Abstract: This paper investigates the average running times and complexities of various root-finding algorithms, including the Affine Method (ARM), Sparse Root Algorithm (SRA), and Branching Tree ...

Ever wonder how quantum computers might change the world? One big area people talk about is factoring numbers. It sounds kind of boring, right? But it’s actually a huge deal for how we keep our online ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Abstract: The article presents a methodology for accurately estimating the Volterra kernels of a discrete-time nonlinear system, even when the system order exceeds that of the Volterra series model.

A method of iteration is developed in terms of a function of somewhat arbitrary character. Sufficient conditions are given for convergence of the process, yielding factors of arbitrary degree for ...

Data-mining of single-cell RNA sequencing (scRNA-seq) is often transformed into learning of lower-dimensional embedding (Becht et al., 2019; Haghverdi et al., 2015; Maaten and Hinton, 2008) of the ...

Methods of polynomial factorization which find the zeros one at a time require the division of the polynomial by the accepted factor. It is shown how the accuracy of this division may be increased by ...

Cross-encoder (CE) models evaluate similarity by simultaneously encoding a query-item pair, outperforming the dot-product with embedding-based models at estimating query-item relevance. Current ...

Accurate phase unwrapping is a critical prerequisite for successful applications in phase-related MRI, including quantitative susceptibility mapping (QSM) and susceptibility weighted imaging. However, ...