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DOE OSTI2020

A Guide to Conquer the Biological Network Era Using Graph Theory

Networks are one of the most common ways to represent biological systems as complex sets of binary interactions or relations between different bioentities. In this article, we discuss the basic graph theory concepts and the various graph types, as well as the available data structures for storing and reading graphs. In addition, we describe several network properties and we highlight some of the widely used network topological features. We briefly mention the network patterns, motifs and models, and we further comment on the types of biological and biomedical networks along with their corresponding computer- and human-readable file formats. Finally, we discuss a variety of algorithms and metrics for network analyses regarding graph drawing, clustering, visualization, link prediction, perturbation, and network alignment as well as the current state-of-the-art tools. We expect this review to reach a very broad spectrum of readers varying from experts to beginners while encouraging them to enhance the field further.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Visualization techniques for the gyrokinetic tokamak simulation code

Gyrokinetic simulations of plasma microturbulence in tokamaks are challenging to visualize because the compute grid follows the magnetic field lines that spiral around the torus. We have overcome this challenge by developing three new approaches that improve visualization of gyrokinetics. Our techniques work directly with the topology of magnetic flux surfaces where the simulation stores variables in concentric rings on poloidal planes (vertical cross sections of the torus). Our visualization preview step triangulates each consecutive pair of rings to display the data on a poloidal plane. The second visualization technique follows spiral field lines around the torus and constructs polygons to visualize a flux surface. Third, the poloidal triangles are connected between planes to form prisms that compose a 3-D model of the entire torus. The visualization workflow produces detailed geometry that matches the high resolution, irregular compute grid for every time step. The surface and solid models are displayed in scientific visualization programs to effectively explore and communicate the results, including fluctuation of electron density, ion temperature, and electrostatic potential. Highly detailed renderings verify plasma behavior along magnetic field lines over time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

Surface flow vectors↗

DOE OSTI2022

Visualization of Tunable Weyl Line in A–A Stacking Kagome Magnets

Abstract Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin–orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle‐resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out‐of‐plane dispersion in the A–A stacked kagome magnet GdMn 6 Sn 6 . Remarkably, the Weyl lines exhibit a strong magnetization‐direction‐tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn 6 Sn 6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Cheng, Zi‐Jia↗

NASA NTRS1984

Flow visualization and interpretation of visualization data for deflected thrust V/STOL nozzles

Flow visualization studies were made for four deflected thrust nozzle models at subsonic speeds. Based on topological rules and the assumption that observed streaks constitute continuous vector fields, available visualization pictures are interpreted and flow patterns on interior surfaces of the nozzles are synthesized. In particular, three dimensional flow structure and separations are discussed. From the synthesized patterns, the overall features of the flow field in a given nozzle can be approximately perceived.

Kao, H. C.↗

NASA NTRS1984

Flow visualization and interpretation of visualization data for deflected thrust V/STOL nozzles

Kao, H. C.↗

DOE OSTI2025

Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be dramatically modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases, forming at the boundaries of two-dimensional (2D) electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here, we use scanning tunneling microscopy (STM) to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for copropagating modes, and induce unexpected edge valley polarization that differ from those of the bulk. While some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Furthermore, our study establishes STM as a promising tool for exploring edge physics of the rapidly expanding 2D topological phases, including newly realized fractional Chern insulators.

Electronic properties and materials↗

DOE OSTI2025

Quantum geometry embedded in unitarity of evolution: Revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands

Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized “step” represents a distinct topological state. Here, we seek a counterpart for “visualizing” quantum geometry, which is a broader concept. Here we show how geometry emerges in quantum as an intrinsic consequence of unitary evolution, composing a framework compatible with quantum metric and independent of specific details or approximations, suggesting quantum geometry may have widespread applicability. Indeed, we exemplify geometric observables, such as oscillation, dephasing, in magnetic resonance or band driving scenarios. Anomalies, supported by both analytic and numerical solutions, underscore the advantages of adopting a geometric perspective, potentially yielding distinguishable experimental signatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclones

