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'It seems like Nature has some secret that lets it make complicated stuff in an effortless way,' Stephen Wolfram recently told an audience at Oxford University’s Mathematical Institute.

In his talk, that you can now watch online, Wolfram, the scientist behind Mathematica and Wolfram Alpha, explored how advances in computation could benefit mathematics.

One of the key ideas he put forward was 'computational irreducibility' – the idea that some computations cannot be sped up by any shortcut, the only way to figure out what is going to happen is to simulate each step.

'People sometimes say that the reason the mathematics that we have is the way it is, is because that's what we need to describe the natural world, I think that's just not true,' he commented.

He suggested that much of the reason mathematics covers the areas it does is historical, building on work begun by the first mathematicians in ancient Babylon.

Computational irreducibility, he said, is a 'junior version of ‘undecidability'' – the idea that when you ask the question of what will ultimately happen the answer is something that is undecidable. Whilst there are over three million theorems in mathematics these are all things that turned out to be decidable/provable.

There isn’t much undecidability in mathematics because maths is set up to examine those things its methods can make progress on: 'mathematics has navigated through these kind of narrow paths in which you don't run into rampant undecidability all over the place.'

Ask mathematical questions at random, he suggested, and you would soon run into undecidability. But perhaps through exploring the space of all possible theorems, using tools such as Wolfram Alpha, you might find new paths.

He described the point of Wolfram Alpha as 'to collect as much knowledge as possible and make it computable', and that this approach could be applied to find out which theorems about a particular structure or system were 'interesting' or 'powerful'.

A pilot study focusing on one particular area of maths, continued fractions, is already showing that the process of organising theorems in a way that’s systematically computable is leading to new advances, he said.

In a contrast to the days when mathematicians did all of their calculations by hand, the future of mathematical process could be that, by entering some details of a system, within seconds they would automatically see a range of theorems about it.

This would give a window on what he called a 'vast ocean of unexplored generalisation of mathematics that exists in this computational universe of possible systems.'

The talk took place at the Mathematical Institute on 12 June 2012.

Costly and rare indium, used in solar cells, and screens for TVs, computers, and mobile phones, could be replaced with abundant and cheap zinc, scientists at Oxford University believe.

Because of its combination of high transparency and high electrical conductivity indium tin oxide (ITO) dominates the global market for coatings for solar cells and LCD displays. The market for the material is estimated to be worth $26.8bn by 2016.

However indium, a so-called 'rare earth' metal, is relatively scarce and expensive and its supply is tightly controlled - China produces over half of the world’s indium and recently reduced its export quotas.

Peter Edwards and colleagues at Oxford University's Department of Chemistry have been investigating how to make alternative coatings from cheaper, more abundant materials. Their research has come up with new coatings based on silicon-doped zinc oxide.

The Oxford team has been working closely with Oxford University Innovation, the University's technology transfer company, to protect and commercialise its research. The team has just won the Materials Science Venture Prize, awarded by the Worshipful Company of Armourers and Brasiers, to develop manufacturing processes for the group's coatings.

Peter comments: 'Zinc is a much more abundant material than indium, and our silicon-doped zinc oxide material offers electrical conductivities around two thirds of ITO, with comparable optical transparency. In addition to solar cells, our new coating could be used with lighting displays and LCD displays used in smart phones, computers and televisions.'

Jamie Ferguson of Isis Innovation said: 'There is an exciting opportunity here for the UK – which already has strong glass and high-technology manufacturing industries – to capitalise on new technologies. Projects such as Professor Edwards' transparent conductors offer the chance to strengthen our advanced materials manufacturing base by producing highly competitive new-generation materials.'

The £25,000 prize money will be used to trial manufacturing techniques and demonstrate the use of the new thin film coatings in photovoltaic products, organic light emitting diodes and LCD displays. The work will be led by Peter Edwards and Vladimir Kuznetsov at the Department of Chemistry.

Technology originally developed to track badgers underground could soon be used to locate people in an emergency situation such as a bomb attack or earthquake.

GPS is good at pinpointing locations in open spaces but below the surface it's a different story. The limitations of conventional tracking technology were exposed in the 2005 London bombings, and numerous earthquakes since, where the emergency services struggled to locate people in underground areas or buried beneath debris.

