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Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…

Higher-order graph clustering aims to partition the graph using frequently occurring subgraphs. Motif conductance is one of the most promising higher-order graph clustering models due to its strong interpretability. However, existing motif…

Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…

Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which hinders their real-world deployment.…

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…

This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…

While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…

This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and…

The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This…

This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…

In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evaluation, we present sub-algorithms allowing substantial…

We introduce a novel bottom-up approach for the extraction of chart data. Our model utilizes images of charts as inputs and learns to detect keypoints (KP), which are used to reconstruct the components within the plot area. Our novelty lies…

Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose…

This work is a continuation of "Fast and backward stable computation of roots of polynomials" by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015. In that paper…

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network…

High-resolution cameras have become very helpful for plant phenotyping by providing a mechanism for tasks such as target versus background discrimination, and the measurement and analysis of fine-above-ground plant attributes. However, the…

We introduce an automated tool for deploying ultra low-latency, low-power deep neural networks with convolutional layers on FPGAs. By extending the hls4ml library, we demonstrate an inference latency of $5\,\mu$s using convolutional…

We report cutting edge performance results for a hybrid CPU-multi GPU implementation of the spin adapted ab initio Density Matrix Renormalization Group (DMRG) method on current state-of-the-art NVIDIA DGX-H100 architectures. We evaluate the…

Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics (QED)-based quantum processors. However, exact diagonalization of the…