Seminars Sorted by Series

Schedule: https://sites.google.com/site/thingroups/schedule

Schedule: https://sites.google.com/site/thingroups/schedule

Schedule: https://sites.google.com/site/thingroups/schedule

Schedule: https://sites.google.com/site/thingroups/schedule

Schedule: https://sites.google.com/site/thingroups/schedule

In this talk, I will try to explain some of the interest in the question of the computation of the homology of a space from noisy data samples as it relates to clustering and other natural problems. Moreover, I will also try to indicate some...

We construct our understanding of the world solely from neuronal activity generated in our brains. How do we do this? Many studies have investigated how the electrical activity of neurons (action potentials) is related to outside stimuli, and maps...

We will see how Hodge theory can be a systemic way of finding geometric structures hidden in (higher dimensional) data.

With recent advances in computing power, numerical studies of nonlinear dynamical systems have become increasingly more popular. However, errors inherent to such studies may obscure the dynamics, or in the very least raise doubts about the existence...

My collaborators and I have spent a the better part of two decades seeking to develop formally and apply empirically methods of programming work: that is, we want to know how to say what we mean, yet mean what we say to a machine built for...

Proteins with knots in their native state were discovered few years ago. Analysis of the entire protein data base indicates that there are quite a few proteins with knots, particularly with slip knots, but still the fraction of proteins with knots...

We discuss some geometric and topological methods that are applied to overcome the large gap problem in Arnold diffusion for a priori unstable Hamiltonian systems. The geometric methods rely on the theory of normally hyperbolic invariant manifolds...

For a planar domain, a finite point configuration is said to be caging, if the set of Euclidean motions of the domain not hitting the point configuration is bounded. Caging configurations are important in robotics and are a popular topic in...

Optical fields propagating in three-dimensional free space are complex scalar fields, and typically contain nodal lines (optical vortices) which may be thought of as interference fringes. Random wave fields, representing speckle patterns randomly...

This will be a report on topics related to topological complexity (TC), introduced by Michael Farber in 2003 as a numerical measure of the complexity of robot motion planning problems. TC of real projective space P^n (lines through the origin in...

The ordinary homology of a subset S of Euclidean space depends only on its topology. By systematically organizing homology of neighborhoods of S, we get quantities that measure the shape of S, rather than just its topology. These quantities can be...

The space of all positions of n disks of radius r in a bounded region has long been studied from the points of view of statistical mechanics and probability. A phase transition is known to occur from simulations, but this is still mysterious to...

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational...

DNA copy number abnormalities (CNAs) play an important role in cancer, and are associated with tumor progression as well as clinical outcome. Using microarray based comparative genomic hybridization (CGH), analysis of CNAs across large cohorts of...

High-dimensional data sets often carry meaningful low-dimensional structures. There are different ways of extracting such structural information. The classic (circa 2000, with some anticipation in the 1990s) strategy of nonlinear dimensionality...