We develop a mathematical theory to explain the mechanism of super-resolution in resonant media which consists of sub-wavelength resonators. Examples includes: Helmholtz resonators, plasmonic particles, and bubbles. For the media consists of small finite number of resonators, we show that super-resolution is due to sub-wavelength propagating mod...
Creator:
Zhang, Hai (Hong Kong University of Science and Technology)
Created:
2017-02-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk presents a Maple/Matlab toolbox for basic polynomial computations with exact or approximate data. The toolbox includes software for computing the approximate GCD, approximate factorization, dual basis and multiplicity identification, as well as numerical elimination in solving polynomial systems. We shall present the underlying theory ...
To achieve personalized medicine, an individualized treatment strategy assigning treatment based on an individual's characteristics that leads to the largest benefit can be considered. Recently, a machine learning approach, O-learning, has been proposed to estimate an optimal individualized treatment rule (ITR), but it is developed to make binar...
Creator:
Zeng, Donglin (University of North Carolina, Chapel Hill)
Created:
2018-11-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Invariant manifolds and foliations have become very useful tools in dynamical systems. For infinite dimensional systems generated by evolutionary PDEs, the mere existence of these structures is non-trivial compared to those of ODEs due to issues such as the non-existence of backward (in time) solutions of some PDEs or nonlinear terms causing der...
Creator:
Zeng, Chongchun (Georgia Institute of Technology)
Created:
2012-09-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We will discuss classical and new results on the existence or non-existence of inertial manifolds (IMs) for semilinear parabolic equation. In particular, we report on the existence of IMs for the 1D reaction-diffusion-advection systems with Dirichlet or Neumann boundary conditions and give the counterexamples for the case of periodic boundary co...
Creator:
Zelik, Sergey (University of Surrey)
Created:
2016-06-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will describe recent results (obtained jointly with A. Guionnet P. Wood) concerning perturbations of non-normal random matrices and their stabilization by additive noise. This builds on techniques introduced earlier inthe context of the 'single ring theorem', by Guionnet, Krishnapur, and the speaker.
Creator:
Zeitouni, Ofer (University of Minnesota, Twin Cities)
Created:
2011-09-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This series will highlight the main steps in the approach to universality based on dynamics and comparisons of Green functions. The emphasis will be on the basic steps, not on sharpest results.
Creator:
Zeitouni, Ofer (University of Minnesota, Twin Cities)
Created:
2012-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The long, rich history of topology in mathematics has provenextremely useful for the study of DNA. DNA, the geneticblueprint for life, undergoes tremendous flux as it ispackaged, replicated, segregated, transcribed, recombined andrepaired. Extremely long and skinny, DNA is prone toentanglement. Every time it is copied, the two resulting'daughter...
Creator:
Zechiedrich, Lynn (Baylor College of Medicine)
Created:
2010-04-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
