Abstract: The Kaczmarz algorithm is a method for solving linear systems of equations that was introduced in 1937. The algorithm is a powerful tool with many applications in signal processing and data science that has enjoyed a resurgence of interest in recent years. We'll discuss some of the history of the Kaczmarz algorithm as well as describ...
Creator:
Weber, Eric (Iowa State University)
Created:
2022-04-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Federated machine learning (FL) is gaining a lot of traction across research communities and industries. FL allows machine learning (ML) model training without sharing data across different parties, thus natively supporting data privacy. However, designing and executing FL jobs is not an easy task today. Flame is an open-source project that aims...
Creator:
Le, Myungjin (Cisco)
Created:
2022-04-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This is an introduction to the lectures and the tutorials. We will study different topics, differential geometric topic using analysis for the lectures and topological topics with numerical experiments for the tutorials. A survey for the knot energies will also be given.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We begin with the generalization of electrostatic energy of charged knots, where we come across the difficulty of divergent integrals. Two kinds of regularization will be introduced, Hadamard regularization and the regularization via analytic continuation, both from the theory of generalized functions.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We will see that Hadamard regularization and the regularization via analytic continuation give essentially the same information. This part is rather technical, although it will save complicated computation afterward.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We apply the regularization via analytic continuation to generalized Riesz energies of submanifolds in Euclidean spaces to obtain Brylinski's beta function, which is a meromorphic function with simple poles. We study geometric information that can be derived from Brylinski's beta function.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A method to construct M\"obius invariant weighted inner products on the tangent spaces of the knot space by using M\"obius invariant knot energies will be introduced. It gives M\"obius invariant gradients of such energies."
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
PhotoAcoustic Tomography (PAT) has become established as a significant imaging modality allowing the qualitative imaging in 3D of absorbed optical energy in the visible and near-infrared range, with high resolution, by exploiting the conversion of optical to acoustic energy and the discontinuity preserving propagation of ultrasound under the ass...
Creator:
Arridge, Simon (University College London)
Created:
2019-04-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A prominent concern, in the age of machine learning and data analysis, is that left to their own devices, algorithms will propagate - even amplify - existing biases. Common definitions of fairness are group-based, typically requiring that a given statistic be equal across a few demographic groups, socially identified as deserving protection. Suc...
Creator:
Reingold, Omer (Stanford University)
Created:
2019-06-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our work is inspired by detection in the...
Creator:
Kushnir, Dan (Nokia Bell Labs)
Created:
2020-11-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
