Category: Publications

In this paper, we leverage persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout by adding and removing contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout.

A key problem in Deep Brain Stimulation (DBS) is determining the optimal parameters for clinical outcome. Current knowledge does not provide a complete deterministic model of DBS neurophysiology. While multiple parameters may influence clinical outcomes in DBS, this paper explores spatial correlation of volume of tissue activated (VTA) to Unified Parkinson’s Disease Rating Scale (UPDRS) scores.

This paper introduces and extension to our previous papers to handle anomalies in the point based object slicing method. The anomalies handled are point, line and plane touch cases as well as overlaps.

In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into a metric space, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data.

We study the topological construction called Mapper in the context of simply connected domains, in particular on images.