Polymers are macromolecules that cannot cross each other without
breaking their bonds. This leads to polymer chain entanglement
which determines bulk viscoelastic responses of the material.
Understanding the relation between entanglement and...
We first describe mathematical foundation of DSGRN (Dynamic
Signatures Generated by Regulatory Networks), an approach that
provides a queryable description of global dynamics of a network
over its entire param- eter space. We describe a connection...
DNA rearrangement is observed at developmental and evolutionary
scale. The recombination process can be directly modeled by
4-regular graphs and Gauss codes, also called double occurrence
words. We discuss properties of these graphs, their spatial...
Motivated by thematic similarities between persistent homology and
magnitude homology, we describe a simplicial construction
associated to a metric space. This construction is determined by
(apart from the metric space itself) a choice of two...
We use persistent homology to analyze predictions of protein
folding by trying to identify global geometric structures that
contribute to the error when the protein is misfolded. The goal is
to find correlations between global geometric structures...
We will showcase persistent homology as a promising new tool for
use in the study of complicated fluid flows. Through a collection
of examples spanning 2D Kolmogorov and Rayleigh-Bénard
convection flows to fully-developed 3D turbulence and...
Extrinsic Flavor: Given a point cloud in R^N sampled from an
unknown probability density, how can we decide whether that
probability density is concentrated near a low-dimensional manifold
M with reasonable...
Using the geometry of sheaves as the common language, this talk
will bridge three separate areas: dynamical systems, signal
processing, and data fusion. Because sheaves model consistency
relationships between local data, they are easily assembled...
Nazarov and Sodin have shown that the zero set of a random real
homogeneous polynomial in n+1 variables and of large degree has
many components and the same is true for the random harmonic such
polynomial ("mono-chromatic waves") .We show that for...
In the first half of the talk I will give a very compressed
introduction into parts of Theoretical Distributed Computing from
the point of view of mathematician. I will describe how to
construct simplicial models whose combinatorics contains...