What is the important part of a matrix? This was the opening question in Professor Strang’s 2016 Alan Tayler Lecture, given at St Catherine's College, Oxford on Monday 28th November. More specifically, if you have a rectangular matrix of real or complex numbers, can you approximate it with another matrix of lower rank and keep […]
A ground-breaking computer model that could reveal why cancer becomes drug-resistant over time, and an equation that could dramatically increase internet speed and capacity, are among four innovations recognised by the Smith Institute as the UK’s best examples of impact from students' mathematical research.
How does the Government currently attempt to boost the UK’s investment in Research and Development? One key policy has been the availability since 2000 of R&D tax credits to UK companies, which help to reduce the cost of investing in research. Unfortunately, the R&D tax credit system is no longer in step with the needs of the modern economy, in large part because of its inequitable treatment of mathematics.
Retrieving relevant information from a large collection of data, for instance using a search engine, is a difficult task. On the one hand we want to be able to use the efficiency of computers to obtain results quickly, on the other hand we would like search results to be as relevant as possible. The discipline Topic modelling can be used to address this problem...
Did you know that our founder, Dr Bruce Smith CBE, was working at Bellcom Inc in Washington D.C. in 1965 in a team selecting the landing site for the first manned moon mission, when he got the idea to create a system engineering company back in the U.K. We now work across ten sectors including aerospace, defence, security, telecommunications, energy and environmental risk, and most of our projects use mathematical models, interrogation of large sets of data and algorithms.
In true festive fashion, this year our Smith Institute staff have come up with a few more teasers for you (and us!) to tackle over the Christmas period. Happy puzzling!
In contrast to statistics which places greater emphasis on inference – finding the model that best explains the data – machine learning emphases a model’s predictive ability. With this in mind, we can form a list of problems that are suitable to a machine learning approach...
Our world’s population is projected to grow. This has sparked international food strategies to support new crop technologies that improve crop output efficiency. Yet limited land available for farming in the UK has been compounded by evolving land use. Weather Logistics, aims to tackle food production issues through better management of UK agricultural risks, by producing fine scale predictions on 25km space-scales at challenging 1-6 month ‘seasonal’ timescales...
Hannah and her sweets have been a hot topic of discussion over the last few days, since the following question appeared on a GCSE mathematics paper, sat by 500,000 teenagers last Thursday: "There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1⁄3. Show that n2-n-90=0." Why were the sweets so sticky?
Since 2007, together with colleagues at the Smith Institute, I have spent a good deal of time working with clients around the globe on auctions for radio spectrum licences. Bearing in mind that auction outcomes can shape a country's mobile telecommunications industry for a decade or more, the tasks of getting the auction designs right […]