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The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior of a scalar function. It supports multi-scale topological analysis and visualization of large scientific data. Its computation poses significant algorithmic challenges when considering large scale data and increased feature complexity. Several parallel algorithms have been proposed towards the fast computation of the 3D Morse-Smale complex. The non-trivial structure of the saddle-saddle connections are not amenable to parallel computation. This paper describes a fine grained parallel method for computing the Morse-Smale complex that is implemented on a GPU. The saddle-saddle reachability is first determined via a transformation into a sequence of vector operations followed by the path traversal, which is achieved via a sequence of matrix operations. Computational experiments show that the method achieves up to 7× speedup over current shared memory implementations.

This article presents a robust Morse theory-1 based framework for segmenting 3D x-ray computed 2 tomography image (CT) and computing the fabric, rel-3 ative arrangement of particles, of granular ensembles. 4 The framework includes an algorithm for computing the 5 segmentation, a data structure for storing the segmenta-6 tion and representing both individual particles and the 7 connectivity network, and visualizations of topological 8 descriptors of the CT image that enable interactive ex-9 ploration. The Morse theory-based framework produces 10 superior quality segmentation of a granular ensemble as 11 compared to prior approaches based on the watershed 12 transform. The accuracy of the connectivity network 13 also improves. Further, the framework supports the effi-14 cient computation of various distribution statistics on 15 the segmentation and the connectivity network. Such 16 a comprehensive characterization and quantification of 17 the fabric of granular ensembles is the first step towards 18 a multiple length scale understanding of the behavior. 19 Keywords Granular ensemble • fabric • segmentation • 20 particle connectivity network • Morse theory • 21 Morse-Smale complex • topological persistence.

Abstract A new method for identifying Rossby wave packets (RWPs) using 6-hourly data from the ERA-Interim is presented. The method operates entirely in the spatial domain and relies on the geometric and topological properties of the meridional wind field to identify RWPs. The method represents RWPs as nodes and edges of a dual graph instead of the more common envelope representation. This novel representation allows access to both RWP phase and amplitude information. Local maxima and minima of the meridional wind field are collected into groups. Each group, called a υ-max cluster or υ-min cluster of the meridional wind field, represents a potential wave component. Nodes of the dual graph represent a υ-max cluster or υ-min cluster. Alternating υ-max clusters and υ-min clusters are linked by edges of the dual graph, called the RWP association graph. Amplitude and discrete gradient-based filtering applied on the association graph helps identify RWPs of interest. The method is inherently robust against noise and does not require smoothing of the input data. The main parameters that control the performance of the method and their impact on the identified RWPs are discussed. All filtering and RWP identification operations are performed on the association graph as opposed to directly on the wind field, leading to computational efficiency. Advantages and limitations of the method are discussed and are compared against (transform-based) envelope methods in a series of experiments.