Related papers: Matrix Completion and Performance Guarantees for S…
DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a…
The amount of completely sequenced chloroplast genomes increases rapidly every day, leading to the possibility to build large-scale phylogenetic trees of plant species. Considering a subset of close plant species defined according to their…
The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…
We study a combinatorial problem arising from microarrays synthesis. The synthesis is done by a light-directed chemical process. The objective is to minimize unintended illumination that may contaminate the quality of experiments.…
We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly…
Motivation: Protein sequence world is discrete as 20 amino acids (AA) while its structure world is continuous, though can be discretized into structural alphabets (SA). In order to reveal the relationship between sequence and structure, it…
DNA has emerged as a promising alternative for long-term data storage due to its high capacity, durability, and low-energy potential. However, storing data in DNA presents several challenges. First, it requires complex and costly…
Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the…
A hardware architecture for the single iteration algorithm is proposed in this paper. Single iteration algorithm enables reconstruction of the full signal when small number of signal samples is available. The algorithm is based on the…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Representing images by compact hash codes is an attractive approach for large-scale content-based image retrieval. In most state-of-the-art hashing-based image retrieval systems, for each image, local descriptors are first aggregated as a…
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require…
Matroids are a fundamental object of study in combinatorial optimization. Three closely related and important problems involving matroids are maximizing the size of the union of $k$ independent sets (that is, $k$-fold matroid union),…
We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
It is not known how a cell manages to find a specific DNA sequence sufficiently fast to repair a broken chromosome through homologous recombination. I propose that the solution is based on a parallelized search implemented by freely…