Tripods Workshop

Geometry and topology play a key role in describing nature at the microscopic scales. Shape determines the function of proteins in biochemistry, macroscopic properties of materials, and even behaviors of organisms. This workshop will bring together researchers interested in using geometric and topological analysis to study the fascinating structures that appear in the micro-world.

Confirmed Speakers

Dunbar Birnie, Professor and Corning/Saint Goban/Malcolm G. McLaren Chair, Materials Science and Engineering, Rutgers University
Zixuan Cang, Department of Math, University of California, Irvine
Chao Chen, Assistant Professor, Department of Biomedical Informatics, Stony Brook University
Pawel Dlotko, Lecturer, Department of Mathematics, Swansea University
Christine Heitsch, Professor, School of Mathematics, Georgia Institute of Technology
Miranda Holmes-Cerfon, Assistant Professor, Courant Institute of Mathematical Sciences, New York University
Jeremy Mason, Assistant Professor, Materials Science and Engineering, University of California, Davis
Julie Mitchell, Director, Biosciences Division, Oak Ridge National Laboratory
Ippei Obayashi, Research Scientist, Center for Advanced Intelligence Project, RIKEN
Ben Schweinhart, Zassenhaus Assistant Professor, Department of Math, The Ohio State University
Tess Smidt, Luis W. Alvarez Postdoctoral Fellow, Berkeley Lab

Conference Details

Machine learning with persistent homology and its applications to materials science
Ippei Obayashi
Abstract: In this talk, I will present our recent research about the combination of persistent homology and machine learning and its applications to materials science. Persistent homology characterizes the shape of data, and machine learning finds the characteristic patterns from data. The combination of these two technique can find the characteristic geometric patterns from data. We use the persistence image method to construct an input for machine learning from persistence diagrams and a linear machine-learning model as machine learning models. Both methods are quite simple, and so we can intuitively interpret the learned result. Some inverse analysis methods for persistent homology are available with our data analysis framework to map the important geometric patterns onto the original input data. I will also present some applications of our method to the data analysis for materials science.

Feature Selection in Biomolecular Models
Julie Mitchell
Abstract: Protein-protein interactions regulate many essential biological processes and play an important role in health and disease. The process of experimentally characterizing protein residues that contribute the most to protein-protein interaction affinity and specificity is laborious. Thus, developing models that accurately characterize hotspots at protein-protein interfaces provides important information about how to drug therapeutically relevant protein-protein interactions. In this work, we combined the KFC2a protein-protein interaction hotspot prediction features with Rosetta scoring function terms and interface filter metrics. A 2-way and 3-way forward selection strategy was employed to train support vector machine classifiers, as was a reverse feature elimination strategy. From these results, we identified subsets of KFC2a and Rosetta combined features that show improved performance over KFC2a features alone. The forward selection algorithm also helped elucidate the biophysical principles that determine whether a given amino acid is a binding hot spot.

Topology (of) matter
Pawel Dlotko
Abstract: From non organic matter all the way to living cells and genome activity we encounter structures with interesting geometrical and topological properties. This structure very often determines function of the matter. In this talk I will give a few examples of cases when tools of computational topology can be useful to analyze and describe it. Starting from nanoporous materials, through shape of neural cells, ending up in gen activity we will show examples how tools from topology can help quantify and understand the considered objects.

Toward the Systematic Generation of Hypothetical Atomic Structures: Geometric Motifs and Neural Networks
Tess Smidt
Abstract: Materials discovery, a multidisciplinary process, now increasingly relies on computational methods. We can now rapidly screen materials for desirable properties by searching materials databases and performing high-throughput first-principles calculations. However, high-throughput computational materials discovery pipelines are bottlenecked by our ability to hypothesize new structures, as these approaches to materials discovery often presuppose that a material already exists and is awaiting identification. In contrast to this assumption, synthesis efforts regularly yield materials that differ substantially from the structures in databases of previously known materials. In this talk, we discuss strategies for generating hypothetical atomic structures using the concepts of geometric motifs (the recurring patterns of atoms in materials) and neural networks that can manipulate discrete geometry in Euclidean space (tensor field networks).

Topological methods for drug design
Zixuan Cang
Abstract: In drug design, accurate structure-based prediction of properties for target proteins, small molecules and protein-ligand complexes is a prerequisite for effective virtual screening of candidate drugs. A concise and informative description of the molecules and the molecular systems is a key to accurate prediction. In this talk I will present an approach using topological data analysis and machine learning which achieves competitive performance in several prediction tasks. Representations of molecules are obtained using persistent homology and the additional atomic features are retained in the representation using cohomology. We will also discuss the potential of integrating persistent homology into an optimization pipeline.

