Mathematics

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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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Watch: Amazing Fluid Dynamics Experiments

Tom Mullin at the University of Oxford introduces some of his favourite fluid dynamics experiments… covering a wide range of fluid mechanics phenomena including turbulence, wave formation, Rayleigh-Taylor instability, viscous effects, magnetism, electricity, segregation, disorder and chaos.…

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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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International Women’s Day 2020: Influential women in STEM

International Women’s Day 2020 falls on Sunday, 8th March this year. In the run up to this date, each week day we’ll be highlighting one woman whose accomplishments in science, technology, engineering and/or mathematics not only elevated their fields but also took us one step closer to a gender-equal world.…

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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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Q&A with Steven Gilmour, Editorial Board Member of Experimental Results, Mathematics, Statistics & Probability Section

This is the latest of an ongoing series of interviews with people involved with our new Open Access journal, Experimental Results – a forum for short research papers from experimental disciplines across Science, Technology and Medicine, providing authors with an outlet for rapid publication of small chunks of research findings with maximum visibility.…

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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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New editor Q&A: Rhonda Righter of UC Berkeley

Rhonda Righter is joining the editorial board of the journal Probability in the Engineering and Informational Sciences. She brings with her a wealth of knowledge in the area of stochastic modelling and optimization; read her full biography here.…

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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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How partial differential equations can unravel information in data

The advance of data science and the solution of big data questions rely heavily on fundamental mathematical techniques. We are surrounded by technology that collects, transmits and manipulates data on an immense scale; the key is the application and development of advanced mathematics for the efficient gathering and manipulation of ‘data’–values of qualitative or quantitative variables–and efficient extraction of ‘information’–the content and meaning present in data.…

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Celebrate Pi Day with Forum of Mathematics

Pi Day is celebrated around the world on the 14th day of the 3rd month. The date representation of 3.14 is the most basic ratio of the circumference of a circle to its diameter, but it also has this going for it: Which, of course, means that mathematicians everywhere love their pi.…

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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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Goldstein wins Batchelor Prize 2016

The G K Batchelor Prize for 2016 is awarded to Professor Raymond E. Goldstein FRS, Schlumberger Professor of Complex Physical Systems in the Department of Applied Mathematics and Theoretical Physics and Fellow of Churchill College, University of Cambridge.

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Stone wins Batchelor Prize 2008

Batchelor prize winner interview Harvard professor’s research recognised by international community An interview with Professor Howard Stone, winner of the Batchelor Prize for Fluid Mechanics Professor Howard Stone, Vicky Joseph Professor of Engineering and Applied Mathematics at Harvard University is the winner of the inaugural Batchelor Prize for Fluid Mechanics.…

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