相关论文: Quadratization of ODEs: Monomial vs. Non-Monomial
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solutions. A global minimizer corresponds to a neural network that…
Quantization of neural networks provides benefits of inference in less compute and memory requirements. Previous work in quantization lack two important aspects which this work provides. First almost all previous work in quantization used a…
Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…
We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is…
The log Euclidean polyrigid registration framework provides a way to smoothly estimate and interpolate poly-rigid/affine transformations for which the invertibility is guaranteed. This powerful and flexible mathematical framework is…
Second order scalar ordinary differential equations ({\sc ode}s) which are linearizable possess special types of symmetries. These are the only symmetries which are non fiber-preserving in the linearized form of the equation, and they are…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still…
Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper,…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…