Pieces of string or curves in three dimensional space may be knotted orbraided. This topological tool can be used to study certain types of nonlineardifferential equations. In particular, such an approach leads to forcingtheorems in the spirit of the famous 'period three implies chaos' for intervalmaps. We have identified three types of differen...
Creator:
Van den Berg, Jan Bouwe (Vrije Universiteit)
Created:
2014-02-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will discuss some stylized topological inference problems and give some information about Kolmogorov, sample and computational complexity. I will then discuss some tentative first steps towards a theory of feasibly computable invariants.
Creator:
Weinberger, Shmuel (University of Chicago)
Created:
2013-10-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets in lower, but still meaningful dimensions for visualization and analysis has grown rapidly over the past decade, including analysis of hyperspectral remote sensing data. The high spectral resolution and the typically continuous bands of hyp...
Creator:
Crawford, Melba (Purdue University)
Created:
2013-09-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Persistent homology and persistent diagrams have been developed as tools of topological data analysis. They provide a robust topological characterization of a given (discrete) geometrical data. In this talk, I will present our recent researches on applying persistent diagrams to protein structural analysis. Topological characterizations of prote...
Creator:
Hiraoka, Yasu (Kyushu University)
Created:
2013-06-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Our work with x-ray micro-CT images of complex porous materials has required the development of topologically valid and efficient algorithms for studying and quantifying their intricate structure. As an example, simulations of two-phase fluid displacements in a porous rock depend on network models that accurately reflect the connectivity and geo...
Creator:
Robins, Vanessa (Australian National University)
Created:
2014-02-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The theory of smectic liquid crystals is notoriously difficult to study. Thermal fluctuations render them disordered through the Landau-Peierls instability, lead to anomalous momentum dependent elasticity, and make the nematic to smectic-A transition enigmatic, at best. I will discuss recent progress in studying large deformations of smectics wh...
Created:
2008-07-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Over the last ten years, a number of methodologies have been developed which leverage topological techniques and ways of thinking to provide understanding of point cloud data. These include ways of 'measuring' shape via homological signatures, topological mapping techniques, and applications of certain kinds of diagram constructions to collectio...
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2012-03-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we introduce the basic construction of topological RNA structures.We introduce shapes and the associated shape polynomial and its connection toRNA folding. We then establish the connection to unicellular maps and outlinethe combinatorial constructions that facilitate genus induction. We furthermoreshow applications of this framework...
Creator:
Reidys, Christian M. (Syddansk Universitet (University of Southern Denmark))
Created:
2013-12-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The hippocampus plays an important role in representing space (for spatial navigation) and time (for episodic memory). Spatial representation of the environment is pivotal for navigation in rodents and primates. Two types of maps, topographical and topological, may be used for spatial representation. Rodent hippocampal place cells exhibit spatia...
Creator:
Chen, Zhe (Sage) (Massachusetts Institute of Technology)
Created:
2013-12-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk I will introduce some techniques for topological reasoning within the purview of graph search-based motion planning. Classically, in robotics and artificial intelligence literature, a popular approach to dealing with complexities in configuration spaces (high dimension or topological non-trivialities) is to create a graph by placing...
Creator:
Bhattacharya, Subhrajit (University of Pennsylvania)
Created:
2014-03-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.