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Computing a Stable Distance on Merge Trees

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological summaries cannot and 2) to still be robust to perturbations in the dataset. The combination of these two properties, known respectively as stability and discriminativity, has led to theoretical distances which are either thought to be or shown to be computationally complex and thus their implementations have been scarce. In order to design similarity measures on merge trees which are computationally feasible for more complex merge trees, many researchers have elected to loosen the restrictions on at least one of these two properties. The question still remains, however, if there are practical situations where trading these desirable properties is necessary. Here we construct a distance between merge trees which is designed to retain both discriminativity and stability. While our approach can be expensive for large merge trees, we illustrate its use in a setting where the number of nodes is small. This setting can be made more practical since we also provide a proof that persistence simplification increases the outputted distance by at most half of the simplified value. As a result, we demonstrate our distance measure on applications in shape comparison and on detection of periodicity in the von Kármán vortex street.

97 MATHEMATICS AND COMPUTING↗

ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. Herein we present a state–of–the–art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time–varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

97 MATHEMATICS AND COMPUTING↗

DEDUPKV: A Space-Efficient and High-Performance Key-Value Store via Fine-Grained Deduplication

Log-Structured Merge Tree (LSM-tree) based key-value stores excel in write-intensive environments but suffer from data duplication, consuming up to 49% of storage space in LSM-tree-based key-value store deployments. Traditional solutions like compression and coarse-grained file system-level deduplication introduce overhead or have limited effectiveness. In this study, we propose DedupKV, a fine-grained deduplication framework tailored for LSM-tree, maximizing data reduction efficiency while minimizing write stalls and read overheads. DedupKV features three key innovations: (1) FLUSH-integrated inline deduplication, which removes duplicates during memory-to-storage writes; (2) WAL file-based offline deduplication, repurposing write-ahead logs to avoid double writes; and (3) elastic execution, dynamically balancing inline and offline deduplication based on memory pressure and workload intensity. Additionally, dynamic granularity management reduces deduplication metadata overhead. We implemented these four ideas in RocksDB for the first time and conducted experiments in a Linux environment. Our evaluation shows that WAL file-based offline deduplication and DedupKV outperform BlobDB by 33% and 23%, respectively, in write-heavy workloads, while reducing write amplification by 1.2 ×, 2 ×, and 1.6 × for real KV datasets.

Jamil, Safdar [Sogang University]↗

A Study of QCD Radiation in VBF Higgs Production with Vincia and Pythia

We discuss and illustrate the properties of several parton-shower algorithms available in Pythia and Vincia, in the context of Higgs production via vector boson fusion (VBF). In particular, the distinctive colour topology of VBF processes allows to define observables sensitive to the coherent radiation pattern of additional jets. We study a set of such observables, using the Vincia sector-antenna shower as our main reference, and contrast it to Pythia's transverse-momentum-ordered DGLAP shower as well as Pythia's dipole-improved shower. We then investigate the robustness of these predictions as successive levels of higher-order perturbative matrix elements are incorporated, including next-to-leading-order matched and tree-level merged calculations, using Powheg Box and Sherpa respectively to generate the hard events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization

Herein this article presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture’s integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.

