8,673 research outputs found
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
Multilayer relationships among entities and information about entities must
be accompanied by the means to analyze, visualize, and obtain insights from
such data. We present open-source software (muxViz) that contains a collection
of algorithms for the analysis of multilayer networks, which are an important
way to represent a large variety of complex systems throughout science and
engineering. We demonstrate the ability of muxViz to analyze and interactively
visualize multilayer data using empirical genetic, neuronal, and transportation
networks. Our software is available at https://github.com/manlius/muxViz.Comment: 18 pages, 10 figures (text of the accepted manuscript
A topological approach for protein classification
Protein function and dynamics are closely related to its sequence and
structure. However prediction of protein function and dynamics from its
sequence and structure is still a fundamental challenge in molecular biology.
Protein classification, which is typically done through measuring the
similarity be- tween proteins based on protein sequence or physical
information, serves as a crucial step toward the understanding of protein
function and dynamics. Persistent homology is a new branch of algebraic
topology that has found its success in the topological data analysis in a
variety of disciplines, including molecular biology. The present work explores
the potential of using persistent homology as an indepen- dent tool for protein
classification. To this end, we propose a molecular topological fingerprint
based support vector machine (MTF-SVM) classifier. Specifically, we construct
machine learning feature vectors solely from protein topological fingerprints,
which are topological invariants generated during the filtration process. To
validate the present MTF-SVM approach, we consider four types of problems.
First, we study protein-drug binding by using the M2 channel protein of
influenza A virus. We achieve 96% accuracy in discriminating drug bound and
unbound M2 channels. Additionally, we examine the use of MTF-SVM for the
classification of hemoglobin molecules in their relaxed and taut forms and
obtain about 80% accuracy. The identification of all alpha, all beta, and
alpha-beta protein domains is carried out in our next study using 900 proteins.
We have found a 85% success in this identifica- tion. Finally, we apply the
present technique to 55 classification tasks of protein superfamilies over 1357
samples. An average accuracy of 82% is attained. The present study establishes
computational topology as an independent and effective alternative for protein
classification
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
This work introduces a number of algebraic topology approaches, such as
multicomponent persistent homology, multi-level persistent homology and
electrostatic persistence for the representation, characterization, and
description of small molecules and biomolecular complexes. Multicomponent
persistent homology retains critical chemical and biological information during
the topological simplification of biomolecular geometric complexity.
Multi-level persistent homology enables a tailored topological description of
inter- and/or intra-molecular interactions of interest. Electrostatic
persistence incorporates partial charge information into topological
invariants. These topological methods are paired with Wasserstein distance to
characterize similarities between molecules and are further integrated with a
variety of machine learning algorithms, including k-nearest neighbors, ensemble
of trees, and deep convolutional neural networks, to manifest their descriptive
and predictive powers for chemical and biological problems. Extensive numerical
experiments involving more than 4,000 protein-ligand complexes from the PDBBind
database and near 100,000 ligands and decoys in the DUD database are performed
to test respectively the scoring power and the virtual screening power of the
proposed topological approaches. It is demonstrated that the present approaches
outperform the modern machine learning based methods in protein-ligand binding
affinity predictions and ligand-decoy discrimination
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