Abstract: An area of interest in statistical mechanics is the study ofstatistical distributions of stochastic currents generated in graphs.It turns out that this problem amounts to the study of periodic familiesof Markov processes that evolve according to the 'master equation.' Physicists have observed that, for almost every generated current, q...
Creator:
Klein, John R. (Wayne State University)
Created:
2013-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint work with S. R. McAllister.The protein folding question has developed over the past four decades as one of the most challenging and potentially rewarding problems in computational biology. Three general classes of algorithms have emerged, based on the techniques of comparativemodeling, fold recognition, and first principles methods. For a ...
Creator:
Floudas, Christodoulos A. (Princeton University)
Created:
2008-01-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Coarse-grained (CG) models provide a promising computational tool for investigating slow complex processes that cannot be adequately studied using more detailed models. However, unless the CG model is consistent with an accurate high-resolution model, the results of CG modeling may be misleading. The present talk describes a statistical mechanic...
Creator:
Noid, William G. (The Pennsylvania State University)
Created:
2008-11-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In order to understand the properties of a real-valued function on a topological space, we can study the Reeb graph of that function. The Reeb graph is a construction which summarizes the connectivity of the level sets. Since it is efficient to compute and is a useful descriptor for the function, it has found its place in many applications. As w...
Creator:
Munch, Elizabeth (University of Minnesota, Twin Cities)
Created:
2014-03-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk focuses on the problem of finding the underlying communitieswithin a network using only knowledge of network topology. We consider agenerative model for a network, namely the planted cluster model, which is asimple extension of the classical stochastic block model. We derive a semidefinite programming (SDP) relaxation of the maximum li...
Creator:
Wu, Yihong (University of Illinois at Urbana-Champaign)
Created:
2015-05-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Recent data sparsification strategies in topological data analysis such as Graph Induced Complex and sparsified Rips complex give rise to a sequence of simplicial complexes connected by simplicial maps rather than inclusions. As a result, the need for computing topological persistence under such maps arises. We propose a practical algorithm for ...
Creator:
Dey, Tamal K. (The Ohio State University)
Created:
2014-05-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
As materials with broken translational symmetry, defects in smectic liquid crystals do not follow the traditional homotopy theoretic classification scheme, and a more geometrical approach is required. Using methods from singularity theory we study the topological classification and combination rules for point and line defects in two and three di...
Creator:
Machon, Thomas (University of Pennsylvania)
Created:
2018-01-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk is about the speaker's recent research work which offers ideas on how a network of dynamical systems is affected by its network topology from the performance and stability perspective. Unlike many existing works, the present talk focuses on the interplay between network topology and 'local dynamics'. More specifically, the present talk...
Creator:
Kim, Yoonsoo (Gyeongsang National University)
Created:
2016-02-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
As one of the most fundamental concepts in wave physics, resonance can give rise to a lot of interesting phenomena including low frequency band gaps. Because of its "divergent" nature, resonance also adds complexity into the modeling, and may even cause the failure of some widely adopted theories like quasi-static homogenization. In this talk, I...
Creator:
Wu, Ying (King Abdullah University of Science & Technology)
Created:
2017-03-13
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.
Problems in applied topology often require computation of an optimal (in some sense) representative among shapes satisfying particular topological constraints. In many cases this is a very challenging, if not infeasible task. Interestingly, such complex problem often can be tackled using biologically inspired algorithms. For example, slime mold ...
Creator:
Mileyko, Yuriy (University of Hawaii at Manoa)
Created:
2013-10-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will discuss the effect of geometric transformations on the topology of data. Geometric transformations are central in highlighting characteristics in the data that extract information. A common feature is that the same data set can provide answers to multiple problems. Thus the choice of underlying geometry is crucial in highlighting the answ...
Creator:
Nicolau, Monica (Stanford University)
Created:
2013-10-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we will describe methodologies to localize both a single and a team of vehicles navigating in a complex environment without GPS. During the first part of the talk, we will consider the situation when vehicles (or a single vehicle navigating in an environment with multiple beacons) can measure their relative (inter-vehicle) distances...
Creator:
Speranzon, Alberto (United Technologies Corporation)
Created:
2014-03-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
To solve real-world data analysis questions, researchers from different fields must collaborate. Topological data analysis (TDA) combines algebraic topology (mathematics) and algorithmic developments (computer science). Recent developments in the field introduce statistical concepts to TDA.In Part I, we will discuss general questions we face in ...
Creator:
Terese, Brittany (Montana State University)
Created:
2018-08-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Recently, sheaves have become useful for addressing problems in signal processing. Morphisms between sheaves provide a handy formal construct for understanding the relationship between measurements, intermediate data, and processed outputs. The resulting topological filters generalize the linear filters that engineers use extensively, but also d...
Creator:
Robinson, Michael (American University)
Created:
2014-03-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The tree structure is currently the accepted paradigm to represent evolutionary relationships between organisms, species or other taxa. However, horizontal, or reticulate, genomic exchanges are pervasive in nature and confound characterization of phylogenetic trees. Drawing from algebraic topology, we present a unique evolutionary framework that...
Creator:
Rabadan, Raul (Columbia University)
Created:
2013-12-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In the first lecture, we will provide an overview of the various ways that topological informationis used in signal detection problems in functional MRI (fMRI) and otherimaging applications. The principal tool used involves computing the expectednumber of critical points of various types of a smooth random field undersome predetermined null hypo...
Creator:
Taylor, Jonathan (Stanford University)
Created:
2013-10-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Topological transport of sound waves and vibrations in solids has attracted considerable attention in the past two years. Several approaches have been proposed and some have been demonstrated. However, it remains an outstanding challenge to create platforms for topological transport of phonons at the nanoscale. In this talk, I will describe thre...
The nature and quantity of data arising out of scientific applications requires novel methods, both for exploratory analysis as well as analysis of significance and validation. One set of new methods relies on ideas and methods from topology. The study of data sets requires an extension of standard methods, which we refer to as persistent topolo...
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2008-10-29
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.
