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All sources NASA NTRS DOE OSTI

DOE OSTI2021

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Computing Hypergraph Homology in Chapel

In this paper, we discuss our experience in implementing homology computation, in particular Betti number calculation in Chapel hypergraph Library (CHGL). Given a dataset represented as a hypergraph, a Betti number for a particular dimension $k$ indicates how many $k$-dimensional `voids' are present in the dataset. Computing Betti number involves various array-centric and linear algebra operations. We demonstrate that implementing these operations in Chapel is both concise and intuitive. In addition, we show that Chapel provides language constructs for implementing parallel and distributed execution of the linear algebra kernels with minimal effort. Syntactically, Chapel provides succinctness of Python, while delivering comparable and better performance than C++-based and Julia-based packages for calculating Betti numbers respectively.

hypergraph, topological data analysis↗

DOE OSTI2026

STM/S Grid LDOS Data and Analysis Code for Deciphering Majorana Zero Modes in Topological Superconductor

This dataset provides raw millikelvin scanning tunneling microscopy/spectroscopy (STM/S) grid spectroscopy data and Python analysis scripts supporting the manuscript “Deciphering Majorana Zero Modes in Topological Superconductor FeTe0.55Se0.45 with Machine-Learning-Assisted Spectral Deconvolution.” The dataset includes a raw grid spectroscopy file acquired on FeTe0.55Se0.45 at 40 mK under magnetic field, together with Python/Jupytext analysis scripts used for STM/S data processing, visualization, spectral deconvolution, Lorentzian peak fitting, feature extraction, machine-learning-assisted clustering, and figure generation. These files support the analysis of vortex-core local density of states and the identification of zero-bias-peak-related spectral components from complex in-gap states. The dataset is intended to provide a citable archival record of the data and analysis code associated with the published manuscript and to support transparency and reproducibility of the reported STM/S and machine-learning workflow.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Topological analysis of X-ray CT data for the recognition and trending of subtle changes in microstructure under material aging

X-ray computed tomography (CT) is an established non-destructive tool for 3D imaging of multiphasic composites. Numerous applications of X-ray CT in medical diagnosis and materials characterization have been reported, many involving field-specific innovations in the imaging technology itself. Yet, quantitative summarization to link image features to properties of interest has been rare. Here we address this issue by employing state-of-the-art technics in scalar field topology for the summarization of X-ray CT images of an example biphasic system. By varying processing-parameters we create different microstructures, evolve them through accelerated thermal aging, CT-image them pre- and post-aged, and demonstrate the ability of our image summarization method to systematically track process- and age-related changes, which can often be very subtle. A novel aspect of the algorithm involves recognition over multiple resolution levels, which provides deeper insight into the pattern relationship between grain-like features and their neighbors. The method is general, adaptable to diverse image reconstruction methods and materials systems, and particularly useful in applications where practical constraints on the sample-size limits the reliable use of more complex models, e.g., convolutional neural networks.

36 MATERIALS SCIENCE↗

NASA NTRS2019

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.

Persistent Homology↗

DOE OSTI2024

Topological Interpretability for Deep Learning

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is an increasing concern, especially in high-risk systems such as criminal justice or medical diagnosis, where incorrect inferences may have tragic consequences. Despite their successes in providing solutions to problems involving real-world data, deep learning (DL) models cannot quantify the certainty of their predictions. These models are frequently quite confident, even when their solutions are incorrect. This work presents a method to infer prominent features in two DL classification models trained on clinical and non-clinical text by employing techniques from topological and geometric data analysis. We create a graph of a model's feature space and cluster the inputs into the graph's vertices by the similarity of features and prediction statistics. We then extract subgraphs demonstrating high-predictive accuracy for a given label. These subgraphs contain a wealth of information about features that the DL model has recognized as relevant to its decisions. We infer these features for a given label using a distance metric between probability measures, and demonstrate the stability of our method compared to the LIME and SHAP interpretability methods. This work establishes that we may gain insights into the decision mechanism of a DL model. This method allows us to ascertain if the model is making its decisions based on information germane to the problem or identifies extraneous patterns within the data.

Spannaus, Adam↗

NASA NTRS2017

Performance Enhancement 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, voids, etc., from a point cloud by finding out when these features appear and disappear in the filtration sequence. In this project, we focus on improving the performance of Eirene, a fancy computational persistent homology package. Eirene is a 5000-line opensource software implemented by using the dynamic programming language Julia. We use the Julia profiling tools to identify the performance bottlenecks and develop different methods to manage the bottlenecks, including the parallelization of some time-consuming functions on the multicore/manycore hardware. The empirical results show that the performance can be greatly improved.

Profiling↗

DOE OSTI2022

A graph signal processing‐based multiple model Kalman filter ( GSP‐MMKF ) tool for predictive analytics: An air separation unit process application

Abstract The industrial Air Separations Unit (ASU) is a complicated and tightly operated process. The use of dynamic process analytics is also a key element of safe and economic operation of these processes, with increasing focus on predictive analytics to take preemptive actions. With the availability of real‐time data from hundreds of sensors, the data analysis process should also consider the topology of the data, as seen in sensor networks. In this paper, a novel tool is presented that considers the complex connectivity patterns in the sensor network and uses local adaptive disturbance estimations to predict global network‐scale trends. The paper introduces the emerging field of Graph Signal Processing (GSP) and presents a rigorous derivation of the tool starting from the extraction of the sensor‐network (in a graph theoretical sense) from the data. This network, which is in the form of a matrix, is then used to derive a Kalman‐filter type of state‐space model driven by input disturbances. Multiple disturbance models (e.g., step, ramp, periodic) are included to allow the model to have different kinds of disturbance propagation. Each graph node (representing the sensors used) dynamically adapts to the most recent detected disturbance individually. These estimated disturbances are propagated to the global network using the graph. Modifications to ensure stability are also discussed. The fidelity of the tool is tested on certain downtime events and the paper concludes by discussing the advantages of the method and planned future improvements.

Ghosh, Sambit↗

DOE OSTI2025

Gene network centrality analysis identifies key regulators coordinating day-night metabolic transitions in Synechococcus elongatus PCC 7942 despite limited accuracy in predicting direct regulator-gene interactions

Synechococcus elongatus PCC 7942 is a model organism for studying circadian regulation and bioproduction, where precise temporal control of metabolism significantly impacts photosynthetic efficiency and CO 2 -to-bioproduct conversion. Despite extensive research on core clock components, our understanding of the broader regulatory network orchestrating genome-wide metabolic transitions remains incomplete. We address this gap by applying machine learning tools and network analysis to investigate the transcriptional architecture governing circadian-controlled gene expression. While our approach showed moderate accuracy in predicting individual transcription factor-gene interactions - a common challenge with real expression data - network-level topological analysis successfully revealed the organizational principles of circadian regulation. Our analysis identified distinct regulatory modules coordinating day-night metabolic transitions, with photosynthesis and carbon/nitrogen metabolism controlled by day-phase regulators, while nighttime modules orchestrate glycogen mobilization and redox metabolism. Through network centrality analysis, we identified potentially significant but previously understudied transcriptional regulators: HimA as a putative DNA architecture regulator, and TetR and SrrB as potential coordinators of nighttime metabolism, working alongside established global regulators RpaA and RpaB. This work demonstrates how network-level analysis can extract biologically meaningful insights despite limitations in predicting direct regulatory interactions. The regulatory principles uncovered here advance our understanding of how cyanobacteria coordinate complex metabolic transitions and may inform metabolic engineering strategies for enhanced photosynthetic bioproduction from CO 2 .

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2015

Hints on nuclear effects from ArgoNeuT data

Initial results from a topological analysis of CC “0 pion” muon neutrino events in LAr collected by the ArgoNeuT experiment on the NuMI LE beam at Fermilab (in the few GeV energy region) are presented and compared with predictions from MC simulations. A new analysis method, based on the reconstruction of exclusive topologies, fully exploiting the LArTPC technique capabilities, is used to analyze the events and study nuclear effects in neutrino interactions on Argon nuclei. Multiple protons accompanying the leading muon and the presence of vertex activity are clearly visible (and measured) in the events. Ratios among rates of different exclusive topologies provide indications of the size of nuclear effects in neutrino-nucleus interactions in LAr.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2014

Topology for Statistical Modeling of Petascale Data

This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Distributed Contour Trees

Topological techniques provide robust tools for data analysis. They are used, for example, for feature extraction, for data de-noising, and for comparison of data sets. This chapter concerns contour trees, a topological descriptor that records the connectivity of the isosurfaces of scalar functions. These trees are fundamental to analysis and visualization of physical phenomena modeled by real-valued measurements. We study the parallel analysis of contour trees. After describing a particular representation of a contour tree, called local{global representation, we illustrate how di erent problems that rely on contour trees can be solved in parallel with minimal communication.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Curvature Energetics Determined by Alchemical Simulation on Four Topologically Distinct Lipid Phases

The relative curvature energetics of two lipids are tested using thermodynamic integration (TI) on four topologically distinct lipid phases. Simulations use TI to switch between choline headgroup lipids (POPC; that prefers to be flat) and ethanolamine headgroup lipids (POPE; that prefer, for example, the inner monolayer of vesicles). Here, the thermodynamical moving of the lipids between planar, inverse hexagonal (H II ), cubic (Q II ; Pn3m space group), and vesicle topologies reveals differences in material parameters that were previously challenging to access. The methodology allows for predictions of two important lipid material properties: the difference in POPC/POPE monolayer intrinsic curvature (ΔJ 0 ) and the difference in POPC/POPE monolayer Gaussian curvature modulus (Δ$\bar{κ_m}$), both of which are connected to the energetics of topological variation. Analysis of the TI data indicates that, consistent with previous experiment and simulation, the J 0 of POPE is more negative than POPC (ΔJ 0 = –0.018 ± 0.001 Å –1 ). The theoretical framework extracts significant differences in $\bar{κ_m}$ of which POPE is less negative than POPC by 2.0 to 4.0 kcal/mol. The range of these values is determined by considering subsets of the simulations, and disagreement between these subsets suggests separate mechanical parameters at very high curvature. Finally, the fit of the TI data to the model indicates that the position of the pivotal plane of curvature is not constant across topologies at high curvature. Overall, the results offer insights into lipid material properties, the limits of a single HC model, and how to test them using simulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

