*William Troiani was one of the recipients of a 2016/17 AMSI Vacation Research Scholarship.*

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This story was syndicated across News Limited publications nationally and in the New York Post.

]]>Head of Research at the Bureau of Meteorology and Australian Mathematical Sciences Institute (AMSI) Winter School 2017 public lecturer, Dr Peter May, says computer modelling and data science has dramatically transformed forecast accuracy and extending weather predication capability.

“These tools have changed the scale and capability of our research, we now produce five day forecasts as accurate as three day forecasts were just ten years ago. The Bureau’s modeling ranges from hours to two years and climate projections over the next 100,” he says.

With climate change leaving greater concentrations of people in vulnerable locations and increasing stress on agricultural industry and water supply, long-term outlooks and understanding of impact on communities and economies is critical.

“Providing ever finer detail means we can provide increasing accurate modeling to inform long-term planning. Working on time scales of as little as a day, we can also link critical flood risk and fire forecasts to their impact for those down at the farm or catchment,” says Dr May.

A leader in understanding the physics of thunderstorms and tropical cyclones, Dr May warns a flood of data without long-term mathematical, social science and advanced computing capability poses a risk.

“Long-term, it is vital we maintain the tools and workforce to turn this data into information to make better decisions, otherwise we risk drowning our forecasters in data with little impact where it is needed,” he says.

Dr May will deliver this year’s AMSI Winter School public lecture at the Queensland University of Technology from 6.30 pm on Monday, 3 July 2017.

AMSI Director, Professor Geoff Prince says the Institute is excited to partner with QUT and event sponsors to showcase the multi-discipline impact of mathematics to the broader community.

“This research illustrates the power of mathematics and statistics to deliver real community and economic impacts that will benefit Australians now and into the future,” says AMSI Director, Professor Geoff Prince.

AMSI Winter School 2017 will run over two weeks in from 26 June to 7 July. Headlined by national and global field leaders, this year’s program will provide students with cutting-edge insights into computational data science.

AMSI Winter 2017 is sponsored by AMSI, QUT, the Department of Education and Training, the BHP Billiton Foundation, SGI, ACEMS, Tech One, QCIF and, the Simulation Group.

For public lecture registrations visit: https://ws.amsi.org.au/public-lecture-2017/

]]>What can and can’t a computer do This question is central to the area of Mathematics now referred to as computability theory. In the early 1900’s, there was interest in not only finding solutions to specific questions in mathematics, but also in finding algorithms which can solve these problems for us. The first step towards achieving this is to first answer the question “what is an algorithm”?

Godel, Church, and Turing all came up with different looking, but logically equivalent definitions of exploring what kinds of problems can be solved by following an algorithm, and what kinds of problems can’t. Perhaps surprisingly, there are some general problems for which there exists no algorithmic solution. For example, it has been proven that there exists no algorithm which takes as input a mathematical statement, and returns “true” if the statement is true, and “false” if the statement is false. Note: the phrase “Mathematical statement” here means a statement of 1^{st} order logic.

For this project, we focused on Church’s approach, which is that of the lambda calculus. Essentially, lambda calculus is a formal language used to describe functions. According to Church, an algorithm is a list of instructions to follow, where the tasks in the list can be described and executed in this language.

There has been a huge rush of developments in computer science over the past fifty years, and it is natural for one to wonder what the effects this explosion has had in the world of Mathematics. Alongside this muse, one might also consider the fact that it is frequently mentioned how hand in hand Pure Mathematics goes with Computer Science. This is an example of a somewhat strange phenomenon where the strength of such a connection seems so obvious, that one can’t help but to feel almost embarrassed when the inevitable realisation that explicit relationships are actually far from common knowledge comes to dawn. Alas, such relationships do exist, and they extend beyond the monogamy of Mathematics and Computer Science, indeed certain areas of Logic also become helpful along the way. We wish to explore such connections, whilst coming to grasp with the foundations of these topics outside of Mathematics, as this content is rarely introduced at undergraduate level, at least as far as the Mathematics department is concerned.

Suppose you and your friend each read a book on a difficult subject. You think your book is harder than your friend’s, but your friend thinks the opposite. How can you work out which one is more complex? Perhaps you could count up how many different words appear in each book and say the book with the largest number of different words is more complex. Or maybe you could try to make the book shorter, without losing any information. Then the book that can be made the shortest is the least complex.

But doing that sounds really tricky. Instead, why not get a computer to do it? There are computer programs, called compressors, that can make digital files smaller without losing information. This is what you do when you make a .zip file. Now, imagine you had the best compressor ever. It takes any file and outputs the smallest possible .zip of that file. To compare the difficult of the your two books, you could run this compressor on the two books and say that the book with the biggest .zip would be the most complex.

This idea is called Kolmogorov complexity, which is named after the prolific Russian mathematician Andrey Kolmogorov. There is a huge range of applications of Kolmogorov complexity through maths, physics, biology and computer science. In particular, it is very useful in Artificial Intelligence. A robot often needs to learn about its environment so it can make the right decisions and actions. However, because of chance and randomness, this can often be very difficult. Sometimes the robot does the same action and gets different results. How does the robot work out how the world works? A good principle would be to choose the simplest model that explains all the things the robot has seen. How do you decide which is the simplest explanation? Well, it’s the one with the smallest Kolmogorov complexity!

The only problem with Kolmogorov complexity (and it’s a big problem) is that it is incomputable. That means it has been mathematically proven that the best possible compressor cannot possibly exist! There is actually no way to work out the size of the smallest .zip of a file, in general.

Despite this major drawback, Kolmogorov complexity is an extremely powerful idea. If you want to read more about it, try Li and Vitanyi’s book ‘An Introduction to Kolmogorov Complexity and Its Applications’. If you’re intrigued by the concept that certain computer programs cannot exist, then google the ‘halting problem’.