This talk will present an introduction to some of the key principles and tools from feedback control theory. The two main design principles that will be explored is the role of feedback as a tool for managing uncertainty, and the use of feedback to design the dynamics of a system. Examples from engineering and nature will be used to illustrate s...
Creator:
Murray, Richard M. (California Institute of Technology)
Created:
2008-04-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this tutorial, we will present the hybridizable discontinuous Galerkin (HDG) methods for diffusion problems. We will describe the main idea for devising them and will explain how to implement them efficiently. We will then compare the methods with mixed methods and the continuous Galerkin methods. Finally, we will discuss the convergence prop...
Creator:
Cockburn, Bernardo (University of Minnesota, Twin Cities)
Created:
2010-10-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
* Expressing variational problems in FEniCS* Annotation and visualizing the computational graph* Adjoining and using the adjoint for optimization* Mesh independence and optimization libraries* Possible examples:- standard linear-quadratic elliptic problem - Dirichlet control of Stokes- topology optimization of pipes in Stokes flow- MPECs via reg...
Creator:
Farrell, Patrick (University of Oxford)
Created:
2016-06-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
1. Introduction and Motivation-What are Inverse problems?-Examples: detection of contaminant sources, image and voice recognition, medical imaging, subsurface imaging, materials identification2. Theoretical aspects of (discrete) inverse problems-Why are inverse problems (oftentimes) difficult to solve?-Well-posed and ill-posed problems: existenc...
Creator:
Aquino, Wilkins (Duke University)
Created:
2016-06-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Julia is a relatively new programming language that combines many of the best features of languages like Python and tools like Matlab. One interacts with Julia like other high-level scripting languages, e.g., through Jupyter notebooks, yet Julia has excellent computational performance because it is built on top of the LLVM compiler. This tutoria...
Creator:
Fessler, Jeff (University of Michigan)
Created:
2019-10-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
1. Quick intro of example shape optimization problems.2. Review differential geometry for curves/surfaces: parametric surfaces, normal vector, curvature, shape operator, etc.3. Review surface differential operators: surface gradient/Laplacian, shape operator, integration by parts on surfaces, etc.4. Intro shape perturbations: material and shape ...
Creator:
Walker, Shawn W. (Louisiana State University)
Created:
2016-06-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Many people find time-dependent quantum mechanics the most interesting and understandable part of quantum mechanics. However, standard courses in quantum mechanics devote little attention to this perspective, and its relationship to the rest of the syllabus is disjointed. Yet it is possible to develop quantum mechanics from beginning to end from...
Creator:
Tannor, David J. (Weizmann Institute of Science)
Created:
2009-01-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
1. Basic Concepts2. Brief Historical Overview3. Density Method in Solid Mechanicsa. Homogenization and Explicit Interpolation Approachesb. Ill-posedness issuesc. Regularization Methods4. Level-set Methods in Solid Mechanicsa. Explicit Methods and Hamilton-Jacobi Approachesb. Ersatz and Immersed boundary Methods5. Overview of Applications in Soli...
Creator:
Maute, Kurt (University of Colorado)
Created:
2016-06-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Online social media represent a fundamental shift of how informationis being produced, transferred and consumed. User generated content inthe form of blog posts, comments, and tweets establishes a connectionbetween the producers and the consumers of information. Tracking thepulse of the social media outlets, enables companies to gain feedbackand...
Creator:
Leskovec, Jure (Stanford University)
Created:
2012-03-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Although the continuous circulation of information, news, jokes,and opinions is ubiquitous in the worldwide social network, theactual mechanics of how any single piece of information spreadson a global scale have largely remained mysterious. A majorchallenge lies in the difficulty of acquisition of large-scaledata recording the diffusion of any ...
Creator:
Liben-Nowell, David (Carleton College)
Created:
2012-02-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Tutorial room at the Jewish Community Center to help students with high school math and other subjects. Included in the photograph: Erwin Froude, Debbie Winer, Jean Weiner, and Rich Kleugman.
Created:
1966
Contributed By:
University of Minnesota Libraries, Nathan and Theresa Berman Upper Midwest Jewish Archives.
My talk will be a tutorial about sparse signal recovery but, more importantly, I will provide an overview of what the research problems are at the intersection of biological applications of group testing, streaming algorithms, sparse signal recovery, and coding theory. The talk should help set the stage for the rest of the workshop.
Creator:
Gilbert, Anna (University of Michigan)
Created:
2012-02-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In recent years network analysis have become the focus of muchresearch in many fields including biology, communication studies, economics, information science, organizational studies, and social psychology. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral cluste...
Creator:
Yu, Bin (University of California, Berkeley)
Created:
2011-09-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Sparse methods for supervised learning aim at ï¬ nding goodlinear predictors from as few variables as possible, i.e., with smallcardinality of their supports. This combinatorial selection problem isoften turned into a convex optimization problem by replacing thecardinality function by its convex envelope (tightest convex lower bound),in this cas...
Creator:
Bach, Francis (École Normale Supérieure)
Created:
2011-09-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The data stream model has emerged as a way of analyzing algorithmic efficiency in the presence of massive data sets. Typically the algorithm is allowed a few (usually one) passes over the input, and must use limited memory and have very fast per input item processing time. I will give a survey of algorithms and lower bounds in this area, with an...
Creator:
Woodruff, David P. (IBM Research Division)
Created:
2012-02-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk I will describe some of our efforts in the area of translational medical imaging,and illustrate how mathematics and formalism play a fundamental role.I will start with our work on brain imaging, where we have developedentire analysis pipelines, going fromfixing basic mathematical errors in the classical formulasof high resolution di...
Creator:
Sapiro, Guillermo R. (University of Minnesota, Twin Cities)
Created:
2011-11-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We introduce a new methodology for studying the maximum eigenvalue of a sum of independent, symmetric random matrices. This approach results in a complete set of extensions to the classical tail bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Freedman, Hoeffding, and McDiarmid. Results for rectangular random matrices follow...
Creator:
Tropp, Joel (California Institute of Technology)
Created:
2011-09-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.