97 MATHEMATICS AND COMPUTING↗

A Mountaintop View Requires Minimal Sorting: A Faster Contour Tree Algorithm

Consider a scalar field f : M → R, where M is a triangulated simplicial mesh in R d . A level set, or contour, at value v is a connected component of f –1 (v). As v is changed, these contours change topology, merge into each other, or split. Contour trees are concise representations of f that track this contour behavior. The vertices of these trees are the critical points of f, where the gradient is zero. The edges represent changes in the topology of contours. It is a fundamental data structure in data analysis and visualization, and there is significant previous work (both theoretical and practical) on algorithms for constructing contour trees. Suppose M has n vertices, N facets, and t critical points. A classic result of Carr, Snoeyink, and Axen (2000) gives an algorithm that takes O(n log n+Nα(N)) time (where α(·) is the inverse Ackermann function). A further improvement to O(t log t + N) time was given by Chiang et al. All these algorithms involve a global sort of the critical points, a significant computational bottleneck. Unfortunately, lower bounds of Ω(t log t) also exist. We present the first algorithm that can avoid the global sort and has a refined time complexity that depends on the contour tree structure. Intuitively, if the tree is short and fat, we get significant improvements in running time. For a partition of the contour tree into a set of descending paths, P, our algorithm runs in O($\Sigma$ pϵP |p| log |p| + tα(t) + N). This is at most O(t log D + N), where D is the diameter of the contour tree. Moreover, it is O(tα(t) + N) for balanced trees, a significant improvement over the previous complexity. Our algorithm requires numerous ideas: partitioning the contour tree into join and split trees, a local growing procedure to iteratively build contour trees, and the use of heavy path decompositions for the time complexity analysis. There is a crucial use of a family of binomial heaps to maintain priorities, ensuring that any comparison made is between comparable nodes of the contour tree. We also prove lower bounds showing that the $\Sigma$ pϵP |p| log |p| complexity is inherent to computing contour trees.

97 MATHEMATICS AND COMPUTING↗

The Global LAnd Surface Satellite (GLASS) evapotranspiration product Version 5.0: Algorithm development and preliminary validation

An accurate estimation of spatially and temporally continuous global terrestrial evapotranspiration (ET) is essential in the assessment of surface energy, water and carbon cycles. The Global LAnd Surface Satellite (GLASS) ET product Version 4.0 (v4.0) based on the Bayesian model averaging (BMA) method was generated to estimate global terrestrial ET. However, certain uncertainty for the GLASS ET product v4.0 limits its application. In this study, we introduced the deep neural networks (DNN) merging framework to improve terrestrial ET estimation for GLASS ET product Version 5.0 (v5.0) generation by integrating five satellite-derived ET products [Moderate Resolution Imaging Spectroradiometer (MODIS) ET product (MOD16), Shuttleworth–Wallace dual-source ET product (SW), Priestley–Taylor-based ET product (PT-JPL), modified satellite-based Priestley–Taylor ET product (MS-PT) and simple hybrid ET product (SIM)]. We compared the performance of DNN method against other merging methods, including GLASS ET algorithm v4.0 (BMA), the gradient boosting regression tree (GBRT) method and the random forest (RF) method, based on 195 global eddy covariance (EC) flux towers covering observations from 2000 through 2015. Validations indicated that the DNN had the highest accuracy among four merging methods across different land cover types, yielding the highest average determination coefficients (R 2 , 0.62), root-mean-squared-error (RMSE, 24.1 W/m 2 ) and Kling–Gupta efficiency (KGE, 0.77) with a of 99% confidence interval. Compared with GLASS ET algorithm v4.0, the DNN improved on the R 2 by approximately 7% (p < 0.01) and the KGE by 10%. Based on the DNN, we then generated 8-day GLASS ET product v5.0 globally with a 1 km spatial resolution from 2001 to 2015 driven by GLASS vegetation and surface net radiation (R n ) datasets and Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA2) datasets. Finally, this global terrestrial ET product provides a valuable dataset for monitoring regional and global water resources and environmental changes.

54 ENVIRONMENTAL SCIENCES↗

Evaluation of Programming Language-Aware Diffs for Improving Developer Productivity

As the number of supported platforms for SNL software increases, so do the testing requirements. This increases the total time spent between when a developer submits code for testing, and when tests are completed. This in turn leads developers to hold off submitting code for testing, meaning that when code is ready for testing there's a lot more of it. This increases the likelihood of merge conflicts which the developer must resolve by hand -- because someone else touched the files near the lines the developer touched. Current text-based diff tools often have trouble resolving conflicts in these cases. Work in Europe and Japan has demonstrated that, using programming language aware diff tools (e.g., using the abstract syntax tree (AST) a compiler might generate) can reduce the manual labor necessary to resolve merge conflicts. These techniques can detect code blocks which have moved, as opposed than current text-based diff tools, which only detect insertions / deletions of text blocks. In this study, we evaluate one such tool, GumTree, and see how effective it is as a replacement for traditional text-based diff approaches.

