Related papers: LinCbO: fast algorithm for computation of the Duqu…

We state and analyze a generalization of the "truncation trick" suggested by Gourdon and Sebah to improve the performance of power series evaluation by binary splitting. It follows from our analysis that the values of D-finite functions…

This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea of Faug\`ere and Lachartre (GB reduction). We further exploit underlying structures in matrices generated during Gr\"obner basis…

We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of the concepts of localization and…

This paper introduces a novel method for finding integer sets that satisfy the Pythagorean theorem by leveraging the Higher-Order Binary Optimization (HOBO) formulation. Unlike the Quadratic Unconstrained Binary Optimization (QUBO)…

Whittle index is a generalization of Gittins index that provides very efficient allocation rules for restless multi-armed bandits. In this work, we develop an algorithm to test the indexability and compute the Whittle indices of any…

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the…

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…

Elegant and general algorithms for handling upwards-closed and downwards-closed subsets of WQOs can be developed using the filter-based and ideal-based representation for these sets. These algorithms can be built in a generic or…

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

The problem of counting collisions or interactions is common in areas as computer graphics and scientific simulations. Since it is a major bottleneck in applications of these areas, a lot of research has been carried out on such subject,…

We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control…

With the advent of high-performance computing techniques, the data for analysis has grown significantly. Here, graphic processing unit (GPU) based program kernels are discussed to exploit parallelism in the analysis codes specific to…

The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…

Neighbourhood-based Collaborative Filtering (CF) has been applied in the industry for several decades, because of the easy implementation and high recommendation accuracy. As the core of neighbourhood-based CF, the task of dynamically…

We revisit the stochastic limited-memory BFGS (L-BFGS) algorithm. By proposing a new framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to…

Advances in gene sequencing have enabled in silico analyses of microbial genomes and have led to the revision of concepts of microbial taxonomy and evolution. We explore deficiencies in existing multiple sequence global alignment algorithms…

This note describes a new efficient bit-slice implementation DenseQMC of the Quine-McCluskey algorithm for finding all prime implicants of a Boolean function in the dense case. It is practically feasible for n <= 23 when run on a common…