Geometry of a Phase Transition
Jeremy Mason
Abstract: A “phase” of matter is traditionally defined as a region of material throughout which all physical properties are essentially uniform. Water and steam are certainly distinct phases by this definition, but the situation is not always so clear—at sufficiently high pressures, the properties of water and steam converge and only a single “fluid” phase remains. The definition is still less clear at the atomic level, where the macroscopic properties used to distinguish phases are not even well-defined (e.g., what is the appropriate volume over which to average?). This talk explores the idea that the ambiguity in our definition of a phase is intimately related to our ignorance about the topography of a configuration space that governs the average properties of the physical system. Recent computational results concerning the topology of this configuration space for several examples systems will also be presented. This work is done in collaboration with Matthew Kahle and Facundo Memoli.

Microstructural Templating for Enhancing the Performance of Electrochemical Devices
Dunbar P. Birnie, III, Anand Patel, and Deborah Silver – and OSU collaborators
Abstract: Electrochemical devices often require microstructures with distinct regions where electronic and ionic charge motion must occur – separately, but also in unison – as the battery or solar cell device operates. We review our prior research in templated microstructures applied to dye-sensitized solar cells – where the templated microstructures have demonstrated enhanced ionic conductivity. Within this framework we also examine the gradation in microstructure that might ideally be required to fully optimize these devices (because of the variation of ionic-vs-electronic conduction that would be required as a function of depth). This analysis highlights microstructural and topological features that we will be trying to enhance for improvement of lithium battery systems performance in the future phases of this program.

Local Configurations in Cell Complexes, and Applications to Oxide Glasses
Benjamin Schweinhart
Abstract: The method of swatches describes the local topology of a cell complex in terms of discrete probability distributions of local configurations. In previous work, local configurations were considered equivalent if they shared the same graph isomorphism type. More recently, we have developed coarser notions of equivalence that result in more informative probability distributions in some applications. In my talk, I will introduce the method of swatches, describe different notions of equivalence for local configurations, and present preliminary results from ongoing research on oxide glasses. This is joint work with Jeremy Mason.

Spaces of RNA branching configurations
Christine Heitsch
Abstract: Understanding the folding of RNA sequences into three-dimensional structures is one of the fundamental challenges in molecular biology. For example, the branching of an RNA secondary structure is an important molecular characteristic yet difficult to predict correctly, especially for sequences on the scale of viral genomes. However, mathematical analysis of discrete models can characterize different types of branching landscapes. These theorems yield insights into RNA structure formation, and suggest new directions in viral capsid assembly.

Rigidity theory at the microscale
Miranda Holmes-Cerfon
Abstract: Colloids, particles with diameters of nanometres to micrometres, form the building blocks of many of the materials around us, and are widely studied both to understand existing materials, and to design new ones. A unique property of such particles is they are “sticky”: the range over which they interact attractively, is much shorter than their diameters. It is often effective to treat attractive interactions as distance constraints, so a system of sticky particles can be modeled as a framework, with vertices at the particle centres, and edges between particles in contact. I will describe how the mathematical theory of the rigidity of frameworks, which has been used to design bridges, buildings, and play structures, gives insight into various physical properties of these microscale particles. I will also describe its limitations, such as its inability to handle imperfections in particle sizes or elastic behaviour of the edges, and some of the theoretical progress we have made toward addressing these limitations from a purely geometric perspective.

Using Topology as a Structural Prior in Data Analysis
Chao Chen
Abstract:In various applications, it is crucial yet challenging to model global structures/behavior of large scale complex systems. In this talk, we discuss how topological information can be incorporated as structural prior/penalty/loss. A differentiable view of the topological computation enables us to seamlessly incorporate it into our learning framework. The topological prior helps extracting complex structural systems in biomedicine, e.g., neuronal systems and cardiac trabeculae. Meanwhile, in generic machine learning context, we use topological simplicity to improve the generalization ability and the robustness of a classifier.

Tripods Workshop

Tripods Workshop

Confirmed Speakers

Conference Details

Organizing Committee

Acknowledgments

Tripods Workshop

Tripods Workshop

Confirmed Speakers

Conference Details

Schedule

Titles and Abstracts

Travel and Lodging

Organizing Committee and Acknowledgements

Organizing Committee

Acknowledgments