相关论文: BTAS: A Library for Tropical Algebra

We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is…

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs have been two significant challenges for developing a programmable high-performance graph library.…

Tremendous advances in parallel computing and graphics hardware opened up several novel real-time GPU applications in the fields of computer vision, computer graphics as well as augmented reality (AR) and virtual reality (VR). Although…

In his preprint https://arxiv.org/abs/1308.3813, Cartwright introduced the notion of a weak tropical complex in order to generalize the concepts of divisors and the Picard group on graphs from Baker and Norine's paper Riemann-Roch and…

In this article we present our relocatable distributed collections library. Building on top of the AGPAS for Java library, we provide a number of useful intra-node parallel patterns as well as the features necessary to support the…

Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing…

GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More' and Toraldo, this algorithm was designed for large-scale problems but had been…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Algorithm Operating System (AlgOS) is an unopinionated, extensible, modular framework for algorithmic implementations. AlgOS offers numerous features: integration with Optuna for automated hyperparameter tuning; automated argument parsing…

We propose a GPU fine-grained load-balancing abstraction that decouples load balancing from work processing and aims to support both static and dynamic schedules with a programmable interface to implement new load-balancing schedules. Prior…

Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…

General Purpose Graphics Processing Unit (GPGPU) computing plays a transformative role in deep learning and machine learning by leveraging the computational advantages of parallel processing. Through the power of Compute Unified Device…

An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…

This paper is devoted to computational algorithms designed to describe the classical Ising magnet in some specific cases when an additional macroscopic restriction in form of constant charge density exists in the system. We developed and…

Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such…

In many scientific and engineering applications, one has to solve not one but a sequence of instances of the same problem. Often times, the problems in the sequence are linked in a way that allows intermediate results to be reused. A…

Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…

We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…

We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…

PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of…