optimal Transport Problems
Description:
Adversarial training is a framework widely used by machine learning practitioners to enforce robustness of learning models. Despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical quest...
Creator:
Garcia Trillos, Nicolas (University of Wisconsin, Madison)
Created:
2022-03-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On Multiclass Adversarial Training, Perimeter Minimization, and Multimarginal Optimal Transport Problems
On the analyticity of critical points of the Möbius energy
Description:
How nice are critical knots of knot energies? We already know that critical knots of the Möbius energy are smooth. This leads to the question whether critical knots of the Möbius energy are not only smooth, but also analytic. In this lecture, we give a short overview on the regularity results for the Möbius energy and present techniques with whi...
Creator:
Vorderobermeier, Nicole (Universität Salzburg)
Created:
2019-06-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On the analyticity of critical points of the Möbius energy
On The Convergence of MMD GANs: A Theory via Parametric Kernelized Gradient Flows
Description:
We consider the maximum mean discrepancy MMD GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN. We show that this flow provides a descent direction minimizing the MMD on a statistical manifold of probability distributions. We then derive an explicit condition which ensures ...
Creator:
Mroueh, Youssef (IBM)
Created:
2020-11-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On The Convergence of MMD GANs: A Theory via Parametric Kernelized Gradient Flows
On the Knotting Probability of Random Equilateral Polygons
Description:
A n-sided polygon in 3-space can be described as a point in 3n-space by listing in order the coordinates of it vertices. In this way, the space of embedded n-sided polygons is a manifold in which points correspond to piecewise linear knots and paths correspond to isotopies which preserve the geometric structure of these knots. In this talk, we w...
Creator:
Hake, Kate (Carleton College)
Created:
2019-06-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On the Knotting Probability of Random Equilateral Polygons
On Wasserstein Gradient Flows and the Search of Neural Network Architectures
Description:
Neural networks have revolutionized machine learning and artificial intelligence in unprecedented ways, establishing new benchmarks in performance in applications such as image recognition and language processing. Such success has motivated researchers and practitioners in multiple fields to develop further applications. This environment has dri...
Creator:
Garcia Trillos, Nicolas (University of Wisconsin, Madison)
Created:
2020-09-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2022-04-22
On Wasserstein Gradient Flows and the Search of Neural Network Architectures