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05/26/2023
Bilipschitz group invariants
Consider the quotient of a real Hilbert space by a subgroup of its ortho...
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12/23/2022
Equi-isoclinic subspaces, covers of the complete graph, and complex conference matrices
In 1992, Godsil and Hensel published a ground-breaking study of distance...
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12/21/2022
Injectivity, stability, and positive definiteness of max filtering
Given a real inner product space V and a group G of linear isometries, m...
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12/09/2022
Max filtering with reflection groups
Given a finite-dimensional real inner product space V and a finite subgr...
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11/28/2022
Sketch-and-solve approaches to k-means clustering by semidefinite programming
We introduce a sketch-and-solve approach to speed up the Peng-Wei semide...
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05/27/2022
Group-invariant max filtering
Given a real inner product space V and a group G of linear isometries, w...
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12/28/2021
Harmonic Grassmannian codes
An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian c...
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08/28/2021
Asymptotic Frame Theory for Analog Coding
Over-complete systems of vectors, or in short, frames, play the role of ...
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05/12/2021
Sketching with Kerdock's crayons: Fast sparsifying transforms for arbitrary linear maps
Given an arbitrary matrix A∈ℝ^n× n, we consider the fundamental problem ...
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01/28/2021
A note on tight projective 2-designs
We study tight projective 2-designs in three different settings. In the ...
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11/23/2020
Neural collapse with unconstrained features
Neural collapse is an emergent phenomenon in deep learning that was rece...
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08/28/2020
Uniquely optimal codes of low complexity are symmetric
We formulate explicit predictions concerning the symmetry of optimal cod...
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08/10/2020
Parameter estimation in the SIR model from early infections
A standard model for epidemics is the SIR model on a graph. We introduce...
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08/10/2020
Lie PCA: Density estimation for symmetric manifolds
We introduce an extension to local principal component analysis for lear...
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08/10/2020
Sketching semidefinite programs for faster clustering
Many clustering problems enjoy solutions by semidefinite programming. Th...
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12/27/2019
Derandomized compressed sensing with nonuniform guarantees for ℓ_1 recovery
We extend the techniques of Hügel, Rauhut and Strohmer (Found. Comput. M...
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12/06/2019
Globally optimizing small codes in real projective spaces
For d∈{5,6}, we classify arrangements of d + 2 points in RP^d-1 for whic...
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09/04/2019
Matching Component Analysis for Transfer Learning
We introduce a new Procrustes-type method called matching component anal...
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07/12/2019
Linear programming bounds for cliques in Paley graphs
The Lovász theta number is a semidefinite programming bound on the cliqu...
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05/15/2019
Doubly transitive lines II: Almost simple symmetries
We study lines through the origin of finite-dimensional complex vector s...
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05/10/2019
Kesten-McKay law for random subensembles of Paley equiangular tight frames
We apply the method of moments to prove a recent conjecture of Haikin, Z...
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02/26/2019
The optimal packing of eight points in the real projective plane
How can we arrange n lines through the origin in three-dimensional Eucli...
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02/03/2019
A Delsarte-Style Proof of the Bukh-Cox Bound
The line packing problem is concerned with the optimal packing of points...
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01/29/2019
Exact Line Packings from Numerical Solutions
Recent progress in Zauner's conjecture has leveraged deep conjectures in...
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12/19/2018
Derandomizing compressed sensing with combinatorial design
Compressed sensing is the art of reconstructing structured n-dimensional...
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12/14/2018
Utility Ghost: Gamified redistricting with partisan symmetry
Inspired by the word game Ghost, we propose a new protocol for bipartisa...
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12/06/2018
SqueezeFit: Label-aware dimensionality reduction by semidefinite programming
Given labeled points in a high-dimensional vector space, we seek a low-d...
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08/27/2018
Fair redistricting is hard
Gerrymandering is a long-standing issue within the U.S. political system...
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06/23/2018
Doubly transitive lines I: Higman pairs and roux
We study lines through the origin of finite-dimensional complex vector s...
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03/25/2018
SUNLayer: Stable denoising with generative networks
It has been experimentally established that deep neural networks can be ...
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10/03/2017
Monte Carlo approximation certificates for k-means clustering
Efficient algorithms for k-means clustering frequently converge to subop...
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02/22/2016
Clustering subgaussian mixtures by semidefinite programming
We introduce a model-free relax-and-round algorithm for k-means clusteri...
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05/18/2015
On the tightness of an SDP relaxation of k-means
Recently, Awasthi et al. introduced an SDP relaxation of the k-means pro...
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10/08/2012