Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

Everything and nothing project

An EPRSC ‘Partnerships for Public Engagement’ scheme 2010. FEC 122,545.56/UoR 10K everything and nothing is a performance and workshop which engages the public creatively with mathematical concepts: the Poincare conjecture, the shape of the universe, topology, and the nature of infinity are explored through an original, thought provoking piece of music theatre. Jorge Luis Borges' short story 'The Library of Babel' and the aviator Amelia Earhart’s attempt to circumnavigate the globe combine to communicate to audience key mathematical concepts of Poincare’s conjecture. The project builds on a 2008 EPSRC early development project (EP/G001650/1) and is led by an interdisciplinary team the19thstep consisting of composer Dorothy Ker, sculptor Kate Allen and mathematician Marcus du Sautoy. everything and nothing has been devised by Dorothy Ker and Kate Allen, is performed by percussionist Chris Brannick, mezzo soprano Lucy Stevens and sound designer Kelcey Swain. The UK tour targets arts-going audiences, from the Green Man Festival to the British Science Festival. Each performance is accompanied with a workshop led by Topologist Katie Steckles. Alongside the performances and workshops is a website, http://www.everythingandnothingproject.com/ The Public engagement evaluation and monitoring for the project are carried out by evaluator Bea Jefferson. The project is significant in its timely relation to contemporary mathematics and arts-science themes delivering an extensive programme of public engagement.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

A technique for delivering individualised formative problems and examples

Active learning plays a strong role in mathematics and statistics, and formative problems are vital for developing key problem-solving skills. To keep students engaged and help them master the fundamentals before challenging themselves further, we have developed a system for delivering problems tailored to a student‟s current level of understanding. Specifically, by adapting simple methodology from clinical trials, a framework for delivering existing problems and other illustrative material has been developed, making use of macros in Excel. The problems are assigned a level of difficulty (a „dose‟), and problems are presented to the student in an order depending on their ability, i.e. based on their performance so far on other problems. We demonstrate and discuss the application of the approach with formative examples developed for a first year course on plane coordinate geometry, and also for problems centred on the topic of chi-square tests.

Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev

Modeling migratory grazing of zooplankton on toxic and non-toxic phytoplankton

Migratory grazing of zooplankton between non-toxic phytoplankton (NTP) and toxic phytoplankton (TPP) is a realistic phenomena unexplored so far. The present article is a first step in this direction. A mathematical model of NTP–TPP-zooplankton with constant and variable zooplankton migration is proposed and analyzed. The asymptotic dynamics of the model system around the biologically feasible equilibria is explored through local stability analysis. The dynamics of the proposed system is explored and displayed for different combination of migratory parameters and toxin inhibition parameters. Our analysis suggests that the migratory grazing of zooplankton has a significant role in determining the dynamic stability and oscillation of phytoplankton zooplankton systems.

Pension scheme redesign and wealth redistribution between the members and sponsor: the USS rule change in October 2011

The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.