An empirical assessment of a single family‐wide hybrid capture locus set at multiple evolutionary timescales in Asteraceae

Premise Hybrid capture with high‐throughput sequencing (Hyb‐Seq) is a powerful tool for evolutionary studies. The applicability of an Asteraceae family‐specific Hyb‐Seq probe set and the outcomes of different phylogenetic analyses are investigated here. Methods Hyb‐Seq data from 112 Asteraceae samples were organized into groups at different taxonomic levels (tribe, genus, and species). For each group, data sets of non‐paralogous loci were built and proportions of parsimony informative characters estimated. The impacts of analyzing alternative data sets, removing long branches, and type of analysis on tree resolution and inferred topologies were investigated in tribe Cichorieae. Results Alignments of the Asteraceae family‐wide Hyb‐Seq locus set were parsimony informative at all taxonomic levels. Levels of resolution and topologies inferred at shallower nodes differed depending on the locus data set and the type of analysis, and were affected by the presence of long branches. Discussion The approach used to build a Hyb‐Seq locus data set influenced resolution and topologies inferred in phylogenetic analyses. Removal of long branches improved the reliability of topological inferences in maximum likelihood analyses. The Astereaceae Hyb‐Seq probe set is applicable at multiple taxonomic depths, which demonstrates that probe sets do not necessarily need to be lineage‐specific.

Jones, Katy E.↗

DOE OSTI2013

Distributed merge trees

Improved simulations and sensors are producing datasets whose increasing complexity exhausts our ability to visualize and comprehend them directly. To cope with this problem, we can detect and extract significant features in the data and use them as the basis for subsequent analysis. Topological methods are valuable in this context because they provide robust and general feature definitions. As the growth of serial computational power has stalled, data analysis is becoming increasingly dependent on massively parallel machines. To satisfy the computational demand created by complex datasets, algorithms need to effectively utilize these computer architectures. The main strength of topological methods, their emphasis on global information, turns into an obstacle during parallelization. We present two approaches to alleviate this problem. We develop a distributed representation of the merge tree that avoids computing the global tree on a single processor and lets us parallelize subsequent queries. To account for the increasing number of cores per processor, we develop a new data structure that lets us take advantage of multiple shared-memory cores to parallelize the work on a single node. Finally, we present experiments that illustrate the strengths of our approach as well as help identify future challenges. Copyright © 2013 ACM 978-1-4503-1922-5/13/ 02...$15.00.

Morozov, D↗

DOE OSTI2018

PIPER: Performance Insights for Programmers and Exascale Runtimes

During the lifetime of the project, the PIPER at the University of Utah worked in collaboration with the team from the partner institutions to establish a set of software tools for analyzing and improving the performance parallel computing tools. These activities complement and complete the work performed by the other X-Stack 2 projects with the definition of a common data models and computing infrastructures, which have been a central element in the targeted performance analysis pipeline and new programming models. The University of Utah team have focused mainly on developing data analysis and visualization systems to facilitate exploration, comparison and evaluation of the behavior and performance of complex algorithms in modern HPC infrastructures. This is involved several demonstrations of the performance achieved and presentation of the results in a way that facilitates the users understand bottlenecks and ways to overcome them. One major focus of the University of Utah activities has been the analysis of the performance characteristics of Fat-Tree and Dragonfly topology networks. The work involved the development of practical visualization systems especially in collaboration with the team at LLNL, and published several papers and gave invited talks at prestigious venues such as the Salishan Conference on High-Speed Computing or the International Conference on High Performance Computing, Data, and Analytics. In addition, the university of Utah team has advanced the core activities on analyzing the performance characteristics of I/O and other data movement systems and their practical use for scaling Uintah and other simulation codes poised for use in the exascale computing environments of the future.

42 ENGINEERING↗

NASA NTRS1991

Analysis and representation of complex structures in separated flows

We discuss our recent work on extraction and visualization of topological information in separated fluid flow data sets. As with scene analysis, an abstract representation of a large data set can greatly facilitate the understanding of complex, high-level structures. When studying flow topology, such a representation can be produced by locating and characterizing critical points in the velocity field and generating the associated stream surfaces. In 3D flows, the surface topology serves as the starting point. The 2D tangential velocity field near the surface of the body is examined for critical points. The tangential velocity field is integrated out along the principal directions of certain classes of critical points to produce curves depicting the topology of the flow near the body. The points and curves are linked to form a skeleton representing the 2D vector field topology. This skeleton provides a basis for analyzing the 3D structures associated with the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations. Integration origins are successively refined to produce stream surfaces. The map of the global topology is completed by generating those stream surfaces associated with 3D critical points.

Helman, James↗

DOE OSTI2015

Multiresolution persistent homology for excessively large biomolecular datasets

Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