Related papers: Rational sphere maps, linear programming, and comp…
Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…
Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a…
The recently developed theory of higher--rank numerical ranges originated in problems of error correction in quantum information theory but its mathematical implications now include a quite satisfactory understanding of \emph{scalar}…
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Deep ReLU Networks can be decomposed into a collection of linear models, each defined in a region of a partition of the input space. This paper provides three results extending this theory. First, we extend this linear decompositions to…
We prove a new classification result for (CR) rational maps from the unit sphere in some ${\mathbb C}^n$ to the unit sphere in ${\mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include…
A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a…
In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a projective line. We extend this to linear sets in arbitrary…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…
This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
We consider the sets of dimensions for which there is an optimal sphere packing with special regularity properties (respectively, a lattice, or a periodic set with a given bound on the number of translations, or an arbitrary periodic set).…