相关论文: Reducing the Computational Requirements of the Dif…

This paper presents enhanced reductions of the bounded-weight and exact-weight Syndrome Decoding Problem (SDP) to a system of quadratic equations. Over $\mathbb{F}_2$, we improve on a previous work and study the degree of regularity of the…

We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…

In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erd\H{o}s-Mordell inequality, we establish…

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…

Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…

The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…

In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…

The lattice QCD simulation with the lattice chiral symmetry is very attractive, however, it is difficult to maintain the symmetry at a modest numerical computation cost. A candidate to reduce the computational cost during the configuration…

The large computing and memory cost of deep neural networks (DNNs) often precludes their use in resource-constrained devices. Quantizing the parameters and operations to lower bit-precision offers substantial memory and energy savings for…

Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…

Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but there are no satisfactory results to date. To address this…

Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…

We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…

Deep neural networks have achieved state-of-the-art results in a wide range of applications, from natural language processing and computer vision to speech recognition. However, as tasks become increasingly complex, model sizes continue to…

Compressing large neural networks with minimal performance loss is crucial to enabling their deployment on edge devices. (Cho et al., 2022) proposed a weight quantization method that uses an attention-based clustering algorithm called…

Gradient quantization is an emerging technique in reducing communication costs in distributed learning. Existing gradient quantization algorithms often rely on engineering heuristics or empirical observations, lacking a systematic approach…

Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…