Related papers: FastMinors package for Macaulay2
Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Several ways to accelerate the solution of 2D/3D linear min-max problems in $n$ constraints are discussed. We also present an algorithm for solving such problems in the 2D case, which is superior to CGAL's linear programming solver, both in…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…
Recently, Multi-modal Large Language Models (MLLMs) have shown remarkable effectiveness for multi-modal tasks due to their abilities to generate and understand cross-modal data. However, processing long sequences of visual tokens extracted…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…
In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range…
Wiedemann's paper, introducing his algorithm for sparse and structured matrix computations over arbitrary fields, also presented a pair of matrix preconditioners for computations over small fields. The analysis of the second of these is…
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
CalcHEP is a package for computation of Feynman diagrams and integration over multi-particle phase space. The main idea prescribed into CalcHEP is to make available passing on from Lagrangians to the final distributions effectively with a…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
Fine-grained monitoring is crucial for multiple data-driven tasks such as debugging, provisioning, and securing networks. Yet, practical constraints in collecting, extracting, and storing data often force operators to use coarse-grained…
We introduce DDE-Solver, a Maple package designed for solving Discrete Differential Equations (DDEs). These equations are functional equations relating algebraically a formal power series F(t, u) with polynomial coefficients in a…
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
Many artificial intelligence models process input data of different lengths and resolutions, making the shape of the tensors dynamic. The performance of these models depends on the shape of the tensors, which makes it difficult to optimize…
We consider multidimensional optimization problems in the framework of tropical mathematics. The problems are formulated to minimize a nonlinear objective function that is defined on vectors over an idempotent semifield and calculated by…
Stereo image matching is a fundamental task in computer vision, photogrammetry and remote sensing, but there is an almost unexplored field, i.e., polygon matching, which faces the following challenges: disparity discontinuity, scale…