Sparsity matroids generalize the combinatorics behind several types of rigidity (2D bar-and-joint, arbitrary dimension body-and-bar, etc.). A conspicuous open problem is to find geometric representations for ALL of them. We present some partial answers. This is joint work with Louis Theran from UMass Amherst.
Creator:
Streinu, Ileana (Smith College)
Created:
2007-06-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Combining different basis to build a more efficient combined representation of complex data has a long history in harmonic analysis and signal processing. More recently, a rigorous mathematical framework was proposed to formalize the problem of separating data into morphologically distinct components based on the microlocal properties of the dat...
Creator:
Labate, Demetrio (University of Houston)
Created:
2018-10-22
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Solved protein structures from PDB depict a static picture, but proteins are flexible. We are interested in understanding how they move near the native conformation, or between two given conformations, without resorting to heavy-duty molecular dynamics techniques. Geometric simulations focus on motions of constrained structures behaving much lik...
Creator:
Streinu, Ileana (Smith College)
Created:
2008-01-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a scheme of studying the geometry of high-dimensional data to discover patterns in it, using minimal parametric distributional assumptions. Our approach is to define multivariate quantiles and extremes, and develop a method of center-outward partial ordering of observations. We formulate methods for quantifying relationships among obs...
Creator:
Chatterjee, Singdhansu (University of Minnesota, Twin Cities)
Created:
2018-04-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
For the last 50 years or longer, it has been a basic question in topology to study differential structures of a given manifold. In the early 80's, Donaldson used anti-self solutions of the Yang-Mills equation to study differentiable 4-manifolds and construct a very useful class of differentiable invariants for 4-manifolds. In particular, he was ...
Creator:
Tian, Gang (Princeton University)
Created:
2012-01-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The L2 or H0 metric on the space of smooth plane regularclosed curves induces vanishing geodesic distance on the quotientImm(S1,R2)/Diff(S1).This is a general phenomenon and holds on all fulldiffeomorphism groups andspaces Imm(M,N)/Diff(M) for a compact manifold M and aRiemanninan manifoldN. Thus we have to consider more complicated Riemannian m...
Creator:
Michor, Peter W. (Universität Wien)
Created:
2006-04-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint work with Yang Liu.Motivated by applications in modeling glass structures inarchitecture, we consider the geometry and computation of meshsurfaces with planar hexagonal faces from the point of viewof discrete differential geometry. It is shown that themesh structure is naturally related to conjugate curve networks onits underlying smooth s...
Creator:
Wang, Wenping (University of Hong Kong)
Created:
2007-05-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will discuss several probabilistic models producing simplicial complexes, manifolds and discretegroups. Random simplicial complexes are high dimensional analogues of random graphs and can beused for studying the behaviour of large systems or networks depending on many randomparameters. We are interested in properties of random spaces which are...
Creator:
Farber, Michael (University of Warwick)
Created:
2014-03-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will present a survey of recent results on geometry-based image processing. The topics will include wavelet-based diffuse interface methods, pan sharpening and hyperspectral sharpening, and sparse image representation.
Creator:
Bertozzi, Andrea L. (University of California, Los Angeles)
Created:
2009-10-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite 'length'. The basic question he addressed was whether the infinitesimal properties of the 'length' of a set E in the plane yield geometric information on E itself. This simple question marks the beginning of the study of the geometry of meas...
Creator:
Toro, Tatiana (University of Washington)
Created:
2015-05-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
