Related papers: A computation of D(9) using FPGA Supercomputing

A new implementation of many-body calculations is of paramount importance in the field of computational physics. In this study, we leverage the capabilities of Field Programmable Gate Arrays (FPGAs) for conducting quantum many-body…

FPGA is appropriate for fix-point neural networks computing due to high power efficiency and configurability. However, its design must be intensively refined to achieve high performance using limited hardware resources. We present an…

In many important applications -- such as search engines and relational database systems -- data is stored in the form of arrays of integers. Encoding and, most importantly, decoding of these arrays consumes considerable CPU time.…

This research introduces an FPGA-based hardware accelerator to optimize the Singular Value Decomposition (SVD) and Fast Fourier transform (FFT) operations in AI models. The proposed design aims to improve processing speed and reduce…

To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…

Deep Forest is a prominent machine learning algorithm known for its high accuracy in forecasting. Compared with deep neural networks, Deep Forest has almost no multiplication operations and has better performance on small datasets. However,…

The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…

Extreme edge platforms, such as in-vehicle smart devices, require efficient deployment of quantized deep neural networks (DNNs) to enable intelligent applications with limited amounts of energy, memory, and computing resources. However,…

The main result of this thesis is to show that there are only finitely many integers $n$ such that both $n$ and $d(n)$ are highly composite numbers at the same time, where $d(n)$ is the divisor function. Bertrand's postulate [4] is used…

In this paper I describe some results on the use of virtual processors technology for parallelize some SPMD computational programs in a cluster environment. The tested technology is the INTEL Hyper Threading on real processors, and the…

In this paper, we reveal an internal structure within Dedekind numbers, demonstrating that they can be expressed as polynomials of powers of 2. This discovery is based on innovative concepts and methods, offering a new perspective on the…

This paper reports on the computation of a discrete logarithm in the finite field $\mathbb F_{2^{30750}}$, breaking by a large margin the previous record, which was set in January 2014 by a computation in $\mathbb F_{2^{9234}}$. The present…

We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…

An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.

Convolutional neural networks (CNNs) with large kernels, drawing inspiration from the key operations of vision transformers (ViTs), have demonstrated impressive performance in various vision-based applications. To address the issue of…

The formulation of quantum programs in terms of the fewest number of gate operations is crucial to retrieve meaningful results from the noisy quantum processors accessible these days. In this work, we demonstrate a use-case for Field…

Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like…

In fault-tolerant quantum computing, soft outputs from real-time decoders play a crucial role in improving decoding accuracy, post-selecting magic states, and accelerating lattice surgery. A recent paper by Meister et al. [arXiv:2405.07433…

Bitmap index is recognized as a promising candidate for online analytics processing systems, because it effectively supports not only parallel processing but also complex and multi-dimensional queries. However, bitmap index creation is a…