In conversation with Andrea Bertozzi

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Crime prediction, robotics, big data, image processing, fluid dynamics. Andrea Bertozzi, professor of applied mathematics at the University of California, Los Angeles (UCLA), has worked in all these areas and more. Her curiosity and many collaborations have made a real impact in our modern world.

We meet Bertozzi at the lobby of her London hotel for breakfast. It’s a typical week for her: she has already given a lecture at the University of Oxford on image processing and is preparing to give yet another talk about big data at the British Library. However, she has still found the time to welcome us warmly and share some fascinating anecdotes from her varied research career.

Bertozzi has always been surrounded by science: her father is a nuclear physicist at the Massachusetts Institute of Technology (MIT), and her sister a chemist at Stanford. “As a young kid, my parents would take us to the science museums so that we could pick one area to study seriously as an adult. But the problem was that I liked everything! So that’s why I moved into applied maths. With that, you can do everything, from science to engineering and even social sciences.” Indeed, her career as an applied mathematician has seen her accomplish that goal. While she began her research with largely theoretical work on nonlinear partial differential equations, she has more recently studied collaborative robots, image processing, big data and crime sciences.

She was always an outstanding student: when challenged to work on a project during her undergraduate degree at Princeton, she remembers that she had handwritten about 10 pages as the solution for a fluids problem. Her undergraduate advisor, Andrew Majda, convinced her to write it up as a paper; this became her first publication, a single author paper at the age of 22, when she was in her first year of graduate school. It was the first of many to come: Bertozzi has written nearly 200 scientific papers and been cited thousands of times. Amazingly, during 2015, she published a scientific paper every three weeks and gave a talk every 10 days.

Not many researchers work in so many branches of mathematics and science, but it is precisely this that gives Bertozzi such a vast array of methods to tackle whatever problem she is currently working on. When presented with a new and difficult challenge, she describes the feeling when “suddenly a light bulb comes on: if we write that equation from image processing in a different way, we are solving an equation found in incompressible fluid dynamics. We are actually solving the Euler equations with the Navier–Stokes boundary conditions. So if we add diffusion we will have the right equations with the right boundary conditions!”

That realisation led to a whole new method in image inpainting (the process of reconstructing parts of an image that might be deteriorated or corrupted). The ability to make such surprising connections is a crucial part of interdisciplinary research. She describes her research process as “going out there and talking to people. When you work in other fields, you need to work with a person who knows the right questions to be asking, believes in the scientific process and has some data.” For Bertozzi, science is like “walking around with a jigsaw puzzle with a missing piece, and sometimes you meet the person who holds that piece”.

Perhaps inspired by those childhood science museum visits, Bertozzi now runs an experimental laboratory in addition to doing her mathematical work. This is unusual for a mathematician but in keeping with Bertozzi’s broad outlook on the world. In her lab, her group studies collaborating robots (where robots have to perform a joint task, forcing them to coordinate) and complex fluid flow—allowing Bertozzi to pair her mathematical models with experimental observations. She even has a couple of patents, one for inpainting and one for data fusion mapping estimation (a method that gives more geographically accurate probability density estimates).

She lived through the computer revolution in the early years of her career. As a college student, she had a summer job with a management consultancy firm where she worked with first generation commercial desktop computers writing billing software, installing hardware and working on clients’ datasets.

Although Bertozzi left the business world to pursue an academic career, her interest in computing remained. She enthuses about the opportunities that scientific programming creates: “you are handed a tool that allows you to visualise the mathematics you have been studying—so all of a sudden we knew what questions we should be asking. Computers had a big impact on my research.” Now she insists that all her students learn programming, even those working on proving theorems, “because otherwise, you cut yourself off from two-thirds of the problems you could be working on”.

Her incursion into crime research is perhaps the most surprising of the many fields she has worked on. While she was initially hesitant about working on social issues, due in part to the availability of reliable data, a meeting with the anthropologist Jeffrey Brantingham was enough to change her mind. “We started working with more than 48,000 automobile thefts registered by the Los Angeles Police Department, with the location, time and details recorded. At the time I had no idea what sort of maths we could use and how interesting it could be, but I gave it a try.” It certainly paid off. Her group developed several models to predict where and when a crime is likely to occur based on past events. One particular model by George Mohler and Bertozzi used a mathematical structure called a self-exciting point process (similar to a Poisson process, but with history playing an additional role). This looked very promising, and within a year of its publication, the Santa Cruz Police Department used it to deploy officers to the areas with the highest probability of a crime occurring. The results were astonishing: in the first month, they reported a 27% decrease in the crime rate. The software developed using this model, PredPol, is currently used in more than 30 cities worldwide to make better policing decisions, prevent crime and keep cities safer.

As a result of the success it has had in reducing crime, this research has been covered many times on TV and in the media, but for her, it is a superficial thing. “Getting the stuff on the news was kind of fun, sure. You’re a rock star for a day, but as a mathematician, what is really exciting is when you figure something out. I remember discovering under-compressible shocks in the 90s and that was one of the most exciting days. The impact you have is fulfilling in a different way.”

Bertozzi describes her multidisciplinary approach as “having a foot in mathematics but having another foot in many other fields”. Her perception is that “sometimes mathematicians live in a bubble, doing things only in the world of mathematics, without seeing how science works in other fields. But to be collaborative you need to see how others do science.”

Bertozzi has more than 120 co-authors on research papers, including top researchers in their own fields: Stanley Osher and Guillermo Sapiro (experts in image processing), Paul Weiss (expert in atomic scale measurements and control), and Bob Behringer and Anne-Marie Cazabat (experts in soft condensed matter). One day she is working with robotics and the next she is meeting with the chief of the Los Angeles Police Department.

Bertozzi attributes her academic success to being lucky: “I had to be given the right problem to start with and I had to meet the right people.” She extends this selfless attitude towards her group: she says proudly that “this work would not have been done without these really talented young people”. To date, she has supervised nearly 30 postgraduate students and over 40 postdocs—and she sees much of her role today as one of a human resources developer: “I feel very strongly that it is not just about me. I can only do maths for 24 hours a day, but when you work with others, you really multiply that time. That is when you can have an impact on society. I care deeply about developing the next generation and helping them to become great scientists.”

And so, our interview ended, allowing Bertozzi to head over to the British Library to give her talk on big data and do exactly that: share her knowledge and experience with tomorrow’s scientists.

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Don´t miss this video explaining PredPol to the media:

https://www.youtube.com/watch?v=U0gX_z0V0nE

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Also, here is Bertozzi’s public lecture: the Mathematics of Crime:

https://www.youtube.com/watch?v=SHgxq0uC5Ng