Tropical cyclones (TCs) are among the most destructive weather systems. Realistically and efficiently detecting and tracking TCs are critical for assessing their impacts and risks. In particular, the eye is a signature feature of a mature TC. Therefore, knowing the eyes’ locations and movements is crucial for both operational weather forecasts and climate risk assessments. Recently, a multilevel robustness framework has been introduced to study the critical points of time-varying vector fields. The framework quantifies the robustness (i.e., structural stability) of critical points across varying neighborhoods. By relating the multilevel robustness with critical point tracking, the framework has demonstrated its potential in cyclone tracking. An advantage is that it identifies cyclonic features using only 2D wind vector fields, which is encouraging as most tracking algorithms require multiple dynamic and thermodynamic variables at different altitudes. A disadvantage is that the framework does not scale well computationally for datasets containing a large number of cyclones. Herein this paper introduces a topologically robust physics-informed tracking framework (TROPHY) for TC tracking. The main idea is to integrate physical knowledge of TC to drastically improve the computational efficiency of multilevel robustness framework for large-scale climate datasets. First, during preprocessing, we propose a physics-informed feature selection strategy to filter 90% of critical points that are short-lived and have low stability, thus preserving good candidates for TC tracking. Second, during in-processing, we impose constraints during the multilevel robustness computation to focus only on physics-informed neighborhoods of TCs. We apply TROPHY to 30 years of 2D wind fields from reanalysis data in ERA5 and generate a number of TC tracks. In comparison with the observed tracks, we demonstrate that TROPHY can capture TC characteristics (e.g., frequency, intensity, duration, latitudes with maximum intensity, and genesis) that are comparable to and sometimes even better than a well-validated TC tracking algorithm that requires multiple dynamic and thermodynamic scalar fields.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1971

Topological solution of bilateral switching networks

Bilateral switching networks synthesis by topological technique, tracing truth table optimum path by visual pattern detection

Mazer, L.↗

NASA NTRS1976

An algorithm for automatic reduction of complex signal flow graphs

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

Young, K. R.↗

DOE OSTI2022

Visualizing discrete Fermi surfaces and possible nodal-line to Weyl state evolution in ZrSiTe

Topological nodal line semimetals (TNLSMs) represent a quantum state of topological matter. When the crystal/time-reversal symmetry is broken, a nodal line state is expected to evolve into a Dirac semimetal, a Weyl semimetal, or other topological phases according to theoretical studies. Here, we report scanning tunneling microscopy (STM) based quasiparticle interference (QPI) measurements performed on the surface of TNLSM ZrSiTe single crystal. A discrete Fermi surface with multiple electron/hole pockets and the impurity-induced inter-/intra- pockets scatterings are directly visualized from QPI patterns. Moreover, the degenerated Dirac points at X point evolve into the pairs of Weyl nodes when Fe atoms are deposited, suggesting a possible phase transition from the nodal line to the Weyl state. The calculated band structures and the Weyl points by applying Zeeman splitting energies along x-direction, further confirm the existence of Weyl points in the Fe-doped ZrSiTe induced by the broken of time-reversal symmetry.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗

DOE OSTI2020

Magnetic Imaging of Domain Walls in the Antiferromagnetic Topological Insulator MnBi 2 Te 4

The control of domain walls or spin textures is crucial for spintronic applications of antiferromagnets. Despite many efforts, it has been challenging to directly visualize antiferromagnetic domains or domain walls with nanoscale resolution, especially in magnetic field. Here, we report magnetic imaging of domain walls in several uniaxial antiferromagnets, the topological insulator MnBi 2 Te 4 family, using cryogenic magnetic force microscopy (MFM). Our MFM results reveal higher magnetic susceptibility inside the domain walls than in domains. Domain walls in these antiferromagnets form randomly with strong thermal and magnetic field dependence. Here, the direct visualization of these domain walls and domain structures in the magnetic field will not only facilitate the exploration of intrinsic topological phenomena in antiferromagnetic topological insulators but will also open a new path toward control and manipulation of domain walls or spin textures in functional antiferromagnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Scalable Computation of Topological Abstractions for Scalar Data

Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial and on single machines. This paper presents the state of the art in the scalable computation of topological abstractions on scalar data, in shared memory parallel on single machines, and in distributed memory parallel on multiple machines. We highlight results for set‐based, graph‐based and complex‐based abstractions and organize the state of the art based on this taxonomy. The paper identifies parallelization and distribution techniques common in topological algorithms and highlights further areas of interest with underdeveloped efforts.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

A Deterministic Self-Organizing Map Approach and its Application on Satellite Data based Cloud Type Classification

A self-organizing map (SOM) is a type of competitive artificial neural network, which projects the high dimensional input space of the training samples into a low dimensional space with the topology relations preserved. This makes SOMs supportive of organizing and visualizing complex data sets and have been pervasively used among numerous disciplines with different applications. Notwithstanding its wide applications, the self-organizing map is perplexed by its inherent randomness, which produces dissimilar SOM patterns even when being trained on identical training samples with the same parameters every time, and thus causes usability concerns for other domain practitioners and precludes more potential users from exploring SOM based applications in a broader spectrum. Motivated by this practical concern, we propose a deterministic approach as a supplement to the standard self-organizing map. In accordance with the theoretical design, the experimental results with satellite cloud data demonstrate the effective and efficient organization as well as simplification capabilities of the proposed approach.

Initialization method↗