Positioning indoors is also a challenge, with no clear winning technology that is able to address people's day-to-day needs, such as finding their way around an airport.

In 2009 Andrew Markham and Niki Trigoni, from Oxford University's Department of Computer Science, faced similar problems when they joined a project to study badgers in Oxford's Wytham Woods. The animals spend much of their lives underground where conventional technology couldn't keep tabs on them.

The solution developed by Andrew and Niki is a technology based on generating very low frequency fields. This has the unique advantage of penetrating obstacles, enabling positioning and communication even through thick layers of rock, soil and concrete.

'Most technologies are only checking the magnitude of the signal – the signal strength from each transmitter – to work out distance,' Andrew told Mark Piesing of Wired.co.uk. In contrast the new technology measures 'vectors, which give you the magnitude and direction… Our technology can work out your position in three dimensions from a single transmitter.' This contrasts with other approaches such as GPS or WiFi which are based on triangulation and typically require signals from at least four transmitters.

After the work with badgers the team realised the technology had potential applications in many areas such as location-based advertising, finding victims in emergencies, and tracking people and equipment in modern mines. They started working with Oxford University Innovation to commercialise their research and are currently raising money for a spinout firm, OneTriax, to be led by CEO Jean-Paul van de Ven, who has significant experience in mobile location based services.

The basic software has already been developed and the team believe that obstacles, such as the fact that low frequency fields vanish very quickly, can be overcome with clever signal-processing algorithms.

The aim is to incorporate the new technology into smart mobile devices: a demonstrator on an Android platform is being developed and, once the technology is perfected, versions suitable for popular smart phones, such as the iPhone, shouldn't be far behind. 

Transit of venus

Photo: Andrew Steele

Venus is visible as the dark spot at the extreme right on the face of the Sun.

Andrew, from Oxford University's Department of Physics, told me:

‘The shots were taken with a normal digital SLR and a fairly long lens (70–200 mm plus a 1.7x teleconverter), but nothing more complex than that. You should of course never look at the Sun with the naked eye, especially through a camera or telescope, but on this occasion the thick clouds had a silver lining and protected me - and, as a bonus, made the shot a lot more atmospheric too!’

Even people at low risk of heart problems would benefit from statins, cheap drugs that lower levels of ‘bad’ cholesterol in the blood.

That’s the main finding of a giant collaborative study coordinated by Oxford’s Clinical Trial Service Unit and the Health Economics Research Centre, and published in The Lancet today.

About half of deaths from cardiovascular disease occur in people with no previous history of the disease, so preventing such deaths can only be done by targeting seemingly healthy people. The new research shows that treating healthy people who are for some reason at increased risk of disease would be effective, and safe, and it could see moves made toward offering these drugs to many millions of middle-aged people around the world, saving hundreds of thousands of lives.

‘The study settles once and for all previous uncertainties about whether people at low-risk of heart disease – healthy, middle-aged people – would see benefits from taking statins,’ says Professor Colin Baigent, who led the study. There would be fewer ‘events’ such as heart attacks and strokes, and this would greatly outweigh risks of any side-effects of the drugs.

The study used data for 175,000 individual participants taking part in 27 different randomised trials of statins that on average ran for around 5 years. Well over 50,000 of those people included in the analysis were at low risk of heart disease, with this group experiencing around 2000 heart attacks, strokes or similar.

With the potential of statins to save many lives, low risks of known side-effects, and the cheap cost of the pills (now that generic versions have become available over recent years), the question now switches to what should the guidelines be: how low should your risk of heart problems be before your doctor starts prescribing these pills?

Colin puts it like this: ‘To what extent should society spend resources on healthy people where there are small individual benefits but it offers the possibility of saving more lives across populations?

‘Should everyone get a statin? No. But where do you draw the line? GPs currently offer statins to people with a previous history of cardiovascular disease, and also to healthy people whose risk of such an event exceeds about 20% over 10 years. Our work suggests that we could save many more lives if we lowered that threshold, and we think that it would be sensible for NICE to review their recommendations in the UK to see whether they agree.’

