25 Feb 2011 11:15 a.m. in room 383 N
25 Mar 2011 11 a.m. in room 380 D
Analyzing systems is a difficult problem that is often made much easier by a good choice of parametrization. A natural choice for dynamical systems is the mapping to the circle. This mapping can describe a variety of behaviour including (quasi)-periodicity and recurrence. This talk will introduce a topological approach for understanding dynamical systems from measurements. Starting with a time series measurement of a dynamical system, using a pipeline based in the framework of computational topology, we can recover an astonishing amount of information about the system. We begin by embedding the time series in a higher dimension and use persistent cohomology to construct a natural parameterization which makes further analysis much easier. I will discuss the individual components of the pipeline as well as show results on several examples of synthetic and real data.
22 Apr 2011 10:30 a.m. in room Gates 392
During most of the cell cycle each chromosome occupies a roughly spherical domain called a chromosome territory. Chromosome territories can overlap and their radial and relative positions are non-random and similar among similar cell types. A chromosome arrangement can be viewed as a packing of overlapping spheres of various sizes inside an ellipsoid, the cell nucleus. We present a non-convex model for chromosome arrangements and are particularly interested in the resulting number and volume of internal 'holes', which make chromosomes deep inside accessible to regulatory factors.
3 Oct 2011 4:15 a.m. in room 380-380C (ICME Colloquium)
An important aspect of understanding large and complex data sets is the large scale organization, or the shape, of the data. Topology is a mathematical discipline whose explicit goal is the study of shape. It constructs for representing shape in compressed, combinatorial manners, and also provides methods for measuring shape, where the notion of measurement is suitably defined. Topological methods have recently been adapted to for the study of finite samples from shapes. I will discuss these methods, with examples.
28 Oct 2011 11 a.m. in room 383-N