42,880 research outputs found
Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology
Topological data analysis is an emerging area in exploratory data analysis
and data mining. Its main tool, persistent homology, has become a popular
technique to study the structure of complex, high-dimensional data. 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 metric spaces, 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. To validate our
approach, we conduct several case studies on real world data sets and show how
our method can find cyclic patterns, deviations from those patterns, and
one-time events in time-varying graphs. We also examine whether
persistence-based similarity measure as a graph metric satisfies a set of
well-established, desirable properties for graph metrics
MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME
Computational experiments using spatial stochastic simulations have led to
important new biological insights, but they require specialized tools, a
complex software stack, as well as large and scalable compute and data analysis
resources due to the large computational cost associated with Monte Carlo
computational workflows. The complexity of setting up and managing a
large-scale distributed computation environment to support productive and
reproducible modeling can be prohibitive for practitioners in systems biology.
This results in a barrier to the adoption of spatial stochastic simulation
tools, effectively limiting the type of biological questions addressed by
quantitative modeling. In this paper, we present PyURDME, a new, user-friendly
spatial modeling and simulation package, and MOLNs, a cloud computing appliance
for distributed simulation of stochastic reaction-diffusion models. MOLNs is
based on IPython and provides an interactive programming platform for
development of sharable and reproducible distributed parallel computational
experiments
Tuning the Performance of a Computational Persistent Homology Package
In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved
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