Measures for preventing cardiovascular disease include encouraging healthy exercise, improving diet and stopping smoking, and all have their part to play in preventing these problems. But Colin emphasises that additional benefits are possible through wider use of statin therapy.

‘Now we have these enormously beneficial tablets that our research shows could play an even greater role in an effective public health strategy,’ says Colin.

Statins are not just for people with high cholesterol, but may be appropriate for anyone who is at increased risk. ‘The emphasis has been on treating according to people’s cholesterol levels,’ says Colin. ‘We need to get away from that focus on cholesterol levels in people’s blood and instead think about their level of risk of cardiovascular problems. Our research shows that if a person has an increased risk of heart attacks, perhaps because they are overweight or a smoker, and yet have normal cholesterol levels, then that person would benefit if their cholesterol was reduced to lower levels. It’s a different way of thinking about it, because we have been encouraged to know our ‘cholesterol level’, whereas what we really need to know is our ‘risk level’, and we should base our decisions about whether to commence statin treatment on that information and not solely on cholesterol levels.’

So what did the study published today in The Lancet do?

Colin explains: ‘We were interested in low-risk people and whether these very healthy people would still experience a benefit from taking statins. There had been controversy over whether there was a benefit of statins for those at low risk of heart attacks. Some studies suggested it didn’t exist, some did.

‘We used information recorded in the trials to set participants [all 175,000] in order of risk. We used measures like cholesterol level, blood pressure, whether or not someone was a smoker to calculate their risk of a heart attack or stroke. We worked out who had the lowest, who the highest and ordered them in line for every trial.’

The researchers then grouped everyone into brackets of risk of having a major cardiovascular event over the course of five years, from those who had <5% risk at one end to >30% risk at the other.

‘Because we had all the data on heart attacks and strokes from the trials we could check the risk scores accurately described what happened,’ Colin explains.

Those in the bottom risk groups do come predominantly from six or seven of the 27 randomised trials included in the analysis. But Colin says including all people from all the trials meant they didn’t just look at those trials that set out to look at low-risk healthy people, they looked at all the available data.

And the results across all risk groups were comparable: Those with low risk of heart events see similar proportional reductions in heart problems to those at much greater initial risk.

But those with a much bigger risk to begin with would see a larger drop in risk, so it’s important to look at the absolute figures.

The researchers estimate that for every 1000 largely healthy people (less than a 10% risk of heart problems over five years) lowering their ‘bad’ cholesterol levels by 1 mmol/litre through taking statins (a fair outcome of statin therapy, stay with me), there would be 11 fewer heart attacks or strokes over a 5 year period. That’s perhaps hard to work through what those numbers mean. It’s perhaps not a huge change for each individual.

But would add up to many heart attacks, strokes, and deaths prevented in healthy people if lots of people were taking the pills.

A better way of looking at these numbers is probably visually. A figure at the end of the Lancet paper makes clear the number of heart attacks and strokes avoided through taking statins. There are many more heart events prevented in the high risk groups, of course. But the benefits do extend right the way to the bottom, with measurable bars still appearing for the much larger population of people at very low risk of heart problems only lowering their bad cholesterol by a bit.

In taking any drug there is the potential for side-effects, and when so many people are taking statins, these are important to consider even if they occur at low rates.

There are a number of known side-effects of statins but these are uncommon and the beneficial effects in terms of preventing heart attacks and strokes greatly exceed the small risks, even among those at very low risk. ‘These are very safe drugs,’ emphasises Colin.

Statins can cause muscle problems, and problems in the liver – though these reverse on stopping taking the pills. Recently, statins have been linked with an increased risk of bleeding in the brain. These are rare, unusual but real side-effects, the evidence shows. Statins may also increase the risk of developing diabetes, but the cardiovascular benefits of statins in low-risk people are substantial even after allowing for this increase in diabetes.

That’s very reassuring when hearing stories of people experiencing muscle pain after starting statins. Some of these may not be connected to the statin and may have happened anyway. But without evidence like this it is certainly harder to compare these tales of side-effects against the heart attacks that didn’t happen, where there is no tale to be told.

The study received public and charity funding from the British Heart Foundation, the UK Medical Research Council, Cancer Research UK and others. The trials included in the analysis were mostly supported by research grants from the pharmaceutical industry.