Refine
Document Type
- Article (5)
- In Proceedings (2)
Language
- English (7)
Has Fulltext
- no (7)
Is part of the Bibliography
- no (7)
An atmospheric front is an imaginary surface that separates two distinct air masses and is commonly defined as the warm-air side of a frontal zone with high gradients of atmospheric temperature and humidity. These fronts are a widely used conceptual model in meteorology, which are often encountered in the literature as two-dimensional (2D) front lines on surface analysis charts. This paper presents a method for computing three-dimensional (3D) atmospheric fronts as surfaces that is capable of extracting continuous and well-confined features suitable for 3D visual analysis, spatio-temporal tracking, and statistical analyses. Recently developed contour-based methods for 3D front extraction rely on computing the third derivative of a moist potential temperature field. Additionally, they require the field to be smoothed to obtain continuous large-scale structures. This paper demonstrates the feasibility of an alternative method to front extraction using ridge surface computation. The proposed method requires only the sec- ond derivative of the input field and produces accurate structures even from unsmoothed data. An application of the ridge-based method to a data set corresponding to Cyclone Friederike demonstrates its benefits and utility towards visual analysis of the full 3D structure of fronts.
The Bay of Bengal (BoB) has maintained its salinity distribution over the years despite a continuous flow of fresh water entering it through rivers on the northern coast, which is capable of diluting the salinity. This can be attributed to the cyclic flow of high salinity water (>= 35 psu), coming from Arabian sea and entering BoB from the south, which moves northward and mixes with this fresh water. The movement of this high salinity water has been studied and analyzed in previous work (Singh et al., 2022). This paper extends the computational methods and analysis of salinity movement. Specifically, we introduce an advection based feature definition that represents the movement of high salinity water, and describe algorithms to track their evolution over time. This method allows us to trace the movement of high salinity water caused due to ocean currents. The method is validated via comparison with established observations on the flow of high salinity water in the BoB, including its entry from the Arabian Sea and its movement near Sri Lanka. Further, the visual analysis and tracking framework enables us to compare it with previous work and analyze the contribution of advection to salinity transport.
The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features.
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes geometrically and admits a stability property under the setting of persistent homology. We present a geometric optimization of the cycles that is computable in polynomial time and is stable in an approximate sense. Tailoring our search criterion to different settings, we obtain various optimization problems like optimal homologous cycle, minimum homology basis, and minimum persistent
homology basis. In practice, the (trivial) exact algorithm is computationally expensive despite having a worst case polynomial runtime. Therefore, we design approximation algorithms for the above problems and study their performance experimentally. These algorithms have reasonable runtimes for moderate sized datasets and the cycles computed by these algorithms
are consistently of high quality as demonstrated via experiments on multiple datasets.
Time-varying Extremum Graphs
(2024)
We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time- varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the TVEG as a time-varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the TVEG as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of TVEG towards identification and exploration of topological events such as deletion, generation, split, and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset.
Molecular Dynamics simulations are indispensable tools for comprehending the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of high dimensional data. In this work, we present Molecular Kinetics via Topology (MoKiTo), a novel approach that combines the ISOKANN algorithm to determine the membership function of a molecular system with a topological analysis tool inspired by the Mapper algorithm. Our strategy efficiently identifies and characterizes distinct molecular pathways, enabling the detection and visualization of critical conformational transitions and rare events. This method offers deeper insights into molecular mechanisms, facilitating the design of targeted interventions in drug discovery and protein engineering.