# Spotlight on Professor Sofia Olhede

** 1 May 2014**

This week the spotlight is on Professor Sofia Olhede, UCL Statistical Science.

## What is your role and what does it involve?

I am a researcher. I study patterns in time and space. Examples of my work include making sense of processes as diverse as neuroscience patterns of brain activity and characterising global circulation oceanographic observations, important for quantifying climate change.

These patterns are fascinating to me both because of the application importance and their mathematical richness. Real patterns inspire most of my theoretical work.

Understanding real patterns requires building mathematical models. This takes hours of intense conversations with application experts in order to extract the essence of the data without making the model too complicated.

Statistical models are special because we can use them to generate pseudo-data where each new dataset is different but still reflective of the underlying scientific phenomenon, helping us to understand variability.

The gold standard in my work is being able to fool the scientific experts into thinking that my pseudo-data is the real thing! In this sense, statistical models are magical.

My more theoretical work is aimed at understanding properties of the tools that we use to analyse data. This requires one to understand what patterns we could potentially see under all possible ways the data could have been generated, while still conforming to the model that we think should regulate the generation of the data.

Such thinking helps us separate what is “normal” variation from more “extreme” behaviour. A good mathematical model is useful to an important practical problem, but will be judged by other mathematicians on its mathematical aesthetics, or basically, on its beauty.

## How long have you been at UCL and what was your previous role?

I have been at UCL for seven years. Before that, I was Senior Lecturer in Statistics at Imperial College London, where I studied as an undergraduate and postgraduate.

My friends from this period then referred to me as “little miss Imperial”. I have always been a researcher and could not imagine being anything else.

## What working achievement or initiative are you most proud of?

Usually whatever I just finished! Jokes aside: my work on understanding evolving oscillations is important to me. I was obsessed by oscillations for years (I think I have finally put it behind me).

Evolving oscillations are a bit of a contradiction in terms because an oscillatory phenomenon is supposed to repeat perfectly – once you start to make a cycle change in nature, it is no longer strictly an oscillation.

Now, working in one dimension is no challenge at all. One of my favourite sources of inspiration is oceanography. There we have two-dimensional oscillations because particles are moving in, for example, whirling bodies of water.

My collaborators and I spent several years understanding what changes in the properties of the water whirls could be extracted and quantified by observing the location of the particles moving in the water.

It was hard because it is fundamentally trying to make predictions about something that we are far from observing directly. I am proud of the work because many of the technical aspects were very laborious and hard.

Thinking about variation as the dimensions increase (much beyond two) is difficult, and my collaborator and I spent considerable time making the proofs correct and verified.

We also spent a lot of time arguing about intuitive understanding of a pattern and mathematical proof.

One of the amazing things about mathematics is that techniques developed will have utility far beyond their intended scope of usage.

The techniques I constructed for the oceanographic problem later worked themselves into a problem of understanding pain perception in prematurely born infants, a project I have jointly led with the Fitzgerald group, also based at UCL. Their goal is to understand the developing brain, a highly complex system.

This problem is observed on completely different length scales (milliseconds rather than the years of the measurement devices in water whirls), but we could use the methods we had developed for the oceanographic problem almost out of the box for quantifying the response to stimuli in the infants.

These methods led us to discover the maturation of functional patterns of pain circuits in the human cortex. The patterns provide insights into the onset of functional regionalisation of pain in the human brain and open the door to other fundamental questions in the developing cortical pain processing and better medication of pain.

I am proud of the work because it adds to the mathematical theory of oscillations in many dimensions, and I get a special kick out of the fact that it has helped us understand two important application problems.

Mathematics is universal and does not care about scale or application type, only patterns of structure.

## Tell us about a project you are working on now which is top of you to-do list?

That is a loaded question. I always have unrealistic expectations of my own ability to achieve.

Working out the mathematical properties of a cool problem is like having a box of different sweets, and one always wonders if the next one will be challenging in a completely different way.

Therefore, I have too much on my to-do list, or too many sweets in my kitchen to eat. I think subconsciously one collects too many problems out of fear of having nothing to do, and because of mathematical greed. This is plainly stupid, as far too many problems come to mind that take too long to solve.

At the moment, I am working on network models, and trying to understand how to generally represent their structure in the abstract.

A network to a mathematician is just a set of entities and relationships between them, even if in a modern setting, these inevitably get described in terms of LinkedIn or Facebook.

This is because humans are fascinated by studying human behaviour and human interaction. Networks are currently very fashionable from a mathematical point of view, and so proving results about them is a race. I am strongly competitive and enjoy racing. Well, as long as I win.

A collaborator and I have just finished some theoretical work showing that a large class of networks can be understood from data, so that as the networks that we observe grow in size, we understand everything about their generation.

In classical statistics, for more standard data types most results of a similar nature are already known, but because people have studied large networks less from a statistical point of view, many problems about them remain unanswered.

