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Research in the Mathematical Sciences

Subject Areas: Applied Mathematics
Publisher: Springer International Publishing - Springer Journals
SJR: 17

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Journal Article

Fully hyperbolic convolutional neural networks

Lensink, Keegan; Peters, Bas; Haber, Eldad

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00343-1

Convolutional neural networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various...
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Journal Article

Quantized convolutional neural networks through the lens of partial differential equations

Ben-Yair, Ido; Ben Shalom, Gil; Eliasof, Moshe; Treister, Eran

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00354-y

Quantization of convolutional neural networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the type of computations involved in neural networks. In this...
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Journal Article

Extendable orthogonal sets of integral vectors

Chamizo, Fernando; Jiménez-Urroz, Jorge

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00357-9

Motivated by a model in quantum computation, we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the quaternions and other hypercomplex numbers.
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Journal Article

Performance assessment of the maximum likelihood ensemble filter and the ensemble Kalman filters for nonlinear problems

Wang, Yijun; Zupanski, Milija; Tu, Xuemin; Gao, Xinfeng

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00359-7

This study presents a thorough investigation of the performance comparison of three ensemble data assimilation (DA) methods, including the maximum likelihood ensemble filter (MLEF), the ensemble Kalman filter (EnKF), and the iterative EnKF (IEnKF), with respect to solution accuracy and...
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Journal Article

Asymptotics for the twisted eta-product and applications to sign changes in partitions

Bridges, Walter; Franke, Johann; Garnowski, Taylor

2022 Research in the Mathematical Sciences

doi:10.1007/s40687-022-00355-x

We prove asymptotic formulas for the complex coefficients of (ζq;q)∞-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\zeta...

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