相关论文: Efficient dot product over word-size finite fields

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…

Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…

The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…

Recently, there has been a lot of effort to represent words in continuous vector spaces. Those representations have been shown to capture both semantic and syntactic information about words. However, distributed representations of phrases…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…

A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…

Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…

Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…

Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics…

Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly…

In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary $d$-dimensional integrals based on tensor product approximations. It reduces the computational complexity (in terms of the CPU…

We derive a closed-form expression for the orthogonal polynomials associated with the general lognormal density. The result can be utilized to construct easily computable approximations for probability density function of a product of…

We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…

Montgomery modular multiplication is widely-used in public key cryptosystems (PKC) and affects the efficiency of upper systems directly. However, modulus is getting larger due to the increasing demand of security, which results in a heavy…

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.

This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…

Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…