Being first is exciting because you have to construct all the tools you will use to understand the problem. This is extremely fun. I would compare it to making up Lego at the same time that you are trying to build with it.

## What is your favourite album, film and novel?

My favourite novel is *Foucault’s Pendulum *by Umberto Eco. It has a sense of the absurdity of our perception of reality.

My appreciation is perhaps not unsurprising, as I am a mathematician. I read this as a teenager, and it still stands out as one of the books I like best. It questions how we perceive reality rather than what is reality.

My favourite album is probably something by Nicki Minaj. I listen to bad popular music, especially if I am working on something that is difficult.

I have had bad moments listening to music in professional settings – for instance, a senior mathematician Skyped me on a Saturday night when I was listening to ASAP Rocky, and as I am incompetent with technical matters, he got to hear something explicit before I managed to switch off Spotify.

By mutual unstated consent (or British tact), we both pretended that he had heard nothing. I also love opera, especially Mozart operas.

Who wouldn’t love a piece of art where two women are mistaken for each other because they exchange clothes? Also, Mozart has a unique sense of tune that is inimitable.

Who else could have written “Soave sia il vento”? However, normally I refuse to say what I am currently listening to.

My favourite film is hard. Here my sense of the ridiculous combats my love of period drama. I shall say nothing further.

## What is your favourite joke (pre-watershed)?

My favourite joke is about a mathematician, physicist and astronomer on the train. They are travelling through Scotland and see a sheep.

The astronomer announces: “All sheep in Scotland are black.” The physicist shakes her head and says, “No, no, no, sheep in Scotland are black.” The mathematician shakes her head and smiles. “No, there is at least one sheep in Scotland who has at least one side that is black.”

## Who would be your dream dinner guests?

My dream dinner guest would be Hilary Clinton. I admire persistent people who refuse to yield to outside pressure. Hilary Clinton is a perfect example of this, and I would ask her what her trick to persisting is.

I also admire that she does not pretend to be softer or conform to acceptable female modes of behaviour, which hurts her politically. I also would think it is time the US got a female president.

## What advice would you give your younger self?

Work harder, but only when it is fun, only with people you find it enjoyable to play with and never doubt yourself. I only produce good mathematics when I am having fun.

This took me a long time to learn, as when I was very young I tried to work on problems that were perceived as ‘hot’ rather than those that piqued my curiosity. I felt I had to produce results rather than just freewheel and enjoy myself.

Eventually I learned that if I let my intrinsic aesthetics choose, it works well in terms of both being strategic and generally having mathematical importance.

I think when I was younger I wanted other people to approve of the work I was doing, and over the course of time I stopped caring about what other people thought.

Trying to do hard maths requires one to believe in oneself – it is a bit like walking on thin air, and it always feels like if you take the first step and start walking it will subsequently be fine.

The hard thing is having that belief to start walking. Every now and then, I get a bump in my self-confidence, and that usually has a considerably strong negative impact on my research output.

It usually takes me a while to start believing in myself again sufficiently to be able to produce good mathematics.

I produce my best work when I am not trying to do so, and when I’m enjoying myself with people that I like. It took me a long time to give myself permission to do so, because I felt that I should be working rather than just playing.** **

Fundamentally, I am a curiosity- rather than esteem-driven researcher.

## What would it surprise people to know about you?

Despite being strongly driven by mathematical problems, I am not impractical. I own a house in Sweden and spend much of my holidays maintaining it.

I like doing this, as staying physically active is a means to switch off my mathematical thinking. If one is actually fixing a problem on the roof, one can’t think about abstract mathematics, or indeed, one will fall off.

I can completely switch off and go into practical mode, which most people wouldn’t imagine me capable of. I also wrote bad poetry in my younger days, whereof the less is said, the better.

## What is your favourite place?

My favourite place varies depending on my mood, which is 100% mercurial. My father’s family is from the west coast of Sweden, and there are some amazing stretches of land there where the sea meets the cliffs.

The landscape there is very sparse and windswept. Usually, it is windy when I visit and I like the drama of seeing the sea meet the sky.

I sometimes get the urge to be away from people, where no one can find me and just think, or not think at all.

One of my other favourite places is Seattle. I have a collaborator there (Jonathan) who is an oceanographer who is deeply creative. It is one of the places where I don’t feel driven to produce, but feel I have licence to just dream.

Jonathan and I have spent a lot of time in coffee shops, dreaming up new models of signal behaviour and drawing impossible diagrams in my notebook.

I do some of my best work when I feel no pressure, and Seattle is so laid-back that it is impossible to get stressed. I love the view of the mountains, which is so different from Europe that it feels I am out of space and time.

I also love London. I have by choice lived here all of my adult life. It has energy and buoyancy, both qualities that inspire action.

I love drinking coffee in the coffee shops near UCL with my collaborators, talking science and solving mathematical problems. This is probably my very favourite activity.