Upcoming MAMS Seminar Series
Spring 2023
Tuesday 3/7— 2:30-3:30 pm at Yost 306
Speaker: Mark Meckes
Title: Magnitude of metric spaces and intrinsic volumes in normed spaces
Abstract: Magnitude is an isometric invariant of metric spaces which was originally motivated by category theory, and has turned out to be closely related to a wide variety of other geometric quantities, from dimension to volume to persistent homology. I will give a survey of this subject, focusing in particular on results relating magnitude to intrinsic volumes in both Euclidean and more general normed spaces, and some recent applications of these connections.
Spring 2023
Wednesday 3/8— 4:00-5:00 pm at Yost 306
Speaker: Xiaofeng Wang, PhD Department of Quantitative Health Sciences
Lerner Research Institute
Cleveland Clinic
Title: Adaptive Density Peak Clustering for Complex Data
Abstract: Common limitations of existing clustering methods include slow algorithm convergence,
instability of the pre-specification on intrinsic parameters, and the lack of robustness to
outliers. In this talk, we present a novel clustering method using an adaptive density peak
detection technique. It is a quick cluster center identification algorithm based on the two
measures of each data observation: the density estimate and the distance to the closest
observation with a higher functional density. Our clustering method is computationally fast
since it does not need an iterative process. We apply our approach to mixed data with both
categorical and continuous variables, as well as complex multivariate functional data. The
flexibility and advantages of the method are examined by comparing it with other existing
clustering methods in simulation studies. Two user-friendly R packages, ADPclust and
FADPclust, have been developed for public use. Finally, the new clustering method is applied to
a real case study in lung cancer research.
Wednesday 4/12— 4:00-5:00 pm at Yost 306
Speaker: Dr. Ulises Fidalgo
Title: A multi-orthogonal polynomials’ approach to a bulk queueing model
Abstract: We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal polynomials with respect to a system of distributions that contain measures supported on starlike subsets of the complex plane. We give explicit expressions for such polynomials and distributions in terms of the solution of an algebraic equation. We also verify that all the states can be reached from each other.