Maths

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The latest research in training modern machine learning models: ‘A deterministic modification of gradient descent that avoids saddle points

Machine learning models, particularly those based on deep neural networks, have revolutionized the fields of data analysis, image recognition, and natural language processing. A key factor in the training of these models is the use of variants of gradient descent algorithms, which optimize model parameters by minimizing a loss function. However, the training optimization problem for neural networks is highly non-convex, presenting unique challenges.

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The PageRank algorithm analysed by EJAM

The PageRank algorithm was developed by Google co-founder Larry Page, and first introduced in 1998. It is based on the idea that a website’s importance can be measured by the number of other websites that link to it. Here, EJAM researchers study the PageRank algorithm.

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John Ockendon Prize 2022 winner announced

The John Ockendon Prize launched in 2016 and is named after the founding editor of the European Journal of Applied Mathematics. This award recognises researchers for their contribution to applied mathematical research. In this article, Journal Editor Martin Burger discusses the 2022 winning paper.

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Mahony Neumann Room Prize 2021

About the Mahony Neumann Room Prize This prize, for outstanding contributions to the Australian Mathematical Society’s research publications, is fittingly named after the founding editors of these journals.…

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Arguing about sets

Sets are ubiquitous and familiar: children get acquainted with sets of objects surrounding them very early on; secondary school students typically encounter sets of natural numbers and sets of real numbers in their maths curriculum. …

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Compressed sensing, image reconstruction and limited measurements

Beyond its theoretical contribution, this work also has signi cant practical impact. It provides new and important insight into how to adapt and optimize the performance of compressed sensing in practical applications. It introduces a new generation of sampling strategies based on multilevel random sampling which are both theoretically optimal and outperform previous state-of-the-art approaches in practice. It has led to new approaches in MRI, NMR, uorescence microscopy and helium atom scattering which offer signi cant performance gains.

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Remembering Sir Michael Atiyah and Sir Peter Swinnerton-Dyer

Cambridge is saddened by the passing of two remarkable mathematicians in recent weeks, Sir Michael Atiyah and Sir Peter Swinnerton-Dyer. Both men made an indelible mark in the subject, with Atiyah receiving the Fields Medal in 1966, and Swinnerton-Dyer postulating the Birch Swinnerton-Dyer Conjecture.…

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Singular perturbations in noisy dynamical systems

The lead article for Issue 4, Voume 29 from the European Journal of Applied Mathematics is Professor Bernard J. Matkowsky’s personalized survey-style article on the theory and application of ‘Singular perturbation methods to noisy dynamical systems’ in the limit of small noise.…

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John Ockendon Prize 2016: Winner Announced

The European Journal of Applied Mathematics and Cambridge University Press are pleased to award the 2016 John Ockendon Prize to S. J Chapman and S. E McBurnie for their winning article ‘Integral constraints in multiple-scales problems’ published in EJAM’s Special Anniversary Issue, October 2015.

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