97 MATHEMATICS AND COMPUTING↗

Constructing high-fidelity halo merger trees in abacussummit

ABSTRACT Tracking the formation and evolution of dark matter haloes is a critical aspect of any analysis of cosmological N-body simulations. In particular, the mass assembly of a halo and its progenitors, encapsulated in the form of its merger tree, serves as a fundamental input for constructing semi-analytic models of galaxy formation and, more generally, for building mock catalogues that emulate galaxy surveys. We present an algorithm for constructing halo merger trees from abacussummit, the largest suite of cosmological N-body simulations performed to date consisting of nearly 60 trillion particles, and which has been designed to meet the Cosmological Simulation Requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. Our method tracks the cores of haloes to determine associations between objects across multiple time slices, yielding lists of halo progenitors and descendants for the several tens of billions of haloes identified across the entire suite. We present an application of these merger trees as a means to enhance the fidelity of abacussummit halo catalogues by flagging and ‘merging’ haloes deemed to exhibit non-monotonic past merger histories. We show that this cleaning technique identifies portions of the halo population that have been deblended due to choices made by the halo finder, but which could have feasibly been part of larger aggregate systems. We demonstrate that by cleaning halo catalogues in this post-processing step, we remove potentially unphysical features in the default halo catalogues, leaving behind a more robust halo population that can be used to create highly accurate mock galaxy realizations from abacussummit.

79 ASTRONOMY AND ASTROPHYSICS↗

A New Member of the Milky Way’s Family Tree: Characterizing the Pontus Merger of Our Galaxy

We study the Pontus structure—a recently discovered merger that brought in ~7 globular clusters in the course of the hierarchical buildup of the Milky Way’s halo. Here, we analyze the stellar population of Pontus and examine (1) its phase-space distribution using the ESA/Gaia data set, (2) its metallicity and chemical abundances (i.e., [Fe/H], [ α /Fe], [Mg/Fe], and [Al/Fe]) using the spectroscopic catalog of APOGEE DR17, and (3) the color–magnitude diagram that shows interesting features, including a possibly double horizontal branch and a small population of blue stragglers. In sum, the Pontus stars show some unique properties that suggest they likely originated from the merging of an independent satellite galaxy; however, future analysis will shed more light on the true nature of this structure. This chemodynamical analysis of Pontus stars is another step forward in our bigger quest to characterize all the merging events of our Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗

An automated procedure built on MTEX for reconstructing deformation twin hierarchies from electron backscattered diffraction datasets of heavily twinned microstructures

Here we present a set of algorithms built on the MTEX and MATLAB graph toolboxes for automatic reconstruction of deformation twin hierarchies from Electron Backscatter Diffraction (EBSD) datasets with a focus on developing methods for heavily twinned microstructures (twin fractions >0.5). The algorithms address key issues arising at large strains, mainly: missing twin relationships, grouping of heavily deformed grain fragments into families of similar orientation originating from a single initial grain, identification of parent fragments for large twin volume fractions, and classification of families having twin relationships with multiple families. To facilitate the development of these algorithms, large-grained ultra-high purity α-Ti deformed in compression along two directions is investigated. Graphs are utilized to handle non-local geometric merging and to represent relationships throughout the reconstruction process. When determining if a grain fragment is from the undeformed microstructure, the combined metrics of the fragment's orientation volume fraction in the initial texture and the directed graph centrality measure of out-closeness (the number of nodes reached in a graph from a given node) are essential. To address automation in reconstructing the sequence of twinning and relating fragments originating from a single grain in the initial microstructure, the twin family tree is formulated as a minimum spanning tree emanating from the initial grain family. A scheme constructing the distances associated with twin relationship comprising the spanning tree is developed, and a novel quasi-directional Prim spanning tree algorithm is used to determine the twin family tree. The procedure is demonstrated to significantly improve the level of automation in reconstructing twin hierarchies in heavily twinned microstructure compared to other methodologies in literature. The procedure can readily be applied to analyses of twinning in metals, as well as provide an approach for routinely extracting twin statistics at larger deformation levels than previously possible. Significantly, the procedure is demonstrated to be capable of identifying third generation twinning in α-Ti microstructures.

36 MATERIALS SCIENCE↗