52 citations · 58 across the 30 of their papers we have counts for
32 papers
Exponential Convergence of Deep Composite Polynomial Approximation for Cusp-Type Functions
Kingsley Yeon, Steven B. Damelin, Michael Werman
We investigate deep composite polynomial approximations of continuous but non-differentiable functions with algebraic cusp singularities. The functions in focus consist of finitely…
A family of interaction energy minimizers supported on two intervals
Steven B. Damelin, Ruiwen Shu
In this paper, we consider the one-dimensional interaction energy where the interaction potential $W(x)= -\…
Uniform Approximation of Functions with Asymmetric Growth and Decay by Deep Weighted Polynomials
Kingsley Yeon, Steven B. Damelin
Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains. Motivat…
Subharmonic Kernels and Energy Minimizing Measures, with Applications to the Flat Torus
Steven B. Damelin, Joel Nathe
We study the minimization of the energy integral over all Borel probability measures , where is a compact connected metric sp…
Partial Transport for Point-Cloud Registration
Yikun Bai, Huy Tran, Steven B. Damelin +1
Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships…
A Multiple Parameter Linear Scale-Space for one dimensional Signal Classification
Leon A. Luxemburg, Steven B. Damelin
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensiona…
The Geometric Approach to the Classification of Signals via a Maximal Set of Signals
Leon A. Luxemburg, Steven B. Damelin
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter varia…
Whitney extensions and orthonormal expansions
S. B. Damelin
The Whitney near extension problem for finite sets in asks the following: Let be a near distortion on a finite set $E\subset \mathbb R…
On best uniform approximation of finite sets by linear combinations of real valued functions using linear programming
Steven B. Damelin, Michael Werman
We study the best approximation problem: \[ \displaystyle \min_{α\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m α_j Γ_j ({\bf x}_i) \right|. \] Here: $Γ:=\left\{Γ_1,..…
On a realization of motion and similarity group equivalence classes of labeled points in with applications to computer vision
Steven B. Damelin, David L. Ragozin, Michael Werman
We study a realization of motion and similarity group equivalence classes of labeled points in as a metric space with a computable metric. Our st…
Preprocessing power weighted shortest path data using a s-Well Separated Pair Decomposition
Gurpreet S. Kalsi, Steven B. Damelin
For 0, we consider an algorithm that computes all -well separated pairs in certain point sets in , . For an integer , we also consider an…
On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment
Steven B. Damelin
This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approxim…
Power Weighted Shortest Paths for Clustering Euclidean Data
Daniel Mckenzie, Steven Damelin
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of…
On Min-Max affine approximants of convex or concave real valued functions from , Chebyshev equioscillation and graphics
Steven B. Damelin, David L. Ragozin, Michael Werman
We study Min-Max affine approximants of a continuous convex or concave function where is a convex compact subset of $\mathbb R^…
An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on
S. B. Damelin, K. Diethelm
This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights with finite moments and with smooth e…
A Note on a Quantitative Form of the Solovay-Kitaev Theorem
S. B. Damelin, B. A. W. Mode
The problem of finding good approximations of arbitrary 1-qubit gates is identical to that of finding a dense group generated by a universal subset of to approximate an arb…
A Koksma-Hlawka-Potential Identity on the Dimensional Sphere and its Applications to Discrepancy
S. B. Damelin
Let be an integer, the unit sphere and a finite signed measure whose positive and negative parts are supported on with finite ene…
On surface completion and image inpainting by biharmonic functions: Numerical aspects
S. B. Damelin, N. S. Hoang
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic…
Isometries and Equivalences Between Point Configurations, Extended To -diffeomorphisms
Neophytos Charalambides, Steven B. Damelin, Bradley Swartz
In this announcement, we deal with the Orthogonal Procrustes Problem, in which two point configurations are compared in order to construct a map to optimally align the two sets. Th…
An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture
Steven B. Damelin, Daniel Kaiser, Jeffrey Sun +1
In this paper, we provide Algebraic-Coding necessary and sufficient conditions for the Maximum Distance Separable Conjecture to hold.
On a condition equivalent to the Maximum Distance Separable conjecture
Jeffery Sun, Steven Damelin, Daniel Kaiser
We denote by the vector space of functions from a finite field to itself, which can be represented as the space $\mathcal{P}_q := \mathbb{F}_q[x]/(x^…
A BMO theorem for distorted diffeomorphisms from to with applications to manifolds of speech and sound
C. Fefferman, S. B. Damelin, W. Glover
This paper deals with a BMO Theorem for distorted diffeomorphisms from to with applications to manifolds of speech and sound. The material for this…
A Constructive Finite Field Method for Scattering Points on the Surface of -Dimensional Spheres
Béla Bajnok, Steven B. Damelin, Jenny Li +1
In this exploratory article, we present a constructive method for scattering points on the surface of dimensional spheres which we believe is new and of interest. Indeed, the p…
The Truncated & Supplemented Pascal Matrix and Applications
M. Hua, S. B. Damelin, J. Sun +1
In this paper, we introduce the (with ) truncated, supplemented Pascal matrix which has the property that any columns form a linearly independent set. This…