Saturday, March 29
MS5: Topology and Dynamical SystemsPart I of II
9:30am11:30am
Room: Crawford 526
For Part 2: MS 21
Organizers: Sergii Kutsak skutsak@ufl.edu Florida Institute of Technology Alexander Dranishnikov dranish at math dot ufl dot edu University of Florida
 9:30am10:00am Topological data analysis through directed filtrations Abstract
 Greg Bell, University of North Carolina at Greensboro
To a finite point cloud, one can associate a barcode (or persistence diagram) by computing homologies of a sequence of Čech complexes. In this talk we'll describe the advantages of replacing the balls that determine the Čech complex with ellipsoids. This is joint work with Thanos Gentimis.
 10:00am10:30am On topological complexity of twisted products Abstract
 Alexander Dranishnikov, University of Florida
The topological complexity was defined by M. Farber to measure robot navigational complexity of a configuration space. We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate of the topological complexity of a space in terms of its dimension and the complexity of its fundamental group.
 10:30am11:00am Wheeze detection using Topological Data Analysis Abstract
 Thanos Gentimis, North Carolina State University
Wheezes are abnormal lung sounds which usually imply obstructive airway diseases. In this talk, we will present a characterization of wheezes using tools from Topological Data Analysis. Namely, the shape of the time delay embedding of a wheeze signal is fundamentally different from that of a normal breathing signal; We used this difference to construct a robust algorithm, based on persistent homology, that distinguishes between the two. This paradigm can be generalized to other signals where almost periodic behavior is a characteristic feature of the signal.
 11:00am11:30am Extending Group Actions Abstract
 James Maissen, University of Florida
We will show sufficient criteria for a group of homeomorphisms acting on a metric space $X$ to extend to one acting on a given compactification of $X$. We give examples illustrating when this can fail when one of the criteria is not met. We then provide some quick applications of this theorem.
 11:30am12:00am A General Theorem About Queueing Networks Abstract
 James Keesling, University of Florida
Let N be a queueing network with $n$ nodes. Suppose that each node represents a queue of the form M/M/m/FIFO. Arrivals come to this system at a rate $\alpha$. The initial arrivals are directed to the various nodes by a probability vector $\{p_i\}_{i=1}^n$. Once in the system, at each node $i$ the clients are served and then directed to another node with probability $p_{ij}$. Certain nodes represent final disposition of the clients. Let $M$ be this transition matrix. It is essentially an absorbing Markov Chain. We show how to analyze this very general queueing system and how to distribute resources to minimize the total waiting time for the clients.
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