Related papers: Rational sphere maps, linear programming, and comp…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
To alleviate the problem of information explosion, recommender systems are widely deployed to provide personalized information filtering services. Usually, embedding tables are employed in recommender systems to transform high-dimensional…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Like [1], we present an algorithm to compute the simulation of a query pattern in a graph of labeled nodes and unlabeled edges. However, our algorithm works on a compressed graph grammar, instead of on the original graph. The speed-up of…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
The intuitive sphere-packing argument is used to obtain analytically-tractable closed-form approximations for achievable information rates of coded modulation transmission systems, for which only analytically-intractable expressions are…
We investigate conditions under which a co-computably enumerable set in a computable metric space is computable. Using higher-dimensional chains and spherical chains we prove that in each computable metric space which is locally computable…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
Camera sensors have been widely used in intelligent robotic systems. Developing camera sensors with high sensing efficiency has always been important to reduce the power, memory, and other related resources. Inspired by recent success on…
Inspired by the linear programming method developed by Cohn and Elkies (Ann. Math. 157(2): 689-714, 2003), we introduce a new linear programming method to solve the sphere packing problem. More concretely, we consider sequences of auxiliary…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
The work that consists of two parts is devoted to the problem of enumerating unrooted $r$-regular maps on the torus up to all its symmetries. We begin with enumerating near-$r$-regular rooted maps on the torus, projective plane and the…
We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena.