Related papers: An Empirically Fast Las Vegas Algorithm for Algebr…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
Important problems across multiple disciplines involve computations on the semiring $(\times, \max)$ (or its equivalents, the negated version $(\times, \min)$), the log-transformed version $(+, \max)$, or the negated log-transformed version…
We study the complexity of some fundamental operations for triangular sets in dimension zero. Using Las-Vegas algorithms, we prove that one can perform such operations as change of order, equiprojectable decomposition, or quasi-inverse…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…
We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane and D an effective divisor supported on the boundary of…
We give a Las Vegas algorithm which computes the shifted Popov form of an $m \times m$ nonsingular polynomial matrix of degree $d$ in expected $\widetilde{\mathcal{O}}(m^\omega d)$ field operations, where $\omega$ is the exponent of matrix…
We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the \NPAz. They are made in the same spirit as the dynamic algebraic closure of a field. They give a concrete content to the theorem…
We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more…
In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used,…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for…
This paper proposes an algorithm for oblivious transfer using elliptic curves. Also, we present its application to chosen one-out-of-two oblivious transfer.
In the estimation of causal effects, one common method for removing the influence of confounders is to adjust the variables that satisfy the back-door criterion. However, it is not always possible to uniquely determine sets of such…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…