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Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…

This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined…

We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…

For a smooth near identity map, we introduce the notion of an interpolating vector field written in terms of iterates of the map. Our construction is based on Lagrangian interpolation and provides an explicit expressions for autonomous…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…

In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs.…

Curve-based representations, particularly integral curves, are often used to represent large-scale computational fluid dynamic simulations. Processing and analyzing curve-based vector field data sets often involves searching for neighboring…

We construct a Floer type boundary operator for generalised Morse-Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed (both homoclinic and periodic) orbits and isolated critical…

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence…

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…

Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to…

Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical…

Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…

This work presents a progressive image vectorization technique that reconstructs the raster image as layer-wise vectors from semantic-aligned macro structures to finer details. Our approach introduces a new image simplification method…

Integration of scalar and vector visualization has been an interesting topic. This paper presents a technique to appropriately select and display multiple streamlines while overlaying with isosurfaces, aiming an integrated scalar and vector…

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data…

The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…