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Found 9 papers, 7 papers with code
Predictive Analytics of Varieties of Potatoes
We explore the application of machine learning algorithms to predict the suitability of Russet potato clones for advancement in breeding trials.
A Normalized Bottleneck Distance on Persistence Diagrams and Homology Preservation under Dimension Reduction
Persistence diagrams are used as signatures of point cloud data assumed to be sampled from manifolds, and represent their topology in a compact fashion.
Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space, i. e. 2- or 3-dimensions.
Chemical Physics Mathematical Physics Algebraic Topology Mathematical Physics
The Maximum Distance Problem and Minimal Spanning Trees
For $E\subset \mathbb{R}^2$, we prove that minimizing over minimum spanning trees that connect the centers of balls of radius $s$, which cover $E$, solves the maximum distance problem.
Classical Analysis and ODEs Computational Geometry Optimization and Control 28A75, 49Q15, 49Q20
Cover Filtration and Stable Paths in the Mapper
Our framework provides an alternative way of building a filtration from a single mapper that is then used to explore stable paths.
Steinhaus Filtration and Stable Paths in the Mapper
We prove a stability result: the cover filtrations of two covers are $\alpha/m$ interleaved, where $\alpha$ is a bound on bottleneck distance between covers and $m$ is the size of smallest set in either cover.
Median Shapes
When the input shapes are modeled by integral currents with shared boundaries in codimension $1$, we show that the median is guaranteed to exist, and is contained in the \emph{envelope} of the input currents.
Differential Geometry Computational Geometry Algebraic Topology Optimization and Control 49Q20 (Primary), 49Q15, 49Q05, 49Q10, 28A75, 58A25, 62-04, 62-07, 65C60, 65D18, 05C10
Interesting Paths in the Mapper
For the special case when G is a directed acyclic graph (DAG), we show that Max-IP can be solved in polynomial time - in O(mnd_i) where d_i is the maximum indegree of a vertex in G. In the more general problem IP, the goal is to find a collection of edge-disjoint interesting paths such that the overall sum of their interestingness scores is maximized.
Computational Geometry Data Structures and Algorithms Algebraic Topology 05C85, 68Q25, 62H30, 55U99 G.2.2; F.2.2
Hyppo-X: A Scalable Exploratory Framework for Analyzing Complex Phenomics Data
Notably, our approach shows how environmental factors could influence phenotypic behavior, and how that effect varies across different genotypes and different time scales.
