172 citations · 196 across the 7 of their papers we have counts for
8 papers
An Algorithm for Persistent Homology Computation Using Homomorphic Encryption
Dominic Gold, Koray Karabina, Francis C. Motta
Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and pre…
Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complex
Amish Mishra, Francis C. Motta
In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Ri…
State dependent delay maps: numerical algorithms and dynamics of projections
J. D. Mireles James, Francis Motta, Vincent Naudot
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differe…
Informing the structure of complex Hadamard matrix spaces using a flow
Francis C. Motta, Patrick D. Shipman
The defect of a complex Hadamard matrix is an upper bound for the dimension of a continuous Hadamard orbit stemming from . We provide a new interpretation of the defect as t…
An Unoriented Variation on de Bruijn Sequences
Christie S. Burris, Francis C. Motta, Patrick D. Shipman
For positive integers , a de Bruijn sequence is a finite sequence of elements drawn from characters whose subwords of length are exactly the words of le…
Producing nanodot arrays with improved hexagonal order by patterning surfaces before ion sputtering
Daniel A. Pearson, R. Mark Bradley, Francis C. Motta +1
When the surface of a nominally flat binary material is bombarded with a broad, normally-incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley ha…
Random cyclic dynamical systems
Michał Adamaszek, Henry Adams, Francis Motta
For X a finite subset of the circle and for 0 < r <= 1 fixed, consider the function f_r : X -> X which maps each point to the clockwise furthest element of X within angular distanc…
Persistence Images: A Stable Vector Representation of Persistent Homology
Henry Adams, Sofya Chepushtanova, Tegan Emerson +7
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discov…