Local Simplification

Why Local Search Excels in Expression Simplification

Simplifying expressions is important to make numerical integration of large expressions from High Energy Physics tractable. To this end, Horner’s method can be used. Finding suitable Horner schemes is assumed to be hard, due to the lack of local heuristics. Recently, MCTS was reported to be able to find near optimal schemes. However, several parameters had to be fine-tuned manually. In this wor...

Local Gradient Descent Methods for GMM Simplification

Gaussian mixture model simplification is a powerful technique for reducing the number of components of an existing mixture model without having to re-cluster the original data set. Instead, a simplified GMM with fewer components is computed by minimizing some distance metric between the two models. In this paper, we derive an analytical expression for the difference between the probability dens...

Local, smooth, and consistent Jacobi set simplification

The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces have shown to be useful in various applications. Unfortunately, in practice functions often contain noise and...

Contour Tree Simplification With Local Geometric Measures

The contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, has several potential applications in scientific and medical visualization, but noise in experimentally-acquired data results in unmanageably large trees. We attach geometric properties of the contours to the branches of the tree and apply simplification by persistence to reduce the size of...

Over-Simplification